Update GLM to latest version (0.9.9.3). This includes GLM's change of matrices no longer default initializing to the identity matrix. This commit thus also includes the update of all of LearnOpenGL's code to reflect this: all matrices are now constructor-initialized to the identity matrix where relevant.

This commit is contained in:
Joey de Vries
2018-12-30 14:27:14 +01:00
parent 239c456ae9
commit f4b6763356
474 changed files with 38219 additions and 38025 deletions

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/// @ref ext_matrix_clip_space
/// @file glm/ext/matrix_clip_space.hpp
///
/// @defgroup ext_matrix_clip_space GLM_EXT_matrix_clip_space
/// @ingroup ext
///
/// Defines functions that generate clip space transformation matrices.
///
/// The matrices generated by this extension use standard OpenGL fixed-function
/// conventions. For example, the lookAt function generates a transform from world
/// space into the specific eye space that the projective matrix functions
/// (perspective, ortho, etc) are designed to expect. The OpenGL compatibility
/// specifications defines the particular layout of this eye space.
///
/// Include <glm/ext/matrix_clip_space.hpp> to use the features of this extension.
///
/// @see ext_matrix_transform
/// @see ext_matrix_projection
#pragma once
// Dependencies
#include "../ext/scalar_constants.hpp"
#include "../geometric.hpp"
#include "../trigonometric.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_matrix_clip_space extension included")
#endif
namespace glm
{
/// @addtogroup ext_matrix_clip_space
/// @{
/// Creates a matrix for projecting two-dimensional coordinates onto the screen.
///
/// @tparam T A floating-point scalar type
///
/// @see - glm::ortho(T const& left, T const& right, T const& bottom, T const& top, T const& zNear, T const& zFar)
/// @see <a href="https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluOrtho2D.xml">gluOrtho2D man page</a>
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> ortho(
T left, T right, T bottom, T top);
/// Creates a matrix for an orthographic parallel viewing volume, using left-handed coordinates.
/// The near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
///
/// @tparam T A floating-point scalar type
///
/// @see - glm::ortho(T const& left, T const& right, T const& bottom, T const& top)
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> orthoLH_ZO(
T left, T right, T bottom, T top, T zNear, T zFar);
/// Creates a matrix for an orthographic parallel viewing volume using right-handed coordinates.
/// The near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @tparam T A floating-point scalar type
///
/// @see - glm::ortho(T const& left, T const& right, T const& bottom, T const& top)
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> orthoLH_NO(
T left, T right, T bottom, T top, T zNear, T zFar);
/// Creates a matrix for an orthographic parallel viewing volume, using left-handed coordinates.
/// The near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
///
/// @tparam T A floating-point scalar type
///
/// @see - glm::ortho(T const& left, T const& right, T const& bottom, T const& top)
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> orthoRH_ZO(
T left, T right, T bottom, T top, T zNear, T zFar);
/// Creates a matrix for an orthographic parallel viewing volume, using right-handed coordinates.
/// The near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @tparam T A floating-point scalar type
///
/// @see - glm::ortho(T const& left, T const& right, T const& bottom, T const& top)
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> orthoRH_NO(
T left, T right, T bottom, T top, T zNear, T zFar);
/// Creates a matrix for an orthographic parallel viewing volume, using left-handed coordinates.
/// The near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
///
/// @tparam T A floating-point scalar type
///
/// @see - glm::ortho(T const& left, T const& right, T const& bottom, T const& top)
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> orthoZO(
T left, T right, T bottom, T top, T zNear, T zFar);
/// Creates a matrix for an orthographic parallel viewing volume, using left-handed coordinates if GLM_FORCE_LEFT_HANDED if defined or right-handed coordinates otherwise.
/// The near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @tparam T A floating-point scalar type
///
/// @see - glm::ortho(T const& left, T const& right, T const& bottom, T const& top)
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> orthoNO(
T left, T right, T bottom, T top, T zNear, T zFar);
/// Creates a matrix for an orthographic parallel viewing volume, using left-handed coordinates.
/// If GLM_FORCE_DEPTH_ZERO_TO_ONE is defined, the near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
/// Otherwise, the near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @tparam T A floating-point scalar type
///
/// @see - glm::ortho(T const& left, T const& right, T const& bottom, T const& top)
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> orthoLH(
T left, T right, T bottom, T top, T zNear, T zFar);
/// Creates a matrix for an orthographic parallel viewing volume, using right-handed coordinates.
/// If GLM_FORCE_DEPTH_ZERO_TO_ONE is defined, the near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
/// Otherwise, the near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @tparam T A floating-point scalar type
///
/// @see - glm::ortho(T const& left, T const& right, T const& bottom, T const& top)
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> orthoRH(
T left, T right, T bottom, T top, T zNear, T zFar);
/// Creates a matrix for an orthographic parallel viewing volume, using the default handedness and default near and far clip planes definition.
/// To change default handedness use GLM_FORCE_LEFT_HANDED. To change default near and far clip planes definition use GLM_FORCE_DEPTH_ZERO_TO_ONE.
///
/// @tparam T A floating-point scalar type
///
/// @see - glm::ortho(T const& left, T const& right, T const& bottom, T const& top)
/// @see <a href="https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glOrtho.xml">glOrtho man page</a>
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> ortho(
T left, T right, T bottom, T top, T zNear, T zFar);
/// Creates a left handed frustum matrix.
/// The near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> frustumLH_ZO(
T left, T right, T bottom, T top, T near, T far);
/// Creates a left handed frustum matrix.
/// The near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> frustumLH_NO(
T left, T right, T bottom, T top, T near, T far);
/// Creates a right handed frustum matrix.
/// The near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> frustumRH_ZO(
T left, T right, T bottom, T top, T near, T far);
/// Creates a right handed frustum matrix.
/// The near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> frustumRH_NO(
T left, T right, T bottom, T top, T near, T far);
/// Creates a frustum matrix using left-handed coordinates if GLM_FORCE_LEFT_HANDED if defined or right-handed coordinates otherwise.
/// The near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> frustumZO(
T left, T right, T bottom, T top, T near, T far);
/// Creates a frustum matrix using left-handed coordinates if GLM_FORCE_LEFT_HANDED if defined or right-handed coordinates otherwise.
/// The near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> frustumNO(
T left, T right, T bottom, T top, T near, T far);
/// Creates a left handed frustum matrix.
/// If GLM_FORCE_DEPTH_ZERO_TO_ONE is defined, the near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
/// Otherwise, the near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> frustumLH(
T left, T right, T bottom, T top, T near, T far);
/// Creates a right handed frustum matrix.
/// If GLM_FORCE_DEPTH_ZERO_TO_ONE is defined, the near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
/// Otherwise, the near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> frustumRH(
T left, T right, T bottom, T top, T near, T far);
/// Creates a frustum matrix with default handedness, using the default handedness and default near and far clip planes definition.
/// To change default handedness use GLM_FORCE_LEFT_HANDED. To change default near and far clip planes definition use GLM_FORCE_DEPTH_ZERO_TO_ONE.
///
/// @tparam T A floating-point scalar type
/// @see <a href="https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glFrustum.xml">glFrustum man page</a>
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> frustum(
T left, T right, T bottom, T top, T near, T far);
/// Creates a matrix for a right handed, symetric perspective-view frustum.
/// The near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
///
/// @param fovy Specifies the field of view angle, in degrees, in the y direction. Expressed in radians.
/// @param aspect Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height).
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveRH_ZO(
T fovy, T aspect, T near, T far);
/// Creates a matrix for a right handed, symetric perspective-view frustum.
/// The near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @param fovy Specifies the field of view angle, in degrees, in the y direction. Expressed in radians.
/// @param aspect Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height).
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveRH_NO(
T fovy, T aspect, T near, T far);
/// Creates a matrix for a left handed, symetric perspective-view frustum.
/// The near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
///
/// @param fovy Specifies the field of view angle, in degrees, in the y direction. Expressed in radians.
/// @param aspect Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height).
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveLH_ZO(
T fovy, T aspect, T near, T far);
/// Creates a matrix for a left handed, symetric perspective-view frustum.
/// The near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @param fovy Specifies the field of view angle, in degrees, in the y direction. Expressed in radians.
/// @param aspect Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height).
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveLH_NO(
T fovy, T aspect, T near, T far);
/// Creates a matrix for a symetric perspective-view frustum using left-handed coordinates if GLM_FORCE_LEFT_HANDED if defined or right-handed coordinates otherwise.
/// The near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
///
/// @param fovy Specifies the field of view angle, in degrees, in the y direction. Expressed in radians.
/// @param aspect Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height).
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveZO(
T fovy, T aspect, T near, T far);
/// Creates a matrix for a symetric perspective-view frustum using left-handed coordinates if GLM_FORCE_LEFT_HANDED if defined or right-handed coordinates otherwise.
/// The near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @param fovy Specifies the field of view angle, in degrees, in the y direction. Expressed in radians.
/// @param aspect Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height).
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveNO(
T fovy, T aspect, T near, T far);
/// Creates a matrix for a right handed, symetric perspective-view frustum.
/// If GLM_FORCE_DEPTH_ZERO_TO_ONE is defined, the near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
/// Otherwise, the near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @param fovy Specifies the field of view angle, in degrees, in the y direction. Expressed in radians.
/// @param aspect Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height).
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveRH(
T fovy, T aspect, T near, T far);
/// Creates a matrix for a left handed, symetric perspective-view frustum.
/// If GLM_FORCE_DEPTH_ZERO_TO_ONE is defined, the near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
/// Otherwise, the near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @param fovy Specifies the field of view angle, in degrees, in the y direction. Expressed in radians.
/// @param aspect Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height).
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveLH(
T fovy, T aspect, T near, T far);
/// Creates a matrix for a symetric perspective-view frustum based on the default handedness and default near and far clip planes definition.
/// To change default handedness use GLM_FORCE_LEFT_HANDED. To change default near and far clip planes definition use GLM_FORCE_DEPTH_ZERO_TO_ONE.
///
/// @param fovy Specifies the field of view angle in the y direction. Expressed in radians.
/// @param aspect Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height).
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
/// @see <a href="https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluPerspective.xml">gluPerspective man page</a>
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspective(
T fovy, T aspect, T near, T far);
/// Builds a perspective projection matrix based on a field of view using right-handed coordinates.
/// The near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
///
/// @param fov Expressed in radians.
/// @param width Width of the viewport
/// @param height Height of the viewport
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveFovRH_ZO(
T fov, T width, T height, T near, T far);
/// Builds a perspective projection matrix based on a field of view using right-handed coordinates.
/// The near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @param fov Expressed in radians.
/// @param width Width of the viewport
/// @param height Height of the viewport
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveFovRH_NO(
T fov, T width, T height, T near, T far);
/// Builds a perspective projection matrix based on a field of view using left-handed coordinates.
/// The near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
///
/// @param fov Expressed in radians.
/// @param width Width of the viewport
/// @param height Height of the viewport
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveFovLH_ZO(
T fov, T width, T height, T near, T far);
/// Builds a perspective projection matrix based on a field of view using left-handed coordinates.
/// The near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @param fov Expressed in radians.
/// @param width Width of the viewport
/// @param height Height of the viewport
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveFovLH_NO(
T fov, T width, T height, T near, T far);
/// Builds a perspective projection matrix based on a field of view using left-handed coordinates if GLM_FORCE_LEFT_HANDED if defined or right-handed coordinates otherwise.
/// The near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
///
/// @param fov Expressed in radians.
/// @param width Width of the viewport
/// @param height Height of the viewport
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveFovZO(
T fov, T width, T height, T near, T far);
/// Builds a perspective projection matrix based on a field of view using left-handed coordinates if GLM_FORCE_LEFT_HANDED if defined or right-handed coordinates otherwise.
/// The near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @param fov Expressed in radians.
/// @param width Width of the viewport
/// @param height Height of the viewport
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveFovNO(
T fov, T width, T height, T near, T far);
/// Builds a right handed perspective projection matrix based on a field of view.
/// If GLM_FORCE_DEPTH_ZERO_TO_ONE is defined, the near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
/// Otherwise, the near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @param fov Expressed in radians.
/// @param width Width of the viewport
/// @param height Height of the viewport
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveFovRH(
T fov, T width, T height, T near, T far);
/// Builds a left handed perspective projection matrix based on a field of view.
/// If GLM_FORCE_DEPTH_ZERO_TO_ONE is defined, the near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
/// Otherwise, the near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @param fov Expressed in radians.
/// @param width Width of the viewport
/// @param height Height of the viewport
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveFovLH(
T fov, T width, T height, T near, T far);
/// Builds a perspective projection matrix based on a field of view and the default handedness and default near and far clip planes definition.
/// To change default handedness use GLM_FORCE_LEFT_HANDED. To change default near and far clip planes definition use GLM_FORCE_DEPTH_ZERO_TO_ONE.
///
/// @param fov Expressed in radians.
/// @param width Width of the viewport
/// @param height Height of the viewport
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param far Specifies the distance from the viewer to the far clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> perspectiveFov(
T fov, T width, T height, T near, T far);
/// Creates a matrix for a left handed, symmetric perspective-view frustum with far plane at infinite.
///
/// @param fovy Specifies the field of view angle, in degrees, in the y direction. Expressed in radians.
/// @param aspect Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height).
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> infinitePerspectiveLH(
T fovy, T aspect, T near);
/// Creates a matrix for a right handed, symmetric perspective-view frustum with far plane at infinite.
///
/// @param fovy Specifies the field of view angle, in degrees, in the y direction. Expressed in radians.
/// @param aspect Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height).
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> infinitePerspectiveRH(
T fovy, T aspect, T near);
/// Creates a matrix for a symmetric perspective-view frustum with far plane at infinite with default handedness.
///
/// @param fovy Specifies the field of view angle, in degrees, in the y direction. Expressed in radians.
/// @param aspect Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height).
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> infinitePerspective(
T fovy, T aspect, T near);
/// Creates a matrix for a symmetric perspective-view frustum with far plane at infinite for graphics hardware that doesn't support depth clamping.
///
/// @param fovy Specifies the field of view angle, in degrees, in the y direction. Expressed in radians.
/// @param aspect Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height).
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> tweakedInfinitePerspective(
T fovy, T aspect, T near);
/// Creates a matrix for a symmetric perspective-view frustum with far plane at infinite for graphics hardware that doesn't support depth clamping.
///
/// @param fovy Specifies the field of view angle, in degrees, in the y direction. Expressed in radians.
/// @param aspect Specifies the aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height).
/// @param near Specifies the distance from the viewer to the near clipping plane (always positive).
/// @param ep Epsilon
///
/// @tparam T A floating-point scalar type
template<typename T>
GLM_FUNC_DECL mat<4, 4, T, defaultp> tweakedInfinitePerspective(
T fovy, T aspect, T near, T ep);
/// @}
}//namespace glm
#include "matrix_clip_space.inl"

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namespace glm
{
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> ortho(T left, T right, T bottom, T top)
{
mat<4, 4, T, defaultp> Result(static_cast<T>(1));
Result[0][0] = static_cast<T>(2) / (right - left);
Result[1][1] = static_cast<T>(2) / (top - bottom);
Result[2][2] = - static_cast<T>(1);
Result[3][0] = - (right + left) / (right - left);
Result[3][1] = - (top + bottom) / (top - bottom);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> orthoLH_ZO(T left, T right, T bottom, T top, T zNear, T zFar)
{
mat<4, 4, T, defaultp> Result(1);
Result[0][0] = static_cast<T>(2) / (right - left);
Result[1][1] = static_cast<T>(2) / (top - bottom);
Result[2][2] = static_cast<T>(1) / (zFar - zNear);
Result[3][0] = - (right + left) / (right - left);
Result[3][1] = - (top + bottom) / (top - bottom);
Result[3][2] = - zNear / (zFar - zNear);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> orthoLH_NO(T left, T right, T bottom, T top, T zNear, T zFar)
{
mat<4, 4, T, defaultp> Result(1);
Result[0][0] = static_cast<T>(2) / (right - left);
Result[1][1] = static_cast<T>(2) / (top - bottom);
Result[2][2] = static_cast<T>(2) / (zFar - zNear);
Result[3][0] = - (right + left) / (right - left);
Result[3][1] = - (top + bottom) / (top - bottom);
Result[3][2] = - (zFar + zNear) / (zFar - zNear);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> orthoRH_ZO(T left, T right, T bottom, T top, T zNear, T zFar)
{
mat<4, 4, T, defaultp> Result(1);
Result[0][0] = static_cast<T>(2) / (right - left);
Result[1][1] = static_cast<T>(2) / (top - bottom);
Result[2][2] = - static_cast<T>(1) / (zFar - zNear);
Result[3][0] = - (right + left) / (right - left);
Result[3][1] = - (top + bottom) / (top - bottom);
Result[3][2] = - zNear / (zFar - zNear);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> orthoRH_NO(T left, T right, T bottom, T top, T zNear, T zFar)
{
mat<4, 4, T, defaultp> Result(1);
Result[0][0] = static_cast<T>(2) / (right - left);
Result[1][1] = static_cast<T>(2) / (top - bottom);
Result[2][2] = - static_cast<T>(2) / (zFar - zNear);
Result[3][0] = - (right + left) / (right - left);
Result[3][1] = - (top + bottom) / (top - bottom);
Result[3][2] = - (zFar + zNear) / (zFar - zNear);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> orthoZO(T left, T right, T bottom, T top, T zNear, T zFar)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_LH_BIT)
return orthoLH_ZO(left, right, bottom, top, zNear, zFar);
else
return orthoRH_ZO(left, right, bottom, top, zNear, zFar);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> orthoNO(T left, T right, T bottom, T top, T zNear, T zFar)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_LH_BIT)
return orthoLH_NO(left, right, bottom, top, zNear, zFar);
else
return orthoRH_NO(left, right, bottom, top, zNear, zFar);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> orthoLH(T left, T right, T bottom, T top, T zNear, T zFar)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_ZO_BIT)
return orthoLH_ZO(left, right, bottom, top, zNear, zFar);
else
return orthoLH_NO(left, right, bottom, top, zNear, zFar);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> orthoRH(T left, T right, T bottom, T top, T zNear, T zFar)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_ZO_BIT)
return orthoRH_ZO(left, right, bottom, top, zNear, zFar);
else
return orthoRH_NO(left, right, bottom, top, zNear, zFar);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> ortho(T left, T right, T bottom, T top, T zNear, T zFar)
{
if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_LH_ZO)
return orthoLH_ZO(left, right, bottom, top, zNear, zFar);
else if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_LH_NO)
return orthoLH_NO(left, right, bottom, top, zNear, zFar);
else if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_RH_ZO)
return orthoRH_ZO(left, right, bottom, top, zNear, zFar);
else if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_RH_NO)
return orthoRH_NO(left, right, bottom, top, zNear, zFar);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> frustumLH_ZO(T left, T right, T bottom, T top, T nearVal, T farVal)
{
mat<4, 4, T, defaultp> Result(0);
Result[0][0] = (static_cast<T>(2) * nearVal) / (right - left);
Result[1][1] = (static_cast<T>(2) * nearVal) / (top - bottom);
Result[2][0] = (right + left) / (right - left);
Result[2][1] = (top + bottom) / (top - bottom);
Result[2][2] = farVal / (farVal - nearVal);
Result[2][3] = static_cast<T>(1);
Result[3][2] = -(farVal * nearVal) / (farVal - nearVal);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> frustumLH_NO(T left, T right, T bottom, T top, T nearVal, T farVal)
{
mat<4, 4, T, defaultp> Result(0);
Result[0][0] = (static_cast<T>(2) * nearVal) / (right - left);
Result[1][1] = (static_cast<T>(2) * nearVal) / (top - bottom);
Result[2][0] = (right + left) / (right - left);
Result[2][1] = (top + bottom) / (top - bottom);
Result[2][2] = (farVal + nearVal) / (farVal - nearVal);
Result[2][3] = static_cast<T>(1);
Result[3][2] = - (static_cast<T>(2) * farVal * nearVal) / (farVal - nearVal);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> frustumRH_ZO(T left, T right, T bottom, T top, T nearVal, T farVal)
{
mat<4, 4, T, defaultp> Result(0);
Result[0][0] = (static_cast<T>(2) * nearVal) / (right - left);
Result[1][1] = (static_cast<T>(2) * nearVal) / (top - bottom);
Result[2][0] = (right + left) / (right - left);
Result[2][1] = (top + bottom) / (top - bottom);
Result[2][2] = farVal / (nearVal - farVal);
Result[2][3] = static_cast<T>(-1);
Result[3][2] = -(farVal * nearVal) / (farVal - nearVal);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> frustumRH_NO(T left, T right, T bottom, T top, T nearVal, T farVal)
{
mat<4, 4, T, defaultp> Result(0);
Result[0][0] = (static_cast<T>(2) * nearVal) / (right - left);
Result[1][1] = (static_cast<T>(2) * nearVal) / (top - bottom);
Result[2][0] = (right + left) / (right - left);
Result[2][1] = (top + bottom) / (top - bottom);
Result[2][2] = - (farVal + nearVal) / (farVal - nearVal);
Result[2][3] = static_cast<T>(-1);
Result[3][2] = - (static_cast<T>(2) * farVal * nearVal) / (farVal - nearVal);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> frustumZO(T left, T right, T bottom, T top, T nearVal, T farVal)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_LH_BIT)
return frustumLH_ZO(left, right, bottom, top, nearVal, farVal);
else
return frustumRH_ZO(left, right, bottom, top, nearVal, farVal);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> frustumNO(T left, T right, T bottom, T top, T nearVal, T farVal)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_LH_BIT)
return frustumLH_NO(left, right, bottom, top, nearVal, farVal);
else
return frustumRH_NO(left, right, bottom, top, nearVal, farVal);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> frustumLH(T left, T right, T bottom, T top, T nearVal, T farVal)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_ZO_BIT)
return frustumLH_ZO(left, right, bottom, top, nearVal, farVal);
else
return frustumLH_NO(left, right, bottom, top, nearVal, farVal);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> frustumRH(T left, T right, T bottom, T top, T nearVal, T farVal)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_ZO_BIT)
return frustumRH_ZO(left, right, bottom, top, nearVal, farVal);
else
return frustumRH_NO(left, right, bottom, top, nearVal, farVal);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> frustum(T left, T right, T bottom, T top, T nearVal, T farVal)
{
if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_LH_ZO)
return frustumLH_ZO(left, right, bottom, top, nearVal, farVal);
else if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_LH_NO)
return frustumLH_NO(left, right, bottom, top, nearVal, farVal);
else if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_RH_ZO)
return frustumRH_ZO(left, right, bottom, top, nearVal, farVal);
else if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_RH_NO)
return frustumRH_NO(left, right, bottom, top, nearVal, farVal);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveRH_ZO(T fovy, T aspect, T zNear, T zFar)
{
assert(abs(aspect - std::numeric_limits<T>::epsilon()) > static_cast<T>(0));
T const tanHalfFovy = tan(fovy / static_cast<T>(2));
mat<4, 4, T, defaultp> Result(static_cast<T>(0));
Result[0][0] = static_cast<T>(1) / (aspect * tanHalfFovy);
Result[1][1] = static_cast<T>(1) / (tanHalfFovy);
Result[2][2] = zFar / (zNear - zFar);
Result[2][3] = - static_cast<T>(1);
Result[3][2] = -(zFar * zNear) / (zFar - zNear);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveRH_NO(T fovy, T aspect, T zNear, T zFar)
{
assert(abs(aspect - std::numeric_limits<T>::epsilon()) > static_cast<T>(0));
T const tanHalfFovy = tan(fovy / static_cast<T>(2));
mat<4, 4, T, defaultp> Result(static_cast<T>(0));
Result[0][0] = static_cast<T>(1) / (aspect * tanHalfFovy);
Result[1][1] = static_cast<T>(1) / (tanHalfFovy);
Result[2][2] = - (zFar + zNear) / (zFar - zNear);
Result[2][3] = - static_cast<T>(1);
Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveLH_ZO(T fovy, T aspect, T zNear, T zFar)
{
assert(abs(aspect - std::numeric_limits<T>::epsilon()) > static_cast<T>(0));
T const tanHalfFovy = tan(fovy / static_cast<T>(2));
mat<4, 4, T, defaultp> Result(static_cast<T>(0));
Result[0][0] = static_cast<T>(1) / (aspect * tanHalfFovy);
Result[1][1] = static_cast<T>(1) / (tanHalfFovy);
Result[2][2] = zFar / (zFar - zNear);
Result[2][3] = static_cast<T>(1);
Result[3][2] = -(zFar * zNear) / (zFar - zNear);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveLH_NO(T fovy, T aspect, T zNear, T zFar)
{
assert(abs(aspect - std::numeric_limits<T>::epsilon()) > static_cast<T>(0));
T const tanHalfFovy = tan(fovy / static_cast<T>(2));
mat<4, 4, T, defaultp> Result(static_cast<T>(0));
Result[0][0] = static_cast<T>(1) / (aspect * tanHalfFovy);
Result[1][1] = static_cast<T>(1) / (tanHalfFovy);
Result[2][2] = (zFar + zNear) / (zFar - zNear);
Result[2][3] = static_cast<T>(1);
Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveZO(T fovy, T aspect, T zNear, T zFar)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_LH_BIT)
return perspectiveLH_ZO(fovy, aspect, zNear, zFar);
else
return perspectiveRH_ZO(fovy, aspect, zNear, zFar);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveNO(T fovy, T aspect, T zNear, T zFar)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_LH_BIT)
return perspectiveLH_NO(fovy, aspect, zNear, zFar);
else
return perspectiveRH_NO(fovy, aspect, zNear, zFar);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveLH(T fovy, T aspect, T zNear, T zFar)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_ZO_BIT)
return perspectiveLH_ZO(fovy, aspect, zNear, zFar);
else
return perspectiveLH_NO(fovy, aspect, zNear, zFar);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveRH(T fovy, T aspect, T zNear, T zFar)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_ZO_BIT)
return perspectiveRH_ZO(fovy, aspect, zNear, zFar);
else
return perspectiveRH_NO(fovy, aspect, zNear, zFar);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspective(T fovy, T aspect, T zNear, T zFar)
{
if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_LH_ZO)
return perspectiveLH_ZO(fovy, aspect, zNear, zFar);
else if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_LH_NO)
return perspectiveLH_NO(fovy, aspect, zNear, zFar);
else if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_RH_ZO)
return perspectiveRH_ZO(fovy, aspect, zNear, zFar);
else if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_RH_NO)
return perspectiveRH_NO(fovy, aspect, zNear, zFar);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveFovRH_ZO(T fov, T width, T height, T zNear, T zFar)
{
assert(width > static_cast<T>(0));
assert(height > static_cast<T>(0));
assert(fov > static_cast<T>(0));
T const rad = fov;
T const h = glm::cos(static_cast<T>(0.5) * rad) / glm::sin(static_cast<T>(0.5) * rad);
T const w = h * height / width; ///todo max(width , Height) / min(width , Height)?
mat<4, 4, T, defaultp> Result(static_cast<T>(0));
Result[0][0] = w;
Result[1][1] = h;
Result[2][2] = zFar / (zNear - zFar);
Result[2][3] = - static_cast<T>(1);
Result[3][2] = -(zFar * zNear) / (zFar - zNear);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveFovRH_NO(T fov, T width, T height, T zNear, T zFar)
{
assert(width > static_cast<T>(0));
assert(height > static_cast<T>(0));
assert(fov > static_cast<T>(0));
T const rad = fov;
T const h = glm::cos(static_cast<T>(0.5) * rad) / glm::sin(static_cast<T>(0.5) * rad);
T const w = h * height / width; ///todo max(width , Height) / min(width , Height)?
mat<4, 4, T, defaultp> Result(static_cast<T>(0));
Result[0][0] = w;
Result[1][1] = h;
Result[2][2] = - (zFar + zNear) / (zFar - zNear);
Result[2][3] = - static_cast<T>(1);
Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveFovLH_ZO(T fov, T width, T height, T zNear, T zFar)
{
assert(width > static_cast<T>(0));
assert(height > static_cast<T>(0));
assert(fov > static_cast<T>(0));
T const rad = fov;
T const h = glm::cos(static_cast<T>(0.5) * rad) / glm::sin(static_cast<T>(0.5) * rad);
T const w = h * height / width; ///todo max(width , Height) / min(width , Height)?
mat<4, 4, T, defaultp> Result(static_cast<T>(0));
Result[0][0] = w;
Result[1][1] = h;
Result[2][2] = zFar / (zFar - zNear);
Result[2][3] = static_cast<T>(1);
Result[3][2] = -(zFar * zNear) / (zFar - zNear);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveFovLH_NO(T fov, T width, T height, T zNear, T zFar)
{
assert(width > static_cast<T>(0));
assert(height > static_cast<T>(0));
assert(fov > static_cast<T>(0));
T const rad = fov;
T const h = glm::cos(static_cast<T>(0.5) * rad) / glm::sin(static_cast<T>(0.5) * rad);
T const w = h * height / width; ///todo max(width , Height) / min(width , Height)?
mat<4, 4, T, defaultp> Result(static_cast<T>(0));
Result[0][0] = w;
Result[1][1] = h;
Result[2][2] = (zFar + zNear) / (zFar - zNear);
Result[2][3] = static_cast<T>(1);
Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear);
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveFovZO(T fov, T width, T height, T zNear, T zFar)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_LH_BIT)
return perspectiveFovLH_ZO(fov, width, height, zNear, zFar);
else
return perspectiveFovRH_ZO(fov, width, height, zNear, zFar);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveFovNO(T fov, T width, T height, T zNear, T zFar)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_LH_BIT)
return perspectiveFovLH_NO(fov, width, height, zNear, zFar);
else
return perspectiveFovRH_NO(fov, width, height, zNear, zFar);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveFovLH(T fov, T width, T height, T zNear, T zFar)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_ZO_BIT)
return perspectiveFovLH_ZO(fov, width, height, zNear, zFar);
else
return perspectiveFovLH_NO(fov, width, height, zNear, zFar);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveFovRH(T fov, T width, T height, T zNear, T zFar)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_ZO_BIT)
return perspectiveFovRH_ZO(fov, width, height, zNear, zFar);
else
return perspectiveFovRH_NO(fov, width, height, zNear, zFar);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveFov(T fov, T width, T height, T zNear, T zFar)
{
if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_LH_ZO)
return perspectiveFovLH_ZO(fov, width, height, zNear, zFar);
else if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_LH_NO)
return perspectiveFovLH_NO(fov, width, height, zNear, zFar);
else if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_RH_ZO)
return perspectiveFovRH_ZO(fov, width, height, zNear, zFar);
else if(GLM_CONFIG_CLIP_CONTROL == GLM_CLIP_CONTROL_RH_NO)
return perspectiveFovRH_NO(fov, width, height, zNear, zFar);
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> infinitePerspectiveRH(T fovy, T aspect, T zNear)
{
T const range = tan(fovy / static_cast<T>(2)) * zNear;
T const left = -range * aspect;
T const right = range * aspect;
T const bottom = -range;
T const top = range;
mat<4, 4, T, defaultp> Result(static_cast<T>(0));
Result[0][0] = (static_cast<T>(2) * zNear) / (right - left);
Result[1][1] = (static_cast<T>(2) * zNear) / (top - bottom);
Result[2][2] = - static_cast<T>(1);
Result[2][3] = - static_cast<T>(1);
Result[3][2] = - static_cast<T>(2) * zNear;
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> infinitePerspectiveLH(T fovy, T aspect, T zNear)
{
T const range = tan(fovy / static_cast<T>(2)) * zNear;
T const left = -range * aspect;
T const right = range * aspect;
T const bottom = -range;
T const top = range;
mat<4, 4, T, defaultp> Result(T(0));
Result[0][0] = (static_cast<T>(2) * zNear) / (right - left);
Result[1][1] = (static_cast<T>(2) * zNear) / (top - bottom);
Result[2][2] = static_cast<T>(1);
Result[2][3] = static_cast<T>(1);
Result[3][2] = - static_cast<T>(2) * zNear;
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> infinitePerspective(T fovy, T aspect, T zNear)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_LH_BIT)
return infinitePerspectiveLH(fovy, aspect, zNear);
else
return infinitePerspectiveRH(fovy, aspect, zNear);
}
// Infinite projection matrix: http://www.terathon.com/gdc07_lengyel.pdf
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> tweakedInfinitePerspective(T fovy, T aspect, T zNear, T ep)
{
T const range = tan(fovy / static_cast<T>(2)) * zNear;
T const left = -range * aspect;
T const right = range * aspect;
T const bottom = -range;
T const top = range;
mat<4, 4, T, defaultp> Result(static_cast<T>(0));
Result[0][0] = (static_cast<T>(2) * zNear) / (right - left);
Result[1][1] = (static_cast<T>(2) * zNear) / (top - bottom);
Result[2][2] = ep - static_cast<T>(1);
Result[2][3] = static_cast<T>(-1);
Result[3][2] = (ep - static_cast<T>(2)) * zNear;
return Result;
}
template<typename T>
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> tweakedInfinitePerspective(T fovy, T aspect, T zNear)
{
return tweakedInfinitePerspective(fovy, aspect, zNear, epsilon<T>());
}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double2x2.hpp
#pragma once
#include "../detail/type_mat2x2.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 2 columns of 2 components matrix of double-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<2, 2, double, defaultp> dmat2x2;
/// 2 columns of 2 components matrix of double-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<2, 2, double, defaultp> dmat2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double2x2_precision.hpp
#pragma once
#include "../detail/type_mat2x2.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 2 columns of 2 components matrix of double-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 2, double, lowp> lowp_dmat2;
/// 2 columns of 2 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 2, double, mediump> mediump_dmat2;
/// 2 columns of 2 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 2, double, highp> highp_dmat2;
/// 2 columns of 2 components matrix of double-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 2, double, lowp> lowp_dmat2x2;
/// 2 columns of 2 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 2, double, mediump> mediump_dmat2x2;
/// 2 columns of 2 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 2, double, highp> highp_dmat2x2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double2x3.hpp
#pragma once
#include "../detail/type_mat2x3.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 2 columns of 3 components matrix of double-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<2, 3, double, defaultp> dmat2x3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double2x3_precision.hpp
#pragma once
#include "../detail/type_mat2x3.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 2 columns of 3 components matrix of double-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 3, double, lowp> lowp_dmat2x3;
/// 2 columns of 3 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 3, double, mediump> mediump_dmat2x3;
/// 2 columns of 3 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 3, double, highp> highp_dmat2x3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double2x4.hpp
#pragma once
#include "../detail/type_mat2x4.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 2 columns of 4 components matrix of double-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<2, 4, double, defaultp> dmat2x4;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double2x4_precision.hpp
#pragma once
#include "../detail/type_mat2x4.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 2 columns of 4 components matrix of double-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 4, double, lowp> lowp_dmat2x4;
/// 2 columns of 4 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 4, double, mediump> mediump_dmat2x4;
/// 2 columns of 4 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 4, double, highp> highp_dmat2x4;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double3x2.hpp
#pragma once
#include "../detail/type_mat3x2.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 3 columns of 2 components matrix of double-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<3, 2, double, defaultp> dmat3x2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double3x2_precision.hpp
#pragma once
#include "../detail/type_mat3x2.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 3 columns of 2 components matrix of double-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 2, double, lowp> lowp_dmat3x2;
/// 3 columns of 2 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 2, double, mediump> mediump_dmat3x2;
/// 3 columns of 2 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 2, double, highp> highp_dmat3x2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double3x3.hpp
#pragma once
#include "../detail/type_mat3x3.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 3 columns of 3 components matrix of double-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<3, 3, double, defaultp> dmat3x3;
/// 3 columns of 3 components matrix of double-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<3, 3, double, defaultp> dmat3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double3x3_precision.hpp
#pragma once
#include "../detail/type_mat3x3.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 3 columns of 3 components matrix of double-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 3, double, lowp> lowp_dmat3;
/// 3 columns of 3 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 3, double, mediump> mediump_dmat3;
/// 3 columns of 3 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 3, double, highp> highp_dmat3;
/// 3 columns of 3 components matrix of double-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 3, double, lowp> lowp_dmat3x3;
/// 3 columns of 3 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 3, double, mediump> mediump_dmat3x3;
/// 3 columns of 3 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 3, double, highp> highp_dmat3x3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double3x4.hpp
#pragma once
#include "../detail/type_mat3x4.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 3 columns of 4 components matrix of double-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<3, 4, double, defaultp> dmat3x4;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double3x4_precision.hpp
#pragma once
#include "../detail/type_mat3x4.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 3 columns of 4 components matrix of double-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 4, double, lowp> lowp_dmat3x4;
/// 3 columns of 4 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 4, double, mediump> mediump_dmat3x4;
/// 3 columns of 4 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 4, double, highp> highp_dmat3x4;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double4x2.hpp
#pragma once
#include "../detail/type_mat4x2.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 4 columns of 2 components matrix of double-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<4, 2, double, defaultp> dmat4x2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double4x2_precision.hpp
#pragma once
#include "../detail/type_mat4x2.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 4 columns of 2 components matrix of double-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 2, double, lowp> lowp_dmat4x2;
/// 4 columns of 2 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 2, double, mediump> mediump_dmat4x2;
/// 4 columns of 2 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 2, double, highp> highp_dmat4x2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double4x3.hpp
#pragma once
#include "../detail/type_mat4x3.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 4 columns of 3 components matrix of double-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<4, 3, double, defaultp> dmat4x3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double4x3_precision.hpp
#pragma once
#include "../detail/type_mat4x3.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 4 columns of 3 components matrix of double-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 3, double, lowp> lowp_dmat4x3;
/// 4 columns of 3 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 3, double, mediump> mediump_dmat4x3;
/// 4 columns of 3 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 3, double, highp> highp_dmat4x3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double4x4.hpp
#pragma once
#include "../detail/type_mat4x4.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 4 columns of 4 components matrix of double-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<4, 4, double, defaultp> dmat4x4;
/// 4 columns of 4 components matrix of double-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<4, 4, double, defaultp> dmat4;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_double4x4_precision.hpp
#pragma once
#include "../detail/type_mat4x4.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 4 columns of 4 components matrix of double-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 4, double, lowp> lowp_dmat4;
/// 4 columns of 4 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 4, double, mediump> mediump_dmat4;
/// 4 columns of 4 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 4, double, highp> highp_dmat4;
/// 4 columns of 4 components matrix of double-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 4, double, lowp> lowp_dmat4x4;
/// 4 columns of 4 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 4, double, mediump> mediump_dmat4x4;
/// 4 columns of 4 components matrix of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 4, double, highp> highp_dmat4x4;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float2x2.hpp
#pragma once
#include "../detail/type_mat2x2.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 2 columns of 2 components matrix of single-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<2, 2, float, defaultp> mat2x2;
/// 2 columns of 2 components matrix of single-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<2, 2, float, defaultp> mat2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float2x2_precision.hpp
#pragma once
#include "../detail/type_mat2x2.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 2 columns of 2 components matrix of single-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 2, float, lowp> lowp_mat2;
/// 2 columns of 2 components matrix of single-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 2, float, mediump> mediump_mat2;
/// 2 columns of 2 components matrix of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 2, float, highp> highp_mat2;
/// 2 columns of 2 components matrix of single-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 2, float, lowp> lowp_mat2x2;
/// 2 columns of 2 components matrix of single-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 2, float, mediump> mediump_mat2x2;
/// 2 columns of 2 components matrix of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 2, float, highp> highp_mat2x2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float2x3.hpp
#pragma once
#include "../detail/type_mat2x3.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 2 columns of 3 components matrix of single-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<2, 3, float, defaultp> mat2x3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float2x3_precision.hpp
#pragma once
#include "../detail/type_mat2x3.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 2 columns of 3 components matrix of single-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 3, float, lowp> lowp_mat2x3;
/// 2 columns of 3 components matrix of single-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 3, float, mediump> mediump_mat2x3;
/// 2 columns of 3 components matrix of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 3, float, highp> highp_mat2x3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float2x4.hpp
#pragma once
#include "../detail/type_mat2x4.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 2 columns of 4 components matrix of single-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<2, 4, float, defaultp> mat2x4;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float2x4_precision.hpp
#pragma once
#include "../detail/type_mat2x4.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 2 columns of 4 components matrix of single-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 4, float, lowp> lowp_mat2x4;
/// 2 columns of 4 components matrix of single-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 4, float, mediump> mediump_mat2x4;
/// 2 columns of 4 components matrix of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<2, 4, float, highp> highp_mat2x4;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float3x2.hpp
#pragma once
#include "../detail/type_mat3x2.hpp"
namespace glm
{
/// @addtogroup core
/// @{
/// 3 columns of 2 components matrix of single-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<3, 2, float, defaultp> mat3x2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float3x2_precision.hpp
#pragma once
#include "../detail/type_mat3x2.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 3 columns of 2 components matrix of single-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 2, float, lowp> lowp_mat3x2;
/// 3 columns of 2 components matrix of single-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 2, float, mediump> mediump_mat3x2;
/// 3 columns of 2 components matrix of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 2, float, highp> highp_mat3x2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float3x3.hpp
#pragma once
#include "../detail/type_mat3x3.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 3 columns of 3 components matrix of single-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<3, 3, float, defaultp> mat3x3;
/// 3 columns of 3 components matrix of single-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<3, 3, float, defaultp> mat3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float3x3_precision.hpp
#pragma once
#include "../detail/type_mat3x3.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 3 columns of 3 components matrix of single-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 3, float, lowp> lowp_mat3;
/// 3 columns of 3 components matrix of single-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 3, float, mediump> mediump_mat3;
/// 3 columns of 3 components matrix of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 3, float, highp> highp_mat3;
/// 3 columns of 3 components matrix of single-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 3, float, lowp> lowp_mat3x3;
/// 3 columns of 3 components matrix of single-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 3, float, mediump> mediump_mat3x3;
/// 3 columns of 3 components matrix of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 3, float, highp> highp_mat3x3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float3x4.hpp
#pragma once
#include "../detail/type_mat3x4.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 3 columns of 4 components matrix of single-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<3, 4, float, defaultp> mat3x4;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float3x4_precision.hpp
#pragma once
#include "../detail/type_mat3x4.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 3 columns of 4 components matrix of single-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 4, float, lowp> lowp_mat3x4;
/// 3 columns of 4 components matrix of single-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 4, float, mediump> mediump_mat3x4;
/// 3 columns of 4 components matrix of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<3, 4, float, highp> highp_mat3x4;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float4x2.hpp
#pragma once
#include "../detail/type_mat4x2.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 4 columns of 2 components matrix of single-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<4, 2, float, defaultp> mat4x2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float2x2_precision.hpp
#pragma once
#include "../detail/type_mat2x2.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 4 columns of 2 components matrix of single-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 2, float, lowp> lowp_mat4x2;
/// 4 columns of 2 components matrix of single-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 2, float, mediump> mediump_mat4x2;
/// 4 columns of 2 components matrix of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 2, float, highp> highp_mat4x2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float4x3.hpp
#pragma once
#include "../detail/type_mat4x3.hpp"
namespace glm
{
/// @addtogroup core_matrix
/// @{
/// 4 columns of 3 components matrix of single-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<4, 3, float, defaultp> mat4x3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float4x3_precision.hpp
#pragma once
#include "../detail/type_mat4x3.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 4 columns of 3 components matrix of single-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 3, float, lowp> lowp_mat4x3;
/// 4 columns of 3 components matrix of single-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 3, float, mediump> mediump_mat4x3;
/// 4 columns of 3 components matrix of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 3, float, highp> highp_mat4x3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float4x4.hpp
#pragma once
#include "../detail/type_mat4x4.hpp"
namespace glm
{
/// @ingroup core_matrix
/// @{
/// 4 columns of 4 components matrix of single-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<4, 4, float, defaultp> mat4x4;
/// 4 columns of 4 components matrix of single-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
typedef mat<4, 4, float, defaultp> mat4;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/matrix_float4x4_precision.hpp
#pragma once
#include "../detail/type_mat4x4.hpp"
namespace glm
{
/// @addtogroup core_matrix_precision
/// @{
/// 4 columns of 4 components matrix of single-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 4, float, lowp> lowp_mat4;
/// 4 columns of 4 components matrix of single-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 4, float, mediump> mediump_mat4;
/// 4 columns of 4 components matrix of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 4, float, highp> highp_mat4;
/// 4 columns of 4 components matrix of single-precision floating-point numbers using low precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 4, float, lowp> lowp_mat4x4;
/// 4 columns of 4 components matrix of single-precision floating-point numbers using medium precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 4, float, mediump> mediump_mat4x4;
/// 4 columns of 4 components matrix of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.6 Matrices</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef mat<4, 4, float, highp> highp_mat4x4;
/// @}
}//namespace glm

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/// @ref ext_matrix_projection
/// @file glm/ext/matrix_projection.hpp
///
/// @defgroup ext_matrix_projection GLM_EXT_matrix_projection
/// @ingroup ext
///
/// Functions that generate common projection transformation matrices.
///
/// The matrices generated by this extension use standard OpenGL fixed-function
/// conventions. For example, the lookAt function generates a transform from world
/// space into the specific eye space that the projective matrix functions
/// (perspective, ortho, etc) are designed to expect. The OpenGL compatibility
/// specifications defines the particular layout of this eye space.
///
/// Include <glm/ext/matrix_projection.hpp> to use the features of this extension.
///
/// @see ext_matrix_transform
/// @see ext_matrix_clip_space
#pragma once
// Dependencies
#include "../gtc/constants.hpp"
#include "../geometric.hpp"
#include "../trigonometric.hpp"
#include "../matrix.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_matrix_projection extension included")
#endif
namespace glm
{
/// @addtogroup ext_matrix_projection
/// @{
/// Map the specified object coordinates (obj.x, obj.y, obj.z) into window coordinates.
/// The near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
///
/// @param obj Specify the object coordinates.
/// @param model Specifies the current modelview matrix
/// @param proj Specifies the current projection matrix
/// @param viewport Specifies the current viewport
/// @return Return the computed window coordinates.
/// @tparam T Native type used for the computation. Currently supported: half (not recommended), float or double.
/// @tparam U Currently supported: Floating-point types and integer types.
///
/// @see <a href="https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluProject.xml">gluProject man page</a>
template<typename T, typename U, qualifier Q>
GLM_FUNC_DECL vec<3, T, Q> projectZO(
vec<3, T, Q> const& obj, mat<4, 4, T, Q> const& model, mat<4, 4, T, Q> const& proj, vec<4, U, Q> const& viewport);
/// Map the specified object coordinates (obj.x, obj.y, obj.z) into window coordinates.
/// The near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @param obj Specify the object coordinates.
/// @param model Specifies the current modelview matrix
/// @param proj Specifies the current projection matrix
/// @param viewport Specifies the current viewport
/// @return Return the computed window coordinates.
/// @tparam T Native type used for the computation. Currently supported: half (not recommended), float or double.
/// @tparam U Currently supported: Floating-point types and integer types.
///
/// @see <a href="https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluProject.xml">gluProject man page</a>
template<typename T, typename U, qualifier Q>
GLM_FUNC_DECL vec<3, T, Q> projectNO(
vec<3, T, Q> const& obj, mat<4, 4, T, Q> const& model, mat<4, 4, T, Q> const& proj, vec<4, U, Q> const& viewport);
/// Map the specified object coordinates (obj.x, obj.y, obj.z) into window coordinates using default near and far clip planes definition.
/// To change default near and far clip planes definition use GLM_FORCE_DEPTH_ZERO_TO_ONE.
///
/// @param obj Specify the object coordinates.
/// @param model Specifies the current modelview matrix
/// @param proj Specifies the current projection matrix
/// @param viewport Specifies the current viewport
/// @return Return the computed window coordinates.
/// @tparam T Native type used for the computation. Currently supported: half (not recommended), float or double.
/// @tparam U Currently supported: Floating-point types and integer types.
///
/// @see <a href="https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluProject.xml">gluProject man page</a>
template<typename T, typename U, qualifier Q>
GLM_FUNC_DECL vec<3, T, Q> project(
vec<3, T, Q> const& obj, mat<4, 4, T, Q> const& model, mat<4, 4, T, Q> const& proj, vec<4, U, Q> const& viewport);
/// Map the specified window coordinates (win.x, win.y, win.z) into object coordinates.
/// The near and far clip planes correspond to z normalized device coordinates of 0 and +1 respectively. (Direct3D clip volume definition)
///
/// @param win Specify the window coordinates to be mapped.
/// @param model Specifies the modelview matrix
/// @param proj Specifies the projection matrix
/// @param viewport Specifies the viewport
/// @return Returns the computed object coordinates.
/// @tparam T Native type used for the computation. Currently supported: half (not recommended), float or double.
/// @tparam U Currently supported: Floating-point types and integer types.
///
/// @see <a href="https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluUnProject.xml">gluUnProject man page</a>
template<typename T, typename U, qualifier Q>
GLM_FUNC_DECL vec<3, T, Q> unProjectZO(
vec<3, T, Q> const& win, mat<4, 4, T, Q> const& model, mat<4, 4, T, Q> const& proj, vec<4, U, Q> const& viewport);
/// Map the specified window coordinates (win.x, win.y, win.z) into object coordinates.
/// The near and far clip planes correspond to z normalized device coordinates of -1 and +1 respectively. (OpenGL clip volume definition)
///
/// @param win Specify the window coordinates to be mapped.
/// @param model Specifies the modelview matrix
/// @param proj Specifies the projection matrix
/// @param viewport Specifies the viewport
/// @return Returns the computed object coordinates.
/// @tparam T Native type used for the computation. Currently supported: half (not recommended), float or double.
/// @tparam U Currently supported: Floating-point types and integer types.
///
/// @see <a href="https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluUnProject.xml">gluUnProject man page</a>
template<typename T, typename U, qualifier Q>
GLM_FUNC_DECL vec<3, T, Q> unProjectNO(
vec<3, T, Q> const& win, mat<4, 4, T, Q> const& model, mat<4, 4, T, Q> const& proj, vec<4, U, Q> const& viewport);
/// Map the specified window coordinates (win.x, win.y, win.z) into object coordinates using default near and far clip planes definition.
/// To change default near and far clip planes definition use GLM_FORCE_DEPTH_ZERO_TO_ONE.
///
/// @param win Specify the window coordinates to be mapped.
/// @param model Specifies the modelview matrix
/// @param proj Specifies the projection matrix
/// @param viewport Specifies the viewport
/// @return Returns the computed object coordinates.
/// @tparam T Native type used for the computation. Currently supported: half (not recommended), float or double.
/// @tparam U Currently supported: Floating-point types and integer types.
///
/// @see <a href="https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluUnProject.xml">gluUnProject man page</a>
template<typename T, typename U, qualifier Q>
GLM_FUNC_DECL vec<3, T, Q> unProject(
vec<3, T, Q> const& win, mat<4, 4, T, Q> const& model, mat<4, 4, T, Q> const& proj, vec<4, U, Q> const& viewport);
/// Define a picking region
///
/// @param center Specify the center of a picking region in window coordinates.
/// @param delta Specify the width and height, respectively, of the picking region in window coordinates.
/// @param viewport Rendering viewport
/// @tparam T Native type used for the computation. Currently supported: half (not recommended), float or double.
/// @tparam U Currently supported: Floating-point types and integer types.
///
/// @see <a href="https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluPickMatrix.xml">gluPickMatrix man page</a>
template<typename T, qualifier Q, typename U>
GLM_FUNC_DECL mat<4, 4, T, Q> pickMatrix(
vec<2, T, Q> const& center, vec<2, T, Q> const& delta, vec<4, U, Q> const& viewport);
/// @}
}//namespace glm
#include "matrix_projection.inl"

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namespace glm
{
template<typename T, typename U, qualifier Q>
GLM_FUNC_QUALIFIER vec<3, T, Q> projectZO(vec<3, T, Q> const& obj, mat<4, 4, T, Q> const& model, mat<4, 4, T, Q> const& proj, vec<4, U, Q> const& viewport)
{
vec<4, T, Q> tmp = vec<4, T, Q>(obj, static_cast<T>(1));
tmp = model * tmp;
tmp = proj * tmp;
tmp /= tmp.w;
tmp.x = tmp.x * static_cast<T>(0.5) + static_cast<T>(0.5);
tmp.y = tmp.y * static_cast<T>(0.5) + static_cast<T>(0.5);
tmp[0] = tmp[0] * T(viewport[2]) + T(viewport[0]);
tmp[1] = tmp[1] * T(viewport[3]) + T(viewport[1]);
return vec<3, T, Q>(tmp);
}
template<typename T, typename U, qualifier Q>
GLM_FUNC_QUALIFIER vec<3, T, Q> projectNO(vec<3, T, Q> const& obj, mat<4, 4, T, Q> const& model, mat<4, 4, T, Q> const& proj, vec<4, U, Q> const& viewport)
{
vec<4, T, Q> tmp = vec<4, T, Q>(obj, static_cast<T>(1));
tmp = model * tmp;
tmp = proj * tmp;
tmp /= tmp.w;
tmp = tmp * static_cast<T>(0.5) + static_cast<T>(0.5);
tmp[0] = tmp[0] * T(viewport[2]) + T(viewport[0]);
tmp[1] = tmp[1] * T(viewport[3]) + T(viewport[1]);
return vec<3, T, Q>(tmp);
}
template<typename T, typename U, qualifier Q>
GLM_FUNC_QUALIFIER vec<3, T, Q> project(vec<3, T, Q> const& obj, mat<4, 4, T, Q> const& model, mat<4, 4, T, Q> const& proj, vec<4, U, Q> const& viewport)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_ZO_BIT)
return projectZO(obj, model, proj, viewport);
else
return projectNO(obj, model, proj, viewport);
}
template<typename T, typename U, qualifier Q>
GLM_FUNC_QUALIFIER vec<3, T, Q> unProjectZO(vec<3, T, Q> const& win, mat<4, 4, T, Q> const& model, mat<4, 4, T, Q> const& proj, vec<4, U, Q> const& viewport)
{
mat<4, 4, T, Q> Inverse = inverse(proj * model);
vec<4, T, Q> tmp = vec<4, T, Q>(win, T(1));
tmp.x = (tmp.x - T(viewport[0])) / T(viewport[2]);
tmp.y = (tmp.y - T(viewport[1])) / T(viewport[3]);
tmp.x = tmp.x * static_cast<T>(2) - static_cast<T>(1);
tmp.y = tmp.y * static_cast<T>(2) - static_cast<T>(1);
vec<4, T, Q> obj = Inverse * tmp;
obj /= obj.w;
return vec<3, T, Q>(obj);
}
template<typename T, typename U, qualifier Q>
GLM_FUNC_QUALIFIER vec<3, T, Q> unProjectNO(vec<3, T, Q> const& win, mat<4, 4, T, Q> const& model, mat<4, 4, T, Q> const& proj, vec<4, U, Q> const& viewport)
{
mat<4, 4, T, Q> Inverse = inverse(proj * model);
vec<4, T, Q> tmp = vec<4, T, Q>(win, T(1));
tmp.x = (tmp.x - T(viewport[0])) / T(viewport[2]);
tmp.y = (tmp.y - T(viewport[1])) / T(viewport[3]);
tmp = tmp * static_cast<T>(2) - static_cast<T>(1);
vec<4, T, Q> obj = Inverse * tmp;
obj /= obj.w;
return vec<3, T, Q>(obj);
}
template<typename T, typename U, qualifier Q>
GLM_FUNC_QUALIFIER vec<3, T, Q> unProject(vec<3, T, Q> const& win, mat<4, 4, T, Q> const& model, mat<4, 4, T, Q> const& proj, vec<4, U, Q> const& viewport)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_ZO_BIT)
return unProjectZO(win, model, proj, viewport);
else
return unProjectNO(win, model, proj, viewport);
}
template<typename T, qualifier Q, typename U>
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> pickMatrix(vec<2, T, Q> const& center, vec<2, T, Q> const& delta, vec<4, U, Q> const& viewport)
{
assert(delta.x > static_cast<T>(0) && delta.y > static_cast<T>(0));
mat<4, 4, T, Q> Result(static_cast<T>(1));
if(!(delta.x > static_cast<T>(0) && delta.y > static_cast<T>(0)))
return Result; // Error
vec<3, T, Q> Temp(
(static_cast<T>(viewport[2]) - static_cast<T>(2) * (center.x - static_cast<T>(viewport[0]))) / delta.x,
(static_cast<T>(viewport[3]) - static_cast<T>(2) * (center.y - static_cast<T>(viewport[1]))) / delta.y,
static_cast<T>(0));
// Translate and scale the picked region to the entire window
Result = translate(Result, Temp);
return scale(Result, vec<3, T, Q>(static_cast<T>(viewport[2]) / delta.x, static_cast<T>(viewport[3]) / delta.y, static_cast<T>(1)));
}
}//namespace glm

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/// @ref ext_matrix_relational
/// @file glm/ext/matrix_relational.hpp
///
/// @defgroup ext_matrix_relational GLM_EXT_matrix_relational
/// @ingroup ext
///
/// Exposes comparison functions for matrix types that take a user defined epsilon values.
///
/// Include <glm/ext/matrix_relational.hpp> to use the features of this extension.
///
/// @see ext_vector_relational
/// @see ext_scalar_relational
/// @see ext_quaternion_relational
#pragma once
// Dependencies
#include "../detail/qualifier.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_matrix_relational extension included")
#endif
namespace glm
{
/// @addtogroup ext_matrix_relational
/// @{
/// Perform a component-wise equal-to comparison of two matrices.
/// Return a boolean vector which components value is True if this expression is satisfied per column of the matrices.
///
/// @tparam C Integer between 1 and 4 included that qualify the number of columns of the matrix
/// @tparam R Integer between 1 and 4 included that qualify the number of rows of the matrix
/// @tparam T Floating-point or integer scalar types
/// @tparam Q Value from qualifier enum
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_DECL GLM_CONSTEXPR vec<C, bool, Q> equal(mat<C, R, T, Q> const& x, mat<C, R, T, Q> const& y);
/// Perform a component-wise not-equal-to comparison of two matrices.
/// Return a boolean vector which components value is True if this expression is satisfied per column of the matrices.
///
/// @tparam C Integer between 1 and 4 included that qualify the number of columns of the matrix
/// @tparam R Integer between 1 and 4 included that qualify the number of rows of the matrix
/// @tparam T Floating-point or integer scalar types
/// @tparam Q Value from qualifier enum
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_DECL GLM_CONSTEXPR vec<C, bool, Q> notEqual(mat<C, R, T, Q> const& x, mat<C, R, T, Q> const& y);
/// Returns the component-wise comparison of |x - y| < epsilon.
/// True if this expression is satisfied.
///
/// @tparam C Integer between 1 and 4 included that qualify the number of columns of the matrix
/// @tparam R Integer between 1 and 4 included that qualify the number of rows of the matrix
/// @tparam T Floating-point or integer scalar types
/// @tparam Q Value from qualifier enum
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_DECL GLM_CONSTEXPR vec<C, bool, Q> equal(mat<C, R, T, Q> const& x, mat<C, R, T, Q> const& y, T epsilon);
/// Returns the component-wise comparison of |x - y| < epsilon.
/// True if this expression is satisfied.
///
/// @tparam C Integer between 1 and 4 included that qualify the number of columns of the matrix
/// @tparam R Integer between 1 and 4 included that qualify the number of rows of the matrix
/// @tparam T Floating-point or integer scalar types
/// @tparam Q Value from qualifier enum
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_DECL GLM_CONSTEXPR vec<C, bool, Q> equal(mat<C, R, T, Q> const& x, mat<C, R, T, Q> const& y, vec<C, T, Q> const& epsilon);
/// Returns the component-wise comparison of |x - y| < epsilon.
/// True if this expression is not satisfied.
///
/// @tparam C Integer between 1 and 4 included that qualify the number of columns of the matrix
/// @tparam R Integer between 1 and 4 included that qualify the number of rows of the matrix
/// @tparam T Floating-point or integer scalar types
/// @tparam Q Value from qualifier enum
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_DECL GLM_CONSTEXPR vec<C, bool, Q> notEqual(mat<C, R, T, Q> const& x, mat<C, R, T, Q> const& y, T epsilon);
/// Returns the component-wise comparison of |x - y| >= epsilon.
/// True if this expression is not satisfied.
///
/// @tparam C Integer between 1 and 4 included that qualify the number of columns of the matrix
/// @tparam R Integer between 1 and 4 included that qualify the number of rows of the matrix
/// @tparam T Floating-point or integer scalar types
/// @tparam Q Value from qualifier enum
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_DECL GLM_CONSTEXPR vec<C, bool, Q> notEqual(mat<C, R, T, Q> const& x, mat<C, R, T, Q> const& y, vec<C, T, Q> const& epsilon);
/// Returns the component-wise comparison between two vectors in term of ULPs.
/// True if this expression is satisfied.
///
/// @tparam C Integer between 1 and 4 included that qualify the number of columns of the matrix
/// @tparam R Integer between 1 and 4 included that qualify the number of rows of the matrix
/// @tparam T Floating-point
/// @tparam Q Value from qualifier enum
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_DECL GLM_CONSTEXPR vec<C, bool, Q> equal(mat<C, R, T, Q> const& x, mat<C, R, T, Q> const& y, int ULPs);
/// Returns the component-wise comparison between two vectors in term of ULPs.
/// True if this expression is satisfied.
///
/// @tparam C Integer between 1 and 4 included that qualify the number of columns of the matrix
/// @tparam R Integer between 1 and 4 included that qualify the number of rows of the matrix
/// @tparam T Floating-point
/// @tparam Q Value from qualifier enum
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_DECL GLM_CONSTEXPR vec<C, bool, Q> equal(mat<C, R, T, Q> const& x, mat<C, R, T, Q> const& y, vec<C, int, Q> const& ULPs);
/// Returns the component-wise comparison between two vectors in term of ULPs.
/// True if this expression is not satisfied.
///
/// @tparam C Integer between 1 and 4 included that qualify the number of columns of the matrix
/// @tparam R Integer between 1 and 4 included that qualify the number of rows of the matrix
/// @tparam T Floating-point
/// @tparam Q Value from qualifier enum
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_DECL GLM_CONSTEXPR vec<C, bool, Q> notEqual(mat<C, R, T, Q> const& x, mat<C, R, T, Q> const& y, int ULPs);
/// Returns the component-wise comparison between two vectors in term of ULPs.
/// True if this expression is not satisfied.
///
/// @tparam C Integer between 1 and 4 included that qualify the number of columns of the matrix
/// @tparam R Integer between 1 and 4 included that qualify the number of rows of the matrix
/// @tparam T Floating-point
/// @tparam Q Value from qualifier enum
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_DECL GLM_CONSTEXPR vec<C, bool, Q> notEqual(mat<C, R, T, Q> const& x, mat<C, R, T, Q> const& y, vec<C, int, Q> const& ULPs);
/// @}
}//namespace glm
#include "matrix_relational.inl"

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/// @ref ext_vector_relational
/// @file glm/ext/vector_relational.inl
// Dependency:
#include "../ext/vector_relational.hpp"
#include "../common.hpp"
namespace glm
{
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR vec<C, bool, Q> equal(mat<C, R, T, Q> const& a, mat<C, R, T, Q> const& b)
{
return equal(a, b, static_cast<T>(0));
}
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR vec<C, bool, Q> equal(mat<C, R, T, Q> const& a, mat<C, R, T, Q> const& b, T Epsilon)
{
return equal(a, b, vec<C, T, Q>(Epsilon));
}
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR vec<C, bool, Q> equal(mat<C, R, T, Q> const& a, mat<C, R, T, Q> const& b, vec<C, T, Q> const& Epsilon)
{
vec<C, bool, Q> Result(true);
for(length_t i = 0; i < C; ++i)
Result[i] = all(equal(a[i], b[i], Epsilon[i]));
return Result;
}
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR vec<C, bool, Q> notEqual(mat<C, R, T, Q> const& x, mat<C, R, T, Q> const& y)
{
return notEqual(x, y, static_cast<T>(0));
}
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR vec<C, bool, Q> notEqual(mat<C, R, T, Q> const& x, mat<C, R, T, Q> const& y, T Epsilon)
{
return notEqual(x, y, vec<C, T, Q>(Epsilon));
}
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR vec<C, bool, Q> notEqual(mat<C, R, T, Q> const& a, mat<C, R, T, Q> const& b, vec<C, T, Q> const& Epsilon)
{
vec<C, bool, Q> Result(true);
for(length_t i = 0; i < C; ++i)
Result[i] = any(notEqual(a[i], b[i], Epsilon[i]));
return Result;
}
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR vec<C, bool, Q> equal(mat<C, R, T, Q> const& a, mat<C, R, T, Q> const& b, int MaxULPs)
{
return equal(a, b, vec<C, int, Q>(MaxULPs));
}
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR vec<C, bool, Q> equal(mat<C, R, T, Q> const& a, mat<C, R, T, Q> const& b, vec<C, int, Q> const& MaxULPs)
{
vec<C, bool, Q> Result(true);
for(length_t i = 0; i < C; ++i)
Result[i] = all(equal(a[i], b[i], MaxULPs[i]));
return Result;
}
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR vec<C, bool, Q> notEqual(mat<C, R, T, Q> const& x, mat<C, R, T, Q> const& y, int MaxULPs)
{
return notEqual(x, y, vec<C, int, Q>(MaxULPs));
}
template<length_t C, length_t R, typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR vec<C, bool, Q> notEqual(mat<C, R, T, Q> const& a, mat<C, R, T, Q> const& b, vec<C, int, Q> const& MaxULPs)
{
vec<C, bool, Q> Result(true);
for(length_t i = 0; i < C; ++i)
Result[i] = any(notEqual(a[i], b[i], MaxULPs[i]));
return Result;
}
}//namespace glm

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/// @ref ext_matrix_transform
/// @file glm/ext/matrix_transform.hpp
///
/// @defgroup ext_matrix_transform GLM_EXT_matrix_transform
/// @ingroup ext
///
/// Defines functions that generate common transformation matrices.
///
/// The matrices generated by this extension use standard OpenGL fixed-function
/// conventions. For example, the lookAt function generates a transform from world
/// space into the specific eye space that the projective matrix functions
/// (perspective, ortho, etc) are designed to expect. The OpenGL compatibility
/// specifications defines the particular layout of this eye space.
///
/// Include <glm/ext/matrix_transform.hpp> to use the features of this extension.
///
/// @see ext_matrix_projection
/// @see ext_matrix_clip_space
#pragma once
// Dependencies
#include "../gtc/constants.hpp"
#include "../geometric.hpp"
#include "../trigonometric.hpp"
#include "../matrix.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_matrix_transform extension included")
#endif
namespace glm
{
/// @addtogroup ext_matrix_transform
/// @{
/// Builds an identity matrix.
template<typename genType>
GLM_FUNC_DECL GLM_CONSTEXPR genType identity();
/// Builds a translation 4 * 4 matrix created from a vector of 3 components.
///
/// @param m Input matrix multiplied by this translation matrix.
/// @param v Coordinates of a translation vector.
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
///
/// @code
/// #include <glm/glm.hpp>
/// #include <glm/gtc/matrix_transform.hpp>
/// ...
/// glm::mat4 m = glm::translate(glm::mat4(1.0f), glm::vec3(1.0f));
/// // m[0][0] == 1.0f, m[0][1] == 0.0f, m[0][2] == 0.0f, m[0][3] == 0.0f
/// // m[1][0] == 0.0f, m[1][1] == 1.0f, m[1][2] == 0.0f, m[1][3] == 0.0f
/// // m[2][0] == 0.0f, m[2][1] == 0.0f, m[2][2] == 1.0f, m[2][3] == 0.0f
/// // m[3][0] == 1.0f, m[3][1] == 1.0f, m[3][2] == 1.0f, m[3][3] == 1.0f
/// @endcode
///
/// @see - translate(mat<4, 4, T, Q> const& m, T x, T y, T z)
/// @see - translate(vec<3, T, Q> const& v)
/// @see <a href="https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glTranslate.xml">glTranslate man page</a>
template<typename T, qualifier Q>
GLM_FUNC_DECL mat<4, 4, T, Q> translate(
mat<4, 4, T, Q> const& m, vec<3, T, Q> const& v);
/// Builds a rotation 4 * 4 matrix created from an axis vector and an angle.
///
/// @param m Input matrix multiplied by this rotation matrix.
/// @param angle Rotation angle expressed in radians.
/// @param axis Rotation axis, recommended to be normalized.
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
///
/// @see - rotate(mat<4, 4, T, Q> const& m, T angle, T x, T y, T z)
/// @see - rotate(T angle, vec<3, T, Q> const& v)
/// @see <a href="https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glRotate.xml">glRotate man page</a>
template<typename T, qualifier Q>
GLM_FUNC_DECL mat<4, 4, T, Q> rotate(
mat<4, 4, T, Q> const& m, T angle, vec<3, T, Q> const& axis);
/// Builds a scale 4 * 4 matrix created from 3 scalars.
///
/// @param m Input matrix multiplied by this scale matrix.
/// @param v Ratio of scaling for each axis.
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
///
/// @see - scale(mat<4, 4, T, Q> const& m, T x, T y, T z)
/// @see - scale(vec<3, T, Q> const& v)
/// @see <a href="https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glScale.xml">glScale man page</a>
template<typename T, qualifier Q>
GLM_FUNC_DECL mat<4, 4, T, Q> scale(
mat<4, 4, T, Q> const& m, vec<3, T, Q> const& v);
/// Build a right handed look at view matrix.
///
/// @param eye Position of the camera
/// @param center Position where the camera is looking at
/// @param up Normalized up vector, how the camera is oriented. Typically (0, 0, 1)
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
///
/// @see - frustum(T const& left, T const& right, T const& bottom, T const& top, T const& nearVal, T const& farVal) frustum(T const& left, T const& right, T const& bottom, T const& top, T const& nearVal, T const& farVal)
template<typename T, qualifier Q>
GLM_FUNC_DECL mat<4, 4, T, Q> lookAtRH(
vec<3, T, Q> const& eye, vec<3, T, Q> const& center, vec<3, T, Q> const& up);
/// Build a left handed look at view matrix.
///
/// @param eye Position of the camera
/// @param center Position where the camera is looking at
/// @param up Normalized up vector, how the camera is oriented. Typically (0, 0, 1)
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
///
/// @see - frustum(T const& left, T const& right, T const& bottom, T const& top, T const& nearVal, T const& farVal) frustum(T const& left, T const& right, T const& bottom, T const& top, T const& nearVal, T const& farVal)
template<typename T, qualifier Q>
GLM_FUNC_DECL mat<4, 4, T, Q> lookAtLH(
vec<3, T, Q> const& eye, vec<3, T, Q> const& center, vec<3, T, Q> const& up);
/// Build a look at view matrix based on the default handedness.
///
/// @param eye Position of the camera
/// @param center Position where the camera is looking at
/// @param up Normalized up vector, how the camera is oriented. Typically (0, 0, 1)
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
///
/// @see - frustum(T const& left, T const& right, T const& bottom, T const& top, T const& nearVal, T const& farVal) frustum(T const& left, T const& right, T const& bottom, T const& top, T const& nearVal, T const& farVal)
/// @see <a href="https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluLookAt.xml">gluLookAt man page</a>
template<typename T, qualifier Q>
GLM_FUNC_DECL mat<4, 4, T, Q> lookAt(
vec<3, T, Q> const& eye, vec<3, T, Q> const& center, vec<3, T, Q> const& up);
/// @}
}//namespace glm
#include "matrix_transform.inl"

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namespace glm
{
template<typename genType>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR genType identity()
{
return detail::init_gentype<genType, detail::genTypeTrait<genType>::GENTYPE>::identity();
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> translate(mat<4, 4, T, Q> const& m, vec<3, T, Q> const& v)
{
mat<4, 4, T, Q> Result(m);
Result[3] = m[0] * v[0] + m[1] * v[1] + m[2] * v[2] + m[3];
return Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> rotate(mat<4, 4, T, Q> const& m, T angle, vec<3, T, Q> const& v)
{
T const a = angle;
T const c = cos(a);
T const s = sin(a);
vec<3, T, Q> axis(normalize(v));
vec<3, T, Q> temp((T(1) - c) * axis);
mat<4, 4, T, Q> Rotate;
Rotate[0][0] = c + temp[0] * axis[0];
Rotate[0][1] = temp[0] * axis[1] + s * axis[2];
Rotate[0][2] = temp[0] * axis[2] - s * axis[1];
Rotate[1][0] = temp[1] * axis[0] - s * axis[2];
Rotate[1][1] = c + temp[1] * axis[1];
Rotate[1][2] = temp[1] * axis[2] + s * axis[0];
Rotate[2][0] = temp[2] * axis[0] + s * axis[1];
Rotate[2][1] = temp[2] * axis[1] - s * axis[0];
Rotate[2][2] = c + temp[2] * axis[2];
mat<4, 4, T, Q> Result;
Result[0] = m[0] * Rotate[0][0] + m[1] * Rotate[0][1] + m[2] * Rotate[0][2];
Result[1] = m[0] * Rotate[1][0] + m[1] * Rotate[1][1] + m[2] * Rotate[1][2];
Result[2] = m[0] * Rotate[2][0] + m[1] * Rotate[2][1] + m[2] * Rotate[2][2];
Result[3] = m[3];
return Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> rotate_slow(mat<4, 4, T, Q> const& m, T angle, vec<3, T, Q> const& v)
{
T const a = angle;
T const c = cos(a);
T const s = sin(a);
mat<4, 4, T, Q> Result;
vec<3, T, Q> axis = normalize(v);
Result[0][0] = c + (static_cast<T>(1) - c) * axis.x * axis.x;
Result[0][1] = (static_cast<T>(1) - c) * axis.x * axis.y + s * axis.z;
Result[0][2] = (static_cast<T>(1) - c) * axis.x * axis.z - s * axis.y;
Result[0][3] = static_cast<T>(0);
Result[1][0] = (static_cast<T>(1) - c) * axis.y * axis.x - s * axis.z;
Result[1][1] = c + (static_cast<T>(1) - c) * axis.y * axis.y;
Result[1][2] = (static_cast<T>(1) - c) * axis.y * axis.z + s * axis.x;
Result[1][3] = static_cast<T>(0);
Result[2][0] = (static_cast<T>(1) - c) * axis.z * axis.x + s * axis.y;
Result[2][1] = (static_cast<T>(1) - c) * axis.z * axis.y - s * axis.x;
Result[2][2] = c + (static_cast<T>(1) - c) * axis.z * axis.z;
Result[2][3] = static_cast<T>(0);
Result[3] = vec<4, T, Q>(0, 0, 0, 1);
return m * Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> scale(mat<4, 4, T, Q> const& m, vec<3, T, Q> const& v)
{
mat<4, 4, T, Q> Result;
Result[0] = m[0] * v[0];
Result[1] = m[1] * v[1];
Result[2] = m[2] * v[2];
Result[3] = m[3];
return Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> scale_slow(mat<4, 4, T, Q> const& m, vec<3, T, Q> const& v)
{
mat<4, 4, T, Q> Result(T(1));
Result[0][0] = v.x;
Result[1][1] = v.y;
Result[2][2] = v.z;
return m * Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> lookAtRH(vec<3, T, Q> const& eye, vec<3, T, Q> const& center, vec<3, T, Q> const& up)
{
vec<3, T, Q> const f(normalize(center - eye));
vec<3, T, Q> const s(normalize(cross(f, up)));
vec<3, T, Q> const u(cross(s, f));
mat<4, 4, T, Q> Result(1);
Result[0][0] = s.x;
Result[1][0] = s.y;
Result[2][0] = s.z;
Result[0][1] = u.x;
Result[1][1] = u.y;
Result[2][1] = u.z;
Result[0][2] =-f.x;
Result[1][2] =-f.y;
Result[2][2] =-f.z;
Result[3][0] =-dot(s, eye);
Result[3][1] =-dot(u, eye);
Result[3][2] = dot(f, eye);
return Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> lookAtLH(vec<3, T, Q> const& eye, vec<3, T, Q> const& center, vec<3, T, Q> const& up)
{
vec<3, T, Q> const f(normalize(center - eye));
vec<3, T, Q> const s(normalize(cross(up, f)));
vec<3, T, Q> const u(cross(f, s));
mat<4, 4, T, Q> Result(1);
Result[0][0] = s.x;
Result[1][0] = s.y;
Result[2][0] = s.z;
Result[0][1] = u.x;
Result[1][1] = u.y;
Result[2][1] = u.z;
Result[0][2] = f.x;
Result[1][2] = f.y;
Result[2][2] = f.z;
Result[3][0] = -dot(s, eye);
Result[3][1] = -dot(u, eye);
Result[3][2] = -dot(f, eye);
return Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> lookAt(vec<3, T, Q> const& eye, vec<3, T, Q> const& center, vec<3, T, Q> const& up)
{
if(GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_LH_BIT)
return lookAtLH(eye, center, up);
else
return lookAtRH(eye, center, up);
}
}//namespace glm

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/// @ref ext_quaternion_common
/// @file glm/ext/quaternion_common.hpp
///
/// @defgroup ext_quaternion_common GLM_EXT_quaternion_common
/// @ingroup ext
///
/// Provides common functions for quaternion types
///
/// Include <glm/ext/quaternion_common.hpp> to use the features of this extension.
///
/// @see ext_scalar_common
/// @see ext_vector_common
/// @see ext_quaternion_float
/// @see ext_quaternion_double
/// @see ext_quaternion_exponential
/// @see ext_quaternion_geometric
/// @see ext_quaternion_relational
/// @see ext_quaternion_trigonometric
/// @see ext_quaternion_transform
#pragma once
// Dependency:
#include "../ext/scalar_constants.hpp"
#include "../ext/quaternion_geometric.hpp"
#include "../common.hpp"
#include "../trigonometric.hpp"
#include "../exponential.hpp"
#include <limits>
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_quaternion_common extension included")
#endif
namespace glm
{
/// @addtogroup ext_quaternion_common
/// @{
/// Spherical linear interpolation of two quaternions.
/// The interpolation is oriented and the rotation is performed at constant speed.
/// For short path spherical linear interpolation, use the slerp function.
///
/// @param x A quaternion
/// @param y A quaternion
/// @param a Interpolation factor. The interpolation is defined beyond the range [0, 1].
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
///
/// @see - slerp(qua<T, Q> const& x, qua<T, Q> const& y, T const& a)
template<typename T, qualifier Q>
GLM_FUNC_DECL qua<T, Q> mix(qua<T, Q> const& x, qua<T, Q> const& y, T a);
/// Linear interpolation of two quaternions.
/// The interpolation is oriented.
///
/// @param x A quaternion
/// @param y A quaternion
/// @param a Interpolation factor. The interpolation is defined in the range [0, 1].
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL qua<T, Q> lerp(qua<T, Q> const& x, qua<T, Q> const& y, T a);
/// Spherical linear interpolation of two quaternions.
/// The interpolation always take the short path and the rotation is performed at constant speed.
///
/// @param x A quaternion
/// @param y A quaternion
/// @param a Interpolation factor. The interpolation is defined beyond the range [0, 1].
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL qua<T, Q> slerp(qua<T, Q> const& x, qua<T, Q> const& y, T a);
/// Returns the q conjugate.
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL qua<T, Q> conjugate(qua<T, Q> const& q);
/// Returns the q inverse.
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL qua<T, Q> inverse(qua<T, Q> const& q);
/// Returns true if x holds a NaN (not a number)
/// representation in the underlying implementation's set of
/// floating point representations. Returns false otherwise,
/// including for implementations with no NaN
/// representations.
///
/// /!\ When using compiler fast math, this function may fail.
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL vec<4, bool, Q> isnan(qua<T, Q> const& x);
/// Returns true if x holds a positive infinity or negative
/// infinity representation in the underlying implementation's
/// set of floating point representations. Returns false
/// otherwise, including for implementations with no infinity
/// representations.
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL vec<4, bool, Q> isinf(qua<T, Q> const& x);
/// @}
} //namespace glm
#include "quaternion_common.inl"

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namespace glm
{
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> mix(qua<T, Q> const& x, qua<T, Q> const& y, T a)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'mix' only accept floating-point inputs");
T const cosTheta = dot(x, y);
// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator
if(cosTheta > static_cast<T>(1) - epsilon<T>())
{
// Linear interpolation
return qua<T, Q>(
mix(x.w, y.w, a),
mix(x.x, y.x, a),
mix(x.y, y.y, a),
mix(x.z, y.z, a));
}
else
{
// Essential Mathematics, page 467
T angle = acos(cosTheta);
return (sin((static_cast<T>(1) - a) * angle) * x + sin(a * angle) * y) / sin(angle);
}
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> lerp(qua<T, Q> const& x, qua<T, Q> const& y, T a)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'lerp' only accept floating-point inputs");
// Lerp is only defined in [0, 1]
assert(a >= static_cast<T>(0));
assert(a <= static_cast<T>(1));
return x * (static_cast<T>(1) - a) + (y * a);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> slerp(qua<T, Q> const& x, qua<T, Q> const& y, T a)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'slerp' only accept floating-point inputs");
qua<T, Q> z = y;
T cosTheta = dot(x, y);
// If cosTheta < 0, the interpolation will take the long way around the sphere.
// To fix this, one quat must be negated.
if(cosTheta < static_cast<T>(0))
{
z = -y;
cosTheta = -cosTheta;
}
// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator
if(cosTheta > static_cast<T>(1) - epsilon<T>())
{
// Linear interpolation
return qua<T, Q>(
mix(x.w, z.w, a),
mix(x.x, z.x, a),
mix(x.y, z.y, a),
mix(x.z, z.z, a));
}
else
{
// Essential Mathematics, page 467
T angle = acos(cosTheta);
return (sin((static_cast<T>(1) - a) * angle) * x + sin(a * angle) * z) / sin(angle);
}
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> conjugate(qua<T, Q> const& q)
{
return qua<T, Q>(q.w, -q.x, -q.y, -q.z);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> inverse(qua<T, Q> const& q)
{
return conjugate(q) / dot(q, q);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> isnan(qua<T, Q> const& q)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isnan' only accept floating-point inputs");
return vec<4, bool, Q>(isnan(q.x), isnan(q.y), isnan(q.z), isnan(q.w));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> isinf(qua<T, Q> const& q)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isinf' only accept floating-point inputs");
return vec<4, bool, Q>(isinf(q.x), isinf(q.y), isinf(q.z), isinf(q.w));
}
}//namespace glm
#if GLM_CONFIG_SIMD == GLM_ENABLE
# include "quaternion_common_simd.inl"
#endif

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#if GLM_ARCH & GLM_ARCH_SSE2_BIT
namespace glm{
namespace detail
{
template<qualifier Q>
struct compute_dot<qua<float, Q>, float, true>
{
static GLM_FUNC_QUALIFIER float call(qua<float, Q> const& x, qua<float, Q> const& y)
{
return _mm_cvtss_f32(glm_vec1_dot(x.data, y.data));
}
};
}//namespace detail
}//namespace glm
#endif//GLM_ARCH & GLM_ARCH_SSE2_BIT

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/// @ref ext_quaternion_double
/// @file glm/ext/quaternion_double.hpp
///
/// @defgroup ext_quaternion_double GLM_EXT_quaternion_double
/// @ingroup ext
///
/// Exposes double-precision floating point quaternion type.
///
/// Include <glm/ext/quaternion_double.hpp> to use the features of this extension.
///
/// @see ext_quaternion_float
/// @see ext_quaternion_double_precision
/// @see ext_quaternion_common
/// @see ext_quaternion_exponential
/// @see ext_quaternion_geometric
/// @see ext_quaternion_relational
/// @see ext_quaternion_transform
/// @see ext_quaternion_trigonometric
#pragma once
// Dependency:
#include "../detail/type_quat.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_quaternion_double extension included")
#endif
namespace glm
{
/// @addtogroup ext_quaternion_double
/// @{
/// Quaternion of double-precision floating-point numbers.
typedef qua<double, defaultp> dquat;
/// @}
} //namespace glm

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/// @ref ext_quaternion_double_precision
/// @file glm/ext/quaternion_double_precision.hpp
///
/// @defgroup ext_quaternion_double_precision GLM_EXT_quaternion_double_precision
/// @ingroup ext
///
/// Exposes double-precision floating point quaternion type with various precision in term of ULPs.
///
/// Include <glm/ext/quaternion_double_precision.hpp> to use the features of this extension.
#pragma once
// Dependency:
#include "../detail/type_quat.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_quaternion_double_precision extension included")
#endif
namespace glm
{
/// @addtogroup ext_quaternion_double_precision
/// @{
/// Quaternion of double-precision floating-point numbers using high precision arithmetic in term of ULPs.
///
/// @see ext_quaternion_double_precision
typedef qua<double, lowp> lowp_dquat;
/// Quaternion of medium double-qualifier floating-point numbers using high precision arithmetic in term of ULPs.
///
/// @see ext_quaternion_double_precision
typedef qua<double, mediump> mediump_dquat;
/// Quaternion of high double-qualifier floating-point numbers using high precision arithmetic in term of ULPs.
///
/// @see ext_quaternion_double_precision
typedef qua<double, highp> highp_dquat;
/// @}
} //namespace glm

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/// @ref ext_quaternion_exponential
/// @file glm/ext/quaternion_exponential.hpp
///
/// @defgroup ext_quaternion_exponential GLM_EXT_quaternion_exponential
/// @ingroup ext
///
/// Provides exponential functions for quaternion types
///
/// Include <glm/ext/quaternion_exponential.hpp> to use the features of this extension.
///
/// @see core_exponential
/// @see ext_quaternion_float
/// @see ext_quaternion_double
#pragma once
// Dependency:
#include "../common.hpp"
#include "../trigonometric.hpp"
#include "../geometric.hpp"
#include "../ext/scalar_constants.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_quaternion_exponential extension included")
#endif
namespace glm
{
/// @addtogroup ext_quaternion_transform
/// @{
/// Returns a exponential of a quaternion.
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL qua<T, Q> exp(qua<T, Q> const& q);
/// Returns a logarithm of a quaternion
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL qua<T, Q> log(qua<T, Q> const& q);
/// Returns a quaternion raised to a power.
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL qua<T, Q> pow(qua<T, Q> const& q, T y);
/// Returns the square root of a quaternion
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL qua<T, Q> sqrt(qua<T, Q> const& q);
/// @}
} //namespace glm
#include "quaternion_exponential.inl"

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namespace glm
{
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> exp(qua<T, Q> const& q)
{
vec<3, T, Q> u(q.x, q.y, q.z);
T const Angle = glm::length(u);
if (Angle < epsilon<T>())
return qua<T, Q>();
vec<3, T, Q> const v(u / Angle);
return qua<T, Q>(cos(Angle), sin(Angle) * v);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> log(qua<T, Q> const& q)
{
vec<3, T, Q> u(q.x, q.y, q.z);
T Vec3Len = length(u);
if (Vec3Len < epsilon<T>())
{
if(q.w > static_cast<T>(0))
return qua<T, Q>(log(q.w), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0));
else if(q.w < static_cast<T>(0))
return qua<T, Q>(log(-q.w), pi<T>(), static_cast<T>(0), static_cast<T>(0));
else
return qua<T, Q>(std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity());
}
else
{
T t = atan(Vec3Len, T(q.w)) / Vec3Len;
T QuatLen2 = Vec3Len * Vec3Len + q.w * q.w;
return qua<T, Q>(static_cast<T>(0.5) * log(QuatLen2), t * q.x, t * q.y, t * q.z);
}
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> pow(qua<T, Q> const& x, T y)
{
//Raising to the power of 0 should yield 1
//Needed to prevent a division by 0 error later on
if(y > -epsilon<T>() && y < epsilon<T>())
return qua<T, Q>(1,0,0,0);
//To deal with non-unit quaternions
T magnitude = sqrt(x.x * x.x + x.y * x.y + x.z * x.z + x.w *x.w);
//Equivalent to raising a real number to a power
//Needed to prevent a division by 0 error later on
if(abs(x.w / magnitude) > static_cast<T>(1) - epsilon<T>() && abs(x.w / magnitude) < static_cast<T>(1) + epsilon<T>())
return qua<T, Q>(pow(x.w, y), 0, 0, 0);
T Angle = acos(x.w / magnitude);
T NewAngle = Angle * y;
T Div = sin(NewAngle) / sin(Angle);
T Mag = pow(magnitude, y - static_cast<T>(1));
return qua<T, Q>(cos(NewAngle) * magnitude * Mag, x.x * Div * Mag, x.y * Div * Mag, x.z * Div * Mag);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> sqrt(qua<T, Q> const& x)
{
return pow(x, static_cast<T>(0.5));
}
}//namespace glm

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/// @ref ext_quaternion_float
/// @file glm/ext/quaternion_float.hpp
///
/// @defgroup ext_quaternion_float GLM_EXT_quaternion_float
/// @ingroup ext
///
/// Exposes single-precision floating point quaternion type.
///
/// Include <glm/ext/quaternion_float.hpp> to use the features of this extension.
///
/// @see ext_quaternion_double
/// @see ext_quaternion_float_precision
/// @see ext_quaternion_common
/// @see ext_quaternion_exponential
/// @see ext_quaternion_geometric
/// @see ext_quaternion_relational
/// @see ext_quaternion_transform
/// @see ext_quaternion_trigonometric
#pragma once
// Dependency:
#include "../detail/type_quat.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_quaternion_float extension included")
#endif
namespace glm
{
/// @addtogroup ext_quaternion_float
/// @{
/// Quaternion of single-precision floating-point numbers.
typedef qua<float, defaultp> quat;
/// @}
} //namespace glm

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/// @ref ext_quaternion_float_precision
/// @file glm/ext/quaternion_float_precision.hpp
///
/// @defgroup ext_quaternion_float_precision GLM_EXT_quaternion_float_precision
/// @ingroup ext
///
/// Exposes single-precision floating point quaternion type with various precision in term of ULPs.
///
/// Include <glm/ext/quaternion_float_precision.hpp> to use the features of this extension.
#pragma once
// Dependency:
#include "../detail/type_quat.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_quaternion_float_precision extension included")
#endif
namespace glm
{
/// @addtogroup ext_quaternion_float_precision
/// @{
/// Quaternion of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
typedef qua<float, lowp> lowp_quat;
/// Quaternion of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
typedef qua<float, mediump> mediump_quat;
/// Quaternion of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
typedef qua<float, highp> highp_quat;
/// @}
} //namespace glm

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/// @ref ext_quaternion_geometric
/// @file glm/ext/quaternion_geometric.hpp
///
/// @defgroup ext_quaternion_geometric GLM_EXT_quaternion_geometric
/// @ingroup ext
///
/// Provides geometric functions for quaternion types
///
/// Include <glm/ext/quaternion_geometric.hpp> to use the features of this extension.
///
/// @see core_geometric
/// @see ext_quaternion_float
/// @see ext_quaternion_double
#pragma once
// Dependency:
#include "../geometric.hpp"
#include "../exponential.hpp"
#include "../ext/vector_relational.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_quaternion_geometric extension included")
#endif
namespace glm
{
/// @addtogroup ext_quaternion_geometric
/// @{
/// Returns the norm of a quaternions
///
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
///
/// @see ext_quaternion_geometric
template<typename T, qualifier Q>
GLM_FUNC_DECL T length(qua<T, Q> const& q);
/// Returns the normalized quaternion.
///
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
///
/// @see ext_quaternion_geometric
template<typename T, qualifier Q>
GLM_FUNC_DECL qua<T, Q> normalize(qua<T, Q> const& q);
/// Returns dot product of q1 and q2, i.e., q1[0] * q2[0] + q1[1] * q2[1] + ...
///
/// @tparam T Floating-point scalar types.
/// @tparam Q Value from qualifier enum
///
/// @see ext_quaternion_geometric
template<typename T, qualifier Q>
GLM_FUNC_DECL T dot(qua<T, Q> const& x, qua<T, Q> const& y);
/// Compute a cross product.
///
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
///
/// @see ext_quaternion_geometric
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> cross(qua<T, Q> const& q1, qua<T, Q> const& q2);
/// @}
} //namespace glm
#include "quaternion_geometric.inl"

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namespace glm
{
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER T dot(qua<T, Q> const& x, qua<T, Q> const& y)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'dot' accepts only floating-point inputs");
return detail::compute_dot<qua<T, Q>, T, detail::is_aligned<Q>::value>::call(x, y);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER T length(qua<T, Q> const& q)
{
return glm::sqrt(dot(q, q));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> normalize(qua<T, Q> const& q)
{
T len = length(q);
if(len <= static_cast<T>(0)) // Problem
return qua<T, Q>(static_cast<T>(1), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0));
T oneOverLen = static_cast<T>(1) / len;
return qua<T, Q>(q.w * oneOverLen, q.x * oneOverLen, q.y * oneOverLen, q.z * oneOverLen);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> cross(qua<T, Q> const& q1, qua<T, Q> const& q2)
{
return qua<T, Q>(
q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z,
q1.w * q2.x + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y,
q1.w * q2.y + q1.y * q2.w + q1.z * q2.x - q1.x * q2.z,
q1.w * q2.z + q1.z * q2.w + q1.x * q2.y - q1.y * q2.x);
}
}//namespace glm

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/// @ref ext_quaternion_relational
/// @file glm/ext/quaternion_relational.hpp
///
/// @defgroup ext_quaternion_relational GLM_EXT_quaternion_relational
/// @ingroup ext
///
/// Exposes comparison functions for quaternion types that take a user defined epsilon values.
///
/// Include <glm/ext/quaternion_relational.hpp> to use the features of this extension.
///
/// @see core_vector_relational
/// @see ext_vector_relational
/// @see ext_matrix_relational
/// @see ext_quaternion_float
/// @see ext_quaternion_double
#pragma once
// Dependency:
#include "../vector_relational.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_quaternion_relational extension included")
#endif
namespace glm
{
/// @addtogroup ext_quaternion_relational
/// @{
/// Returns the component-wise comparison of result x == y.
///
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL vec<4, bool, Q> equal(qua<T, Q> const& x, qua<T, Q> const& y);
/// Returns the component-wise comparison of |x - y| < epsilon.
///
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL vec<4, bool, Q> equal(qua<T, Q> const& x, qua<T, Q> const& y, T epsilon);
/// Returns the component-wise comparison of result x != y.
///
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL vec<4, bool, Q> notEqual(qua<T, Q> const& x, qua<T, Q> const& y);
/// Returns the component-wise comparison of |x - y| >= epsilon.
///
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL vec<4, bool, Q> notEqual(qua<T, Q> const& x, qua<T, Q> const& y, T epsilon);
/// @}
} //namespace glm
#include "quaternion_relational.inl"

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namespace glm
{
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> equal(qua<T, Q> const& x, qua<T, Q> const& y)
{
vec<4, bool, Q> Result;
for(length_t i = 0; i < x.length(); ++i)
Result[i] = x[i] == y[i];
return Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> equal(qua<T, Q> const& x, qua<T, Q> const& y, T epsilon)
{
vec<4, T, Q> v(x.x - y.x, x.y - y.y, x.z - y.z, x.w - y.w);
return lessThan(abs(v), vec<4, T, Q>(epsilon));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> notEqual(qua<T, Q> const& x, qua<T, Q> const& y)
{
vec<4, bool, Q> Result;
for(length_t i = 0; i < x.length(); ++i)
Result[i] = x[i] != y[i];
return Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> notEqual(qua<T, Q> const& x, qua<T, Q> const& y, T epsilon)
{
vec<4, T, Q> v(x.x - y.x, x.y - y.y, x.z - y.z, x.w - y.w);
return greaterThanEqual(abs(v), vec<4, T, Q>(epsilon));
}
}//namespace glm

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/// @ref ext_quaternion_transform
/// @file glm/ext/quaternion_transform.hpp
///
/// @defgroup ext_quaternion_transform GLM_EXT_quaternion_transform
/// @ingroup ext
///
/// Provides transformation functions for quaternion types
///
/// Include <glm/ext/quaternion_transform.hpp> to use the features of this extension.
///
/// @see ext_quaternion_float
/// @see ext_quaternion_double
/// @see ext_quaternion_exponential
/// @see ext_quaternion_geometric
/// @see ext_quaternion_relational
/// @see ext_quaternion_trigonometric
#pragma once
// Dependency:
#include "../common.hpp"
#include "../trigonometric.hpp"
#include "../geometric.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_quaternion_transform extension included")
#endif
namespace glm
{
/// @addtogroup ext_quaternion_transform
/// @{
/// Rotates a quaternion from a vector of 3 components axis and an angle.
///
/// @param q Source orientation
/// @param angle Angle expressed in radians.
/// @param axis Axis of the rotation
///
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL qua<T, Q> rotate(qua<T, Q> const& q, T const& angle, vec<3, T, Q> const& axis);
/// @}
} //namespace glm
#include "quaternion_transform.inl"

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namespace glm
{
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> rotate(qua<T, Q> const& q, T const& angle, vec<3, T, Q> const& v)
{
vec<3, T, Q> Tmp = v;
// Axis of rotation must be normalised
T len = glm::length(Tmp);
if(abs(len - static_cast<T>(1)) > static_cast<T>(0.001))
{
T oneOverLen = static_cast<T>(1) / len;
Tmp.x *= oneOverLen;
Tmp.y *= oneOverLen;
Tmp.z *= oneOverLen;
}
T const AngleRad(angle);
T const Sin = sin(AngleRad * static_cast<T>(0.5));
return q * qua<T, Q>(cos(AngleRad * static_cast<T>(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin);
}
}//namespace glm

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/// @ref ext_quaternion_trigonometric
/// @file glm/ext/quaternion_trigonometric.hpp
///
/// @defgroup ext_quaternion_trigonometric GLM_EXT_quaternion_trigonometric
/// @ingroup ext
///
/// Provides trigonometric functions for quaternion types
///
/// Include <glm/ext/quaternion_trigonometric.hpp> to use the features of this extension.
///
/// @see ext_quaternion_float
/// @see ext_quaternion_double
/// @see ext_quaternion_exponential
/// @see ext_quaternion_geometric
/// @see ext_quaternion_relational
/// @see ext_quaternion_transform
#pragma once
// Dependency:
#include "../trigonometric.hpp"
#include "../exponential.hpp"
#include "scalar_constants.hpp"
#include "vector_relational.hpp"
#include <limits>
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_quaternion_trigonometric extension included")
#endif
namespace glm
{
/// @addtogroup ext_quaternion_trigonometric
/// @{
/// Returns the quaternion rotation angle.
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL T angle(qua<T, Q> const& x);
/// Returns the q rotation axis.
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL vec<3, T, Q> axis(qua<T, Q> const& x);
/// Build a quaternion from an angle and a normalized axis.
///
/// @param angle Angle expressed in radians.
/// @param axis Axis of the quaternion, must be normalized.
///
/// @tparam T A floating-point scalar type
/// @tparam Q A value from qualifier enum
template<typename T, qualifier Q>
GLM_FUNC_DECL qua<T, Q> angleAxis(T const& angle, vec<3, T, Q> const& axis);
/// @}
} //namespace glm
#include "quaternion_trigonometric.inl"

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namespace glm
{
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER T angle(qua<T, Q> const& x)
{
return acos(x.w) * static_cast<T>(2);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<3, T, Q> axis(qua<T, Q> const& x)
{
T const tmp1 = static_cast<T>(1) - x.w * x.w;
if(tmp1 <= static_cast<T>(0))
return vec<3, T, Q>(0, 0, 1);
T const tmp2 = static_cast<T>(1) / sqrt(tmp1);
return vec<3, T, Q>(x.x * tmp2, x.y * tmp2, x.z * tmp2);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> angleAxis(T const& angle, vec<3, T, Q> const& v)
{
T const a(angle);
T const s = glm::sin(a * static_cast<T>(0.5));
return qua<T, Q>(glm::cos(a * static_cast<T>(0.5)), v * s);
}
}//namespace glm

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/// @ref ext_scalar_common
/// @file glm/ext/scalar_common.hpp
///
/// @defgroup ext_scalar_common GLM_EXT_scalar_common
/// @ingroup ext
///
/// Exposes min and max functions for 3 to 4 scalar parameters.
///
/// Include <glm/ext/scalar_common.hpp> to use the features of this extension.
///
/// @see core_func_common
/// @see ext_vector_common
#pragma once
// Dependency:
#include "../common.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_scalar_common extension included")
#endif
namespace glm
{
/// @addtogroup ext_scalar_common
/// @{
/// Returns the minimum component-wise values of 3 inputs
///
/// @tparam T A floating-point scalar type.
template<typename T>
GLM_FUNC_DECL T min(T a, T b, T c);
/// Returns the minimum component-wise values of 4 inputs
///
/// @tparam T A floating-point scalar type.
template<typename T>
GLM_FUNC_DECL T min(T a, T b, T c, T d);
/// Returns the maximum component-wise values of 3 inputs
///
/// @tparam T A floating-point scalar type.
template<typename T>
GLM_FUNC_DECL T max(T a, T b, T c);
/// Returns the maximum component-wise values of 4 inputs
///
/// @tparam T A floating-point scalar type.
template<typename T>
GLM_FUNC_DECL T max(T a, T b, T c, T d);
/// Returns the minimum component-wise values of 2 inputs. If one of the two arguments is NaN, the value of the other argument is returned.
///
/// @tparam T A floating-point scalar type.
///
/// @see <a href="http://en.cppreference.com/w/cpp/numeric/math/fmin">std::fmin documentation</a>
template<typename T>
GLM_FUNC_DECL T fmin(T a, T b);
/// Returns the minimum component-wise values of 3 inputs. If one of the two arguments is NaN, the value of the other argument is returned.
///
/// @tparam T A floating-point scalar type.
///
/// @see <a href="http://en.cppreference.com/w/cpp/numeric/math/fmin">std::fmin documentation</a>
template<typename T>
GLM_FUNC_DECL T fmin(T a, T b, T c);
/// Returns the minimum component-wise values of 4 inputs. If one of the two arguments is NaN, the value of the other argument is returned.
///
/// @tparam T A floating-point scalar type.
///
/// @see <a href="http://en.cppreference.com/w/cpp/numeric/math/fmin">std::fmin documentation</a>
template<typename T>
GLM_FUNC_DECL T fmin(T a, T b, T c, T d);
/// Returns the maximum component-wise values of 2 inputs. If one of the two arguments is NaN, the value of the other argument is returned.
///
/// @tparam T A floating-point scalar type.
///
/// @see <a href="http://en.cppreference.com/w/cpp/numeric/math/fmax">std::fmax documentation</a>
template<typename T>
GLM_FUNC_DECL T fmax(T a, T b);
/// Returns the maximum component-wise values of 3 inputs. If one of the two arguments is NaN, the value of the other argument is returned.
///
/// @tparam T A floating-point scalar type.
///
/// @see <a href="http://en.cppreference.com/w/cpp/numeric/math/fmax">std::fmax documentation</a>
template<typename T>
GLM_FUNC_DECL T fmax(T a, T b, T C);
/// Returns the maximum component-wise values of 4 inputs. If one of the two arguments is NaN, the value of the other argument is returned.
///
/// @tparam T A floating-point scalar type.
///
/// @see <a href="http://en.cppreference.com/w/cpp/numeric/math/fmax">std::fmax documentation</a>
template<typename T>
GLM_FUNC_DECL T fmax(T a, T b, T C, T D);
/// @}
}//namespace glm
#include "scalar_common.inl"

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namespace glm
{
template<typename T>
GLM_FUNC_QUALIFIER T min(T a, T b, T c)
{
return glm::min(glm::min(a, b), c);
}
template<typename T>
GLM_FUNC_QUALIFIER T min(T a, T b, T c, T d)
{
return glm::min(glm::min(a, b), glm::min(c, d));
}
template<typename T>
GLM_FUNC_QUALIFIER T max(T a, T b, T c)
{
return glm::max(glm::max(a, b), c);
}
template<typename T>
GLM_FUNC_QUALIFIER T max(T a, T b, T c, T d)
{
return glm::max(glm::max(a, b), glm::max(c, d));
}
# if GLM_HAS_CXX11_STL
using std::fmin;
# else
template<typename T>
GLM_FUNC_QUALIFIER T fmin(T a, T b)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'fmin' only accept floating-point input");
if (isnan(a))
return b;
return min(a, b);
}
# endif
template<typename T>
GLM_FUNC_QUALIFIER T fmin(T a, T b, T c)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'fmin' only accept floating-point input");
if (isnan(a))
return fmin(b, c);
if (isnan(b))
return fmin(a, c);
if (isnan(c))
return min(a, b);
return min(a, b, c);
}
template<typename T>
GLM_FUNC_QUALIFIER T fmin(T a, T b, T c, T d)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'fmin' only accept floating-point input");
if (isnan(a))
return fmin(b, c, d);
if (isnan(b))
return min(a, fmin(c, d));
if (isnan(c))
return fmin(min(a, b), d);
if (isnan(d))
return min(a, b, c);
return min(a, b, c, d);
}
# if GLM_HAS_CXX11_STL
using std::fmax;
# else
template<typename T>
GLM_FUNC_QUALIFIER T fmax(T a, T b)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'fmax' only accept floating-point input");
if (isnan(a))
return b;
return max(a, b);
}
# endif
template<typename T>
GLM_FUNC_QUALIFIER T fmax(T a, T b, T c)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'fmax' only accept floating-point input");
if (isnan(a))
return fmax(b, c);
if (isnan(b))
return fmax(a, c);
if (isnan(c))
return max(a, b);
return max(a, b, c);
}
template<typename T>
GLM_FUNC_QUALIFIER T fmax(T a, T b, T c, T d)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'fmax' only accept floating-point input");
if (isnan(a))
return fmax(b, c, d);
if (isnan(b))
return max(a, fmax(c, d));
if (isnan(c))
return fmax(max(a, b), d);
if (isnan(d))
return max(a, b, c);
return max(a, b, c, d);
}
}//namespace glm

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/// @ref ext_scalar_constants
/// @file glm/ext/scalar_constants.hpp
///
/// @defgroup ext_scalar_constants GLM_EXT_scalar_constants
/// @ingroup ext
///
/// Provides a list of constants and precomputed useful values.
///
/// Include <glm/ext/scalar_constants.hpp> to use the features of this extension.
#pragma once
// Dependencies
#include "../detail/setup.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_scalar_constants extension included")
#endif
namespace glm
{
/// @addtogroup ext_scalar_constants
/// @{
/// Return the epsilon constant for floating point types.
template<typename genType>
GLM_FUNC_DECL GLM_CONSTEXPR genType epsilon();
/// Return the pi constant for floating point types.
template<typename genType>
GLM_FUNC_DECL GLM_CONSTEXPR genType pi();
/// @}
} //namespace glm
#include "scalar_constants.inl"

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#include <limits>
namespace glm
{
template<typename genType>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR genType epsilon()
{
GLM_STATIC_ASSERT(std::numeric_limits<genType>::is_iec559, "'epsilon' only accepts floating-point inputs");
return std::numeric_limits<genType>::epsilon();
}
template<typename genType>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR genType pi()
{
GLM_STATIC_ASSERT(std::numeric_limits<genType>::is_iec559, "'epsilon' only accepts floating-point inputs");
return static_cast<genType>(3.14159265358979323846264338327950288);
}
} //namespace glm

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/// @ref ext_scalar_int_sized
/// @file glm/ext/scalar_int_sized.hpp
///
/// @defgroup ext_scalar_int_sized GLM_EXT_scalar_int_sized
/// @ingroup ext
///
/// Exposes sized signed integer scalar types.
///
/// Include <glm/ext/scalar_int_sized.hpp> to use the features of this extension.
///
/// @see ext_scalar_uint_sized
#pragma once
#include "../detail/setup.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_scalar_int_sized extension included")
#endif
namespace glm{
namespace detail
{
# if GLM_HAS_EXTENDED_INTEGER_TYPE
typedef std::int8_t int8;
typedef std::int16_t int16;
typedef std::int32_t int32;
# else
typedef char int8;
typedef short int16;
typedef int int32;
#endif//
template<>
struct is_int<int8>
{
enum test {value = ~0};
};
template<>
struct is_int<int16>
{
enum test {value = ~0};
};
template<>
struct is_int<int64>
{
enum test {value = ~0};
};
}//namespace detail
/// @addtogroup ext_scalar_int_sized
/// @{
/// 8 bit signed integer type.
typedef detail::int8 int8;
/// 16 bit signed integer type.
typedef detail::int16 int16;
/// 32 bit signed integer type.
typedef detail::int32 int32;
/// 64 bit signed integer type.
typedef detail::int64 int64;
/// @}
}//namespace glm

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/// @ref ext_scalar_relational
/// @file glm/ext/scalar_relational.hpp
///
/// @defgroup ext_scalar_relational GLM_EXT_scalar_relational
/// @ingroup ext
///
/// Exposes comparison functions for scalar types that take a user defined epsilon values.
///
/// Include <glm/ext/scalar_relational.hpp> to use the features of this extension.
///
/// @see core_vector_relational
/// @see ext_vector_relational
/// @see ext_matrix_relational
#pragma once
// Dependencies
#include "../detail/qualifier.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_scalar_relational extension included")
#endif
namespace glm
{
/// Returns the component-wise comparison of |x - y| < epsilon.
/// True if this expression is satisfied.
///
/// @tparam genType Floating-point or integer scalar types
template<typename genType>
GLM_FUNC_DECL GLM_CONSTEXPR bool equal(genType const& x, genType const& y, genType const& epsilon);
/// Returns the component-wise comparison of |x - y| >= epsilon.
/// True if this expression is not satisfied.
///
/// @tparam genType Floating-point or integer scalar types
template<typename genType>
GLM_FUNC_DECL GLM_CONSTEXPR bool notEqual(genType const& x, genType const& y, genType const& epsilon);
/// Returns the component-wise comparison between two scalars in term of ULPs.
/// True if this expression is satisfied.
///
/// @param x First operand.
/// @param y Second operand.
/// @param ULPs Maximum difference in ULPs between the two operators to consider them equal.
///
/// @tparam genType Floating-point or integer scalar types
template<typename genType>
GLM_FUNC_DECL GLM_CONSTEXPR bool equal(genType const& x, genType const& y, int ULPs);
/// Returns the component-wise comparison between two scalars in term of ULPs.
/// True if this expression is not satisfied.
///
/// @param x First operand.
/// @param y Second operand.
/// @param ULPs Maximum difference in ULPs between the two operators to consider them not equal.
///
/// @tparam genType Floating-point or integer scalar types
template<typename genType>
GLM_FUNC_DECL GLM_CONSTEXPR bool notEqual(genType const& x, genType const& y, int ULPs);
/// @}
}//namespace glm
#include "scalar_relational.inl"

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#include "../common.hpp"
#include "../ext/scalar_int_sized.hpp"
#include "../ext/scalar_uint_sized.hpp"
#include "../detail/type_float.hpp"
namespace glm
{
template<typename genType>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR bool equal(genType const& x, genType const& y, genType const& epsilon)
{
return abs(x - y) <= epsilon;
}
template<typename genType>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR bool notEqual(genType const& x, genType const& y, genType const& epsilon)
{
return abs(x - y) > epsilon;
}
template<typename genType>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR bool equal(genType const& x, genType const& y, int MaxULPs)
{
detail::float_t<genType> const a(x);
detail::float_t<genType> const b(y);
// Different signs means they do not match.
if(a.negative() != b.negative())
{
// Check for equality to make sure +0==-0
return a.mantissa() == b.mantissa() && a.exponent() == b.exponent();
}
// Find the difference in ULPs.
typename detail::float_t<genType>::int_type const DiffULPs = abs(a.i - b.i);
return DiffULPs <= MaxULPs;
}
template<typename genType>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR bool notEqual(genType const& x, genType const& y, int ULPs)
{
return !equal(x, y, ULPs);
}
}//namespace glm

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/// @ref ext_scalar_uint_sized
/// @file glm/ext/scalar_uint_sized.hpp
///
/// @defgroup ext_scalar_uint_sized GLM_EXT_scalar_uint_sized
/// @ingroup ext
///
/// Exposes sized unsigned integer scalar types.
///
/// Include <glm/ext/scalar_uint_sized.hpp> to use the features of this extension.
///
/// @see ext_scalar_int_sized
#pragma once
#include "../detail/setup.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_scalar_uint_sized extension included")
#endif
namespace glm{
namespace detail
{
# if GLM_HAS_EXTENDED_INTEGER_TYPE
typedef std::uint8_t uint8;
typedef std::uint16_t uint16;
typedef std::uint32_t uint32;
# else
typedef unsigned char uint8;
typedef unsigned short uint16;
typedef unsigned int uint32;
#endif
template<>
struct is_int<uint8>
{
enum test {value = ~0};
};
template<>
struct is_int<uint16>
{
enum test {value = ~0};
};
template<>
struct is_int<uint64>
{
enum test {value = ~0};
};
}//namespace detail
/// @addtogroup ext_scalar_uint_sized
/// @{
/// 8 bit unsigned integer type.
typedef detail::uint8 uint8;
/// 16 bit unsigned integer type.
typedef detail::uint16 uint16;
/// 32 bit unsigned integer type.
typedef detail::uint32 uint32;
/// 64 bit unsigned integer type.
typedef detail::uint64 uint64;
/// @}
}//namespace glm

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/// @ref ext_scalar_ulp
/// @file glm/ext/scalar_ulp.hpp
///
/// @defgroup ext_scalar_ulp GLM_EXT_scalar_ulp
/// @ingroup ext
///
/// Allow the measurement of the accuracy of a function against a reference
/// implementation. This extension works on floating-point data and provide results
/// in ULP.
///
/// Include <glm/ext/scalar_ulp.hpp> to use the features of this extension.
///
/// @see ext_vector_ulp
/// @see ext_scalar_relational
#pragma once
// Dependencies
#include "../ext/scalar_int_sized.hpp"
#include "../common.hpp"
#include "../detail/qualifier.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_scalar_ulp extension included")
#endif
namespace glm
{
/// Return the next ULP value(s) after the input value(s).
///
/// @tparam genType A floating-point scalar type.
///
/// @see ext_scalar_ulp
template<typename genType>
GLM_FUNC_DECL genType next_float(genType x);
/// Return the previous ULP value(s) before the input value(s).
///
/// @tparam genType A floating-point scalar type.
///
/// @see ext_scalar_ulp
template<typename genType>
GLM_FUNC_DECL genType prev_float(genType x);
/// Return the value(s) ULP distance after the input value(s).
///
/// @tparam genType A floating-point scalar type.
///
/// @see ext_scalar_ulp
template<typename genType>
GLM_FUNC_DECL genType next_float(genType x, int ULPs);
/// Return the value(s) ULP distance before the input value(s).
///
/// @tparam genType A floating-point scalar type.
///
/// @see ext_scalar_ulp
template<typename genType>
GLM_FUNC_DECL genType prev_float(genType x, int ULPs);
/// Return the distance in the number of ULP between 2 single-precision floating-point scalars.
///
/// @see ext_scalar_ulp
GLM_FUNC_DECL int float_distance(float x, float y);
/// Return the distance in the number of ULP between 2 double-precision floating-point scalars.
///
/// @see ext_scalar_ulp
GLM_FUNC_DECL int64 float_distance(double x, double y);
/// @}
}//namespace glm
#include "scalar_ulp.inl"

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/// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
///
/// Developed at SunPro, a Sun Microsystems, Inc. business.
/// Permission to use, copy, modify, and distribute this
/// software is freely granted, provided that this notice
/// is preserved.
#include "../detail/type_float.hpp"
#include "../ext/scalar_constants.hpp"
#include <cmath>
#include <cfloat>
#if(GLM_COMPILER & GLM_COMPILER_VC)
# pragma warning(push)
# pragma warning(disable : 4127)
#endif
typedef union
{
float value;
/* FIXME: Assumes 32 bit int. */
unsigned int word;
} ieee_float_shape_type;
typedef union
{
double value;
struct
{
int lsw;
int msw;
} parts;
} ieee_double_shape_type;
#define GLM_EXTRACT_WORDS(ix0,ix1,d) \
do { \
ieee_double_shape_type ew_u; \
ew_u.value = (d); \
(ix0) = ew_u.parts.msw; \
(ix1) = ew_u.parts.lsw; \
} while (0)
#define GLM_GET_FLOAT_WORD(i,d) \
do { \
ieee_float_shape_type gf_u; \
gf_u.value = (d); \
(i) = gf_u.word; \
} while (0)
#define GLM_SET_FLOAT_WORD(d,i) \
do { \
ieee_float_shape_type sf_u; \
sf_u.word = (i); \
(d) = sf_u.value; \
} while (0)
#define GLM_INSERT_WORDS(d,ix0,ix1) \
do { \
ieee_double_shape_type iw_u; \
iw_u.parts.msw = (ix0); \
iw_u.parts.lsw = (ix1); \
(d) = iw_u.value; \
} while (0)
namespace glm{
namespace detail
{
GLM_FUNC_QUALIFIER float nextafterf(float x, float y)
{
volatile float t;
int hx, hy, ix, iy;
GLM_GET_FLOAT_WORD(hx, x);
GLM_GET_FLOAT_WORD(hy, y);
ix = hx & 0x7fffffff; // |x|
iy = hy & 0x7fffffff; // |y|
if((ix > 0x7f800000) || // x is nan
(iy > 0x7f800000)) // y is nan
return x + y;
if(abs(y - x) <= epsilon<float>())
return y; // x=y, return y
if(ix == 0)
{ // x == 0
GLM_SET_FLOAT_WORD(x, (hy & 0x80000000) | 1);// return +-minsubnormal
t = x * x;
if(abs(t - x) <= epsilon<float>())
return t;
else
return x; // raise underflow flag
}
if(hx >= 0)
{ // x > 0
if(hx > hy) // x > y, x -= ulp
hx -= 1;
else // x < y, x += ulp
hx += 1;
}
else
{ // x < 0
if(hy >= 0 || hx > hy) // x < y, x -= ulp
hx -= 1;
else // x > y, x += ulp
hx += 1;
}
hy = hx & 0x7f800000;
if(hy >= 0x7f800000)
return x + x; // overflow
if(hy < 0x00800000) // underflow
{
t = x * x;
if(abs(t - x) > epsilon<float>())
{ // raise underflow flag
GLM_SET_FLOAT_WORD(y, hx);
return y;
}
}
GLM_SET_FLOAT_WORD(x, hx);
return x;
}
GLM_FUNC_QUALIFIER double nextafter(double x, double y)
{
volatile double t;
int hx, hy, ix, iy;
unsigned int lx, ly;
GLM_EXTRACT_WORDS(hx, lx, x);
GLM_EXTRACT_WORDS(hy, ly, y);
ix = hx & 0x7fffffff; // |x|
iy = hy & 0x7fffffff; // |y|
if(((ix >= 0x7ff00000) && ((ix - 0x7ff00000) | lx) != 0) || // x is nan
((iy >= 0x7ff00000) && ((iy - 0x7ff00000) | ly) != 0)) // y is nan
return x + y;
if(abs(y - x) <= epsilon<double>())
return y; // x=y, return y
if((ix | lx) == 0)
{ // x == 0
GLM_INSERT_WORDS(x, hy & 0x80000000, 1); // return +-minsubnormal
t = x * x;
if(abs(t - x) <= epsilon<double>())
return t;
else
return x; // raise underflow flag
}
if(hx >= 0) { // x > 0
if(hx > hy || ((hx == hy) && (lx > ly))) { // x > y, x -= ulp
if(lx == 0) hx -= 1;
lx -= 1;
}
else { // x < y, x += ulp
lx += 1;
if(lx == 0) hx += 1;
}
}
else { // x < 0
if(hy >= 0 || hx > hy || ((hx == hy) && (lx > ly))){// x < y, x -= ulp
if(lx == 0) hx -= 1;
lx -= 1;
}
else { // x > y, x += ulp
lx += 1;
if(lx == 0) hx += 1;
}
}
hy = hx & 0x7ff00000;
if(hy >= 0x7ff00000)
return x + x; // overflow
if(hy < 0x00100000)
{ // underflow
t = x * x;
if(abs(t - x) > epsilon<double>())
{ // raise underflow flag
GLM_INSERT_WORDS(y, hx, lx);
return y;
}
}
GLM_INSERT_WORDS(x, hx, lx);
return x;
}
}//namespace detail
}//namespace glm
#if(GLM_COMPILER & GLM_COMPILER_VC)
# pragma warning(pop)
#endif
namespace glm
{
template<>
GLM_FUNC_QUALIFIER float next_float(float x)
{
# if GLM_HAS_CXX11_STL
return std::nextafter(x, std::numeric_limits<float>::max());
# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
return detail::nextafterf(x, FLT_MAX);
# elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID)
return __builtin_nextafterf(x, FLT_MAX);
# else
return nextafterf(x, FLT_MAX);
# endif
}
template<>
GLM_FUNC_QUALIFIER double next_float(double x)
{
# if GLM_HAS_CXX11_STL
return std::nextafter(x, std::numeric_limits<double>::max());
# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
return detail::nextafter(x, std::numeric_limits<double>::max());
# elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID)
return __builtin_nextafter(x, DBL_MAX);
# else
return nextafter(x, DBL_MAX);
# endif
}
template<typename T>
GLM_FUNC_QUALIFIER T next_float(T x, int ULPs)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'next_float' only accept floating-point input");
assert(ULPs >= 0);
T temp = x;
for(int i = 0; i < ULPs; ++i)
temp = next_float(temp);
return temp;
}
GLM_FUNC_QUALIFIER float prev_float(float x)
{
# if GLM_HAS_CXX11_STL
return std::nextafter(x, std::numeric_limits<float>::min());
# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
return detail::nextafterf(x, FLT_MIN);
# elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID)
return __builtin_nextafterf(x, FLT_MIN);
# else
return nextafterf(x, FLT_MIN);
# endif
}
GLM_FUNC_QUALIFIER double prev_float(double x)
{
# if GLM_HAS_CXX11_STL
return std::nextafter(x, std::numeric_limits<double>::min());
# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
return _nextafter(x, DBL_MIN);
# elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID)
return __builtin_nextafter(x, DBL_MIN);
# else
return nextafter(x, DBL_MIN);
# endif
}
template<typename T>
GLM_FUNC_QUALIFIER T prev_float(T x, int ULPs)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'prev_float' only accept floating-point input");
assert(ULPs >= 0);
T temp = x;
for(int i = 0; i < ULPs; ++i)
temp = prev_float(temp);
return temp;
}
GLM_FUNC_QUALIFIER int float_distance(float x, float y)
{
detail::float_t<float> const a(x);
detail::float_t<float> const b(y);
return abs(a.i - b.i);
}
GLM_FUNC_QUALIFIER int64 float_distance(double x, double y)
{
detail::float_t<double> const a(x);
detail::float_t<double> const b(y);
return abs(a.i - b.i);
}
}//namespace glm

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/// @ref ext_vector_bool1
/// @file glm/ext/vector_bool1.hpp
///
/// @defgroup ext_vector_bool1 GLM_EXT_vector_bool1
/// @ingroup ext
///
/// Exposes bvec1 vector type.
///
/// Include <glm/ext/vector_bool1.hpp> to use the features of this extension.
///
/// @see ext_vector_bool1_precision extension.
#pragma once
#include "../detail/type_vec1.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_vector_bool1 extension included")
#endif
namespace glm
{
/// @addtogroup ext_vector_bool1
/// @{
/// 1 components vector of boolean.
typedef vec<1, bool, defaultp> bvec1;
/// @}
}//namespace glm

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/// @ref ext_vector_bool1_precision
/// @file glm/ext/vector_bool1_precision.hpp
///
/// @defgroup ext_vector_bool1_precision GLM_EXT_vector_bool1_precision
/// @ingroup ext
///
/// Exposes highp_bvec1, mediump_bvec1 and lowp_bvec1 types.
///
/// Include <glm/ext/vector_bool1_precision.hpp> to use the features of this extension.
#pragma once
#include "../detail/type_vec1.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_vector_bool1_precision extension included")
#endif
namespace glm
{
/// @addtogroup ext_vector_bool1_precision
/// @{
/// 1 component vector of bool values.
typedef vec<1, bool, highp> highp_bvec1;
/// 1 component vector of bool values.
typedef vec<1, bool, mediump> mediump_bvec1;
/// 1 component vector of bool values.
typedef vec<1, bool, lowp> lowp_bvec1;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_bool2.hpp
#pragma once
#include "../detail/type_vec2.hpp"
namespace glm
{
/// @addtogroup core_vector
/// @{
/// 2 components vector of boolean.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
typedef vec<2, bool, defaultp> bvec2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_bool2_precision.hpp
#pragma once
#include "../detail/type_vec2.hpp"
namespace glm
{
/// @addtogroup core_vector_precision
/// @{
/// 2 components vector of high qualifier bool numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<2, bool, highp> highp_bvec2;
/// 2 components vector of medium qualifier bool numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<2, bool, mediump> mediump_bvec2;
/// 2 components vector of low qualifier bool numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<2, bool, lowp> lowp_bvec2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_bool3.hpp
#pragma once
#include "../detail/type_vec3.hpp"
namespace glm
{
/// @addtogroup core_vector
/// @{
/// 3 components vector of boolean.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
typedef vec<3, bool, defaultp> bvec3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_bool3_precision.hpp
#pragma once
#include "../detail/type_vec3.hpp"
namespace glm
{
/// @addtogroup core_vector_precision
/// @{
/// 3 components vector of high qualifier bool numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<3, bool, highp> highp_bvec3;
/// 3 components vector of medium qualifier bool numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<3, bool, mediump> mediump_bvec3;
/// 3 components vector of low qualifier bool numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<3, bool, lowp> lowp_bvec3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_bool4.hpp
#pragma once
#include "../detail/type_vec4.hpp"
namespace glm
{
/// @addtogroup core_vector
/// @{
/// 4 components vector of boolean.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
typedef vec<4, bool, defaultp> bvec4;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_bool4_precision.hpp
#pragma once
#include "../detail/type_vec4.hpp"
namespace glm
{
/// @addtogroup core_vector_precision
/// @{
/// 4 components vector of high qualifier bool numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<4, bool, highp> highp_bvec4;
/// 4 components vector of medium qualifier bool numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<4, bool, mediump> mediump_bvec4;
/// 4 components vector of low qualifier bool numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<4, bool, lowp> lowp_bvec4;
/// @}
}//namespace glm

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/// @ref ext_vector_common
/// @file glm/ext/vector_common.hpp
///
/// @defgroup ext_vector_common GLM_EXT_vector_common
/// @ingroup ext
///
/// Exposes min and max functions for 3 to 4 vector parameters.
///
/// Include <glm/ext/vector_common.hpp> to use the features of this extension.
///
/// @see core_common
/// @see ext_scalar_common
#pragma once
// Dependency:
#include "../ext/scalar_common.hpp"
#include "../common.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_vector_common extension included")
#endif
namespace glm
{
/// @addtogroup ext_vector_common
/// @{
/// Return the minimum component-wise values of 3 inputs
///
/// @tparam L Integer between 1 and 4 included that qualify the dimension of the vector
/// @tparam T Floating-point or integer scalar types
/// @tparam Q Value from qualifier enum
template<length_t L, typename T, qualifier Q>
GLM_FUNC_DECL GLM_CONSTEXPR vec<L, T, Q> min(vec<L, T, Q> const& a, vec<L, T, Q> const& b, vec<L, T, Q> const& c);
/// Return the minimum component-wise values of 4 inputs
///
/// @tparam L Integer between 1 and 4 included that qualify the dimension of the vector
/// @tparam T Floating-point or integer scalar types
/// @tparam Q Value from qualifier enum
template<length_t L, typename T, qualifier Q>
GLM_FUNC_DECL GLM_CONSTEXPR vec<L, T, Q> min(vec<L, T, Q> const& a, vec<L, T, Q> const& b, vec<L, T, Q> const& c, vec<L, T, Q> const& d);
/// Return the maximum component-wise values of 3 inputs
///
/// @tparam L Integer between 1 and 4 included that qualify the dimension of the vector
/// @tparam T Floating-point or integer scalar types
/// @tparam Q Value from qualifier enum
template<length_t L, typename T, qualifier Q>
GLM_FUNC_DECL GLM_CONSTEXPR vec<L, T, Q> max(vec<L, T, Q> const& x, vec<L, T, Q> const& y, vec<L, T, Q> const& z);
/// Return the maximum component-wise values of 4 inputs
///
/// @tparam L Integer between 1 and 4 included that qualify the dimension of the vector
/// @tparam T Floating-point or integer scalar types
/// @tparam Q Value from qualifier enum
template<length_t L, typename T, qualifier Q>
GLM_FUNC_DECL GLM_CONSTEXPR vec<L, T, Q> max( vec<L, T, Q> const& x, vec<L, T, Q> const& y, vec<L, T, Q> const& z, vec<L, T, Q> const& w);
/// Returns y if y < x; otherwise, it returns x. If one of the two arguments is NaN, the value of the other argument is returned.
///
/// @tparam L Integer between 1 and 4 included that qualify the dimension of the vector
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
///
/// @see <a href="http://en.cppreference.com/w/cpp/numeric/math/fmin">std::fmin documentation</a>
template<length_t L, typename T, qualifier Q>
GLM_FUNC_DECL vec<L, T, Q> fmin(vec<L, T, Q> const& x, T y);
/// Returns y if y < x; otherwise, it returns x. If one of the two arguments is NaN, the value of the other argument is returned.
///
/// @tparam L Integer between 1 and 4 included that qualify the dimension of the vector
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
///
/// @see <a href="http://en.cppreference.com/w/cpp/numeric/math/fmin">std::fmin documentation</a>
template<length_t L, typename T, qualifier Q>
GLM_FUNC_DECL vec<L, T, Q> fmin(vec<L, T, Q> const& x, vec<L, T, Q> const& y);
/// Returns y if y < x; otherwise, it returns x. If one of the two arguments is NaN, the value of the other argument is returned.
///
/// @tparam L Integer between 1 and 4 included that qualify the dimension of the vector
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
///
/// @see <a href="http://en.cppreference.com/w/cpp/numeric/math/fmin">std::fmin documentation</a>
template<length_t L, typename T, qualifier Q>
GLM_FUNC_DECL vec<L, T, Q> fmin(vec<L, T, Q> const& a, vec<L, T, Q> const& b, vec<L, T, Q> const& c);
/// Returns y if y < x; otherwise, it returns x. If one of the two arguments is NaN, the value of the other argument is returned.
///
/// @tparam L Integer between 1 and 4 included that qualify the dimension of the vector
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
///
/// @see <a href="http://en.cppreference.com/w/cpp/numeric/math/fmin">std::fmin documentation</a>
template<length_t L, typename T, qualifier Q>
GLM_FUNC_DECL vec<L, T, Q> fmin(vec<L, T, Q> const& a, vec<L, T, Q> const& b, vec<L, T, Q> const& c, vec<L, T, Q> const& d);
/// Returns y if x < y; otherwise, it returns x. If one of the two arguments is NaN, the value of the other argument is returned.
///
/// @tparam L Integer between 1 and 4 included that qualify the dimension of the vector
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
///
/// @see <a href="http://en.cppreference.com/w/cpp/numeric/math/fmax">std::fmax documentation</a>
template<length_t L, typename T, qualifier Q>
GLM_FUNC_DECL vec<L, T, Q> fmax(vec<L, T, Q> const& a, T b);
/// Returns y if x < y; otherwise, it returns x. If one of the two arguments is NaN, the value of the other argument is returned.
///
/// @tparam L Integer between 1 and 4 included that qualify the dimension of the vector
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
///
/// @see <a href="http://en.cppreference.com/w/cpp/numeric/math/fmax">std::fmax documentation</a>
template<length_t L, typename T, qualifier Q>
GLM_FUNC_DECL vec<L, T, Q> fmax(vec<L, T, Q> const& a, vec<L, T, Q> const& b);
/// Returns y if x < y; otherwise, it returns x. If one of the two arguments is NaN, the value of the other argument is returned.
///
/// @tparam L Integer between 1 and 4 included that qualify the dimension of the vector
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
///
/// @see <a href="http://en.cppreference.com/w/cpp/numeric/math/fmax">std::fmax documentation</a>
template<length_t L, typename T, qualifier Q>
GLM_FUNC_DECL vec<L, T, Q> fmax(vec<L, T, Q> const& a, vec<L, T, Q> const& b, vec<L, T, Q> const& c);
/// Returns y if x < y; otherwise, it returns x. If one of the two arguments is NaN, the value of the other argument is returned.
///
/// @tparam L Integer between 1 and 4 included that qualify the dimension of the vector
/// @tparam T Floating-point scalar types
/// @tparam Q Value from qualifier enum
///
/// @see <a href="http://en.cppreference.com/w/cpp/numeric/math/fmax">std::fmax documentation</a>
template<length_t L, typename T, qualifier Q>
GLM_FUNC_DECL vec<L, T, Q> fmax(vec<L, T, Q> const& a, vec<L, T, Q> const& b, vec<L, T, Q> const& c, vec<L, T, Q> const& d);
/// @}
}//namespace glm
#include "vector_common.inl"

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#include "../detail/_vectorize.hpp"
namespace glm
{
template<length_t L, typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR vec<L, T, Q> min(vec<L, T, Q> const& x, vec<L, T, Q> const& y, vec<L, T, Q> const& z)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'min' only accept floating-point or integer inputs");
return glm::min(glm::min(x, y), z);
}
template<length_t L, typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR vec<L, T, Q> min(vec<L, T, Q> const& x, vec<L, T, Q> const& y, vec<L, T, Q> const& z, vec<L, T, Q> const& w)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'min' only accept floating-point or integer inputs");
return glm::min(glm::min(x, y), glm::min(z, w));
}
template<length_t L, typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR vec<L, T, Q> max(vec<L, T, Q> const& x, vec<L, T, Q> const& y, vec<L, T, Q> const& z)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'max' only accept floating-point or integer inputs");
return glm::max(glm::max(x, y), z);
}
template<length_t L, typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR vec<L, T, Q> max(vec<L, T, Q> const& x, vec<L, T, Q> const& y, vec<L, T, Q> const& z, vec<L, T, Q> const& w)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'max' only accept floating-point or integer inputs");
return glm::max(glm::max(x, y), glm::max(z, w));
}
template<length_t L, typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<L, T, Q> fmin(vec<L, T, Q> const& a, T b)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'fmin' only accept floating-point inputs");
return detail::functor2<vec, L, T, Q>::call(fmin, a, vec<L, T, Q>(b));
}
template<length_t L, typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<L, T, Q> fmin(vec<L, T, Q> const& a, vec<L, T, Q> const& b)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'fmin' only accept floating-point inputs");
return detail::functor2<vec, L, T, Q>::call(fmin, a, b);
}
template<length_t L, typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<L, T, Q> fmin(vec<L, T, Q> const& a, vec<L, T, Q> const& b, vec<L, T, Q> const& c)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'fmin' only accept floating-point inputs");
return fmin(fmin(a, b), c);
}
template<length_t L, typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<L, T, Q> fmin(vec<L, T, Q> const& a, vec<L, T, Q> const& b, vec<L, T, Q> const& c, vec<L, T, Q> const& d)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'fmin' only accept floating-point inputs");
return fmin(fmin(a, b), fmin(c, d));
}
template<length_t L, typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<L, T, Q> fmax(vec<L, T, Q> const& a, T b)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'fmax' only accept floating-point inputs");
return detail::functor2<vec, L, T, Q>::call(fmax, a, vec<L, T, Q>(b));
}
template<length_t L, typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<L, T, Q> fmax(vec<L, T, Q> const& a, vec<L, T, Q> const& b)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'fmax' only accept floating-point inputs");
return detail::functor2<vec, L, T, Q>::call(fmax, a, b);
}
template<length_t L, typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<L, T, Q> fmax(vec<L, T, Q> const& a, vec<L, T, Q> const& b, vec<L, T, Q> const& c)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'fmax' only accept floating-point inputs");
return fmax(fmax(a, b), c);
}
template<length_t L, typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<L, T, Q> fmax(vec<L, T, Q> const& a, vec<L, T, Q> const& b, vec<L, T, Q> const& c, vec<L, T, Q> const& d)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'fmax' only accept floating-point inputs");
return fmax(fmax(a, b), fmax(c, d));
}
}//namespace glm

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/// @ref ext_vector_double1
/// @file glm/ext/vector_double1.hpp
///
/// @defgroup ext_vector_double1 GLM_EXT_vector_double1
/// @ingroup ext
///
/// Exposes double-precision floating point vector type with one component.
///
/// Include <glm/ext/vector_double1.hpp> to use the features of this extension.
///
/// @see ext_vector_double1_precision extension.
/// @see ext_vector_float1 extension.
#pragma once
#include "../detail/type_vec1.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_vector_dvec1 extension included")
#endif
namespace glm
{
/// @addtogroup ext_vector_double1
/// @{
/// 1 components vector of double-precision floating-point numbers.
typedef vec<1, double, defaultp> dvec1;
/// @}
}//namespace glm

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/// @ref ext_vector_double1_precision
/// @file glm/ext/vector_double1_precision.hpp
///
/// @defgroup ext_vector_double1_precision GLM_EXT_vector_double1_precision
/// @ingroup ext
///
/// Exposes highp_dvec1, mediump_dvec1 and lowp_dvec1 types.
///
/// Include <glm/ext/vector_double1_precision.hpp> to use the features of this extension.
///
/// @see ext_vector_double1
#pragma once
#include "../detail/type_vec1.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_vector_double1_precision extension included")
#endif
namespace glm
{
/// @addtogroup ext_vector_double1_precision
/// @{
/// 1 component vector of double-precision floating-point numbers using high precision arithmetic in term of ULPs.
typedef vec<1, double, highp> highp_dvec1;
/// 1 component vector of double-precision floating-point numbers using medium precision arithmetic in term of ULPs.
typedef vec<1, double, mediump> mediump_dvec1;
/// 1 component vector of double-precision floating-point numbers using low precision arithmetic in term of ULPs.
typedef vec<1, double, lowp> lowp_dvec1;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_double2.hpp
#pragma once
#include "../detail/type_vec2.hpp"
namespace glm
{
/// @addtogroup core_vector
/// @{
/// 2 components vector of double-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
typedef vec<2, double, defaultp> dvec2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_double2_precision.hpp
#pragma once
#include "../detail/type_vec2.hpp"
namespace glm
{
/// @addtogroup core_vector_precision
/// @{
/// 2 components vector of high double-qualifier floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<2, double, highp> highp_dvec2;
/// 2 components vector of medium double-qualifier floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<2, double, mediump> mediump_dvec2;
/// 2 components vector of low double-qualifier floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<2, double, lowp> lowp_dvec2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_double3.hpp
#pragma once
#include "../detail/type_vec3.hpp"
namespace glm
{
/// @addtogroup core_vector
/// @{
/// 3 components vector of double-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
typedef vec<3, double, defaultp> dvec3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_double3_precision.hpp
#pragma once
#include "../detail/type_vec3.hpp"
namespace glm
{
/// @addtogroup core_vector_precision
/// @{
/// 3 components vector of high double-qualifier floating-point numbers.
/// There is no guarantee on the actual qualifier.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<3, double, highp> highp_dvec3;
/// 3 components vector of medium double-qualifier floating-point numbers.
/// There is no guarantee on the actual qualifier.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<3, double, mediump> mediump_dvec3;
/// 3 components vector of low double-qualifier floating-point numbers.
/// There is no guarantee on the actual qualifier.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<3, double, lowp> lowp_dvec3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_double4.hpp
#pragma once
#include "../detail/type_vec4.hpp"
namespace glm
{
/// @addtogroup core_vector
/// @{
/// 4 components vector of double-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
typedef vec<4, double, defaultp> dvec4;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_double4_precision.hpp
#pragma once
#include "../detail/setup.hpp"
#include "../detail/type_vec4.hpp"
namespace glm
{
/// @addtogroup core_vector_precision
/// @{
/// 4 components vector of high double-qualifier floating-point numbers.
/// There is no guarantee on the actual qualifier.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<4, double, highp> highp_dvec4;
/// 4 components vector of medium double-qualifier floating-point numbers.
/// There is no guarantee on the actual qualifier.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<4, double, mediump> mediump_dvec4;
/// 4 components vector of low double-qualifier floating-point numbers.
/// There is no guarantee on the actual qualifier.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<4, double, lowp> lowp_dvec4;
/// @}
}//namespace glm

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/// @ref ext_vector_float1
/// @file glm/ext/vector_float1.hpp
///
/// @defgroup ext_vector_float1 GLM_EXT_vector_float1
/// @ingroup ext
///
/// Exposes single-precision floating point vector type with one component.
///
/// Include <glm/ext/vector_float1.hpp> to use the features of this extension.
///
/// @see ext_vector_float1_precision extension.
/// @see ext_vector_double1 extension.
#pragma once
#include "../detail/type_vec1.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_vector_float1 extension included")
#endif
namespace glm
{
/// @addtogroup ext_vector_float1
/// @{
/// 1 components vector of single-precision floating-point numbers.
typedef vec<1, float, defaultp> vec1;
/// @}
}//namespace glm

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/// @ref ext_vector_float1_precision
/// @file glm/ext/vector_float1_precision.hpp
///
/// @defgroup ext_vector_float1_precision GLM_EXT_vector_float1_precision
/// @ingroup ext
///
/// Exposes highp_vec1, mediump_vec1 and lowp_vec1 types.
///
/// Include <glm/ext/vector_float1_precision.hpp> to use the features of this extension.
///
/// @see ext_vector_float1 extension.
#pragma once
#include "../detail/type_vec1.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_vector_float1_precision extension included")
#endif
namespace glm
{
/// @addtogroup ext_vector_float1_precision
/// @{
/// 1 component vector of single-precision floating-point numbers using high precision arithmetic in term of ULPs.
typedef vec<1, float, highp> highp_vec1;
/// 1 component vector of single-precision floating-point numbers using medium precision arithmetic in term of ULPs.
typedef vec<1, float, mediump> mediump_vec1;
/// 1 component vector of single-precision floating-point numbers using low precision arithmetic in term of ULPs.
typedef vec<1, float, lowp> lowp_vec1;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_float2.hpp
#pragma once
#include "../detail/type_vec2.hpp"
namespace glm
{
/// @addtogroup core_vector
/// @{
/// 2 components vector of single-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
typedef vec<2, float, defaultp> vec2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_float2_precision.hpp
#pragma once
#include "../detail/type_vec2.hpp"
namespace glm
{
/// @addtogroup core_vector_precision
/// @{
/// 2 components vector of high single-qualifier floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<2, float, highp> highp_vec2;
/// 2 components vector of medium single-qualifier floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<2, float, mediump> mediump_vec2;
/// 2 components vector of low single-qualifier floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<2, float, lowp> lowp_vec2;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_float3.hpp
#pragma once
#include "../detail/type_vec3.hpp"
namespace glm
{
/// @addtogroup core_vector
/// @{
/// 3 components vector of single-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
typedef vec<3, float, defaultp> vec3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_float3_precision.hpp
#pragma once
#include "../detail/type_vec3.hpp"
namespace glm
{
/// @addtogroup core_vector_precision
/// @{
/// 3 components vector of high single-qualifier floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<3, float, highp> highp_vec3;
/// 3 components vector of medium single-qualifier floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<3, float, mediump> mediump_vec3;
/// 3 components vector of low single-qualifier floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<3, float, lowp> lowp_vec3;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_float4.hpp
#pragma once
#include "../detail/type_vec4.hpp"
namespace glm
{
/// @addtogroup core_vector
/// @{
/// 4 components vector of single-precision floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
typedef vec<4, float, defaultp> vec4;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_float4_precision.hpp
#pragma once
#include "../detail/type_vec4.hpp"
namespace glm
{
/// @addtogroup core_vector_precision
/// @{
/// 4 components vector of high single-qualifier floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<4, float, highp> highp_vec4;
/// 4 components vector of medium single-qualifier floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<4, float, mediump> mediump_vec4;
/// 4 components vector of low single-qualifier floating-point numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.7.2 Precision Qualifier</a>
typedef vec<4, float, lowp> lowp_vec4;
/// @}
}//namespace glm

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/// @ref ext_vector_int1
/// @file glm/ext/vector_int1.hpp
///
/// @defgroup ext_vector_int1 GLM_EXT_vector_int1
/// @ingroup ext
///
/// Exposes ivec1 vector type.
///
/// Include <glm/ext/vector_int1.hpp> to use the features of this extension.
///
/// @see ext_vector_uint1 extension.
/// @see ext_vector_int1_precision extension.
#pragma once
#include "../detail/type_vec1.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_vector_int1 extension included")
#endif
namespace glm
{
/// @addtogroup ext_vector_int1
/// @{
/// 1 component vector of signed integer numbers.
typedef vec<1, int, defaultp> ivec1;
/// @}
}//namespace glm

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/// @ref ext_vector_int1_precision
/// @file glm/ext/vector_int1_precision.hpp
///
/// @defgroup ext_vector_int1_precision GLM_EXT_vector_int1_precision
/// @ingroup ext
///
/// Exposes highp_ivec1, mediump_ivec1 and lowp_ivec1 types.
///
/// Include <glm/ext/vector_int1_precision.hpp> to use the features of this extension.
#pragma once
#include "../detail/type_vec1.hpp"
#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
# pragma message("GLM: GLM_EXT_vector_int1_precision extension included")
#endif
namespace glm
{
/// @addtogroup ext_vector_int1_precision
/// @{
/// 1 component vector of signed integer values.
typedef vec<1, int, highp> highp_ivec1;
/// 1 component vector of signed integer values.
typedef vec<1, int, mediump> mediump_ivec1;
/// 1 component vector of signed integer values.
typedef vec<1, int, lowp> lowp_ivec1;
/// @}
}//namespace glm

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/// @ref core
/// @file glm/ext/vector_int2.hpp
#pragma once
#include "../detail/type_vec2.hpp"
namespace glm
{
/// @addtogroup core_vector
/// @{
/// 2 components vector of signed integer numbers.
///
/// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 4.1.5 Vectors</a>
typedef vec<2, int, defaultp> ivec2;
/// @}
}//namespace glm

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