Quaternion (#456)

* Quat

* format

* checkpoint

* math utils

* update

* Chebyshev

* update utility

* tested

* format

Author: jnyfah

ZEngine/ZEngine/Core/Maths/MathUtils.h

@@ -0,0 +1,177 @@
+#pragma once
+namespace ZEngine::Core::Maths
+{
+    template <typename T>
+    constexpr T DEG_TO_RAD = T(0.017453292519943295769236907684886127);
+
+    template <typename T>
+    constexpr T RAD_TO_DEG = T(57.295779513082320876798154814105170332);
+
+    template <typename T>
+    constexpr T PI = T(3.141592653589793238462643383279502884);
+
+    template <typename T>
+    constexpr T TWO_PI = T(6.283185307179586476925286766559005768);
+
+    template <typename T>
+    constexpr T HALF_PI = T(1.570796326794896619231321691639751442);
+
+    template <typename T>
+    constexpr T clamp(T value, T minVal, T maxVal)
+    {
+        return (value < minVal) ? minVal : (value > maxVal) ? maxVal : value;
+    }
+
+    template <typename T>
+    constexpr T min(T a, T b)
+    {
+        return (a < b) ? a : b;
+    }
+
+    template <typename T>
+    constexpr T max(T a, T b)
+    {
+        return (a > b) ? a : b;
+    }
+
+    template <typename T>
+    constexpr T abs(T value)
+    {
+        return (value < T(0)) ? -value : value;
+    }
+
+    template <typename T>
+    constexpr T radians(T degrees)
+    {
+        return degrees * DEG_TO_RAD<T>;
+    }
+
+    template <typename T>
+    constexpr T degrees(T radians)
+    {
+        return radians * RAD_TO_DEG<T>;
+    }
+
+    template <typename T>
+    constexpr T floor(T x)
+    {
+        T intPart = static_cast<T>(static_cast<long long>(x));
+        return (x < T(0) && x != intPart) ? intPart - T(1) : intPart;
+    }
+
+    template <typename T>
+    T sqrt(T x)
+    {
+        if (x <= T(0))
+        {
+            return T(0);
+        }
+        constexpr T epsilon       = (sizeof(T) == sizeof(float)) ? T(1e-7) : T(1e-15);
+        T           guess         = x;
+        T           prev          = T(0);
+        int         iteration     = 0;
+        const int   max_iteration = 20;
+        while (abs(guess - prev) > epsilon && iteration < max_iteration)
+        {
+            prev  = guess;
+            guess = (guess + x / guess) * T(0.5);
+            ++iteration;
+        }
+        return guess;
+    }
+
+    template <typename T>
+    T sin(T x)
+    {
+        x      -= TWO_PI<T> * floor(x / TWO_PI<T>);
+
+        T sign  = T(1);
+        if (x > HALF_PI<T>)
+        {
+            x    = PI<T> - x;
+            sign = -1;
+        }
+        else if (x < -HALF_PI<T>)
+        {
+            x    = -PI<T> - x;
+            sign = -1;
+        }
+
+        T       x2 = x * x;
+
+        const T c1 = T(-0.16666667);
+        const T c2 = T(0.0083333310);
+        const T c3 = T(-0.00019840874);
+
+        T       t1 = c2 + c3 * x2;
+        T       t2 = c1 + t1 * x2;
+
+        return sign * x * (1 + t2 * x2);
+    }
+
+    template <typename T>
+    T cos(T x)
+    {
+        return sin<T>(HALF_PI<T> - x);
+    }
+
+    template <typename T>
+    T atan(T x)
+    {
+        if (abs(x) > T(1))
+        {
+            T result = (x > T(0) ? HALF_PI<T> : -HALF_PI<T>) -atan(T(1) / x);
+            return result;
+        }
+
+        T       x2 = x * x;
+
+        const T c1 = T(-0.33333333);
+        const T c2 = T(0.2);
+        const T c3 = T(-0.14285714);
+        const T c4 = T(0.11111111);
+
+        T       t1 = c3 + c4 * x2;
+        T       t2 = c2 + t1 * x2;
+        T       t3 = c1 + t2 * x2;
+
+        return x + x * x2 * t3;
+    }
+
+    template <typename T>
+    T atan2(T y, T x)
+    {
+        if (x > T(0))
+            return atan(y / x);
+        else if (x < T(0))
+        {
+            if (y >= T(0))
+                return atan(y / x) + PI<T>;
+            else
+                return atan(y / x) - PI<T>;
+        }
+        else
+        {
+            if (y > T(0))
+                return HALF_PI<T>;
+            else if (y < T(0))
+                return -HALF_PI<T>;
+            else
+                return T(0);
+        }
+    }
+
+    template <typename T>
+    T acos(T x)
+    {
+        if (abs(x) > T(1))
+            return T(0);
+
+        if (x == T(0))
+            return HALF_PI<T>;
+
+        T sqrt_term = sqrt(T(1) - x * x);
+        return atan2(sqrt_term, x);
+    }
+
+} // namespace ZEngine::Core::Maths

ZEngine/ZEngine/Core/Maths/Matrix.h

@@ -1,6 +1,5 @@
 #include <Helpers/MemoryOperations.h>
 #include <Vec.h>
-#include <cstddef>
 
 namespace ZEngine::Core::Maths
 {