55 lines
2.3 KiB
C++
55 lines
2.3 KiB
C++
#include "round-angle.hh"
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#include <eigen3/Eigen/Dense>
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using namespace creeper;
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using Eigen::Vector2d, std::numbers::pi;
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static inline auto impl_round_angle_solution(
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RoundAngleSolution& solution, Vector2d e0, Vector2d e1, Vector2d e2, double radius) -> void {
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// solve the arc origin
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const auto v1 = Vector2d { e1 - e0 };
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const auto v2 = Vector2d { e2 - e0 };
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const auto dot = v1.x() * v2.x() + v1.y() * v2.y();
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const auto det = v1.x() * v2.y() - v1.y() * v2.x();
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const auto angle = std::abs(std::atan2(det, dot));
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const auto width = radius / std::tan(angle / 2);
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const auto point_begin = Vector2d { e0 + width * v1.normalized() };
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const auto point_end = Vector2d { e0 + width * v2.normalized() };
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const auto origin = Vector2d { point_begin + radius * v1.unitOrthogonal() };
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solution.start = QPointF { point_begin.x(), point_begin.y() };
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solution.end = QPointF { point_end.x(), point_end.y() };
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// solve the rect corners
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const auto v3 = Vector2d { e0 - origin }.normalized();
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const auto v4 = Vector2d { v3.unitOrthogonal() };
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const Vector2d corner0 = origin + Vector2d::UnitX() * radius + Vector2d::UnitY() * radius;
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const Vector2d corner1 = origin - Vector2d::UnitX() * radius - Vector2d::UnitY() * radius;
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solution.rect = QRectF { QPointF(corner1.x(), corner1.y()), QPointF(corner0.x(), corner0.y()) };
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// solve the arc angle
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// 角度计算时，注意Qt的系Y的正方向向下，但角度又是从X正方向逆时针开始计算,可谓混乱
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const auto angle_begin_vector = Vector2d { point_begin - origin };
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const auto angle_end_vector = Vector2d { point_end - origin };
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const auto angle_end = std::atan2(-angle_end_vector.y(), angle_end_vector.x());
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solution.angle_begin = std::atan2(-angle_begin_vector.y(), angle_begin_vector.x());
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solution.angle_length = angle_end - solution.angle_begin;
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if (solution.angle_length < -pi) solution.angle_length = 2 * pi + solution.angle_length;
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solution.angle_begin = solution.angle_begin * 180 / pi;
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solution.angle_length = solution.angle_length * 180 / pi;
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}
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RoundAngleSolution::RoundAngleSolution(QPointF e0, QPointF e1, QPointF e2, double radius) noexcept {
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impl_round_angle_solution(
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*this, Eigen::Vector2d { e0.x(), e0.y() }, { e1.x(), e1.y() }, { e2.x(), e2.y() }, radius);
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}
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