diff -r 922662adb72a -r 30204975694a src/geometry.cpp
--- 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];
+}