Math

Linear math function. More...

Collaboration diagram for Math:

Detailed Description

The Math group provides usual facilities for linear math, including

• vector types: bj_vec2, bj_vec3 and bj_vec4
• 4x4 matrix with bj_mat4
• Quaternion with bj_quat

The scalar type is float by is aliased as bj_real_t using a typedef.

This library is a direct conversion of linmath.h by Wolfgang Draxinger.

Macros
#define	bj_real_t   float
	Alias for float type.
#define	bj_quat_add   bj_vec4_add
	Alias for bj_vec4_add, adds two quaternions.
#define	bj_quat_sub   bj_vec4_sub
	Alias for bj_vec4_sub, subtracts two quaternions.
#define	bj_quat_norm   bj_vec4_normalize
	Alias for bj_vec4_normalize, normalizes a quaternion.
#define	bj_quat_scale   bj_vec4_scale
	Alias for bj_vec4_scale, scales a quaternion by a scalar.
#define	bj_quat_dot   bj_vec4_dot
	Alias for bj_vec4_dot, computes the dot product of two quaternions.

Typedefs
typedef bj_real_t	bj_vec2[2]
	Defines a 2D vector type.
typedef bj_real_t	bj_vec3[3]
	Defines a 3D vector type.
typedef bj_real_t	bj_vec4[4]
	Defines a 4D vector type.
typedef bj_vec4	bj_mat4[4]
	Defines a 4x4 matrix type.
typedef bj_real_t	bj_quat[4]
	Defines a quaternion type.

Functions
BJ_INLINE void	bj_vec2_set (bj_vec2 res, bj_real_t a, bj_real_t b)
	Directly set the scalar values of a bj_vec2 object.
BJ_INLINE void	bj_vec2_apply (bj_vec2 res, const bj_vec2 a, bj_real_t(*f)(bj_real_t))
	Invoke the given function to each scalar of the bj_vec2.
BJ_INLINE void	bj_vec2_add (bj_vec2 res, const bj_vec2 lhs, const bj_vec2 rhs)
	Set res to the result of lhs+rhs.
BJ_INLINE void	bj_vec2_sub (bj_vec2 res, const bj_vec2 lhs, const bj_vec2 rhs)
	Set res to the result of lhs-rhs.
BJ_INLINE void	bj_vec2_scale (bj_vec2 res, const bj_vec2 v, bj_real_t s)
	Set res to the result of multiplying v by s.
BJ_INLINE void	bj_vec2_scale_each (bj_vec2 res, const bj_vec2 v, const bj_vec2 s)
	Multiply each scalar of v by the respecting scalar in s.
BJ_INLINE bj_real_t	bj_vec2_dot (const bj_vec2 a, const bj_vec2 b)
	Computes the dot product of a abnd b
BJ_INLINE bj_real_t	bj_vec2_len (const bj_vec2 v)
	Computes the length of the vec2.
BJ_INLINE void	bj_vec2_normalize (bj_vec2 res, const bj_vec2 v)
	Normalizes the provided vec2.
BJ_INLINE void	bj_vec2_min (bj_vec2 res, const bj_vec2 a, const bj_vec2 b)
	Computes the component-wise minimum of two 2D vectors.
BJ_INLINE void	bj_vec2_max (bj_vec2 res, const bj_vec2 a, const bj_vec2 b)
	Computes the component-wise maximum of two 2D vectors.
BJ_INLINE void	bj_vec2_copy (bj_vec2 res, const bj_vec2 src)
	Copies the contents of one 2D vector to another.
BJ_INLINE void	bj_vec3_set (bj_vec2 res, bj_real_t a, bj_real_t b, bj_real_t c)
	Directly set the scalar values of a bj_vec3 object.
BJ_INLINE void	bj_vec3_apply (bj_vec3 res, const bj_vec3 a, bj_real_t(*f)(bj_real_t))
	Invoke the given function to each scalar of the bj_vec3.
BJ_INLINE void	bj_vec3_add (bj_vec3 res, const bj_vec3 lhs, const bj_vec3 rhs)
	Set res to the result of lhs+rhs.
BJ_INLINE void	bj_vec3_sub (bj_vec3 res, const bj_vec3 lhs, const bj_vec3 rhs)
	Set res to the result of lhs-rhs.
BJ_INLINE void	bj_vec3_scale (bj_vec3 res, const bj_vec3 v, bj_real_t s)
	Set res to the result of multiplying v by s.
BJ_INLINE bj_real_t	bj_vec3_dot (const bj_vec3 a, const bj_vec3 b)
	Computes the dot product of a abnd b
BJ_INLINE bj_real_t	bj_vec3_len (const bj_vec3 v)
	Computes the length of the vec3.
BJ_INLINE void	bj_vec3_normalize (bj_vec3 res, const bj_vec3 v)
	Normalizes the provided vec3.
BJ_INLINE void	bj_vec3_min (bj_vec3 res, const bj_vec3 a, const bj_vec3 b)
	Computes the component-wise minimum of two 3D vectors.
BJ_INLINE void	bj_vec3_max (bj_vec3 res, const bj_vec3 a, const bj_vec3 b)
	Computes the component-wise maximum of two 3D vectors.
BJ_INLINE void	bj_vec3_copy (bj_vec3 res, const bj_vec3 src)
	Copies the contents of one 3D vector to another.
BJ_INLINE void	bj_vec3_cross (bj_vec3 res, const bj_vec3 l, const bj_vec3 r)
	Computes the 3D cross product of two 3D vectors.
BJ_INLINE void	bj_vec3_reflect (bj_vec3 res, const bj_vec3 v, const bj_vec3 n)
	Reflects a 3D vector around a given normal.
BJ_INLINE void	bj_vec4_set (bj_vec2 res, bj_real_t a, bj_real_t b, bj_real_t c, bj_real_t d)
	Directly set the scalar values of a bj_vec4 object.
BJ_INLINE void	bj_vec4_apply (bj_vec4 res, const bj_vec4 a, bj_real_t(*f)(bj_real_t))
	Invoke the given function to each scalar of the bj_vec4.
BJ_INLINE void	bj_vec4_add (bj_vec4 res, const bj_vec4 lhs, const bj_vec4 rhs)
	Set res to the result of lhs+rhs.
BJ_INLINE void	bj_vec4_sub (bj_vec4 res, const bj_vec4 lhs, const bj_vec4 rhs)
	Set res to the result of lhs-rhs.
BJ_INLINE void	bj_vec4_scale (bj_vec4 res, const bj_vec4 v, bj_real_t s)
	Set res to the result of multiplying v by s.
BJ_INLINE bj_real_t	bj_vec4_dot (const bj_vec4 a, const bj_vec4 b)
	Computes the dot product of a abnd b
BJ_INLINE bj_real_t	bj_vec4_len (const bj_vec4 v)
	Computes the length of the vec4.
BJ_INLINE void	bj_vec4_normalize (bj_vec4 res, const bj_vec4 v)
	Normalizes the provided vec4.
BJ_INLINE void	bj_vec4_min (bj_vec4 res, const bj_vec4 a, const bj_vec4 b)
	Computes the component-wise minimum of two 4D vectors.
BJ_INLINE void	bj_vec4_max (bj_vec4 res, const bj_vec4 a, const bj_vec4 b)
	Computes the component-wise maximum of two 4D vectors.
BJ_INLINE void	bj_vec4_copy (bj_vec4 res, const bj_vec4 src)
	Copies the contents of one 4D vector to another.
BJ_INLINE void	bj_vec4_cross (bj_vec4 res, const bj_vec4 l, const bj_vec4 r)
	Computes the 3D cross product of two 4D vectors, assuming w = 1.0.
BJ_INLINE void	bj_vec4_reflect (bj_vec4 res, const bj_vec4 v, const bj_vec4 n)
	Reflects a 4D vector around a given normal.
BJ_INLINE void	bj_mat4_identity (bj_mat4 mat)
	Initializes a 4x4 matrix to the identity matrix.
BJ_INLINE void	bj_mat4_copy (bj_mat4 to, const bj_mat4 from)
	Copies a 4x4 matrix from one to another.
BJ_INLINE void	bj_mat4_row (bj_vec4 res, const bj_mat4 mat, int r)
	Retrieves a specific row from a 4x4 matrix.
BJ_INLINE void	bj_mat4_col (bj_vec4 res, const bj_mat4 mat, int c)
	Retrieves a specific column from a 4x4 matrix.
BJ_INLINE void	bj_mat4_transpose (bj_mat4 res, const bj_mat4 mat)
	Transposes a 4x4 matrix.
BJ_INLINE void	bj_mat4_add (bj_mat4 res, const bj_mat4 lhs, const bj_mat4 rhs)
	Adds two 4x4 matrices.
BJ_INLINE void	bj_mat4_sub (bj_mat4 res, const bj_mat4 lhs, const bj_mat4 rhs)
	Subtracts one 4x4 matrix from another.
BJ_INLINE void	bj_mat4_scale (bj_mat4 res, const bj_mat4 lhs, bj_real_t k)
	Scales a 4x4 matrix by a scalar.
BJ_INLINE void	bj_mat4_scale_xyz (bj_mat4 res, const bj_mat4 mat, bj_real_t x, bj_real_t y, bj_real_t z)
	Scales the X, Y, and Z components of a 4x4 matrix.
BJ_INLINE void	bj_mat4_mul (bj_mat4 res, const bj_mat4 lhs, const bj_mat4 rhs)
	Multiplies two 4x4 matrices.
BJ_INLINE void	bj_mat4_mul_vec4 (bj_vec4 res, const bj_mat4 mat, const bj_vec4 v)
	Multiplies a 4x4 matrix by a 4D vector.
BJ_INLINE void	bj_mat4_translation (bj_mat4 res, bj_real_t x, bj_real_t y, bj_real_t z)
	Creates a 4x4 translation matrix.
BJ_INLINE void	bj_mat4_translation_inplace (bj_mat4 M, bj_real_t x, bj_real_t y, bj_real_t z)
	Applies a translation transformation to a 4x4 matrix in-place.
BJ_INLINE void	bj_mat4_mul_outer (bj_mat4 res, const bj_vec3 a, const bj_vec3 b)
	Computes the outer product of two 3D vectors and stores the result in a 4x4 matrix.
BJ_INLINE void	bj_mat4_rotate (bj_mat4 res, const bj_mat4 mat, bj_real_t x, bj_real_t y, bj_real_t z, bj_real_t angle)
	Rotates a 4x4 matrix by a given axis and angle.
BJ_INLINE void	bj_ma4_rotate_x (bj_mat4 res, const bj_mat4 mat, bj_real_t angle)
	Rotates a 4x4 matrix around the X axis by a given angle.
BJ_INLINE void	bj_ma4_rotate_y (bj_mat4 res, const bj_mat4 mat, bj_real_t angle)
	Rotates a 4x4 matrix around the Y axis by a given angle.
BJ_INLINE void	bj_ma4_rotate_z (bj_mat4 res, const bj_mat4 mat, bj_real_t angle)
	Rotates a 4x4 matrix around the Z-axis by a given angle.
BJ_INLINE void	bj_mat4_rotate_arcball (bj_mat4 R, const bj_mat4 M, bj_vec2 const _a, bj_vec2 const _b, bj_real_t s)
	Rotates a matrix based on arcball-style rotation from two 2D vectors.
BJ_INLINE void	bj_mat4_inverse (bj_mat4 res, const bj_mat4 mat)
	Inverts a 4x4 matrix.
BJ_INLINE void	bj_mat4_orthonormalize (bj_mat4 res, const bj_mat4 mat)
	Orthonormalizes the rows of a 4x4 matrix.
BJ_INLINE void	bj_mat4_frustum (bj_mat4 fmat, bj_real_t l, bj_real_t r, bj_real_t b, bj_real_t t, bj_real_t n, bj_real_t f)
	Generates a perspective projection matrix for a frustum.
BJ_INLINE void	bj_mat4_ortho (bj_mat4 omat, bj_real_t l, bj_real_t r, bj_real_t b, bj_real_t t, bj_real_t n, bj_real_t f)
	Generates an orthographic projection matrix.
BJ_INLINE void	bj_mat4_perspective (bj_mat4 pmat, bj_real_t y_fov, bj_real_t aspect, bj_real_t n, bj_real_t f)
	Generates a perspective projection matrix based on field of view.
BJ_INLINE void	bj_mat4_lookat (bj_mat4 m, const bj_vec3 eye, const bj_vec3 center, const bj_vec3 up)
	Generates a look-at matrix.
BJ_INLINE void	bj_quat_identity (bj_quat q)
	Sets a quaternion to the identity quaternion.
BJ_INLINE void	bj_quat_mul (bj_quat res, const bj_quat p, const bj_quat q)
	Multiplies two quaternions.
BJ_INLINE void	bj_quat_conjugate (bj_quat res, const bj_quat q)
	Computes the conjugate of a quaternion.
BJ_INLINE void	bj_quat_rotation (bj_quat res, bj_real_t angle, const bj_vec3 axis)
	Creates a rotation quaternion based on an angle and axis.
BJ_INLINE void	bj_quat_mul_vec3 (bj_vec3 res, const bj_quat q, const bj_vec3 v)
	Applies a quaternion rotation to a 3D vector.
BJ_INLINE void	bj_mat4_from_quat (bj_mat4 res, const bj_quat q)
	Converts a quaternion to a 4x4 rotation matrix.
BJ_INLINE void	bj_mat4_rotate_from_quat (bj_mat4 R, const bj_mat4 M, const bj_quat q)
	Applies a quaternion rotation to each column of a matrix.
BJ_INLINE void	bj_quat_from_mat4 (bj_quat q, const bj_mat4 M)
	Converts a 4x4 rotation matrix to a quaternion.

Typedef Documentation

bj_mat4

typedef bj_vec4 bj_mat4[4]

This type represents a 4x4 matrix, where each row is a bj_vec4 vector. It is commonly used for transformations such as rotations, scaling, and translations.

Note

The matrix is represented as an array of four bj_vec4 values.

See also

bj_vec4

bj_quat

typedef bj_real_t bj_quat[4]

This type represents a quaternion with four components, each of type bj_real_t. Quaternions are used for representing rotations in 3D space.

Note

The quaternion is represented as an array of four bj_real_t values.

See also

bj_real_t

bj_vec2

typedef bj_real_t bj_vec2[2]

This type represents a 2D vector with two components, each of type bj_real_t. It is commonly used for storing 2D coordinates, directions, or other 2D data.

Note

The vector is represented as an array of two bj_real_t values.

See also

bj_real_t

bj_vec3

typedef bj_real_t bj_vec3[3]

This type represents a 3D vector with three components, each of type bj_real_t. It is commonly used for storing 3D coordinates, directions, or other 3D data.

Note

The vector is represented as an array of three bj_real_t values.

See also

bj_real_t

bj_vec4

typedef bj_real_t bj_vec4[4]

This type represents a 4D vector with four components, each of type bj_real_t. It is commonly used for storing 4D homogeneous coordinates or other 4D data.

Note

The vector is represented as an array of four bj_real_t values.

See also

bj_real_t

Function Documentation

bj_ma4_rotate_x()

BJ_INLINE void bj_ma4_rotate_x	(	bj_mat4	res,
		const bj_mat4	mat,
		bj_real_t	angle )

This function performs a rotation of matrix mat around the X axis by angle (in radians), and stores the resulting matrix in res.

Parameters

res	The resulting rotated matrix.
mat	The matrix to rotate.
angle	The angle to rotate by (in radians).

bj_ma4_rotate_y()

BJ_INLINE void bj_ma4_rotate_y	(	bj_mat4	res,
		const bj_mat4	mat,
		bj_real_t	angle )

This function performs a rotation of matrix mat around the Y axis by angle (in radians), and stores the resulting matrix in res.

Parameters

res	The resulting rotated matrix.
mat	The matrix to rotate.
angle	The angle to rotate by (in radians).

bj_ma4_rotate_z()

BJ_INLINE void bj_ma4_rotate_z	(	bj_mat4	res,
		const bj_mat4	mat,
		bj_real_t	angle )

This function applies a rotation to the input matrix around the Z-axis by a specified angle and stores the result in the output matrix.

Parameters

mat	The 4x4 matrix to rotate.
angle	The angle (in radians) to rotate the matrix around the Z-axis.
res	The resulting rotated matrix.

bj_mat4_add()

BJ_INLINE void bj_mat4_add	(	bj_mat4	res,
		const bj_mat4	lhs,
		const bj_mat4	rhs )

Computes the element-wise addition of two matrices lhs and rhs and stores the result in res.

Parameters

res	The resulting matrix after addition.
lhs	The left-hand matrix to add.
rhs	The right-hand matrix to add.

bj_mat4_col()

BJ_INLINE void bj_mat4_col	(	bj_vec4	res,
		const bj_mat4	mat,
		int	c )

Extracts the column at index c from matrix mat and stores it in res.

Parameters

res	The resulting column vector.
mat	The matrix from which to extract the column.
c	The column index (0-based) to extract.

bj_mat4_copy()

BJ_INLINE void bj_mat4_copy	(	bj_mat4	to,
		const bj_mat4	from )

Copies the entire contents of the matrix from to the matrix to.

Parameters

to	The destination matrix.
from	The source matrix to copy from.

bj_mat4_from_quat()

BJ_INLINE void bj_mat4_from_quat	(	bj_mat4	res,
		const bj_quat	q )

This function converts the given quaternion into a 4x4 rotation matrix.

Parameters

res	The resulting 4x4 rotation matrix.
q	The quaternion to convert.

bj_mat4_frustum()

BJ_INLINE void bj_mat4_frustum	(	bj_mat4	fmat,
		bj_real_t	l,
		bj_real_t	r,
		bj_real_t	b,
		bj_real_t	t,
		bj_real_t	n,
		bj_real_t	f )

This function generates a perspective projection matrix based on a frustum defined by the left, right, bottom, top, near, and far clipping planes.

Parameters

l	The left plane of the frustum.
r	The right plane of the frustum.
b	The bottom plane of the frustum.
t	The top plane of the frustum.
n	The near plane of the frustum.
f	The far plane of the frustum.
fmat	The resulting perspective projection matrix.

bj_mat4_identity()

BJ_INLINE void bj_mat4_identity

(

bj_mat4

mat

)

Sets all diagonal elements of the matrix to 1.0 and all off-diagonal elements to 0.0.

Parameters

mat	The matrix to be initialized as the identity matrix.

bj_mat4_inverse()

BJ_INLINE void bj_mat4_inverse	(	bj_mat4	res,
		const bj_mat4	mat )

This function calculates the inverse of the given 4x4 matrix and stores it in the result matrix. It uses a standard matrix inversion method for 4x4 matrices.

Parameters

mat	The matrix to invert.
res	The resulting inverted matrix.

bj_mat4_lookat()

BJ_INLINE void bj_mat4_lookat	(	bj_mat4	m,
		const bj_vec3	eye,
		const bj_vec3	center,
		const bj_vec3	up )

This function generates a view matrix that transforms coordinates from world space to camera space based on the eye position, center (target) position, and up vector.

Parameters

eye	The position of the camera.
center	The target position the camera is looking at.
up	The up vector of the camera.
m	The resulting look-at matrix.

bj_mat4_mul()

BJ_INLINE void bj_mat4_mul	(	bj_mat4	res,
		const bj_mat4	lhs,
		const bj_mat4	rhs )

Computes the matrix product of lhs and rhs and stores the result in res.

Parameters

res	The resulting matrix after multiplication.
lhs	The left-hand matrix.
rhs	The right-hand matrix.

bj_mat4_mul_outer()

BJ_INLINE void bj_mat4_mul_outer	(	bj_mat4	res,
		const bj_vec3	a,
		const bj_vec3	b )

Computes the outer product of vectors a and b and stores the result in matrix res. The result is a matrix where elements are the products of corresponding components of the vectors.

Parameters

res	The resulting 4x4 matrix from the outer product.
a	The first 3D vector.
b	The second 3D vector.

bj_mat4_mul_vec4()

BJ_INLINE void bj_mat4_mul_vec4	(	bj_vec4	res,
		const bj_mat4	mat,
		const bj_vec4	v )

Computes the matrix-vector product of matrix mat and vector v and stores the result in res.

Parameters

res	The resulting vector after multiplication.
mat	The matrix to multiply.
v	The vector to multiply.

bj_mat4_ortho()

BJ_INLINE void bj_mat4_ortho	(	bj_mat4	omat,
		bj_real_t	l,
		bj_real_t	r,
		bj_real_t	b,
		bj_real_t	t,
		bj_real_t	n,
		bj_real_t	f )

This function generates an orthographic projection matrix for the specified left, right, bottom, top, near, and far clipping planes.

Parameters

l	The left plane of the orthographic projection.
r	The right plane of the orthographic projection.
b	The bottom plane of the orthographic projection.
t	The top plane of the orthographic projection.
n	The near plane of the orthographic projection.
f	The far plane of the orthographic projection.
omat	The resulting orthographic projection matrix.

bj_mat4_orthonormalize()

BJ_INLINE void bj_mat4_orthonormalize	(	bj_mat4	res,
		const bj_mat4	mat )

This function orthonormalizes the rows of the matrix, ensuring that the matrix rows are orthogonal and normalized.

Parameters

mat	The 4x4 matrix to orthonormalize.
res	The resulting orthonormalized 4x4 matrix.

bj_mat4_perspective()

BJ_INLINE void bj_mat4_perspective	(	bj_mat4	pmat,
		bj_real_t	y_fov,
		bj_real_t	aspect,
		bj_real_t	n,
		bj_real_t	f )

This function generates a perspective projection matrix based on the field of view (y_fov), aspect ratio, and near and far clipping planes.

Parameters

y_fov	The vertical field of view in radians.
aspect	The aspect ratio (width / height).
n	The near clipping plane.
f	The far clipping plane.
pmat	The resulting perspective projection matrix.

bj_mat4_rotate()

BJ_INLINE void bj_mat4_rotate	(	bj_mat4	res,
		const bj_mat4	mat,
		bj_real_t	x,
		bj_real_t	y,
		bj_real_t	z,
		bj_real_t	angle )

This function performs a 3D rotation on matrix mat around an arbitrary axis (x, y, z) by angle (in radians), and stores the resulting matrix in res. The axis vector is normalized before the rotation.

Parameters

res	The resulting rotated matrix.
mat	The matrix to rotate.
x	The X component of the axis of rotation.
y	The Y component of the axis of rotation.
z	The Z component of the axis of rotation.
angle	The angle to rotate by (in radians).

bj_mat4_rotate_arcball()

BJ_INLINE void bj_mat4_rotate_arcball	(	bj_mat4	R,
		const bj_mat4	M,
		bj_vec2 const	_a,
		bj_vec2 const	_b,
		bj_real_t	s )

This function computes the rotation matrix that represents the arcball rotation based on two 2D input vectors (a, b), the input matrix, and a scaling factor. It normalizes the vectors and calculates the rotation axis and angle, applying the rotation to the matrix.

Parameters

M	The input matrix to rotate.
_a	The first 2D vector for the arcball rotation.
_b	The second 2D vector for the arcball rotation.
s	A scaling factor for the rotation angle.
R	The resulting rotation matrix.

bj_mat4_rotate_from_quat()

BJ_INLINE void bj_mat4_rotate_from_quat	(	bj_mat4	R,
		const bj_mat4	M,
		const bj_quat	q )

This function applies the rotation represented by the given quaternion to each column of the given matrix, transforming it into the rotated matrix.

Parameters

R	The resulting rotated matrix.
M	The matrix to rotate.
q	The quaternion representing the rotation.

bj_mat4_row()

BJ_INLINE void bj_mat4_row	(	bj_vec4	res,
		const bj_mat4	mat,
		int	r )

Extracts the row at index r from matrix mat and stores it in res.

Parameters

res	The resulting row vector.
mat	The matrix from which to extract the row.
r	The row index (0-based) to extract.

bj_mat4_scale()

BJ_INLINE void bj_mat4_scale	(	bj_mat4	res,
		const bj_mat4	lhs,
		bj_real_t	k )

Multiplies each element of the matrix lhs by the scalar k and stores the result in res.

Parameters

res	The resulting scaled matrix.
lhs	The matrix to scale.
k	The scalar by which to scale the matrix.

bj_mat4_scale_xyz()

BJ_INLINE void bj_mat4_scale_xyz	(	bj_mat4	res,
		const bj_mat4	mat,
		bj_real_t	x,
		bj_real_t	y,
		bj_real_t	z )

Scales the X, Y, and Z components of the matrix mat by x, y, and z respectively. The W component is left unchanged and copied directly from mat.

Parameters

res	The resulting scaled matrix.
mat	The matrix to scale.
x	The scaling factor for the X component.
y	The scaling factor for the Y component.
z	The scaling factor for the Z component.

bj_mat4_sub()

BJ_INLINE void bj_mat4_sub	(	bj_mat4	res,
		const bj_mat4	lhs,
		const bj_mat4	rhs )

Computes the element-wise subtraction of two matrices lhs and rhs and stores the result in res.

Parameters

res	The resulting matrix after subtraction.
lhs	The matrix to subtract from.
rhs	The matrix to subtract.

bj_mat4_translation()

BJ_INLINE void bj_mat4_translation	(	bj_mat4	res,
		bj_real_t	x,
		bj_real_t	y,
		bj_real_t	z )

Creates a translation matrix that translates a point by x, y, and z in 3D space.

Parameters

res	The resulting translation matrix.
x	The translation distance along the X axis.
y	The translation distance along the Y axis.
z	The translation distance along the Z axis.

bj_mat4_translation_inplace()

BJ_INLINE void bj_mat4_translation_inplace	(	bj_mat4	M,
		bj_real_t	x,
		bj_real_t	y,
		bj_real_t	z )

This function adds a translation by x, y, and z to the matrix M in-place. The translation vector is applied by modifying the last column of the matrix.

Parameters

[in,out]	M	The matrix to apply the translation to (modified in-place).
	x	The translation distance along the X axis.
	y	The translation distance along the Y axis.
	z	The translation distance along the Z axis.

bj_mat4_transpose()

BJ_INLINE void bj_mat4_transpose	(	bj_mat4	res,
		const bj_mat4	mat )

Computes the transpose of matrix mat and stores it in res. The rows of mat become the columns of res.

Parameters

res	The transposed matrix.
mat	The matrix to transpose.

bj_quat_conjugate()

BJ_INLINE void bj_quat_conjugate	(	bj_quat	res,
		const bj_quat	q )

This function computes the conjugate of the given quaternion, which involves negating the vector part (x, y, z) of the quaternion while keeping the scalar part unchanged.

Parameters

res	The resulting conjugated quaternion.
q	The quaternion to conjugate.

bj_quat_from_mat4()

BJ_INLINE void bj_quat_from_mat4	(	bj_quat	q,
		const bj_mat4	M )

This function converts the given 4x4 rotation matrix into a quaternion.

Parameters

q	The resulting quaternion.
M	The 4x4 rotation matrix to convert.

bj_quat_identity()

BJ_INLINE void bj_quat_identity

(

bj_quat

q

)

This function sets the given quaternion to the identity quaternion (0, 0, 0, 1).

Parameters

q	The quaternion to set as the identity.

bj_quat_mul()

BJ_INLINE void bj_quat_mul	(	bj_quat	res,
		const bj_quat	p,
		const bj_quat	q )

This function computes the product of two quaternions, following the quaternion multiplication rules, and stores the result in the output quaternion.

Parameters

res	The resulting quaternion after multiplication.
p	The first quaternion.
q	The second quaternion.

bj_quat_mul_vec3()

BJ_INLINE void bj_quat_mul_vec3	(	bj_vec3	res,
		const bj_quat	q,
		const bj_vec3	v )

This function rotates a 3D vector using the given quaternion, which represents the rotation.

Parameters

res	The resulting rotated vector.
q	The quaternion representing the rotation.
v	The 3D vector to rotate.

bj_quat_rotation()

BJ_INLINE void bj_quat_rotation	(	bj_quat	res,
		bj_real_t	angle,
		const bj_vec3	axis )

This function generates a quaternion representing a rotation of the specified angle (in radians) around the given axis.

Parameters

res	The resulting rotation quaternion.
angle	The angle (in radians) of rotation.
axis	The axis around which the rotation occurs.

bj_vec2_add()

BJ_INLINE void bj_vec2_add	(	bj_vec2	res,
		const bj_vec2	lhs,
		const bj_vec2	rhs )

Parameters

res	The destination vec2
lhs	The first source vec2
rhs	The second source vec2

bj_vec2_apply()

BJ_INLINE void bj_vec2_apply	(	bj_vec2	res,
		const bj_vec2	a,
		bj_real_t(*	f )(bj_real_t) )

Parameters

res	A location to the target vec2
a	A location to the source vec2
f	The map function

Examples

shaders.c.

bj_vec2_copy()

BJ_INLINE void bj_vec2_copy	(	bj_vec2	res,
		const bj_vec2	src )

Parameters

res	The destination vector.
src	The source vector to copy.

Examples

shaders.c.

bj_vec2_dot()

BJ_INLINE bj_real_t bj_vec2_dot	(	const bj_vec2	a,
		const bj_vec2	b )

Parameters

a	The first vec2
b	The second vec2

Returns

The resulting dot product

bj_vec2_len()

BJ_INLINE bj_real_t bj_vec2_len

(

const bj_vec2

v

)

Parameters

v

The vec2

Returns

The length

Examples

shaders.c.

bj_vec2_max()

BJ_INLINE void bj_vec2_max	(	bj_vec2	res,
		const bj_vec2	a,
		const bj_vec2	b )

Parameters

res	The result vector, where each component is the maximum of a and b.
a	The first input vector.
b	The second input vector.

bj_vec2_min()

BJ_INLINE void bj_vec2_min	(	bj_vec2	res,
		const bj_vec2	a,
		const bj_vec2	b )

Parameters

res	The result vector, where each component is the minimum of a and b.
a	The first input vector.
b	The second input vector.

bj_vec2_normalize()

BJ_INLINE void bj_vec2_normalize	(	bj_vec2	res,
		const bj_vec2	v )

Parameters

res	The resulting vec2
v	The vec2

bj_vec2_scale()

BJ_INLINE void bj_vec2_scale	(	bj_vec2	res,
		const bj_vec2	v,
		bj_real_t	s )

Parameters

res	The destination vec2
v	The source vec2
s	The factor value

Examples

shaders.c.

bj_vec2_scale_each()

BJ_INLINE void bj_vec2_scale_each	(	bj_vec2	res,
		const bj_vec2	v,
		const bj_vec2	s )

Parameters

res	The destination vec2
v	The source vec2
s	The scalar vec2

bj_vec2_set()

BJ_INLINE void bj_vec2_set	(	bj_vec2	res,
		bj_real_t	a,
		bj_real_t	b )

Parameters

res	A location to the target vec4
a	The first scalar value
b	The second scalar value

bj_vec2_sub()

BJ_INLINE void bj_vec2_sub	(	bj_vec2	res,
		const bj_vec2	lhs,
		const bj_vec2	rhs )

Parameters

res	The destination vec2
lhs	The first source vec2
rhs	The second source vec2

Examples

shaders.c.

bj_vec3_add()

BJ_INLINE void bj_vec3_add	(	bj_vec3	res,
		const bj_vec3	lhs,
		const bj_vec3	rhs )

Parameters

res	The destination vec3
lhs	The first source vec3
rhs	The second source vec3

Examples

shaders.c.

bj_vec3_apply()

BJ_INLINE void bj_vec3_apply	(	bj_vec3	res,
		const bj_vec3	a,
		bj_real_t(*	f )(bj_real_t) )

Parameters

res	A location to the target vec3
a	A location to the source vec3
f	The map function

bj_vec3_copy()

BJ_INLINE void bj_vec3_copy	(	bj_vec3	res,
		const bj_vec3	src )

Parameters

res	The destination vector.
src	The source vector to copy.

Examples

shaders.c.

bj_vec3_cross()

BJ_INLINE void bj_vec3_cross	(	bj_vec3	res,
		const bj_vec3	l,
		const bj_vec3	r )

Parameters

res	The resulting vector (cross product of l and r).
l	The left-hand input vector.
r	The right-hand input vector.

bj_vec3_dot()

BJ_INLINE bj_real_t bj_vec3_dot	(	const bj_vec3	a,
		const bj_vec3	b )

Parameters

a	The first vec3
b	The second vec3

Returns

The resulting dot product

bj_vec3_len()

BJ_INLINE bj_real_t bj_vec3_len

(

const bj_vec3

v

)

Parameters

v

The vec3

Returns

The length

bj_vec3_max()

BJ_INLINE void bj_vec3_max	(	bj_vec3	res,
		const bj_vec3	a,
		const bj_vec3	b )

Parameters

res	The result vector, where each component is the maximum of a and b.
a	The first input vector.
b	The second input vector.

bj_vec3_min()

BJ_INLINE void bj_vec3_min	(	bj_vec3	res,
		const bj_vec3	a,
		const bj_vec3	b )

Parameters

res	The result vector, where each component is the minimum of a and b.
a	The first input vector.
b	The second input vector.

bj_vec3_normalize()

BJ_INLINE void bj_vec3_normalize	(	bj_vec3	res,
		const bj_vec3	v )

Parameters

res	The resulting vec3
v	The vec3

bj_vec3_reflect()

BJ_INLINE void bj_vec3_reflect	(	bj_vec3	res,
		const bj_vec3	v,
		const bj_vec3	n )

Computes the reflection of vector v across the normal vector n. Assumes both vectors are 3D, and uses all three components.

Parameters

res	The reflected vector.
v	The incident vector.
n	The normal vector (should be normalized).

bj_vec3_scale()

BJ_INLINE void bj_vec3_scale	(	bj_vec3	res,
		const bj_vec3	v,
		bj_real_t	s )

Parameters

res	The destination vec3
v	The source vec3
s	The factor value

Examples

shaders.c.

bj_vec3_set()

BJ_INLINE void bj_vec3_set	(	bj_vec2	res,
		bj_real_t	a,
		bj_real_t	b,
		bj_real_t	c )

Parameters

res	A location to the target vec4
a	The first scalar value
b	The second scalar value
c	The third scalar value

bj_vec3_sub()

BJ_INLINE void bj_vec3_sub	(	bj_vec3	res,
		const bj_vec3	lhs,
		const bj_vec3	rhs )

Parameters

res	The destination vec3
lhs	The first source vec3
rhs	The second source vec3

bj_vec4_add()

BJ_INLINE void bj_vec4_add	(	bj_vec4	res,
		const bj_vec4	lhs,
		const bj_vec4	rhs )

Parameters

res	The destination vec4
lhs	The first source vec4
rhs	The second source vec4

bj_vec4_apply()

BJ_INLINE void bj_vec4_apply	(	bj_vec4	res,
		const bj_vec4	a,
		bj_real_t(*	f )(bj_real_t) )

Parameters

res	A location to the target vec4
a	A location to the source vec4
f	The map function

bj_vec4_copy()

BJ_INLINE void bj_vec4_copy	(	bj_vec4	res,
		const bj_vec4	src )

Parameters

res	The destination vector.
src	The source vector to copy.

bj_vec4_cross()

BJ_INLINE void bj_vec4_cross	(	bj_vec4	res,
		const bj_vec4	l,
		const bj_vec4	r )

Only the x, y, and z components are used for the cross product. The w component of the result is set to 1.0.

Parameters

res	The resulting vector.
l	The left-hand input vector.
r	The right-hand input vector.

bj_vec4_dot()

BJ_INLINE bj_real_t bj_vec4_dot	(	const bj_vec4	a,
		const bj_vec4	b )

Parameters

a	The first vec4
b	The second vec4

Returns

The resulting dot product

bj_vec4_len()

BJ_INLINE bj_real_t bj_vec4_len

(

const bj_vec4

v

)

Parameters

v

The vec4

Returns

The length

bj_vec4_max()

BJ_INLINE void bj_vec4_max	(	bj_vec4	res,
		const bj_vec4	a,
		const bj_vec4	b )

Parameters

res	The result vector, where each component is the maximum of a and b.
a	The first input vector.
b	The second input vector.

bj_vec4_min()

BJ_INLINE void bj_vec4_min	(	bj_vec4	res,
		const bj_vec4	a,
		const bj_vec4	b )

Parameters

res	The result vector, where each component is the minimum of a and b.
a	The first input vector.
b	The second input vector.

bj_vec4_normalize()

BJ_INLINE void bj_vec4_normalize	(	bj_vec4	res,
		const bj_vec4	v )

Parameters

res	The resulting vec4
v	The vec4

bj_vec4_reflect()

BJ_INLINE void bj_vec4_reflect	(	bj_vec4	res,
		const bj_vec4	v,
		const bj_vec4	n )

Computes the reflection of vector v across the normal vector n. Assumes both vectors are 4D, and uses all four components.

Parameters

res	The reflected vector.
v	The incident vector.
n	The normal vector (should be normalized).

bj_vec4_scale()

BJ_INLINE void bj_vec4_scale	(	bj_vec4	res,
		const bj_vec4	v,
		bj_real_t	s )

Parameters

res	The destination vec2
v	The source vec2
s	The factor value

bj_vec4_set()

BJ_INLINE void bj_vec4_set	(	bj_vec2	res,
		bj_real_t	a,
		bj_real_t	b,
		bj_real_t	c,
		bj_real_t	d )

Parameters

res	A location to the target vec4
a	The first scalar value
b	The second scalar value
c	The third scalar value
d	The fourth scalar value

bj_vec4_sub()

BJ_INLINE void bj_vec4_sub	(	bj_vec4	res,
		const bj_vec4	lhs,
		const bj_vec4	rhs )

Parameters

res	The destination vec4
lhs	The first source vec4
rhs	The second source vec4