Files
HandmadeMath/HandmadeMath.h
2016-04-02 21:10:31 -07:00

1075 lines
19 KiB
C

/*
HandmadeMath.h v0.1
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.
==========================================================================
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@strangedev.net && @strangezak)
Functionality:
Matt Mascarenhas (@miblo_)
Aleph
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 Pi32 3.14159265359f
#define HMM_PI 3.14159265358979323846
#define MIN(a, b) (a) > (b) ? (b) : (a)
#define MAX(a, b) (a) < (b) ? (b) : (a)
#define ABS(a) (a) < 0 ? -(a) : (a)
#define MOD(a, m) ((a) % (m)) >= 0 ? ((a) % (m)) : (((a) % (m)) + (m))
#define Square(x) ((x) * (x))
typedef union vec2
{
struct
{
float X, Y;
};
struct
{
float U, V;
};
struct
{
float Left, Right;
};
float Elements[2];
} vec2;
typedef union vec3
{
struct
{
float X, Y, Z;
};
struct
{
float U, V, W;
};
struct
{
float R, G, B;
};
struct
{
vec2 XY;
float Ignored0_;
};
struct
{
float Ignored1_;
vec2 YZ;
};
struct
{
vec2 UV;
float Ignored2_;
};
struct
{
float Ignored3_;
vec2 VW;
};
float Elements[3];
} vec3;
typedef union vec4
{
struct
{
union
{
vec3 XYZ;
struct
{
float X, Y, Z;
};
};
float W;
};
struct
{
union
{
vec3 RGB;
struct
{
float R, G, B;
};
};
float A;
};
struct
{
vec2 XY;
float Ignored0_;
float Ignored1_;
};
struct
{
float Ignored2_;
vec2 YZ;
float Ignored3_;
};
struct
{
float Ignored4_;
float Ignored5_;
vec2 ZW;
};
float Elements[4];
} vec4;
typedef union mat4
{
float Elements[4][4];
} mat4;
HMMDEF float
Power(float Base, int Exponent);
HMMDEF float
Clamp(float Min, float Value, float Max);
HMMDEF vec3
Normalize(vec3 A);
HMMDEF vec3
Cross(vec3 VecOne, vec3 VecTwo);
HMMDEF float
Dot(vec3 VecOne, vec3 VecTwo);
HMMDEF vec2
Vec2i(int X, int Y);
HMMDEF vec2
Vec2(float X, float Y);
HMMDEF vec3
Vec3(float X, float Y, float Z);
HMMDEF vec3
Vec3i(int X, int Y, int Z);
HMMDEF vec4
Vec4(float X, float Y, float Z, float W);
HMMDEF vec4
Vec4i(int X, int Y, int Z, int W);
HMMDEF vec2
AddVec2(vec2 Left, vec2 Right);
HMMDEF vec3
AddVec3(vec3 Left, vec3 Right);
HMMDEF vec4
AddVec4(vec4 Left, vec4 Right);
HMMDEF vec2
SubtractVec2(vec2 Left, vec2 Right);
HMMDEF vec3
SubtractVec3(vec3 Left, vec3 Right);
HMMDEF vec4
SubtractVec4(vec4 Left, vec4 Right);
HMMDEF vec2
MultiplyVec2(vec2 Left, vec2 Right);
HMMDEF vec3
MultiplyVec3(vec3 Left, vec3 Right);
HMMDEF vec4
MultiplyVec4(vec4 Left, vec4 Right);
HMMDEF vec2
DivideVec2(vec2 Left, vec2 Right);
HMMDEF vec3
DivideVec3(vec3 Left, vec3 Right);
HMMDEF vec4
DivideVec4(vec4 Left, vec4 Right);
HMMDEF mat4
Mat4(void);
HMMDEF mat4
Mat4d(float Diagonal);
HMMDEF mat4
MultiplyMat4(mat4 Left, mat4 Right);
HMMDEF mat4
Orthographic(float Left, float Right, float Bottom, float Top, float Near, float Far);
HMMDEF mat4
Perspective(float FOV, float AspectRatio, float Near, float Far);
HMMDEF mat4
Translate(vec3 Translation);
HMMDEF mat4
Rotate(float Angle, vec3 Axis);
HMMDEF mat4
Scale(vec3 Scale);
HMMDEF mat4
LookAt(vec3 Eye, vec3 Center, vec3 Up);
#ifdef __cplusplus
}
#endif
#ifdef HANDMADE_MATH_CPP_MODE
HMMDEF vec2
Add(int X, int Y);
HMMDEF vec3
Add(int X, int Y, int Z);
HMMDEF vec4
Add(int X, int Y, int Z, int W);
HMMDEF vec2
Subtract(int X, int Y);
HMMDEF vec3
Subtract(int X, int Y, int Z);
HMMDEF vec4
Subtract(int X, int Y, int Z, int W);
HMMDEF vec2
Multiply(int X, int Y);
HMMDEF vec3
Multiply(int X, int Y, int Z);
HMMDEF vec4
Multiply(int X, int Y, int Z, int W);
HMMDEF mat4
Multiply(mat4 Left, mat4 Right);
HMMDEF vec2
Divide(int X, int Y);
HMMDEF vec3
Divide(int X, int Y, int Z);
HMMDEF vec4
Divide(int X, int Y, int Z, int W);
HMMDEF vec2
operator+(vec2 Left, vec2 Right);
HMMDEF vec3
operator+(vec3 Left, vec3 Right);
HMMDEF vec4
operator+(vec4 Left, vec4 Right);
HMMDEF vec2
operator-(vec2 Left, vec2 Right);
HMMDEF vec3
operator-(vec3 Left, vec3 Right);
HMMDEF vec4
operator-(vec4 Left, vec4 Right);
HMMDEF vec2 operator*(vec2 Left, vec2 Right);
HMMDEF vec3 operator*(vec3 Left, vec3 Right);
HMMDEF vec4 operator*(vec4 Left, vec4 Right);
HMMDEF mat4 operator*(mat4 Left, mat4 Right);
HMMDEF vec3 operator*(vec3 Left, float Right);
HMMDEF vec2 operator*(vec2 Left, float Right);
HMMDEF vec2
operator/(vec2 Left, vec2 Right);
HMMDEF vec3
operator/(vec3 Left, vec3 Right);
HMMDEF vec4
operator/(vec4 Left, vec4 Right);
#endif /* HANDMADE_MATH_CPP */
#endif /* HANDMADE_MATH_H */
#ifdef HANDMADE_MATH_IMPLEMENTATION
HMMDEF HINLINE float
ToRadians(float Degrees)
{
float Result = Degrees * (Pi32 / 180.0f);
return (Result);
}
HMMDEF HINLINE float
Inner(vec3 A, vec3 B)
{
float Result = A.X * B.X + A.Y * B.Y + A.Z * B.Z;
return (Result);
}
HMMDEF HINLINE float
SquareRoot(float Float)
{
float Result = sqrtf(Float);
return (Result);
}
HMMDEF HINLINE float
LengthSq(vec3 A)
{
float Result = Inner(A, A);
return (Result);
}
HMMDEF HINLINE float
Length(vec3 A)
{
float Result = SquareRoot(LengthSq(A));
return (Result);
}
HMMDEF HINLINE float
Power(float Base, int Exponent)
{
float Result = 1;
if(Exponent > 0)
{
for(int i = 0; i < Exponent; ++i)
{
Result *= Base;
}
}
else
{
for(int i = 0; i > Exponent; --i)
{
Result /= Base;
}
}
return (Result);
}
HMMDEF HINLINE float
Lerp(float A, float Time, float B)
{
float Result = (1.0f - Time) * A + Time * B;
return (Result);
}
HMMDEF HINLINE float
Clamp(float Min, float Value, float Max)
{
float Result = Value;
if(Result < Min)
{
Result = Min;
}
else if(Result > Max)
{
Result = Max;
}
return (Result);
}
HMMDEF HINLINE vec3
Normalize(vec3 A)
{
vec3 Result = A * (1.0f / Length(A));
return (Result);
}
HMMDEF HINLINE vec3
Cross(vec3 VecOne, vec3 VecTwo)
{
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);
}
HMMDEF HINLINE float
Dot(vec3 VecOne, vec3 VecTwo)
{
float Result = 0;
Result = (VecOne.X * VecTwo.X) + (VecOne.Y * VecTwo.Y) + (VecOne.Z * VecTwo.Z);
return (Result);
}
HMMDEF HINLINE vec2
Vec2(float X, float Y)
{
vec2 Result;
Result.X = X;
Result.Y = Y;
return (Result);
}
HMMDEF HINLINE vec2
Vec2i(int X, int Y)
{
vec2 Result;
Result.X = (float)X;
Result.Y = (float)Y;
return (Result);
}
HMMDEF HINLINE vec3
Vec3(float X, float Y, float Z)
{
vec3 Result;
Result.X = X;
Result.Y = Y;
Result.Z = Z;
return (Result);
}
HMMDEF HINLINE vec3
Vec3i(int X, int Y, int Z)
{
vec3 Result;
Result.X = (float)X;
Result.Y = (float)Y;
Result.Z = (float)Z;
return (Result);
}
HMMDEF HINLINE vec4
Vec4(float X, float Y, float Z, float W)
{
vec4 Result;
Result.X = X;
Result.Y = Y;
Result.Z = Z;
Result.W = W;
return (Result);
}
HMMDEF HINLINE vec4
Vec4i(int X, int Y, int Z, int W)
{
vec4 Result;
Result.X = (float)X;
Result.Y = (float)Y;
Result.Z = (float)Z;
Result.W = (float)W;
return (Result);
}
HMMDEF HINLINE vec2
AddVec2(vec2 Left, vec2 Right)
{
vec2 Result;
Result.X = Left.X + Right.X;
Result.Y = Left.Y + Right.Y;
return (Result);
}
HMMDEF HINLINE vec3
AddVec3(vec3 Left, vec3 Right)
{
vec3 Result;
Result.X = Left.X + Right.X;
Result.Y = Left.Y + Right.Y;
Result.Z = Left.Z + Right.Z;
return (Result);
}
HMMDEF HINLINE vec4
AddVec4(vec4 Left, vec4 Right)
{
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);
}
HMMDEF HINLINE vec2
SubtractVec2(vec2 Left, vec2 Right)
{
vec2 Result;
Result.X = Left.X - Right.X;
Result.Y = Left.Y - Right.Y;
return (Result);
}
HMMDEF HINLINE vec3
SubtractVec3(vec3 Left, vec3 Right)
{
vec3 Result;
Result.X = Left.X - Right.X;
Result.Y = Left.Y - Right.Y;
Result.Z = Left.Z - Right.Z;
return (Result);
}
HMMDEF HINLINE vec4
SubtractVec4(vec4 Left, vec4 Right)
{
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);
}
HMMDEF HINLINE vec2
MultiplyVec2(vec2 Left, vec2 Right)
{
vec2 Result;
Result.X = Left.X * Right.X;
Result.Y = Left.Y * Right.Y;
return (Result);
}
HMMDEF HINLINE vec3
MultiplyVec3(vec3 Left, vec3 Right)
{
vec3 Result;
Result.X = Left.Z * Right.X;
Result.Y = Left.Y * Right.Y;
Result.Z = Left.Z * Right.Z;
return (Result);
}
HMMDEF HINLINE vec4
MultiplyVec4(vec4 Left, vec4 Right)
{
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);
}
HMMDEF HINLINE vec2
DivideVec2(vec2 Left, vec2 Right)
{
vec2 Result;
Result.X = Left.X / Right.X;
Result.Y = Left.Y / Right.Y;
return (Result);
}
HMMDEF HINLINE vec3
DivideVec3(vec3 Left, vec3 Right)
{
vec3 Result;
Result.X = Left.X / Right.X;
Result.Y = Left.Y / Right.Y;
Result.Z = Left.Z / Right.Z;
return (Result);
}
HMMDEF HINLINE vec4
DivideVec4(vec4 Left, vec4 Right)
{
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);
}
HMMDEF mat4
Mat4()
{
mat4 Result;
for(int Rows = 0; Rows < 4; ++Rows)
{
for(int Columns = 0; Columns < 4; ++Columns)
{
Result.Elements[Rows][Columns] = 0.0f;
}
}
return (Result);
}
HMMDEF mat4
Mat4d(float Diagonal)
{
mat4 Result;
for(int Rows = 0; Rows < 4; ++Rows)
{
for(int 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);
}
HMMDEF mat4
MultiplyMat4(mat4 Left, mat4 Right)
{
mat4 Result = Mat4();
for(int Rows = 0; Rows < 4; ++Rows)
{
for(int Columns = 0; Columns < 4; ++Columns)
{
float Sum = 0;
for(int CurrentMatrice = 0; CurrentMatrice < 4; ++CurrentMatrice)
{
Sum += Right.Elements[Rows][CurrentMatrice] * Left.Elements[CurrentMatrice][Columns];
}
Result.Elements[Rows][Columns] = Sum;
}
}
return (Result);
}
HMMDEF mat4
Orthographic(float Left, float Right, float Bottom, float Top, float Near, float Far)
{
mat4 Result = 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);
}
HMMDEF mat4
Perspective(float FOV, float AspectRatio, float Near, float Far)
{
mat4 Result = Mat4d(1.0f);
Result.Elements[0][0] = 1.0f / (AspectRatio * tanf(FOV / 2.0f));
Result.Elements[1][1] = 1.0f / tanf(FOV / 2.0f);
Result.Elements[2][3] = -1.0f;
Result.Elements[2][2] = -(Far + Near) / (Far - Near);
Result.Elements[3][2] = -(2.0f * Far * Near) / (Far - Near);
Result.Elements[3][3] = 0.0f;
return (Result);
}
HMMDEF mat4
Translate(vec3 Translation)
{
mat4 Result = Mat4d(1.0f);
Result.Elements[3][0] = Translation.X;
Result.Elements[3][1] = Translation.Y;
Result.Elements[3][2] = Translation.Z;
return (Result);
}
HMMDEF mat4
Rotate(float Angle, vec3 Axis)
{
mat4 Result = Mat4d(1.0f);
Result.Elements[0][0] = Axis.X * Axis.X * (1.0f - cosf(ToRadians(Angle))) + cosf(ToRadians(Angle));
Result.Elements[0][1] = Axis.Y * Axis.X * (1.0f - cosf(ToRadians(Angle))) + Axis.Z * (sinf(ToRadians(Angle)));
Result.Elements[0][2] = Axis.X * Axis.Z * (1.0f - cosf(ToRadians(Angle))) - Axis.Y * (sinf(ToRadians(Angle)));
Result.Elements[1][0] = Axis.X * Axis.Y * (1.0f - cosf(ToRadians(Angle))) - Axis.Z * (sinf(ToRadians(Angle)));
Result.Elements[1][1] = Axis.Y * Axis.Y * (1.0f - cosf(ToRadians(Angle))) + (cosf(ToRadians(Angle)));
Result.Elements[1][2] = Axis.Y * Axis.Z * (1.0f - cosf(ToRadians(Angle))) + Axis.X * (sinf(ToRadians(Angle)));
Result.Elements[2][0] = Axis.X * Axis.Z * (1.0f - cosf(ToRadians(Angle))) + Axis.Y * (sinf(ToRadians(Angle)));
Result.Elements[2][1] = Axis.Y * Axis.Z * (1.0f - cosf(ToRadians(Angle))) - Axis.X * (sinf(ToRadians(Angle)));
Result.Elements[2][2] = Axis.Z * Axis.Z * (1.0f - cosf(ToRadians(Angle))) * (cosf(ToRadians(Angle)));
return (Result);
}
HMMDEF mat4
LookAt(vec3 Eye, vec3 Center, vec3 Up)
{
mat4 Result = {};
vec3 F = Normalize(Center - Eye);
vec3 S = Normalize(Cross(F, Up));
vec3 U = 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] = -Dot(S, Eye);
Result.Elements[3][1] = -Dot(U, Eye);
Result.Elements[3][2] = Dot(F, Eye);
Result.Elements[3][3] = 1.0f;
return (Result);
}
HMMDEF mat4
Scale(vec3 Scale)
{
mat4 Result = 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
HMMDEF HINLINE vec2
Add(vec2 Left, vec2 Right)
{
vec2 Result = AddVec2(Left, Right);
return (Result);
}
HMMDEF HINLINE vec3
Add(vec3 Left, vec3 Right)
{
vec3 Result = AddVec3(Left, Right);
return (Result);
}
HMMDEF HINLINE vec4
Add(vec4 Left, vec4 Right)
{
vec4 Result = AddVec4(Left, Right);
return (Result);
}
HMMDEF HINLINE vec2
Subtract(vec2 Left, vec2 Right)
{
vec2 Result = SubtractVec2(Left, Right);
return (Result);
}
HMMDEF HINLINE vec3
Subtract(vec3 Left, vec3 Right)
{
vec3 Result = SubtractVec3(Left, Right);
return (Result);
}
HMMDEF HINLINE vec4
Subtract(vec4 Left, vec4 Right)
{
vec4 Result = SubtractVec4(Left, Right);
return (Result);
}
HMMDEF HINLINE vec2
Multiply(vec2 Left, vec2 Right)
{
vec2 Result = MultiplyVec2(Left, Right);
return (Result);
}
HMMDEF HINLINE vec3
Multiply(vec3 Left, vec3 Right)
{
vec3 Result = MultiplyVec3(Left, Right);
return (Result);
}
HMMDEF HINLINE vec4
Multiply(vec4 Left, vec4 Right)
{
vec4 Result = MultiplyVec4(Left, Right);
return (Result);
}
HMMDEF HINLINE mat4
Multiply(mat4 Left, mat4 Right)
{
mat4 Result = MultiplyMat4(Left, Right);
return (Result);
}
HMMDEF HINLINE vec2
Divide(vec2 Left, vec2 Right)
{
vec2 Result = DivideVec2(Left, Right);
return (Result);
}
HMMDEF HINLINE vec3
Divide(vec3 Left, vec3 Right)
{
vec3 Result = DivideVec3(Left, Right);
return (Result);
}
HMMDEF HINLINE vec4
Divide(vec4 Left, vec4 Right)
{
vec4 Result = DivideVec4(Left, Right);
return (Result);
}
HMMDEF HINLINE vec2
operator+(vec2 Left, vec2 Right)
{
vec2 Result = Add(Left, Right);
return (Result);
}
HMMDEF HINLINE vec3
operator+(vec3 Left, vec3 Right)
{
vec3 Result = Add(Left, Right);
return (Result);
}
HMMDEF HINLINE vec4
operator+(vec4 Left, vec4 Right)
{
vec4 Result = Add(Left, Right);
return (Result);
}
HMMDEF HINLINE vec2
operator-(vec2 Left, vec2 Right)
{
vec2 Result = Subtract(Left, Right);
return (Result);
}
HMMDEF HINLINE vec3
operator-(vec3 Left, vec3 Right)
{
vec3 Result = Subtract(Left, Right);
return (Result);
}
HMMDEF HINLINE vec4
operator-(vec4 Left, vec4 Right)
{
vec4 Result = Subtract(Left, Right);
return (Result);
}
HMMDEF HINLINE vec2 operator*(vec2 Left, vec2 Right)
{
vec2 Result = Multiply(Left, Right);
return (Result);
}
HMMDEF HINLINE vec3 operator*(vec3 Left, vec3 Right)
{
vec3 Result = Multiply(Left, Right);
return (Result);
}
HMMDEF HINLINE vec3 operator*(vec3 Left, float Right)
{
vec3 Result;
Result.X = Right * Left.X;
Result.Y = Right * Left.Y;
Result.Z = Right * Left.Z;
return (Result);
}
HMMDEF vec2 operator*(vec2 Left, float Right)
{
vec2 Result;
Result.X = Right * Left.X;
Result.Y = Right * Left.Y;
return (Result);
}
HMMDEF HINLINE vec4 operator*(vec4 Left, vec4 Right)
{
vec4 Result = Multiply(Left, Right);
return (Result);
}
HMMDEF HINLINE mat4 operator*(mat4 Left, mat4 Right)
{
mat4 Result = Multiply(Left, Right);
return (Result);
}
HMMDEF HINLINE vec2
operator/(vec2 Left, vec2 Right)
{
vec2 Result = Divide(Left, Right);
return (Result);
}
HMMDEF HINLINE vec3
operator/(vec3 Left, vec3 Right)
{
vec3 Result = Divide(Left, Right);
return (Result);
}
HMMDEF HINLINE vec4
operator/(vec4 Left, vec4 Right)
{
vec4 Result = Divide(Left, Right);
return (Result);
}
#endif /* HANDMADE_MATH_CPP_MODE */
#endif /* HANDMADE_MATH_IMPLEMENTATION */