Math

Internals of the Vector & Matrix API. More...

Collaboration diagram for Math:

Files
file	mat.c
file	utils.h
file	vec.c
SRP_FORCEINLINE vec4	mat4MultiplyVec4 (const mat4 *restrict m, vec4 v)
SRP_FORCEINLINE mat4	mat4MultiplyMat4 (const mat4 *restrict a, const mat4 *restrict b)
SRP_FORCEINLINE mat4	mat4ConstructIdentity ()
SRP_FORCEINLINE mat4	mat4ConstructScale (float x, float y, float z)
SRP_FORCEINLINE mat4	mat4ConstructTranslate (float x, float y, float z)
SRP_FORCEINLINE mat4	mat4ConstructRotate (float x, float y, float z)
SRP_FORCEINLINE mat4	mat4ConstructTRS (float transX, float transY, float transZ, float rotataionX, float rotataionY, float rotataionZ, float scaleX, float scaleY, float scaleZ)
SRP_FORCEINLINE mat4	mat4ConstructView (float cameraX, float cameraY, float cameraZ, float rotataionX, float rotataionY, float rotataionZ, float scaleX, float scaleY, float scaleZ)
SRP_FORCEINLINE mat4	mat4ConstructOrthogonalProjection (float x_min, float x_max, float y_min, float y_max, float z_min, float z_max)
SRP_FORCEINLINE mat4	mat4ConstructPerspectiveProjection (float x_min_near, float x_max_near, float y_min_near, float y_max_near, float z_near, float z_far)
SRP_FORCEINLINE vec2	vec2Add (vec2 a, vec2 b)
SRP_FORCEINLINE vec2	vec2Subtract (vec2 a, vec2 b)
SRP_FORCEINLINE float	vec2DotProduct (vec2 a, vec2 b)
SRP_FORCEINLINE vec2	vec2MultiplyScalar (vec2 a, float b)
SRP_FORCEINLINE vec3	vec3Add (vec3 a, vec3 b)
SRP_FORCEINLINE vec3	vec3Subtract (vec3 a, vec3 b)
SRP_FORCEINLINE float	vec3DotProduct (vec3 a, vec3 b)
SRP_FORCEINLINE vec3	vec3MultiplyScalar (vec3 a, float b)
SRP_FORCEINLINE vec4	vec4Add (vec4 a, vec4 b)
SRP_FORCEINLINE vec4	vec4Subtract (vec4 a, vec4 b)
SRP_FORCEINLINE float	vec4DotProduct (vec4 a, vec4 b)
SRP_FORCEINLINE vec4	vec4MultiplyScalar (vec4 a, float b)
#define	_USE_MATH_DEFINES
#define	M_PI   3.14159265358979323846
#define	MIN(a, b)   ( (a) > (b) ? (b) : (a) )
#define	MAX(a, b)   ( (a) > (b) ? (a) : (b) )
#define	CLAMP(min, max, value)
#define	FRACTIONAL(x)   ( (x) - floor(x) )
#define	EPSILON   1e-9
#define	ROUGHLY_EQUAL(a, b)   (fabs((a) - (b)) <= EPSILON)
#define	ROUGHLY_ZERO(x)   (fabs(x) <= EPSILON)
#define	ROUGHLY_LESS_OR_EQUAL(a, b)   ((a) <= (b) + EPSILON)
#define	ROUGHLY_GREATER_OR_EQUAL(a, b)   ((a) >= (b) - EPSILON)

Detailed Description

Internals of the Vector & Matrix API.

Macro Definition Documentation

CLAMP

#define CLAMP	(		min,
			max,
			value
	)

Value:

    ( \
        (value < min) ? \
            (min) : \
            (value > max) ? \
                (max) : \
                (value) \
    )

Clamp the value between min and max

Returns

min, if value < min; max, if value > max; value otherwise

FRACTIONAL

#define FRACTIONAL

(

x

)

( (x) - floor(x) )

Get the fractional part of float or double

MAX

#define MAX	(		a,
			b
	)		( (a) > (b) ? (a) : (b) )

Get the maximum of two values

MIN

#define MIN	(		a,
			b
	)		( (a) > (b) ? (b) : (a) )

Get the minimum of two values

ROUGHLY_EQUAL

#define ROUGHLY_EQUAL	(		a,
			b
	)		(fabs((a) - (b)) <= EPSILON)

Determine if two values are roughly equal

ROUGHLY_GREATER_OR_EQUAL

#define ROUGHLY_GREATER_OR_EQUAL	(		a,
			b
	)		((a) >= (b) - EPSILON)

Determine if the first value is roughly greater or equal than the second one

ROUGHLY_LESS_OR_EQUAL

#define ROUGHLY_LESS_OR_EQUAL	(		a,
			b
	)		((a) <= (b) + EPSILON)

Determine if the first value is roughly less or equal than the second one

ROUGHLY_ZERO

#define ROUGHLY_ZERO

(

x

)

(fabs(x) <= EPSILON)

Determine if a value is roughly zero

Function Documentation

mat4ConstructIdentity()

SRP_FORCEINLINE mat4 mat4ConstructIdentity

(

)

Construct a 4x4 identity matrix

Returns

4x4 identity matrix

mat4ConstructOrthogonalProjection()

SRP_FORCEINLINE mat4 mat4ConstructOrthogonalProjection	(	float	x_min,
		float	x_max,
		float	y_min,
		float	y_max,
		float	z_min,
		float	z_max
	)

Construct a 4x4 orthogonal projection matrix. The orthogonal projection matrix transforms arbitrary rectangular parallelepiped (defined by 2 points: "min" and "max" ones) into an NDC cube, so it can be drawn in screen space

Parameters

x_min,y_min,z_min	Coordinates of the "min" point defining a rectangular parallelepiped
x_max,y_max,z_max	Coordinates of the "max" point defining a rectangular parallelepiped

Returns

Orthogonal projection matrix

mat4ConstructPerspectiveProjection()

SRP_FORCEINLINE mat4 mat4ConstructPerspectiveProjection	(	float	x_min_near,
		float	x_max_near,
		float	y_min_near,
		float	y_max_near,
		float	z_near,
		float	z_far
	)

Todo:

Avoid matmul here?

mat4ConstructRotate()

SRP_FORCEINLINE mat4 mat4ConstructRotate	(	float	x,
		float	y,
		float	z
	)

Construct a 4x4 matrix that rotates the points

Parameters

x,y,z

Angle (in radians) by which the points are rotated around X, Y, Z axis respectively

Returns

Rotation matrix

mat4ConstructScale()

SRP_FORCEINLINE mat4 mat4ConstructScale	(	float	x,
		float	y,
		float	z
	)

Construct a 4x4 matrix that scales the X, Y and Z dimensions

Parameters

x,y,z

Scaling coefficients for X, Y, Z dimensions respectively

Returns

Scale matrix

mat4ConstructTranslate()

SRP_FORCEINLINE mat4 mat4ConstructTranslate	(	float	x,
		float	y,
		float	z
	)

Construct a 4x4 matrix that translates the points

Parameters

x,y,z

Translating coefficient for X, Y, Z dimensions respectively

Returns

Translation matrix

mat4ConstructTRS()

SRP_FORCEINLINE mat4 mat4ConstructTRS	(	float	transX,
		float	transY,
		float	transZ,
		float	rotataionX,
		float	rotataionY,
		float	rotataionZ,
		float	scaleX,
		float	scaleY,
		float	scaleZ
	)

Construct a 4x4 matrix that translates, rotates the points and scales the X, Y, and Z dimenstions

See also

mat4ConstructScale() mat4ConstructTranslate() mat4ConstructRotate()

Returns

TRS matrix

mat4ConstructView()

SRP_FORCEINLINE mat4 mat4ConstructView	(	float	cameraX,
		float	cameraY,
		float	cameraZ,
		float	rotationX,
		float	rotationY,
		float	rotationZ,
		float	scaleX,
		float	scaleY,
		float	scaleZ
	)

Construct a 4x4 view matrix

Parameters

cameraX,cameraY,cameraZ	Camera position
rotationX,rotationY,rotationZ	Camera rotation along each dimension
scaleX,scaleY,scaleZ	Camera "zoom" along each dimension

Returns

View matrix

mat4MultiplyMat4()

SRP_FORCEINLINE mat4 mat4MultiplyMat4	(	const mat4 *restrict	a,
		const mat4 *restrict	b
	)

Multiply two 4x4 matrices

Parameters

a	Pointer to a matrix A
b	Pointer to a matrix B

Returns

The product A*B

mat4MultiplyVec4()

SRP_FORCEINLINE vec4 mat4MultiplyVec4	(	const mat4 *restrict	a,
		vec4	b
	)

Multiply mat4 by vec4

Parameters

a	Pointer to a matrix A
b	Vector B

Returns

The product A*B

vec2Add()

SRP_FORCEINLINE vec2 vec2Add	(	vec2	a,
		vec2	b
	)

Add two vectors

vec2DotProduct()

SRP_FORCEINLINE float vec2DotProduct	(	vec2	a,
		vec2	b
	)

Calculate the dot product of two vectors

vec2MultiplyScalar()

SRP_FORCEINLINE vec2 vec2MultiplyScalar	(	vec2	a,
		float	b
	)

Multiply a vector with a scalar value

vec2Subtract()

SRP_FORCEINLINE vec2 vec2Subtract	(	vec2	a,
		vec2	b
	)

Subtract two vectors

vec3Add()

SRP_FORCEINLINE vec3 vec3Add	(	vec3	a,
		vec3	b
	)

Add two vectors

vec3DotProduct()

SRP_FORCEINLINE float vec3DotProduct	(	vec3	a,
		vec3	b
	)

Calculate the dot product of two vectors

vec3MultiplyScalar()

SRP_FORCEINLINE vec3 vec3MultiplyScalar	(	vec3	a,
		float	b
	)

Multiply a vector with a scalar value

vec3Subtract()

SRP_FORCEINLINE vec3 vec3Subtract	(	vec3	a,
		vec3	b
	)

Subtract two vectors

vec4Add()

SRP_FORCEINLINE vec4 vec4Add	(	vec4	a,
		vec4	b
	)

Add two vectors

vec4DotProduct()

SRP_FORCEINLINE float vec4DotProduct	(	vec4	a,
		vec4	b
	)

Calculate the dot product of two vectors

vec4MultiplyScalar()

SRP_FORCEINLINE vec4 vec4MultiplyScalar	(	vec4	a,
		float	b
	)

Multiply a vector with a scalar value

vec4Subtract()

SRP_FORCEINLINE vec4 vec4Subtract	(	vec4	a,
		vec4	b
	)

Subtract two vectors