HandmadeMath/HandmadeMath.h

/*
  HandmadeMath.h v0.2a

  This is a single header file with a bunch of useful functions for
  basic game math operations.
  ==========================================================================
  You MUST

     #define HANDMADE_MATH_IMPLEMENTATION

  in EXACTLY one C or C++ file that includes this header, BEFORE the
  include, like this:

     #define HANDMADE_MATH_IMPLEMENTATION
     #include "HandmadeMath.h"

  All other files should just #include "HandmadeMath.h" without the #define.
  ==========================================================================

  For overloaded, and operator overloaded versions of the base C functions.
  You MUST

  #define HANDMADE_MATH_CPP_MODE

  in EXACTLY one C or C++ file that includes this header, BEFORE the
  include, like this:

     #define HANDMADE_MATH_IMPLEMENTATION
     #define HANDMADE_MATH_CPP_MODE
     #include "HandmadeMath.h"

  All other files should just #include "HandmadeMath.h" without the #define.
  ==========================================================================

  Version History:
      0.2 (*) Updated documentation
          (*) Better C compliance
          (*) Prefix all handmade math functions 
          (*) Better operator overloading
      0.2a
          (*) Prefixed Macros

  LICENSE

  This software is in the public domain. Where that dedication is not
  recognized, you are granted a perpetual, irrevocable license to copy,
  distribute, and modify this file as you see fit.

  CREDITS

  Written by Zakary Strange (zak@handmade.network && @strangezak)

  Functionality:
   Matt Mascarenhas (@miblo_)
   Aleph
   FieryDrake (@fierydrake)

  Fixes:
   Jeroen van Rijn (@J_vanRijn)
   Kiljacken (@Kiljacken)
   Insofaras (@insofaras)
*/

#ifndef HANDMADE_MATH_H
#define HANDMADE_MATH_H

#include <math.h> // TODO(zak): Remove this later on

#ifdef __cplusplus
extern "C"
{
#endif

#ifdef HANDMADEMATH_STATIC
#define HMMDEF static
#else
#define HMMDEF extern
#endif

#if _MSC_VER && !__INTEL_COMPILER
#define HINLINE __inline
#else
#define HINLINE inline
#endif

#define HMM_PI32 3.14159265359f
#define HMM_PI 3.14159265358979323846

#define HMM_MIN(a, b) (a) > (b) ? (b) : (a)
#define HMM_MAX(a, b) (a) < (b) ? (b) : (a)
#define HMN_ABS(a) (a) < 0 ? -(a) : (a)
#define HMM_MOD(a, m) ((a) % (m)) >= 0 ? ((a) % (m)) : (((a) % (m)) + (m))
#define HMM_SQUARE(x) ((x) * (x))

typedef union hmm_vec2
{
    struct
    {
        float X, Y;
    };

    struct
    {
        float U, V;
    };

    struct
    {
        float Left, Right;
    };

    float Elements[2];
} hmm_vec2;

typedef union hmm_vec3
{
    struct
    {
        float X, Y, Z;
    };

    struct
    {
        float U, V, W;
    };

    struct
    {
        float R, G, B;
    };

    struct
    {
        hmm_vec2 XY;
        float Ignored0_;
    };

    struct
    {
        float Ignored1_;
        hmm_vec2 YZ;
    };

    struct
    {
        hmm_vec2 UV;
        float Ignored2_;
    };

    struct
    {
        float Ignored3_;
        hmm_vec2 VW;
    };

    float Elements[3];
} hmm_vec3;

typedef union hmm_vec4
{
    struct
    {
        union
        {
            hmm_vec3 XYZ;
            struct
            {
                float X, Y, Z;
            };
        };

        float W;
    };
    struct
    {
        union
        {
            hmm_vec3 RGB;
            struct
            {
                float R, G, B;
            };
        };

        float A;
    };

    struct
    {
        hmm_vec2 XY;
        float Ignored0_;
        float Ignored1_;
    };

    struct
    {
        float Ignored2_;
        hmm_vec2 YZ;
        float Ignored3_;
    };

    struct
    {
        float Ignored4_;
        float Ignored5_;
        hmm_vec2 ZW;
    };

    float Elements[4];
} hmm_vec4;

typedef union hmm_mat4
{
    float Elements[4][4];
} hmm_mat4;

typedef hmm_vec2 hmm_v2;
typedef hmm_vec3 hmm_v3;
typedef hmm_vec4 hmm_v4;
typedef hmm_mat4 hmm_m4;    

HMMDEF float HMM_ToRadians(float Degrees);
HMMDEF float HMM_Inner(hmm_vec3 A, hmm_vec3 B);
HMMDEF float HMM_SquareRoot(float Float);
HMMDEF float HMM_LengthSquareRoot(hmm_vec3 A);
HMMDEF float HMM_Length(hmm_vec3 A);    
HMMDEF float HMM_Power(float Base, int Exponent);
HMMDEF float HMM_Clamp(float Min, float Value, float Max);

HMMDEF hmm_vec3 HMM_Normalize(hmm_vec3 A);
HMMDEF hmm_vec3 HMM_Cross(hmm_vec3 VecOne, hmm_vec3 VecTwo);
HMMDEF float HMM_Dot(hmm_vec3 VecOne, hmm_vec3 VecTwo);

HMMDEF hmm_vec2 HMM_Vec2i(int X, int Y);
HMMDEF hmm_vec2 HMM_Vec2(float X, float Y);
HMMDEF hmm_vec3 HMM_Vec3(float X, float Y, float Z);
HMMDEF hmm_vec3 HMM_Vec3i(int X, int Y, int Z);
HMMDEF hmm_vec4 HMM_Vec4(float X, float Y, float Z, float W);
HMMDEF hmm_vec4 HMM_Vec4i(int X, int Y, int Z, int W);

HMMDEF hmm_vec2 HMM_AddVec2(hmm_vec2 Left, hmm_vec2 Right);
HMMDEF hmm_vec3 HMM_AddVec3(hmm_vec3 Left, hmm_vec3 Right);
HMMDEF hmm_vec4 HMM_AddVec4(hmm_vec4 Left, hmm_vec4 Right);

HMMDEF hmm_vec2 HMM_SubtractVec2(hmm_vec2 Left, hmm_vec2 Right);
HMMDEF hmm_vec3 HMM_SubtractVec3(hmm_vec3 Left, hmm_vec3 Right);
HMMDEF hmm_vec4 HMM_SubtractVec4(hmm_vec4 Left, hmm_vec4 Right);

HMMDEF hmm_vec2 HMM_MultiplyVec2(hmm_vec2 Left, hmm_vec2 Right);
HMMDEF hmm_vec3 HMM_MultiplyVec3(hmm_vec3 Left, hmm_vec3 Right);
HMMDEF hmm_vec4 HMM_MultiplyVec4(hmm_vec4 Left, hmm_vec4 Right);

HMMDEF hmm_vec2 HMM_DivideVec2(hmm_vec2 Left, hmm_vec2 Right);
HMMDEF hmm_vec3 HMM_DivideVec3(hmm_vec3 Left, hmm_vec3 Right);
HMMDEF hmm_vec4 HMM_DivideVec4(hmm_vec4 Left, hmm_vec4 Right);

HMMDEF hmm_mat4 HMM_Mat4(void);
HMMDEF hmm_mat4 HMM_Mat4d(float Diagonal);
HMMDEF hmm_mat4 HMM_MultiplyMat4(hmm_mat4 Left, hmm_mat4 Right);
HMMDEF hmm_vec4 HMM_MultiplyMat4ByVec4(hmm_mat4 Matrix, hmm_vec4 Vector);

HMMDEF hmm_mat4 HMM_Orthographic(float Left, float Right, float Bottom, float Top, float Near, float Far);
HMMDEF hmm_mat4 HMM_Perspective(float FOV, float AspectRatio, float Near, float Far);
HMMDEF hmm_mat4 HMM_Translate(hmm_vec3 Translation);
HMMDEF hmm_mat4 HMM_Rotate(float Angle, hmm_vec3 Axis);
HMMDEF hmm_mat4 HMM_Scale(hmm_vec3 Scale);

HMMDEF hmm_mat4 HMM_LookAt(hmm_vec3 Eye, hmm_vec3 Center, hmm_vec3 Up);

#ifdef __cplusplus
}
#endif

#ifdef HANDMADE_MATH_CPP_MODE

HMMDEF hmm_vec2 HMM_Add(int X, int Y);
HMMDEF hmm_vec3 HMM_Add(int X, int Y, int Z);
HMMDEF hmm_vec4 HMM_Add(int X, int Y, int Z, int W);

HMMDEF hmm_vec2 HMM_Subtract(int X, int Y);
HMMDEF hmm_vec3 HMM_Subtract(int X, int Y, int Z);
HMMDEF hmm_vec4 HMM_Subtract(int X, int Y, int Z, int W);

HMMDEF hmm_vec2 HMM_Multiply(int X, int Y);
HMMDEF hmm_vec3 HMM_Multiply(int X, int Y, int Z);
HMMDEF hmm_vec4 HMM_Multiply(int X, int Y, int Z, int W);
HMMDEF hmm_mat4 HMM_Multiply(hmm_mat4 Left, hmm_mat4 Right);

HMMDEF hmm_vec2 HMM_Divide(int X, int Y);
HMMDEF hmm_vec3 HMM_Divide(int X, int Y, int Z);
HMMDEF hmm_vec4 HMM_Divide(int X, int Y, int Z, int W);

HMMDEF hmm_vec2 operator+(hmm_vec2 Left, hmm_vec2 Right);
HMMDEF hmm_vec3 operator+(hmm_vec3 Left, hmm_vec3 Right);
HMMDEF hmm_vec4 operator+(hmm_vec4 Left, hmm_vec4 Right);

HMMDEF hmm_vec2 operator-(hmm_vec2 Left, hmm_vec2 Right);
HMMDEF hmm_vec3 operator-(hmm_vec3 Left, hmm_vec3 Right);
HMMDEF hmm_vec4 operator-(hmm_vec4 Left, hmm_vec4 Right);

HMMDEF hmm_vec2 operator*(hmm_vec2 Left, hmm_vec2 Right);
HMMDEF hmm_vec3 operator*(hmm_vec3 Left, hmm_vec3 Right);
HMMDEF hmm_vec4 operator*(hmm_vec4 Left, hmm_vec4 Right);
HMMDEF hmm_mat4 operator*(hmm_mat4 Left, hmm_mat4 Right);

HMMDEF hmm_vec3 operator*(hmm_vec3 Left, float Right);
HMMDEF hmm_vec2 operator*(hmm_vec2 Left, float Right);

HMMDEF hmm_vec2 operator/(hmm_vec2 Left, hmm_vec2 Right);
HMMDEF hmm_vec3 operator/(hmm_vec3 Left, hmm_vec3 Right);
HMMDEF hmm_vec4 operator/(hmm_vec4 Left, hmm_vec4 Right);

#endif /* HANDMADE_MATH_CPP */

#endif /* HANDMADE_MATH_H */

#ifdef HANDMADE_MATH_IMPLEMENTATION

HINLINE float
HMM_ToRadians(float Degrees)
{
    float Result = Degrees * (Pi32 / 180.0f);

    return (Result);
}

HINLINE float
HMM_Inner(hmm_vec3 A, hmm_vec3 B)
{
    float Result = A.X * B.X + A.Y * B.Y + A.Z * B.Z;

    return (Result);
}

HINLINE float
HMM_SquareRoot(float Float)
{    
    float Result = sqrtf(Float);

    return(Result);
}

HINLINE float
HMM_LengthSquareRoot(hmm_vec3 A)
{
    float Result = HMM_Inner(A, A);

    return (Result);
}

HINLINE float
HMM_Length(hmm_vec3 A)
{
    float Result = HMM_SquareRoot(HMM_LengthSquareRoot(A));
    return (Result);
}

HINLINE float
HMM_Power(float Base, int Exponent)
{
    float Result = 1;
    if(Exponent > 0)
    {
        int i;
        for(i = 0; i < Exponent; ++i)
        {
            Result *= Base;
        }
    }
    else
    {
        int i;
        for(i = 0; i > Exponent; --i)
        {
            Result /= Base;
        }
    }
    return (Result);
}

HINLINE float
HMM_Lerp(float A, float Time, float B)
{
    float Result = (1.0f - Time) * A + Time * B;

    return (Result);
}

HINLINE float
HMM_Clamp(float Min, float Value, float Max)
{
    float Result = Value;

    if(Result < Min)
    {
        Result = Min;
    }
    else if(Result > Max)
    {
        Result = Max;
    }

    return (Result);
}

HINLINE hmm_vec3
HMM_Normalize(hmm_vec3 A)
{
    hmm_vec3 Result = {0};

    Result.X = A.X * (1.0f / HMM_Length(A));
    Result.Y = A.Y * (1.0f / HMM_Length(A));
    Result.Z = A.Z * (1.0f / HMM_Length(A));
    
    return (Result);
}

HINLINE hmm_vec3
HMM_Cross(hmm_vec3 VecOne, hmm_vec3 VecTwo)
{
    hmm_vec3 Result;

    Result.X = (VecOne.Y * VecTwo.Z) - (VecOne.Z * VecTwo.Y);
    Result.Y = (VecOne.Z * VecTwo.X) - (VecOne.X * VecTwo.Z);
    Result.Z = (VecOne.X * VecTwo.Y) - (VecOne.Y * VecTwo.X);

    return (Result);
}

HINLINE float
HMM_Dot(hmm_vec3 VecOne, hmm_vec3 VecTwo)
{
    float Result = 0;

    Result = (VecOne.X * VecTwo.X) + (VecOne.Y * VecTwo.Y) + (VecOne.Z * VecTwo.Z);

    return (Result);
}

HINLINE hmm_vec2
HMM_Vec2(float X, float Y)
{
    hmm_vec2 Result;

    Result.X = X;
    Result.Y = Y;

    return (Result);
}

HINLINE hmm_vec2
HMM_Vec2i(int X, int Y)
{
    hmm_vec2 Result;

    Result.X = (float)X;
    Result.Y = (float)Y;

    return (Result);
}

HINLINE hmm_vec3
HMM_Vec3(float X, float Y, float Z)
{
    hmm_vec3 Result;

    Result.X = X;
    Result.Y = Y;
    Result.Z = Z;

    return (Result);
}

HINLINE hmm_vec3
HMM_Vec3i(int X, int Y, int Z)
{
    hmm_vec3 Result;

    Result.X = (float)X;
    Result.Y = (float)Y;
    Result.Z = (float)Z;

    return (Result);
}

HINLINE hmm_vec4
HMM_Vec4(float X, float Y, float Z, float W)
{
    hmm_vec4 Result;

    Result.X = X;
    Result.Y = Y;
    Result.Z = Z;
    Result.W = W;

    return (Result);
}

HINLINE hmm_vec4
HMM_Vec4i(int X, int Y, int Z, int W)
{
    hmm_vec4 Result;

    Result.X = (float)X;
    Result.Y = (float)Y;
    Result.Z = (float)Z;
    Result.W = (float)W;

    return (Result);
}

HINLINE hmm_vec2
HMM_AddVec2(hmm_vec2 Left, hmm_vec2 Right)
{
    hmm_vec2 Result;

    Result.X = Left.X + Right.X;
    Result.Y = Left.Y + Right.Y;

    return (Result);
}

HINLINE hmm_vec3
HMM_AddVec3(hmm_vec3 Left, hmm_vec3 Right)
{
    hmm_vec3 Result;

    Result.X = Left.X + Right.X;
    Result.Y = Left.Y + Right.Y;
    Result.Z = Left.Z + Right.Z;

    return (Result);
}

HINLINE hmm_vec4
HMM_AddVec4(hmm_vec4 Left, hmm_vec4 Right)
{
    hmm_vec4 Result;

    Result.X = Left.X + Right.X;
    Result.Y = Left.Y + Right.Y;
    Result.Z = Left.Z + Right.Z;
    Result.W = Left.W + Right.W;

    return (Result);
}

HINLINE hmm_vec2
HMM_SubtractVec2(hmm_vec2 Left, hmm_vec2 Right)
{
    hmm_vec2 Result;

    Result.X = Left.X - Right.X;
    Result.Y = Left.Y - Right.Y;

    return (Result);
}

HINLINE hmm_vec3
HMM_SubtractVec3(hmm_vec3 Left, hmm_vec3 Right)
{
    hmm_vec3 Result;

    Result.X = Left.X - Right.X;
    Result.Y = Left.Y - Right.Y;
    Result.Z = Left.Z - Right.Z;

    return (Result);
}

HINLINE hmm_vec4
HMM_SubtractVec4(hmm_vec4 Left, hmm_vec4 Right)
{
    hmm_vec4 Result;

    Result.X = Left.X - Right.X;
    Result.Y = Left.Y - Right.Y;
    Result.Z = Left.Z - Right.Z;
    Result.W = Left.W - Right.W;

    return (Result);
}

HINLINE hmm_vec2
HMM_MultiplyVec2(hmm_vec2 Left, hmm_vec2 Right)
{
    hmm_vec2 Result;

    Result.X = Left.X * Right.X;
    Result.Y = Left.Y * Right.Y;

    return (Result);
}

HINLINE hmm_vec3
HMM_MultiplyVec3(hmm_vec3 Left, hmm_vec3 Right)
{
    hmm_vec3 Result;

    Result.X = Left.Z * Right.X;
    Result.Y = Left.Y * Right.Y;
    Result.Z = Left.Z * Right.Z;

    return (Result);
}

HINLINE hmm_vec4
HMM_MultiplyVec4(hmm_vec4 Left, hmm_vec4 Right)
{
    hmm_vec4 Result;

    Result.X = Left.X * Right.X;
    Result.Y = Left.Y * Right.Y;
    Result.Z = Left.Z * Right.Z;
    Result.W = Left.W * Right.W;

    return (Result);
}

HINLINE hmm_vec2
HMM_DivideVec2(hmm_vec2 Left, hmm_vec2 Right)
{
    hmm_vec2 Result;

    Result.X = Left.X / Right.X;
    Result.Y = Left.Y / Right.Y;

    return (Result);
}

HINLINE hmm_vec3
HMM_DivideVec3(hmm_vec3 Left, hmm_vec3 Right)
{
    hmm_vec3 Result;

    Result.X = Left.X / Right.X;
    Result.Y = Left.Y / Right.Y;
    Result.Z = Left.Z / Right.Z;

    return (Result);
}

HINLINE hmm_vec4
HMM_DivideVec4(hmm_vec4 Left, hmm_vec4 Right)
{
    hmm_vec4 Result;

    Result.X = Left.X / Right.X;
    Result.Y = Left.Y / Right.Y;
    Result.Z = Left.Z / Right.Z;
    Result.W = Left.W / Right.W;

    return (Result);
}

HINLINE hmm_mat4
HMM_Mat4()
{
    hmm_mat4 Result = {0};

    return (Result);
}

hmm_mat4
HMM_Mat4d(float Diagonal)
{
    hmm_mat4 Result;

    int Rows;
    for(Rows = 0; Rows < 4; ++Rows)
    {
        int Columns;
        for(Columns = 0; Columns < 4; ++Columns)
        {
            Result.Elements[Rows][Columns] = 0.0f;
        }
    }

    Result.Elements[0][0] = Diagonal;
    Result.Elements[1][1] = Diagonal;
    Result.Elements[2][2] = Diagonal;
    Result.Elements[3][3] = Diagonal;

    return (Result);
}

hmm_mat4
HMM_MultiplyMat4(hmm_mat4 Left, hmm_mat4 Right)
{
    hmm_mat4 Result = HMM_Mat4();

    int Rows;
    for(Rows = 0; Rows < 4; ++Rows)
    {
        int Columns;
        for(Columns = 0; Columns < 4; ++Columns)
        {
            float Sum = 0;
            int CurrentMatrice;
            for(CurrentMatrice = 0; CurrentMatrice < 4; ++CurrentMatrice)
            {
                Sum += Right.Elements[Rows][CurrentMatrice] * Left.Elements[CurrentMatrice][Columns];
            }

            Result.Elements[Rows][Columns] = Sum;
        }
    }

    return (Result);
}

hmm_vec4
HMM_MultiplyMat4ByVec4(hmm_mat4 Matrix, hmm_vec4 Vector)
{
    hmm_vec4 Result = HMM_Vec4(0.0f, 0.0f, 0.0f, 0.0f);
    
    int Rows, Columns;
    for(Rows = 0; Rows < 4; ++Rows)
    {
        float Sum = 0;
        for(Columns = 0; Columns < 4; ++Columns)
        {
            Sum += Matrix.Elements[Rows][Columns] * Vector.Elements[Columns];
        }
        
        Result.Elements[Rows] = Sum;
    }
    
    return (Result);
}

hmm_mat4
HMM_Orthographic(float Left, float Right, float Bottom, float Top, float Near, float Far)
{
    hmm_mat4 Result = HMM_Mat4d(1.0f);

    Result.Elements[0][0] = 2.0f / (Right - Left);
    Result.Elements[1][1] = 2.0f / (Top - Bottom);
    Result.Elements[2][2] = 2.0f / (Near - Far);

    Result.Elements[3][0] = (Left + Right) / (Left - Right);
    Result.Elements[3][1] = (Bottom + Top) / (Bottom - Top);
    Result.Elements[3][2] = (Far + Near) / (Near - Far);

    return (Result);
}

hmm_mat4
HMM_Perspective(float FOV, float AspectRatio, float Near, float Far)
{
    hmm_mat4 Result = HMM_Mat4d(1.0f);

    float TanThetaOver2 = tanf(FOV * (HMM_PI32 / 360.0f));
    
    Result.Elements[0][0] = 1.0f / TanThetaOver2;
    Result.Elements[1][1] = AspectRatio / TanThetaOver2;
    Result.Elements[2][3] = -1.0f;
    Result.Elements[2][2] = (Near + Far) / (Near - Far);
    Result.Elements[3][2] = (2.0f * Near * Far) / (Near - Far);
    Result.Elements[3][3] = 0.0f;

    return (Result);
}

hmm_mat4
HMM_Translate(hmm_vec3 Translation)
{
    hmm_mat4 Result = HMM_Mat4d(1.0f);

    Result.Elements[3][0] = Translation.X;
    Result.Elements[3][1] = Translation.Y;
    Result.Elements[3][2] = Translation.Z;

    return (Result);
}

hmm_mat4
HMM_Rotate(float Angle, hmm_vec3 Axis)
{
    hmm_mat4 Result = HMM_Mat4d(1.0f);

    Result.Elements[0][0] = Axis.X * Axis.X * (1.0f - cosf(HMM_ToRadians(Angle))) + cosf(HMM_ToRadians(Angle));
    Result.Elements[0][1] = Axis.Y * Axis.X * (1.0f - cosf(HMM_ToRadians(Angle))) + Axis.Z * (sinf(HMM_ToRadians(Angle)));
    Result.Elements[0][2] = Axis.X * Axis.Z * (1.0f - cosf(HMM_ToRadians(Angle))) - Axis.Y * (sinf(HMM_ToRadians(Angle)));

    Result.Elements[1][0] = Axis.X * Axis.Y * (1.0f - cosf(HMM_ToRadians(Angle))) - Axis.Z * (sinf(HMM_ToRadians(Angle)));
    Result.Elements[1][1] = Axis.Y * Axis.Y * (1.0f - cosf(HMM_ToRadians(Angle))) + (cosf(HMM_ToRadians(Angle)));
    Result.Elements[1][2] = Axis.Y * Axis.Z * (1.0f - cosf(HMM_ToRadians(Angle))) + Axis.X * (sinf(HMM_ToRadians(Angle)));

    Result.Elements[2][0] = Axis.X * Axis.Z * (1.0f - cosf(HMM_ToRadians(Angle))) + Axis.Y * (sinf(HMM_ToRadians(Angle)));
    Result.Elements[2][1] = Axis.Y * Axis.Z * (1.0f - cosf(HMM_ToRadians(Angle))) - Axis.X * (sinf(HMM_ToRadians(Angle)));
    Result.Elements[2][2] = Axis.Z * Axis.Z * (1.0f - cosf(HMM_ToRadians(Angle))) * (cosf(HMM_ToRadians(Angle)));

    return (Result);
}

hmm_mat4
HMM_LookAt(hmm_vec3 Eye, hmm_vec3 Center, hmm_vec3 Up)
{
    hmm_mat4 Result = {0};

    hmm_vec3 F = HMM_Normalize(HMM_SubtractVec3(Center, Eye));
    hmm_vec3 S = HMM_Normalize(HMM_Cross(F, Up));
    hmm_vec3 U = HMM_Cross(S, F);

    Result.Elements[0][0] = S.X;
    Result.Elements[0][1] = U.X;
    Result.Elements[0][2] = -F.X;

    Result.Elements[1][0] = S.Y;
    Result.Elements[1][1] = U.Y;
    Result.Elements[1][2] = -F.Y;

    Result.Elements[2][0] = S.Z;
    Result.Elements[2][1] = U.Z;
    Result.Elements[2][2] = -F.Z;

    Result.Elements[3][0] = -HMM_Dot(S, Eye);
    Result.Elements[3][1] = -HMM_Dot(U, Eye);
    Result.Elements[3][2] = HMM_Dot(F, Eye);
    Result.Elements[3][3] = 1.0f;

    return (Result);
}

hmm_mat4
HMM_Scale(hmm_vec3 Scale)
{
    hmm_mat4 Result = HMM_Mat4d(1.0f);

    Result.Elements[0][0] = Scale.X;
    Result.Elements[1][1] = Scale.Y;
    Result.Elements[2][2] = Scale.Z;

    return (Result);
}

#ifdef HANDMADE_MATH_CPP_MODE

HINLINE hmm_vec2
Add(hmm_vec2 Left, hmm_vec2 Right)
{
    hmm_vec2 Result = HMM_AddVec2(Left, Right);

    return (Result);
}

HINLINE hmm_vec3
Add(hmm_vec3 Left, hmm_vec3 Right)
{
    hmm_vec3 Result = HMM_AddVec3(Left, Right);

    return (Result);
}

HMMDEF HINLINE hmm_vec4
Add(hmm_vec4 Left, hmm_vec4 Right)
{
    hmm_vec4 Result = HMM_AddVec4(Left, Right);

    return (Result);
}

HINLINE hmm_vec2
Subtract(hmm_vec2 Left, hmm_vec2 Right)
{
    hmm_vec2 Result = HMM_SubtractVec2(Left, Right);

    return (Result);
}

HINLINE hmm_vec3
Subtract(hmm_vec3 Left, hmm_vec3 Right)
{
    hmm_vec3 Result = HMM_SubtractVec3(Left, Right);

    return (Result);
}

HINLINE hmm_vec4
Subtract(hmm_vec4 Left, hmm_vec4 Right)
{
    hmm_vec4 Result = HMM_SubtractVec4(Left, Right);

    return (Result);
}

HINLINE hmm_vec2
Multiply(hmm_vec2 Left, hmm_vec2 Right)
{
    hmm_vec2 Result = HMM_MultiplyVec2(Left, Right);

    return (Result);
}

HINLINE hmm_vec3
Multiply(hmm_vec3 Left, hmm_vec3 Right)
{
    hmm_vec3 Result = HMM_MultiplyVec3(Left, Right);

    return (Result);
}

HINLINE hmm_vec4
Multiply(hmm_vec4 Left, hmm_vec4 Right)
{
    hmm_vec4 Result = HMM_MultiplyVec4(Left, Right);

    return (Result);
}

HINLINE hmm_mat4
Multiply(hmm_mat4 Left, hmm_mat4 Right)
{
    hmm_mat4 Result = HMM_MultiplyMat4(Left, Right);

    return (Result);
}

HINLINE hmm_vec2
Divide(hmm_vec2 Left, hmm_vec2 Right)
{
    hmm_vec2 Result = HMM_DivideVec2(Left, Right);

    return (Result);
}

HINLINE hmm_vec3
Divide(hmm_vec3 Left, hmm_vec3 Right)
{
    hmm_vec3 Result = HMM_DivideVec3(Left, Right);

    return (Result);
}

HINLINE hmm_vec4
Divide(hmm_vec4 Left, hmm_vec4 Right)
{
    hmm_vec4 Result = HMM_DivideVec4(Left, Right);

    return (Result);
}

HINLINE hmm_vec2
operator+(hmm_vec2 Left, hmm_vec2 Right)
{
    hmm_vec2 Result = Add(Left, Right);

    return (Result);
}

HINLINE hmm_vec3
operator+(hmm_vec3 Left, hmm_vec3 Right)
{
    hmm_vec3 Result = Add(Left, Right);

    return (Result);
}

HINLINE hmm_vec4
operator+(hmm_vec4 Left, hmm_vec4 Right)
{
    hmm_vec4 Result = Add(Left, Right);

    return (Result);
}

HINLINE hmm_vec2
operator-(hmm_vec2 Left, hmm_vec2 Right)
{
    hmm_vec2 Result = Subtract(Left, Right);

    return (Result);
}

HINLINE hmm_vec3
operator-(hmm_vec3 Left, hmm_vec3 Right)
{
    hmm_vec3 Result = Subtract(Left, Right);

    return (Result);
}

HINLINE hmm_vec4
operator-(hmm_vec4 Left, hmm_vec4 Right)
{
    hmm_vec4 Result = Subtract(Left, Right);

    return (Result);
}

HINLINE hmm_vec2
operator*(hmm_vec2 Left, hmm_vec2 Right)
{
    hmm_vec2 Result = Multiply(Left, Right);

    return (Result);
}

HINLINE hmm_vec3
operator*(hmm_vec3 Left, hmm_vec3 Right)
{
    hmm_vec3 Result = Multiply(Left, Right);

    return (Result);
}

HINLINE hmm_vec3
operator*(hmm_vec3 Left, float Right)
{
    hmm_vec3 Result;

    Result.X = Right * Left.X;
    Result.Y = Right * Left.Y;
    Result.Z = Right * Left.Z;

    return (Result);
}

HINLINE hmm_vec2
operator*(hmm_vec2 Left, float Right)
{
    hmm_vec2 Result;

    Result.X = Right * Left.X;
    Result.Y = Right * Left.Y;

    return (Result);
}

HINLINE hmm_vec4
operator*(hmm_vec4 Left, hmm_vec4 Right)
{
    hmm_vec4 Result = Multiply(Left, Right);

    return (Result);
}

HINLINE hmm_mat4
operator*(hmm_mat4 Left, hmm_mat4 Right)
{
    hmm_mat4 Result = Multiply(Left, Right);

    return (Result);
}

HINLINE hmm_vec2
operator/(hmm_vec2 Left, hmm_vec2 Right)
{
    hmm_vec2 Result = Divide(Left, Right);

    return (Result);
}

HINLINE hmm_vec3
operator/(hmm_vec3 Left, hmm_vec3 Right)
{
    hmm_vec3 Result = Divide(Left, Right);

    return (Result);
}

HINLINE hmm_vec4
operator/(hmm_vec4 Left, hmm_vec4 Right)
{
    hmm_vec4 Result = Divide(Left, Right);

    return (Result);
}

#endif /* HANDMADE_MATH_CPP_MODE */

#endif /* HANDMADE_MATH_IMPLEMENTATION */