--- a/src/geometry.cpp Thu Apr 14 11:08:20 2022 +0300
+++ b/src/geometry.cpp Mon May 16 01:40:49 2022 +0300
@@ -235,3 +235,43 @@
}
return (sum < 0) ? Winding::Anticlockwise : Winding::Clockwise;
}
+
+/**
+ * @brief computes the point on a Bezier curve
+ * @param curve
+ * @param t scalar between 0 and 1, with t=0 being P0 and t=1 being P3
+ * @return point on curve
+ */
+glm::vec3 geom::pointOnCurve(const BezierCurve &curve, float t)
+{
+ // clamp t as rounding errors might make it slightly out of bounds
+ t = std::clamp(t, 0.0f, 1.0f);
+ const float t_2 = t * t;
+ const float t_3 = t * t * t;
+ const float coeffs[3] = {
+ -1*t_3 +3*t_2 -3*t +1,
+ +3*t_3 -6*t_2 +3*t,
+ -3*t_3 +3*t_2,
+ };
+ return coeffs[0] * curve[0] + coeffs[1] * curve[1] + coeffs[2] * curve[2] + t_3 * curve[3];
+}
+
+/**
+ * @brief computes the derivative of a point on a Bezier curve
+ * @param curve
+ * @param t scalar between 0 and 1, with t=0 being P0 and t=1 being P3
+ * @return point on curve
+ */
+glm::vec3 geom::derivativeOnCurve(const BezierCurve &curve, float t)
+{
+ // clamp t as rounding errors might make it slightly out of bounds
+ t = std::clamp(t, 0.0f, 1.0f);
+ const float t_2 = t * t;
+ const float coeffs[4] = {
+ -3*t_2 + 6*t -3,
+ +9*t_2 -12*t +3,
+ -9*t_2 + 6*t,
+ +3*t_2
+ };
+ return coeffs[0] * curve[0] + coeffs[1] * curve[1] + coeffs[2] * curve[2] + coeffs[3] * curve[3];
+}