Implement 2D Quadratic and Cubic Bezier Curve algorithm

include/J3ML/Algorithm/Bezier.h

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+/// @file       Bezier.h
+/// @desc       Cubic Bezier Curve impl. using De Casteljau's Method
+/// @author     Joshua O'Leary
+/// @edited     20 June 2024
+/// @version    2
+/// @copyright  (c) Redacted Software 2024
+/// @license    Unlicense - Public Domain
+
+#pragma once
+
+// Bezier Method:
+// p = (1-t)^3 * P0 + 3*t*(1-t)^2*P1 + 3*t^2*(1-t)*P2 + t^3*P3;
+
+// For cubics:
+// p = (1-t)^2 * P0 + 2*(1-t)*t*P1 + t*t*P2;
+
+// Transcribed from here: explicit form and derivative
+// https://en.wikipedia.org/wiki/B%C3%A9zier_curve#Cubic_B%C3%A9zier_curves
+
+#include "J3ML/LinearAlgebra/Vector2.h"
+
+namespace J3ML::Algorithm
+{
+    using namespace J3ML::LinearAlgebra;
+
+    template <typename T>
+    inline T Square(T f) { return f * f; }
+
+    template <typename T>
+    inline T Cube(T f) { return f * f * f; }
+
+    template <typename T>
+    inline T Bezier(float t, const T& p0, const T& p1, const T& p2, const T& p3)
+    {
+        return Cube(1 - t) * p0 + 3 * Square(1 - t) * t * p1 + 3 * (1 - t) * Square(t) * p2 + Cube(t) * p3;
+    }
+
+    inline Vector2 Bezier(float t, const Vector2& p0, const Vector2& p1, const Vector2& p2, const Vector2& p3);
+
+    // Tangent
+    Vector2 BezierDerivative(float t, const Vector2& p0, const Vector2& p1, const Vector2& p2, const Vector2& p3);
+
+    // Normal
+    Vector2 BezierNormal(float t, const Vector2& p0, const Vector2& p1, const Vector2& p2, const Vector2& p3);
+}

src/J3ML/Algorithm/Bezier.cpp

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+#include <J3ML/Algorithm/Bezier.h>
+
+namespace J3ML::Algorithm
+{
+    using namespace J3ML::LinearAlgebra;
+    Vector2 BezierNormal(float t, const Vector2 &p0, const Vector2 &p1,
+                                  const Vector2 &p2, const Vector2 &p3) {
+        auto derived = BezierDerivative(t, p0, p1, p2, p3);
+        return derived.Normalized();
+    }
+
+    Vector2 BezierDerivative(float t, const Vector2 &p0, const Vector2 &p1, const Vector2 &p2, const Vector2 &p3) {
+        return 3 * Square(1 - t) * (p1 - p0) + 6 * (1 - t) * t * (p2 - p1) + 3 * Square(t) * (p3 - p2);
+    }
+
+    Vector2 Algorithm::Bezier(float t, const Vector2 &p0, const Vector2 &p1, const Vector2 &p2, const Vector2 &p3) {
+        return {Bezier(t, p0.x, p1.x, p2.x, p3.x), Bezier(t, p0.y, p1.y, p2.y, p3.y)};
+    }
+}
+