first commit

modern-qt/utility/solution/round-angle.cc

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+#include "round-angle.hh"
+#include <eigen3/Eigen/Dense>
+
+using namespace creeper;
+using Eigen::Vector2d, std::numbers::pi;
+
+static inline auto impl_round_angle_solution(
+    RoundAngleSolution& solution, Vector2d e0, Vector2d e1, Vector2d e2, double radius) -> void {
+
+    // solve the arc origin
+    const auto v1 = Vector2d { e1 - e0 };
+    const auto v2 = Vector2d { e2 - e0 };
+
+    const auto dot = v1.x() * v2.x() + v1.y() * v2.y();
+    const auto det = v1.x() * v2.y() - v1.y() * v2.x();
+
+    const auto angle = std::abs(std::atan2(det, dot));
+    const auto width = radius / std::tan(angle / 2);
+
+    const auto point_begin = Vector2d { e0 + width * v1.normalized() };
+    const auto point_end   = Vector2d { e0 + width * v2.normalized() };
+
+    const auto origin = Vector2d { point_begin + radius * v1.unitOrthogonal() };
+
+    solution.start = QPointF { point_begin.x(), point_begin.y() };
+    solution.end   = QPointF { point_end.x(), point_end.y() };
+
+    // solve the rect corners
+    const auto v3          = Vector2d { e0 - origin }.normalized();
+    const auto v4          = Vector2d { v3.unitOrthogonal() };
+    const Vector2d corner0 = origin + Vector2d::UnitX() * radius + Vector2d::UnitY() * radius;
+    const Vector2d corner1 = origin - Vector2d::UnitX() * radius - Vector2d::UnitY() * radius;
+    solution.rect = QRectF { QPointF(corner1.x(), corner1.y()), QPointF(corner0.x(), corner0.y()) };
+
+    // solve the arc angle
+    // 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
+    const auto angle_begin_vector = Vector2d { point_begin - origin };
+    const auto angle_end_vector   = Vector2d { point_end - origin };
+
+    const auto angle_end = std::atan2(-angle_end_vector.y(), angle_end_vector.x());
+
+    solution.angle_begin  = std::atan2(-angle_begin_vector.y(), angle_begin_vector.x());
+    solution.angle_length = angle_end - solution.angle_begin;
+
+    if (solution.angle_length < -pi) solution.angle_length = 2 * pi + solution.angle_length;
+
+    solution.angle_begin  = solution.angle_begin * 180 / pi;
+    solution.angle_length = solution.angle_length * 180 / pi;
+}
+
+RoundAngleSolution::RoundAngleSolution(QPointF e0, QPointF e1, QPointF e2, double radius) noexcept {
+    impl_round_angle_solution(
+        *this, Eigen::Vector2d { e0.x(), e0.y() }, { e1.x(), e1.y() }, { e2.x(), e2.y() }, radius);
+}

modern-qt/utility/solution/round-angle.hh

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+#pragma once
+
+#include <qpoint.h>
+#include <qrect.h>
+
+namespace creeper {
+
+struct RoundAngleSolution {
+
+    /// @brief 给定原点和端点，按逆时针方向计算圆弧
+    /// @note 圆弧注意按照逆时针算
+    /// @param e0 两切线交点
+    /// @param e1 圆弧起始点切线
+    /// @param e2 圆弧终点切线
+    /// @param radius 半径
+    RoundAngleSolution(QPointF e0, QPointF e1, QPointF e2, double radius) noexcept;
+
+    QRectF rect;
+    QPointF start;
+    QPointF end;
+    double angle_begin;
+    double angle_length;
+};
+
+}