Collaboration diagram for Math:

Topics
	Geometry 2D

Data Structures
struct	bj_mat3x3_t
struct	bj_mat3x2_t
struct	bj_mat4x4_t
struct	bj_mat4x3_t
struct	bj_rect_t
struct	bj_vec2_t
struct	bj_vec3_t
struct	bj_vec4_t

Macros
#define	BJ_M3(c, r)
#define	BJ_M32(c, r)
#define	BJ_M4(c, r)
#define	BJ_M43(c, r)
#define	BJ_VEC2_ZERO ((bj_vec2){BJ_FZERO, BJ_FZERO})
#define	BJ_VEC3_ZERO ((bj_vec3){BJ_FZERO, BJ_FZERO, BJ_FZERO})
#define	BJ_VEC4_ZERO ((bj_vec4){BJ_FZERO, BJ_FZERO, BJ_FZERO, BJ_FZERO})

Typedefs
typedef struct bj_mat3x3_t	bj_mat3x3
typedef struct bj_mat3x3_t	bj_mat3
typedef struct bj_mat3x2_t	bj_mat3x2
typedef struct bj_mat4x4_t	bj_mat4x4
typedef struct bj_mat4x4_t	bj_mat4
typedef struct bj_mat4x3_t	bj_mat4x3
typedef struct bj_vec4_t	bj_quat
typedef struct bj_rect_t	bj_rect
typedef struct bj_vec2_t	bj_vec2
typedef struct bj_vec3_t	bj_vec3
typedef struct bj_vec4_t	bj_vec4

Functions
static void	bj_mat3_set_identity (bj_mat3 *restrict M)
static void	bj_mat3_copy (bj_mat3 restrict dst, const bj_mat3 restrict src)
static bj_vec3	bj_mat3_row (const bj_mat3 *restrict M, int r)
static bj_vec3	bj_mat3_col (const bj_mat3 *restrict M, int c)
static void	bj_mat3_transpose (bj_mat3 restrict out, const bj_mat3 restrict A)
static void	bj_mat3_add (bj_mat3 restrict out, const bj_mat3 restrict A, const bj_mat3 *restrict B)
static void	bj_mat3_sub (bj_mat3 restrict out, const bj_mat3 restrict A, const bj_mat3 *restrict B)
static void	bj_mat3_mul_scalar (bj_mat3 restrict out, const bj_mat3 restrict A, bj_real k)
static void	bj_mat3_mul (bj_mat3 restrict out, const bj_mat3 restrict A, const bj_mat3 *restrict B)
static bj_vec3	bj_mat3_transform_vec3 (const bj_mat3 *restrict M, bj_vec3 v)
static bj_vec2	bj_mat3_transform_point (const bj_mat3 *restrict M, bj_vec2 p)
static void	bj_mat3_set_translation (bj_mat3 *restrict M, bj_real tx, bj_real ty)
static void	bj_mat3_translate (bj_mat3 *restrict M, bj_real tx, bj_real ty)
static void	bj_mat3_set_scaling_xy (bj_mat3 *restrict M, bj_real sx, bj_real sy)
static void	bj_mat3_set_shear_xy (bj_mat3 *restrict M, bj_real shx, bj_real shy)
static void	bj_mat3_set_rotation_z (bj_mat3 *restrict M, bj_real angle)
static bj_real	bj_mat3_determinant (const bj_mat3 *restrict A)
static bj_bool	bj_mat3_invert (bj_mat3 restrict out, const bj_mat3 restrict A)
static void	bj_mat3_invert_unsafe (bj_mat3 restrict out, const bj_mat3 restrict A)
static void	bj_mat3_set_ortho (bj_mat3 *restrict M, bj_real l, bj_real r, bj_real b, bj_real t)
static void	bj_mat3_set_viewport (bj_mat3 *restrict M, bj_real x, bj_real y, bj_real w, bj_real h)
static void	bj_mat3x2_set_identity (bj_mat3x2 *restrict M)
static void	bj_mat3x2_set_translation (bj_mat3x2 *restrict M, bj_real tx, bj_real ty)
static void	bj_mat3x2_set_scaling_xy (bj_mat3x2 *restrict M, bj_real sx, bj_real sy)
static void	bj_mat3x2_set_rotation_z (bj_mat3x2 *restrict M, bj_real angle)
static void	bj_mat3x2_mul (bj_mat3x2 restrict out, const bj_mat3x2 restrict A, const bj_mat3x2 *restrict B)
static bj_vec2	bj_mat3x2_transform_point (const bj_mat3x2 *restrict M, bj_vec2 p)
static bj_vec2	bj_mat3x2_transform_dir (const bj_mat3x2 *restrict M, bj_vec2 v)
static void	bj_mat3_from_mat3x2 (bj_mat3 restrict M, const bj_mat3x2 restrict A)
static void	bj_mat3x2_from_mat3 (bj_mat3x2 restrict M, const bj_mat3 restrict A)
static void	bj_mat4_set_identity (bj_mat4 *restrict M)
static void	bj_mat4_copy (bj_mat4 restrict dst, const bj_mat4 restrict src)
static bj_vec4	bj_mat4_row (const bj_mat4 *restrict M, int r)
static bj_vec4	bj_mat4_col (const bj_mat4 *restrict M, int c)
static void	bj_mat4_transpose (bj_mat4 restrict out, const bj_mat4 restrict A)
static void	bj_mat4_add (bj_mat4 restrict out, const bj_mat4 restrict A, const bj_mat4 *restrict B)
static void	bj_mat4_sub (bj_mat4 restrict out, const bj_mat4 restrict A, const bj_mat4 *restrict B)
static void	bj_mat4_mul_scalar (bj_mat4 restrict out, const bj_mat4 restrict A, bj_real k)
static void	bj_mat4_scale_axes (bj_mat4 restrict out, const bj_mat4 restrict A, bj_real sx, bj_real sy, bj_real sz)
static void	bj_mat4_mul (bj_mat4 restrict out, const bj_mat4 restrict A, const bj_mat4 *restrict B)
static bj_vec4	bj_mat4_transform_vec4 (const bj_mat4 *restrict M, bj_vec4 v)
static void	bj_mat4_set_translation (bj_mat4 *restrict M, bj_real x, bj_real y, bj_real z)
static void	bj_mat4_translate (bj_mat4 *restrict M, bj_real x, bj_real y, bj_real z)
static void	bj_mat4_set_outer_product (bj_mat4 *restrict out, bj_vec3 a, bj_vec3 b)
static void	bj_mat4_rotate_axis_andle (bj_mat4 restrict out, const bj_mat4 restrict M, bj_vec3 axis, bj_real angle)
static void	bj_mat4_rotate_x (bj_mat4 restrict out, const bj_mat4 restrict M, bj_real a)
static void	bj_mat4_rotate_y (bj_mat4 restrict out, const bj_mat4 restrict M, bj_real a)
static void	bj_mat4_rotate_z (bj_mat4 restrict out, const bj_mat4 restrict M, bj_real a)
static void	bj_mat4_rotate_arcball (bj_mat4 restrict R, const bj_mat4 restrict M, bj_vec2 a, bj_vec2 b, bj_real s)
static bj_bool	bj_mat4_invert (bj_mat4 restrict out, const bj_mat4 restrict M)
static void	bj_mat4_invert_unsafe (bj_mat4 restrict out, const bj_mat4 restrict M)
static void	bj_mat4_orthonormalize (bj_mat4 restrict out, const bj_mat4 restrict A)
static void	bj_mat4_set_frustum (bj_mat4 *restrict M, bj_real l, bj_real r, bj_real b, bj_real t, bj_real n, bj_real f)
static void	bj_mat4_set_ortho (bj_mat4 *restrict M, bj_real l, bj_real r, bj_real b, bj_real t, bj_real n, bj_real f)
static void	bj_mat4_set_perspective (bj_mat4 *restrict M, bj_real y_fov, bj_real aspect, bj_real n, bj_real f)
static void	bj_mat4_set_viewport (bj_mat4 *restrict M, bj_real x, bj_real y, bj_real w, bj_real h)
static void	bj_mat4_set_lookat (bj_mat4 *restrict M, bj_vec3 eye, bj_vec3 center, bj_vec3 up)
static void	bj_mat4x3_set_identity (bj_mat4x3 *restrict M)
static void	bj_mat4x3_set_translation (bj_mat4x3 *restrict M, bj_real tx, bj_real ty, bj_real tz)
static void	bj_mat4x3_set_scaling_xyz (bj_mat4x3 *restrict M, bj_real sx, bj_real sy, bj_real sz)
static void	bj_mat4x3_set_rotation_x (bj_mat4x3 *restrict M, bj_real a)
static void	bj_mat4x3_set_rotation_y (bj_mat4x3 *restrict M, bj_real a)
static void	bj_mat4x3_set_rotation_z (bj_mat4x3 *restrict M, bj_real a)
static void	bj_mat4x3_mul (bj_mat4x3 restrict out, const bj_mat4x3 restrict A, const bj_mat4x3 *restrict B)
static bj_vec3	bj_mat4x3_transform_point (const bj_mat4x3 *restrict M, bj_vec3 p)
static bj_vec3	bj_mat4x3_transform_dir (const bj_mat4x3 *restrict M, bj_vec3 v)
static void	bj_mat4_from_mat4x3 (bj_mat4 restrict M, const bj_mat4x3 restrict A)
static void	bj_mat4x3_from_mat4 (bj_mat4x3 restrict M, const bj_mat4 restrict A)
static bj_quat	bj_quat_identity (void)
static bj_real	bj_quat_dot (bj_quat a, bj_quat b)
static bj_real	bj_quat_norm2 (bj_quat q)
static bj_real	bj_quat_norm (bj_quat q)
static bj_quat	bj_quat_normalize (bj_quat q)
static bj_quat	bj_quat_conjugate (bj_quat q)
static bj_quat	bj_quat_inverse (bj_quat q)
static bj_quat	bj_quat_mul (bj_quat p, bj_quat q)
static bj_quat	bj_quat_slerp (bj_quat a, bj_quat b, bj_real t)
static bj_quat	bj_quat_from_axis_angle (bj_vec3 axis, bj_real angle_rad)
static bj_vec3	bj_quat_rotate_vec3 (bj_quat q, bj_vec3 v)
static bj_vec4	bj_quat_rotate_vec4 (bj_quat q, bj_vec4 v)
static void	bj_quat_to_mat4 (bj_mat4 *restrict M, bj_quat q)
static bj_quat	bj_quat_from_mat4 (const bj_mat4 *restrict M)
bj_bool	bj_rect_intersection (const bj_rect p_rect_a, const bj_rect p_rect_b, bj_rect *p_result)
static bj_vec2	bj_vec2_map (bj_vec2 a, bj_real(*f)(bj_real))
static bj_vec2	bj_vec2_add (bj_vec2 lhs, bj_vec2 rhs)
static bj_vec2	bj_vec2_add_scaled (bj_vec2 lhs, bj_vec2 rhs, bj_real s)
static bj_vec2	bj_vec2_sub (const bj_vec2 lhs, const bj_vec2 rhs)
static bj_vec2	bj_vec2_scale (bj_vec2 v, bj_real s)
static bj_vec2	bj_vec2_mul_comp (const bj_vec2 v, const bj_vec2 s)
static bj_real	bj_vec2_dot (bj_vec2 a, bj_vec2 b)
static bj_real	bj_vec2_perp_dot (bj_vec2 a, bj_vec2 b)
static bj_real	bj_vec2_len (bj_vec2 v)
static bj_vec2	bj_vec2_scale_to_len (bj_vec2 v, bj_real L)
static bj_real	bj_vec2_distance_sq (bj_vec2 a, bj_vec2 b)
static bj_real	bj_vec2_distance (const bj_vec2 a, const bj_vec2 b)
static bj_vec2	bj_vec2_normalize (bj_vec2 v)
static bj_vec2	bj_vec2_normalize_unsafe (bj_vec2 v)
static bj_vec2	bj_vec2_min (bj_vec2 a, bj_vec2 b)
static bj_vec2	bj_vec2_max (bj_vec2 a, bj_vec2 b)
static bj_vec3	bj_vec3_map (bj_vec3 a, bj_real(*f)(bj_real))
static bj_vec3	bj_vec3_add (bj_vec3 lhs, bj_vec3 rhs)
static bj_vec3	bj_vec3_add_scaled (bj_vec3 lhs, bj_vec3 rhs, bj_real s)
static bj_vec3	bj_vec3_sub (bj_vec3 lhs, bj_vec3 rhs)
static bj_vec3	bj_vec3_scale (bj_vec3 v, bj_real s)
static bj_real	bj_vec3_dot (bj_vec3 a, bj_vec3 b)
static bj_real	bj_vec3_len (bj_vec3 v)
static bj_vec3	bj_vec3_scale_to_len (bj_vec3 v, bj_real L)
static bj_real	bj_vec3_distance_sq (bj_vec3 a, bj_vec3 b)
static bj_real	bj_vec3_distance (bj_vec3 a, bj_vec3 b)
static bj_vec3	bj_vec3_normalize (bj_vec3 v)
static bj_vec3	bj_vec3_normalize_unsafe (bj_vec3 v)
static bj_vec3	bj_vec3_min (bj_vec3 a, bj_vec3 b)
static bj_vec3	bj_vec3_max (bj_vec3 a, bj_vec3 b)
static bj_vec3	bj_vec3_cross (bj_vec3 l, bj_vec3 r)
static bj_vec3	bj_vec3_reflect (bj_vec3 v, bj_vec3 n)
static bj_vec4	bj_vec4_map (bj_vec4 a, bj_real(*f)(bj_real))
static bj_vec4	bj_vec4_add (bj_vec4 lhs, bj_vec4 rhs)
static bj_vec4	bj_vec4_add_scaled (bj_vec4 lhs, bj_vec4 rhs, bj_real s)
static bj_vec4	bj_vec4_sub (bj_vec4 lhs, bj_vec4 rhs)
static bj_vec4	bj_vec4_scale (bj_vec4 v, bj_real s)
static bj_real	bj_vec4_dot (bj_vec4 a, bj_vec4 b)
static bj_real	bj_vec4_len (bj_vec4 v)
static bj_vec4	bj_vec4_normalize (bj_vec4 v)
static bj_vec4	bj_vec4_normalize_unsafe (bj_vec4 v)
static bj_vec4	bj_vec4_min (bj_vec4 a, bj_vec4 b)
static bj_vec4	bj_vec4_max (bj_vec4 a, bj_vec4 b)
static bj_vec4	bj_vec4_cross_xyz (bj_vec4 l, bj_vec4 r)
static bj_vec4	bj_vec4_reflect (bj_vec4 v, bj_vec4 n)

Real type selection and helpers
typedef float	bj_real
#define	BJ_F(x)
#define	BJ_EPSILON (FLT_EPSILON)
#define	BJ_FI(x)
#define	BJ_FZERO (BJ_F(0.0))

Scalar utilities
Generic scalar helpers. All arguments and results are bj_real.
static bj_real	bj_clamp (bj_real x, bj_real lo, bj_real hi)
static bj_real	bj_step (bj_real edge, bj_real x)
static bj_real	bj_smoothstep (bj_real e0, bj_real e1, bj_real x)
static bj_real	bj_fract (bj_real x)
static bj_real	bj_mod (bj_real x, bj_real y)

Absolute-epsilon comparisons
Comparisons using BJ_EPSILON as an absolute tolerance.
static int	bj_real_eq (bj_real a, bj_real b)
static int	bj_real_neq (bj_real a, bj_real b)
static int	bj_real_lt (bj_real a, bj_real b)
static int	bj_real_gt (bj_real a, bj_real b)
static int	bj_real_lte (bj_real a, bj_real b)
static int	bj_real_gte (bj_real a, bj_real b)
static int	bj_real_cmp (bj_real a, bj_real b)

Relative-epsilon comparisons
Comparisons using a scale-dependent tolerance.
static bj_real	bj_real_relative_scale (bj_real a, bj_real b)
static int	bj_real_eq_rel (bj_real a, bj_real b)
static int	bj_real_neq_rel (bj_real a, bj_real b)
static int	bj_real_lt_rel (bj_real a, bj_real b)
static int	bj_real_gt_rel (bj_real a, bj_real b)
static int	bj_real_lte_rel (bj_real a, bj_real b)
static int	bj_real_gte_rel (bj_real a, bj_real b)
static int	bj_real_cmp_rel (bj_real a, bj_real b)

Zero tests and helpers
Utilities for zero checks and safe normalization.
static int	bj_real_is_zero (bj_real x)
static int	bj_real_is_zero_scaled (bj_real x, bj_real scale)
static bj_real	bj_real_snap_zero (bj_real x)
static bj_real	bj_real_snorm_safe (bj_real x, bj_real len)

Circle constants
#define	BJ_PI_F (3.14159265358979323846f)
#define	BJ_TAU_F (6.28318530717958647692f)
#define	BJ_PI_D (3.14159265358979323846264338327950288)
#define	BJ_TAU_D (6.28318530717958647692528676655900576)
#define	BJ_PI_L (3.141592653589793238462643383279502884L)
#define	BJ_TAU_L (6.283185307179586476925286766559005768L)
#define	BJ_PI (BJ_F(3.141592653589793238462643383279502884))
#define	BJ_TAU (BJ_F(6.283185307179586476925286766559005768))

Typed wrappers (float)
Thin aliases to <math.h> float functions.
#define	bj_absf fabsf
#define	bj_acosf acosf
#define	bj_atan2f atan2f
#define	bj_copysignf copysignf
#define	bj_cosf cosf
#define	bj_expf expf
#define	bj_floorf floorf
#define	bj_fmodf fmodf
#define	bj_logf logf
#define	bj_maxf fmaxf
#define	bj_minf fminf
#define	bj_powf powf
#define	bj_roundf roundf
#define	bj_sinf sinf
#define	bj_sqrtf sqrtf
#define	bj_tanf tanf

Typed wrappers (double)
Thin aliases to <math.h> double functions.
#define	bj_absd fabs
#define	bj_acosd acos
#define	bj_atan2d atan2
#define	bj_copysignd copysign
#define	bj_cosd cos
#define	bj_expd exp
#define	bj_floord floor
#define	bj_fmodd fmod
#define	bj_logd log
#define	bj_maxd fmax
#define	bj_mind fmin
#define	bj_powd pow
#define	bj_roundd round
#define	bj_sind sin
#define	bj_sqrtd sqrt
#define	bj_tand tan

Typed wrappers (long double)
Thin aliases to <math.h> long double functions.
#define	bj_absl fabsl
#define	bj_acosl acosl
#define	bj_atan2l atan2l
#define	bj_copysignl copysignl
#define	bj_cosl cosl
#define	bj_expl expl
#define	bj_floorl floorl
#define	bj_fmodl fmodl
#define	bj_logl logl
#define	bj_maxl fmaxl
#define	bj_minl fminl
#define	bj_powl powl
#define	bj_roundl roundl
#define	bj_sinl sinl
#define	bj_sqrtl sqrtl
#define	bj_tanl tanl

Precision-dispatch to match bj_real
Map generic bj_* names to the active precision.
#define	bj_abs bj_absf
#define	bj_acos bj_acosf
#define	bj_atan2 bj_atan2f
#define	bj_copysign bj_copysignf
#define	bj_cos bj_cosf
#define	bj_exp bj_expf
#define	bj_floor bj_floorf
#define	bj_fmod bj_fmodf
#define	bj_log bj_logf
#define	bj_max bj_maxf
#define	bj_min bj_minf
#define	bj_pow bj_powf
#define	bj_round bj_roundf
#define	bj_sin bj_sinf
#define	bj_sqrt bj_sqrtf
#define	bj_tan bj_tanf

Detailed Description

Math utilities (precision abstraction, constants, scalar functions).

This header provides:

Compile-time selection of real precision (bj_real).
Constants such as PI and TAU in multiple precisions.
Typed wrappers for C math functions.
Generic bj_* math macros mapped to the selected bj_real type.
Scalar helpers: clamp, step, smoothstep, fract, modulus.
Floating-point comparison utilities (absolute and relative epsilon).
Zero tests and safe normalization.

All functions are thin wrappers around <math.h> with consistent naming and precision handling. They are dimensionless utilities: values are treated as pure scalars without physical units.

Data Structure Documentation

◆ bj_mat3x3_t

struct bj_mat3x3_t

Data Fields
bj_real	m[9]

◆ bj_mat3x2_t

struct bj_mat3x2_t

bj_mat3x2: 3×2 column-major matrix backed by bj_vec2.

(2D affine: 2×2 linear block plus translation column). Columns are arrays of 2 components.

Data Fields
bj_real	m[6]

◆ bj_mat4x4_t

struct bj_mat4x4_t

bj_mat4x4: 4×4 column-major matrix backed by bj_vec4.

Columns are arrays of 4 components.

Data Fields
bj_real	m[16]

◆ bj_mat4x3_t

struct bj_mat4x3_t

bj_mat4x3: 4×3 column-major matrix backed by bj_vec3.

(3D affine: 3×3 linear block plus translation row). Columns are arrays of 3 components.

Data Fields
bj_real	m[12]

◆ bj_rect_t

struct bj_rect_t

Represents a rectangle with position and dimensions.

Data Fields
uint16_t	h	The height of the rectangle.
uint16_t	w	The width of the rectangle.
int16_t	x	The x-coordinate of the rectangle's top-left corner.
int16_t	y	The y-coordinate of the rectangle's top-left corner.

◆ bj_vec2_t

struct bj_vec2_t

bj_vec2: 2D vector of bj_real values.

Intended for lightweight math operations and POD interop.

Data Fields
bj_real	x
bj_real	y

◆ bj_vec3_t

struct bj_vec3_t

bj_vec3: 3D vector of bj_real values.

Intended for lightweight math operations and POD interop.

Data Fields
bj_real	x
bj_real	y
bj_real	z

◆ bj_vec4_t

struct bj_vec4_t

bj_vec4: 4D vector of bj_real values.

Intended for lightweight math operations and POD interop.

Data Fields
bj_real	w
bj_real	x
bj_real	y
bj_real	z

Macro Definition Documentation

◆ bj_abs

#define bj_abs bj_absf

Absolute value.

◆ bj_absd

#define bj_absd fabs

Absolute value (double)

◆ bj_absf

#define bj_absf fabsf

Absolute value (float)

◆ bj_absl

#define bj_absl fabsl

Absolute value (long double)

◆ bj_acos

#define bj_acos bj_acosf

Arc cosine.

◆ bj_acosd

#define bj_acosd acos

Arc cosine (double)

◆ bj_acosf

#define bj_acosf acosf

Arc cosine (float)

◆ bj_acosl

#define bj_acosl acosl

Arc cosine (long double)

◆ bj_atan2

#define bj_atan2 bj_atan2f

Arc tangent.

◆ bj_atan2d

#define bj_atan2d atan2

Arc tangent (float)

◆ bj_atan2f

#define bj_atan2f atan2f

Arc tangent (float)

◆ bj_atan2l

#define bj_atan2l atan2l

Arc tangent (float)

◆ bj_copysign

#define bj_copysign bj_copysignf

Copy sign.

◆ bj_copysignd

#define bj_copysignd copysign

Copy sign (double)

◆ bj_copysignf

#define bj_copysignf copysignf

Copy sign (float)

◆ bj_copysignl

#define bj_copysignl copysignl

Copy sign (long double)

◆ bj_cos

#define bj_cos bj_cosf

Cosine.

◆ bj_cosd

#define bj_cosd cos

Cosine (double)

◆ bj_cosf

#define bj_cosf cosf

Cosine (float)

◆ bj_cosl

#define bj_cosl cosl

Cosine (long double)

◆ BJ_EPSILON

#define BJ_EPSILON (FLT_EPSILON)

Machine epsilon for bj_real when float is selected.

◆ bj_exp

#define bj_exp bj_expf

Exponential.

◆ bj_expd

#define bj_expd exp

Exponential (double)

◆ bj_expf

#define bj_expf expf

Exponential (float)

◆ bj_expl

#define bj_expl expl

Exponential (long double)

◆ BJ_F

#define BJ_F ( x )

Value:

x##f

Literal suffix helper for bj_real when float is selected.

◆ BJ_FI

#define BJ_FI ( x )

Value:

BJ_F(1.0) / BJ_F(x)

BJ_F

#define BJ_F(x)

Literal suffix helper for bj_real when float is selected.

Definition math.h:53

Convenience reciprocal literal generator.

Parameters

x	Positive scalar literal

Returns: 1.0 / x in bj_real

◆ bj_floor

#define bj_floor bj_floorf

Floor.

◆ bj_floord

#define bj_floord floor

Floor (double)

◆ bj_floorf

#define bj_floorf floorf

Floor (float)

◆ bj_floorl

#define bj_floorl floorl

Floor (long double)

◆ bj_fmod

#define bj_fmod bj_fmodf

Floating modulus.

◆ bj_fmodd

#define bj_fmodd fmod

Floating modulus (double)

◆ bj_fmodf

#define bj_fmodf fmodf

Floating modulus (float)

◆ bj_fmodl

#define bj_fmodl fmodl

Floating modulus (long double)

◆ BJ_FZERO

#define BJ_FZERO (BJ_F(0.0))

Zero constant in bj_real.

◆ bj_log

#define bj_log bj_logf

Natural logarithm.

◆ bj_logd

#define bj_logd log

Natural log (double)

◆ bj_logf

#define bj_logf logf

Natural log (float)

◆ bj_logl

#define bj_logl logl

Natural log (long double)

◆ BJ_M3

#define BJ_M3	(		c,
			r )

Value:

((c)*3 + (r)) /* 0<=c,r<3 */

◆ BJ_M32

#define BJ_M32	(		c,
			r )

Value:

((c)*2 + (r)) /* 0<=c<3, 0<=r<2 */

◆ BJ_M4

#define BJ_M4	(		c,
			r )

Value:

((c)*4 + (r)) /* 0<=c,r<4) */

◆ BJ_M43

#define BJ_M43	(		c,
			r )

Value:

((c)*3 + (r)) /* 0<=c<4, 0<=r<3 */

◆ bj_max

#define bj_max bj_maxf

Maximum of two floats.

◆ bj_maxd

#define bj_maxd fmax

Maximum of two doubles.

◆ bj_maxf

#define bj_maxf fmaxf

Maximum of two floats.

◆ bj_maxl

#define bj_maxl fmaxl

Maximum of two long doubles.

◆ bj_min

#define bj_min bj_minf

Minimum of two floats.

◆ bj_mind

#define bj_mind fmin

Minimum of two doubles.

◆ bj_minf

#define bj_minf fminf

Minimum of two floats.

◆ bj_minl

#define bj_minl fminl

Minimum of two long doubles.

◆ BJ_PI

#define BJ_PI (BJ_F(3.141592653589793238462643383279502884))

PI in the selected bj_real precision.

◆ BJ_PI_D

#define BJ_PI_D (3.14159265358979323846264338327950288)

Double-precision PI.

◆ BJ_PI_F

#define BJ_PI_F (3.14159265358979323846f)

Single-precision PI.

◆ BJ_PI_L

#define BJ_PI_L (3.141592653589793238462643383279502884L)

Long-double PI.

◆ bj_pow

#define bj_pow bj_powf

Power.

◆ bj_powd

#define bj_powd pow

Power (double)

◆ bj_powf

#define bj_powf powf

Power (float)

◆ bj_powl

#define bj_powl powl

Power (long double)

◆ bj_round

#define bj_round bj_roundf

Round to nearest integer.

◆ bj_roundd

#define bj_roundd round

Round to nearest (double)

◆ bj_roundf

#define bj_roundf roundf

Round to nearest (float)

◆ bj_roundl

#define bj_roundl roundl

Round to nearest (long double)

◆ bj_sin

#define bj_sin bj_sinf

Sine.

◆ bj_sind

#define bj_sind sin

Sine (double)

◆ bj_sinf

#define bj_sinf sinf

Sine (float)

◆ bj_sinl

#define bj_sinl sinl

Sine (long double)

◆ bj_sqrt

#define bj_sqrt bj_sqrtf

Square root.

◆ bj_sqrtd

#define bj_sqrtd sqrt

Square root (double)

◆ bj_sqrtf

#define bj_sqrtf sqrtf

Square root (float)

◆ bj_sqrtl

#define bj_sqrtl sqrtl

Square root (long double)

◆ bj_tan

#define bj_tan bj_tanf

Tangent.

◆ bj_tand

#define bj_tand tan

Tangent (double)

◆ bj_tanf

#define bj_tanf tanf

Tangent (float)

◆ bj_tanl

#define bj_tanl tanl

Tangent (long double)

◆ BJ_TAU

#define BJ_TAU (BJ_F(6.283185307179586476925286766559005768))

TAU in the selected bj_real precision.

◆ BJ_TAU_D

#define BJ_TAU_D (6.28318530717958647692528676655900576)

Double-precision TAU (2 * PI).

◆ BJ_TAU_F

#define BJ_TAU_F (6.28318530717958647692f)

Single-precision TAU (2 * PI).

◆ BJ_TAU_L

#define BJ_TAU_L (6.283185307179586476925286766559005768L)

Long-double TAU (2 * PI).

◆ BJ_VEC2_ZERO

#define BJ_VEC2_ZERO ((bj_vec2){BJ_FZERO, BJ_FZERO})

◆ BJ_VEC3_ZERO

#define BJ_VEC3_ZERO ((bj_vec3){BJ_FZERO, BJ_FZERO, BJ_FZERO})

◆ BJ_VEC4_ZERO

#define BJ_VEC4_ZERO ((bj_vec4){BJ_FZERO, BJ_FZERO, BJ_FZERO, BJ_FZERO})

Typedef Documentation

◆ bj_mat3

typedef struct bj_mat3x3_t bj_mat3

◆ bj_mat3x2

typedef struct bj_mat3x2_t bj_mat3x2

◆ bj_mat3x3

typedef struct bj_mat3x3_t bj_mat3x3

◆ bj_mat4

typedef struct bj_mat4x4_t bj_mat4

◆ bj_mat4x3

typedef struct bj_mat4x3_t bj_mat4x3

◆ bj_mat4x4

typedef struct bj_mat4x4_t bj_mat4x4

◆ bj_quat

typedef struct bj_vec4_t bj_quat

Quaternion type alias based on the 4D vector struct.

The layout matches bj_vec4_t fields:

q.x, q.y, q.z // vector part

q.w // scalar part

The alias preserves binary compatibility with bj_vec4_t and allows using quaternion values wherever a 4D vector is accepted, when meaningful.

◆ bj_real

typedef float bj_real

Selected real type for float configuration.

◆ bj_rect

typedef struct bj_rect_t bj_rect

Typedef for bj_rect_t.

◆ bj_vec2

typedef struct bj_vec2_t bj_vec2

◆ bj_vec3

typedef struct bj_vec3_t bj_vec3

◆ bj_vec4

typedef struct bj_vec4_t bj_vec4

Function Documentation

◆ bj_clamp()

bj_real bj_clamp	(	bj_real	x,
		bj_real	lo,
		bj_real	hi )

inlinestatic

Clamp x to the closed interval [lo, hi].

Parameters

x	Input value
lo	Lower bound
hi	Upper bound

Returns: lo if x < lo, hi if x > hi, else x

◆ bj_fract()

bj_real bj_fract ( bj_real x )

inlinestatic

Fractional part of x.

Parameters

x	Input value

Returns: x - floor(x)

◆ bj_mat3_add()

void bj_mat3_add	(	bj_mat3 *restrict	out,
		const bj_mat3 *restrict	A,
		const bj_mat3 *restrict	B )

inlinestatic

Component-wise addition: out = A + B.

Parameters

out	Output 3×3 matrix.
A	Input 3×3 matrix.
B	Input 3×3 matrix.

◆ bj_mat3_col()

bj_vec3 bj_mat3_col	(	const bj_mat3 *restrict	M,
		int	c )

inlinestatic

Extract a matrix column as a vector.

Parameters

M	Input 3×3 matrix.
c	index (0-based).

Returns: 3D vector result.

◆ bj_mat3_copy()

void bj_mat3_copy	(	bj_mat3 *restrict	dst,
		const bj_mat3 *restrict	src )

inlinestatic

Copy a matrix.

Parameters

dst	Output 3×3 matrix.
src	Input 3×3 matrix.

◆ bj_mat3_determinant()

bj_real bj_mat3_determinant ( const bj_mat3 *restrict A )

inlinestatic

Determinant of a 3×3 matrix.

Parameters

A	Input 3×3 matrix.

Returns: bj_real.

◆ bj_mat3_from_mat3x2()

void bj_mat3_from_mat3x2	(	bj_mat3 *restrict	M,
		const bj_mat3x2 *restrict	A )

inlinestatic

Promote a 3×2 affine matrix to 3×3.

Parameters

M	Output 3×3 matrix.
A	Input 3×2 matrix.

◆ bj_mat3_invert()

bj_bool bj_mat3_invert	(	bj_mat3 *restrict	out,
		const bj_mat3 *restrict	A )

inlinestatic

Invert a 3×3 matrix (safe, adjugate).

Computes A^{-1} = adj(A) / det(A). If det(A) is zero by bj_real_is_zero, returns 0 and leaves out unspecified.

Parameters

out	Output 3×3 matrix.
A	Input 3×3 matrix.

Returns: BJ_TRUE on success, BJ_FALSE if singular or near-singular by bj_real_is_zero(det).

Warning: Adj/Det method is numerically unstable for ill-conditioned A.

See also: bj_mat3_invert_unsafe

◆ bj_mat3_invert_unsafe()

void bj_mat3_invert_unsafe	(	bj_mat3 *restrict	out,
		const bj_mat3 *restrict	A )

inlinestatic

Invert a 3×3 matrix (unsafe, adjugate).

Same as bj_mat3_invert but skips the singularity check and divides by det(A) unconditionally. Faster when invertibility is guaranteed.

Parameters

out	Output 3×3 matrix.
A	Input 3×3 matrix (must be nonsingular).

Precondition: det(A) != 0 and A is well-conditioned for numerical stability.

Warning: Division by zero if det(A) == 0. Consider bj_mat3_invert instead.

◆ bj_mat3_mul()

void bj_mat3_mul	(	bj_mat3 *restrict	out,
		const bj_mat3 *restrict	A,
		const bj_mat3 *restrict	B )

inlinestatic

Matrix product: out = A * B.

Parameters

out	Output 3×3 matrix.
A	Input 3×3 matrix.
B	Input 3×3 matrix.

Note: Column-major storage. Vectors are columns. Right-multiply: r = M * v.

◆ bj_mat3_mul_scalar()

void bj_mat3_mul_scalar	(	bj_mat3 *restrict	out,
		const bj_mat3 *restrict	A,
		bj_real	k )

inlinestatic

Scalar multiply: out = A * k.

Parameters

out	Output 3×3 matrix.
A	Input 3×3 matrix.
k	Uniform scale factor.

◆ bj_mat3_row()

bj_vec3 bj_mat3_row	(	const bj_mat3 *restrict	M,
		int	r )

inlinestatic

Extract a matrix row as a vector.

Parameters

M	Input 3×3 matrix.
r	index (0-based).

Returns: 3D vector result.

◆ bj_mat3_set_identity()

void bj_mat3_set_identity ( bj_mat3 *restrict M )

inlinestatic

Set a 3×3 matrix to identity.

Parameters

M	Output 3×3 matrix.

◆ bj_mat3_set_ortho()

void bj_mat3_set_ortho	(	bj_mat3 *restrict	M,
		bj_real	l,
		bj_real	r,
		bj_real	b,
		bj_real	t )

inlinestatic

Build a 2D orthographic projection into a 3×3 matrix.

Parameters

M	Output 3×3 matrix.
l	Input scalar.
r	scalar (0-based).
b	Input scalar.
t	Input scalar.

◆ bj_mat3_set_rotation_z()

void bj_mat3_set_rotation_z	(	bj_mat3 *restrict	M,
		bj_real	angle )

inlinestatic

Matrix operation.

Parameters

M	Output 3×3 matrix.
angle	Rotation angle in radians.

◆ bj_mat3_set_scaling_xy()

void bj_mat3_set_scaling_xy	(	bj_mat3 *restrict	M,
		bj_real	sx,
		bj_real	sy )

inlinestatic

Apply non-uniform XY scale to a 3×3 matrix.

Parameters

M	Output 3×3 matrix.
sx	Scale on x.
sy	Scale on y.

◆ bj_mat3_set_shear_xy()

void bj_mat3_set_shear_xy	(	bj_mat3 *restrict	M,
		bj_real	shx,
		bj_real	shy )

inlinestatic

Build an XY shear into a 3×3 matrix.

Parameters

M	Output 3×3 matrix.
shx	Input scalar.
shy	Input scalar.

◆ bj_mat3_set_translation()

void bj_mat3_set_translation	(	bj_mat3 *restrict	M,
		bj_real	tx,
		bj_real	ty )

inlinestatic

Build a 3×3 translation matrix.

Parameters

M	Output 3×3 matrix.
tx	Translation along x.
ty	Translation along y.

◆ bj_mat3_set_viewport()

void bj_mat3_set_viewport	(	bj_mat3 *restrict	M,
		bj_real	x,
		bj_real	y,
		bj_real	w,
		bj_real	h )

inlinestatic

Build a 2D viewport transform into a 3×3 matrix.

Parameters

M	Output 3×3 matrix.
x	Viewport X origin in pixels.
y	Viewport Y origin in pixels.
w	Viewport width in pixels.
h	Viewport height in pixels.

◆ bj_mat3_sub()

void bj_mat3_sub	(	bj_mat3 *restrict	out,
		const bj_mat3 *restrict	A,
		const bj_mat3 *restrict	B )

inlinestatic

Component-wise subtraction: out = A - B.

Parameters

out	Output 3×3 matrix.
A	Input 3×3 matrix.
B	Input 3×3 matrix.

◆ bj_mat3_transform_point()

bj_vec2 bj_mat3_transform_point	(	const bj_mat3 *restrict	M,
		bj_vec2	p )

inlinestatic

Transform a 2D point by a 3×3 homogeneous transform.

Parameters

M	Input 3×3 matrix.
p	Input point.

Returns: 2D vector result.

Note: Homogeneous 2D. Applies projective divide if w ≠ 0.

◆ bj_mat3_transform_vec3()

bj_vec3 bj_mat3_transform_vec3	(	const bj_mat3 *restrict	M,
		bj_vec3	v )

inlinestatic

Multiply a 3×3 matrix by a 3D vector: r = M * v.

Parameters

M	Input 3×3 matrix.
v	Input vector.

Returns: 3D vector result.

Note: Column-major storage. Vectors are columns. Right-multiply: r = M * v.

◆ bj_mat3_translate()

void bj_mat3_translate	(	bj_mat3 *restrict	M,
		bj_real	tx,
		bj_real	ty )

inlinestatic

Right-multiply by a translation: M = M * T(tx,ty).

Parameters

M	Output 3×3 matrix.
tx	Translation along x.
ty	Translation along y.

Note: Right-multiply in place.

◆ bj_mat3_transpose()

void bj_mat3_transpose	(	bj_mat3 *restrict	out,
		const bj_mat3 *restrict	A )

inlinestatic

Transpose a matrix.

Parameters

out	Output 3×3 matrix.
A	Input 3×3 matrix.

◆ bj_mat3x2_from_mat3()

void bj_mat3x2_from_mat3	(	bj_mat3x2 *restrict	M,
		const bj_mat3 *restrict	A )

inlinestatic

Demote a 3×3 matrix to 3×2 (drop projective terms).

Parameters

M	Output 3×2 matrix.
A	Input 3×3 matrix.

◆ bj_mat3x2_mul()

void bj_mat3x2_mul	(	bj_mat3x2 *restrict	out,
		const bj_mat3x2 *restrict	A,
		const bj_mat3x2 *restrict	B )

inlinestatic

Matrix product: out = A * B.

Parameters

out	Output 3×2 matrix.
A	Input 3×2 matrix.
B	Input 3×2 matrix.

Note: Column-major storage. Vectors are columns. Right-multiply: r = M * v.

◆ bj_mat3x2_set_identity()

void bj_mat3x2_set_identity ( bj_mat3x2 *restrict M )

inlinestatic

Set a 3×2 affine matrix to identity.

Parameters

M	Output 3×2 matrix.

◆ bj_mat3x2_set_rotation_z()

void bj_mat3x2_set_rotation_z	(	bj_mat3x2 *restrict	M,
		bj_real	angle )

inlinestatic

Matrix operation.

Parameters

M	Output 3×2 matrix.
angle	Rotation angle in radians.

◆ bj_mat3x2_set_scaling_xy()

void bj_mat3x2_set_scaling_xy	(	bj_mat3x2 *restrict	M,
		bj_real	sx,
		bj_real	sy )

inlinestatic

Scalar multiply: M = sx * k.

Parameters

M	Output 3×2 matrix.
sx	Scale on x.
sy	Scale on y.

◆ bj_mat3x2_set_translation()

void bj_mat3x2_set_translation	(	bj_mat3x2 *restrict	M,
		bj_real	tx,
		bj_real	ty )

inlinestatic

Matrix operation.

Parameters

M	Output 3×2 matrix.
tx	Translation along x.
ty	Translation along y.

◆ bj_mat3x2_transform_dir()

bj_vec2 bj_mat3x2_transform_dir	(	const bj_mat3x2 *restrict	M,
		bj_vec2	v )

inlinestatic

Transform a direction vector (ignoring translation).

Parameters

M	Input 3×2 matrix.
v	Input vector.

Returns: 2D vector result.

Note: Homogeneous 2D. Applies projective divide if w ≠ 0.

◆ bj_mat3x2_transform_point()

bj_vec2 bj_mat3x2_transform_point	(	const bj_mat3x2 *restrict	M,
		bj_vec2	p )

inlinestatic

Transform a 2D point by a 3×2 affine matrix.

Parameters

M	Input 3×2 matrix.
p	Input point.

Returns: 2D vector result.

Note: Homogeneous 2D. Applies projective divide if w ≠ 0.

◆ bj_mat4_add()

void bj_mat4_add	(	bj_mat4 *restrict	out,
		const bj_mat4 *restrict	A,
		const bj_mat4 *restrict	B )

inlinestatic

Component-wise addition: out = A + B.

Parameters

out	Output 4×4 matrix.
A	Input 4×4 matrix.
B	Input 4×4 matrix.

◆ bj_mat4_col()

bj_vec4 bj_mat4_col	(	const bj_mat4 *restrict	M,
		int	c )

inlinestatic

Extract a matrix column as a vector.

Parameters

M	Input 4×4 matrix.
c	index (0-based).

Returns: 4D vector result.

◆ bj_mat4_copy()

void bj_mat4_copy	(	bj_mat4 *restrict	dst,
		const bj_mat4 *restrict	src )

inlinestatic

Copy a matrix.

Parameters

dst	Output 4×4 matrix.
src	Input 4×4 matrix.

◆ bj_mat4_from_mat4x3()

void bj_mat4_from_mat4x3	(	bj_mat4 *restrict	M,
		const bj_mat4x3 *restrict	A )

inlinestatic

Promote a 4×3 affine matrix to 4×4.

Parameters

M	Output 4×4 matrix.
A	Input 4×3 matrix.

◆ bj_mat4_invert()

bj_bool bj_mat4_invert	(	bj_mat4 *restrict	out,
		const bj_mat4 *restrict	M )

inlinestatic

Invert a 4×4 matrix (safe).

Computes A^{-1} via cofactors. If det(A) is zero by bj_real_is_zero, returns 0 and leaves out unspecified.

Parameters

out	Output 4×4 matrix.
M	Input 4×4 matrix.

Returns: BJ_TRUE on success, BJ_FALSE if singular or near-singular by bj_real_is_zero(det).

Warning: Cofactor-based inversion is costly and can be unstable for ill-conditioned matrices. Prefer affine/orthonormal specializations when possible.

See also: bj_mat4_invert_unsafe

◆ bj_mat4_invert_unsafe()

void bj_mat4_invert_unsafe	(	bj_mat4 *restrict	out,
		const bj_mat4 *restrict	M )

inlinestatic

Invert a 4×4 matrix (unsafe).

Same as bj_mat4_invert but skips the singularity check and divides by det(A) unconditionally.

Parameters

out	Output 4×4 matrix.
M	Input 4×4 matrix (must be nonsingular).

Precondition: det(M) != 0 and M is well-conditioned for numerical stability.

Warning: Division by zero if det(M) == 0. Consider bj_mat4_invert instead.

◆ bj_mat4_mul()

void bj_mat4_mul	(	bj_mat4 *restrict	out,
		const bj_mat4 *restrict	A,
		const bj_mat4 *restrict	B )

inlinestatic

Matrix product: out = A * B.

Parameters

out	Output 4×4 matrix.
A	Input 4×4 matrix.
B	Input 4×4 matrix.

Note: Column-major storage. Vectors are columns. Right-multiply: r = M * v.

◆ bj_mat4_mul_scalar()

void bj_mat4_mul_scalar	(	bj_mat4 *restrict	out,
		const bj_mat4 *restrict	A,
		bj_real	k )

inlinestatic

Scalar multiply: out = A * k.

Parameters

out	Output 4×4 matrix.
A	Input 4×4 matrix.
k	Uniform scale factor.

◆ bj_mat4_orthonormalize()

void bj_mat4_orthonormalize	(	bj_mat4 *restrict	out,
		const bj_mat4 *restrict	A )

inlinestatic

Orthonormalize the 3×3 linear part of a 4×4 matrix.

Parameters

out	Output 4×4 matrix.
A	Input 4×4 matrix.

Warning: If the 3×3 block is degenerate the result may contain NaNs.

◆ bj_mat4_rotate_arcball()

void bj_mat4_rotate_arcball	(	bj_mat4 *restrict	R,
		const bj_mat4 *restrict	M,
		bj_vec2	a,
		bj_vec2	b,
		bj_real	s )

inlinestatic

Build a 4×4 rotation from two unit vectors (arcball).

Parameters

R	Output 4×4 matrix.
M	Input 4×4 matrix.
a	Input 2D vector.
b	Input 2D vector.
s	Scale factors as a vector.

◆ bj_mat4_rotate_axis_andle()

void bj_mat4_rotate_axis_andle	(	bj_mat4 *restrict	out,
		const bj_mat4 *restrict	M,
		bj_vec3	axis,
		bj_real	angle )

inlinestatic

Right-multiply a 4×4 by a rotation around an arbitrary axis.

Parameters

out	Output 4×4 matrix.
M	Input 4×4 matrix.
axis	Unit axis of rotation.
angle	Rotation angle in radians.

◆ bj_mat4_rotate_x()

void bj_mat4_rotate_x	(	bj_mat4 *restrict	out,
		const bj_mat4 *restrict	M,
		bj_real	a )

inlinestatic

Right-multiply by an X-axis rotation.

Parameters

out	Output 4×4 matrix.
M	Input 4×4 matrix.
a	Input scalar.

◆ bj_mat4_rotate_y()

void bj_mat4_rotate_y	(	bj_mat4 *restrict	out,
		const bj_mat4 *restrict	M,
		bj_real	a )

inlinestatic

Right-multiply by a Y-axis rotation.

Parameters

out	Output 4×4 matrix.
M	Input 4×4 matrix.
a	Input scalar.

◆ bj_mat4_rotate_z()

void bj_mat4_rotate_z	(	bj_mat4 *restrict	out,
		const bj_mat4 *restrict	M,
		bj_real	a )

inlinestatic

Right-multiply by a Z-axis rotation.

Parameters

out	Output 4×4 matrix.
M	Input 4×4 matrix.
a	Input scalar.

◆ bj_mat4_row()

bj_vec4 bj_mat4_row	(	const bj_mat4 *restrict	M,
		int	r )

inlinestatic

Extract a matrix row as a vector.

Parameters

M	Input 4×4 matrix.
r	index (0-based).

Returns: 4D vector result.

◆ bj_mat4_scale_axes()

void bj_mat4_scale_axes	(	bj_mat4 *restrict	out,
		const bj_mat4 *restrict	A,
		bj_real	sx,
		bj_real	sy,
		bj_real	sz )

inlinestatic

Scale basis vectors of a 4×4 matrix by per-axis factors.

Parameters

out	Output 4×4 matrix.
A	Input 4×4 matrix.
sx	Scale on x.
sy	Scale on y.
sz	Scale on z.

◆ bj_mat4_set_frustum()

void bj_mat4_set_frustum	(	bj_mat4 *restrict	M,
		bj_real	l,
		bj_real	r,
		bj_real	b,
		bj_real	t,
		bj_real	n,
		bj_real	f )

inlinestatic

Build a perspective frustum into a 4×4 matrix.

Parameters

M	Output 4×4 matrix.
l	Input scalar.
r	scalar (0-based).
b	Input scalar.
t	Input scalar.
n	Near plane distance.
f	Far plane distance.

Warning: Requires r>l, t>b, f>n. Depth maps to [0,1]. Y is inverted.

◆ bj_mat4_set_identity()

void bj_mat4_set_identity ( bj_mat4 *restrict M )

inlinestatic

Set a 4×4 matrix to identity.

Parameters

M	Output 4×4 matrix.

◆ bj_mat4_set_lookat()

void bj_mat4_set_lookat	(	bj_mat4 *restrict	M,
		bj_vec3	eye,
		bj_vec3	center,
		bj_vec3	up )

inlinestatic

Build a right-handed look-at view matrix.

Parameters

M	Output 4×4 matrix.
eye	Camera position.
center	Target point the camera looks at.
up	Approximate up direction.

Note: Right-handed view: +Z looks from eye to center.

◆ bj_mat4_set_ortho()

void bj_mat4_set_ortho	(	bj_mat4 *restrict	M,
		bj_real	l,
		bj_real	r,
		bj_real	b,
		bj_real	t,
		bj_real	n,
		bj_real	f )

inlinestatic

Build a 3D orthographic projection into a 4×4 matrix.

Parameters

M	Output 4×4 matrix.
l	Input scalar.
r	scalar (0-based).
b	Input scalar.
t	Input scalar.
n	Near plane distance.
f	Far plane distance.

Warning: Requires r!=l, t!=b, f!=n. Depth maps to [0,1]. Y is inverted.

◆ bj_mat4_set_outer_product()

void bj_mat4_set_outer_product	(	bj_mat4 *restrict	out,
		bj_vec3	a,
		bj_vec3	b )

inlinestatic

Add outer product r += s * v^T to a 4×4 matrix.

Parameters

out	Output 4×4 matrix.
a	Input 3D vector.
b	Input 3D vector.

◆ bj_mat4_set_perspective()

void bj_mat4_set_perspective	(	bj_mat4 *restrict	M,
		bj_real	y_fov,
		bj_real	aspect,
		bj_real	n,
		bj_real	f )

inlinestatic

Build a 4×4 perspective projection from vertical FOV.

Parameters

M	Output 4×4 matrix.
y_fov	Vertical field of view in radians.
aspect	Aspect ratio width/height.
n	Near plane distance.
f	Far plane distance.

Warning: Requires f > n and aspect > 0. Depth maps to [0,1]. Y is inverted.

◆ bj_mat4_set_translation()

void bj_mat4_set_translation	(	bj_mat4 *restrict	M,
		bj_real	x,
		bj_real	y,
		bj_real	z )

inlinestatic

Build a 4×4 translation matrix.

Parameters

M	Output 4×4 matrix.
x	Viewport X origin in pixels.
y	Viewport Y origin in pixels.
z	Input scalar.

◆ bj_mat4_set_viewport()

void bj_mat4_set_viewport	(	bj_mat4 *restrict	M,
		bj_real	x,
		bj_real	y,
		bj_real	w,
		bj_real	h )

inlinestatic

Build a 3D viewport transform into a 4×4 matrix.

Parameters

M	Output 4×4 matrix.
x	Viewport X origin in pixels.
y	Viewport Y origin in pixels.
w	Viewport width in pixels.
h	Viewport height in pixels.

Note: Maps NDC x,y ∈ [-1,1] and z ∈ [0,1] to window coordinates.

◆ bj_mat4_sub()

void bj_mat4_sub	(	bj_mat4 *restrict	out,
		const bj_mat4 *restrict	A,
		const bj_mat4 *restrict	B )

inlinestatic

Component-wise subtraction: out = A - B.

Parameters

out	Output 4×4 matrix.
A	Input 4×4 matrix.
B	Input 4×4 matrix.

◆ bj_mat4_transform_vec4()

bj_vec4 bj_mat4_transform_vec4	(	const bj_mat4 *restrict	M,
		bj_vec4	v )

inlinestatic

Multiply a 4×4 matrix by a 4D vector: r = M * v.

Parameters

M	Input 4×4 matrix.
v	Input vector.

Returns: 4D vector result.

Note: Column-major storage. Vectors are columns. Right-multiply: r = M * v.

◆ bj_mat4_translate()

void bj_mat4_translate	(	bj_mat4 *restrict	M,
		bj_real	x,
		bj_real	y,
		bj_real	z )

inlinestatic

Right-multiply by a translation: M = M * T(tx,ty,tz).

Parameters

M	Output 4×4 matrix.
x	Viewport X origin in pixels.
y	Viewport Y origin in pixels.
z	Input scalar.

Note: Right-multiply in place.

◆ bj_mat4_transpose()

void bj_mat4_transpose	(	bj_mat4 *restrict	out,
		const bj_mat4 *restrict	A )

inlinestatic

Transpose a matrix.

Parameters

out	Output 4×4 matrix.
A	Input 4×4 matrix.

◆ bj_mat4x3_from_mat4()

void bj_mat4x3_from_mat4	(	bj_mat4x3 *restrict	M,
		const bj_mat4 *restrict	A )

inlinestatic

Demote a 4×4 matrix to 4×3 (drop projective terms).

Parameters

M	Output 4×3 matrix.
A	Input 4×4 matrix.

◆ bj_mat4x3_mul()

void bj_mat4x3_mul	(	bj_mat4x3 *restrict	out,
		const bj_mat4x3 *restrict	A,
		const bj_mat4x3 *restrict	B )

inlinestatic

Matrix product: out = A * B.

Parameters

out	Output 4×3 matrix.
A	Input 4×3 matrix.
B	Input 4×3 matrix.

Note: Column-major storage. Vectors are columns. Right-multiply: r = M * v.

◆ bj_mat4x3_set_identity()

void bj_mat4x3_set_identity ( bj_mat4x3 *restrict M )

inlinestatic

Set a 4×3 affine matrix to identity.

Parameters

M	Output 4×3 matrix.

◆ bj_mat4x3_set_rotation_x()

void bj_mat4x3_set_rotation_x	(	bj_mat4x3 *restrict	M,
		bj_real	a )

inlinestatic

Right-multiply by an X-axis rotation.

Parameters

M	Output 4×3 matrix.
a	Input scalar.

◆ bj_mat4x3_set_rotation_y()

void bj_mat4x3_set_rotation_y	(	bj_mat4x3 *restrict	M,
		bj_real	a )

inlinestatic

Right-multiply by a Y-axis rotation.

Parameters

M	Output 4×3 matrix.
a	Input scalar.

◆ bj_mat4x3_set_rotation_z()

void bj_mat4x3_set_rotation_z	(	bj_mat4x3 *restrict	M,
		bj_real	a )

inlinestatic

Right-multiply by a Z-axis rotation.

Parameters

M	Output 4×3 matrix.
a	Input scalar.

◆ bj_mat4x3_set_scaling_xyz()

void bj_mat4x3_set_scaling_xyz	(	bj_mat4x3 *restrict	M,
		bj_real	sx,
		bj_real	sy,
		bj_real	sz )

inlinestatic

Scalar multiply: M = sx * k.

Parameters

M	Output 4×3 matrix.
sx	Scale on x.
sy	Scale on y.
sz	Scale on z.

◆ bj_mat4x3_set_translation()

void bj_mat4x3_set_translation	(	bj_mat4x3 *restrict	M,
		bj_real	tx,
		bj_real	ty,
		bj_real	tz )

inlinestatic

Matrix operation.

Parameters

M	Output 4×3 matrix.
tx	Translation along x.
ty	Translation along y.
tz	Translation along z.

◆ bj_mat4x3_transform_dir()

bj_vec3 bj_mat4x3_transform_dir	(	const bj_mat4x3 *restrict	M,
		bj_vec3	v )

inlinestatic

Transform a direction vector (ignoring translation).

Parameters

M	Input 4×3 matrix.
v	Input vector.

Returns: 3D vector result.

Note: Affine 3D. Ignores projective terms; no divide.

◆ bj_mat4x3_transform_point()

bj_vec3 bj_mat4x3_transform_point	(	const bj_mat4x3 *restrict	M,
		bj_vec3	p )

inlinestatic

Transform a 3D point by a 4×3 affine matrix.

Parameters

M	Input 4×3 matrix.
p	Input point.

Returns: 3D vector result.

Note: Affine 3D. Ignores projective terms; no divide.

◆ bj_mod()

bj_real bj_mod	(	bj_real	x,
		bj_real	y )

inlinestatic

Positive modulus with non-negative result magnitude.

Parameters

x	Dividend
y	Divisor (must be non-zero)

Returns: Remainder in [0, |y|) with the sign of y

Precondition: y != 0

◆ bj_quat_conjugate()

bj_quat bj_quat_conjugate ( bj_quat q )

inlinestatic

Conjugate of a quaternion.

Negates the vector part and keeps the scalar part: conj(q) = {-x,-y,-z,w}.

Parameters

q	Quaternion.

Returns: Conjugated quaternion.

See also: bj_quat_inverse

◆ bj_quat_dot()

bj_real bj_quat_dot	(	bj_quat	a,
		bj_quat	b )

inlinestatic

4D dot product between two quaternions.

Parameters

a	First quaternion.
b	Second quaternion.

Returns: a·b.

Note: For unit quaternions this equals cos(theta) where theta is the half-angle between orientations used by bj_quat_slerp.

◆ bj_quat_from_axis_angle()

bj_quat bj_quat_from_axis_angle	(	bj_vec3	axis,
		bj_real	angle_rad )

inlinestatic

Build a quaternion from a rotation axis and angle.

Parameters

axis	Rotation axis. Need not be unit length.
angle_rad	Rotation angle in radians.

Returns: Quaternion representing the rotation.

Note: Identity is returned if the axis length is near zero.

◆ bj_quat_from_mat4()

bj_quat bj_quat_from_mat4 ( const bj_mat4 *restrict M )

inlinestatic

Build a quaternion from a 4×4 rotation matrix.

Only the upper-left 3×3 block is used. Assumes it encodes a proper rotation. The result is normalized.

Parameters

M	Source 4×4 matrix (column-major).

Returns: Quaternion representing the rotation.

◆ bj_quat_identity()

bj_quat bj_quat_identity ( void )

inlinestatic

Return the identity quaternion.

Represents a no-rotation. Equivalent to {0,0,0,1}.

Returns: Identity quaternion.

See also: bj_quat_normalize

◆ bj_quat_inverse()

bj_quat bj_quat_inverse ( bj_quat q )

inlinestatic

Multiplicative inverse of a quaternion.

Returns identity if the squared norm is near zero (<= BJ_EPSILON). Otherwise q^{-1} = conj(q) / ||q||^2.

Parameters

q	Quaternion.

Returns: Inverse quaternion.

See also: bj_quat_conjugate, bj_quat_normalize

◆ bj_quat_mul()

bj_quat bj_quat_mul	(	bj_quat	p,
		bj_quat	q )

inlinestatic

Hamilton product p * q.

Composition order follows standard Hamilton convention. When used to rotate vectors via v' = q * v * q^{-1}, apply q on the left.

Parameters

p	Left quaternion.
q	Right quaternion.

Returns: Product p*q.

◆ bj_quat_norm()

bj_real bj_quat_norm ( bj_quat q )

inlinestatic

Euclidean norm (length).

Parameters

q	Quaternion.

Returns: ||q||.

◆ bj_quat_norm2()

bj_real bj_quat_norm2 ( bj_quat q )

inlinestatic

Squared Euclidean norm.

Parameters

q	Quaternion.

Returns: ||q||^2.

See also: bj_quat_norm, bj_quat_normalize

◆ bj_quat_normalize()

bj_quat bj_quat_normalize ( bj_quat q )

inlinestatic

Normalize a quaternion.

Returns identity if the input length is near zero (<= BJ_EPSILON).

Parameters

q	Quaternion.

Returns: Unit-length quaternion.

◆ bj_quat_rotate_vec3()

bj_vec3 bj_quat_rotate_vec3	(	bj_quat	q,
		bj_vec3	v )

inlinestatic

Rotate a 3D vector by a quaternion.

Parameters

q	Rotation quaternion. Expected to be unit length for pure rotation.
v	Vector to rotate.

Returns: Rotated vector.

Note: For performance, q is not normalized inside the function. Call bj_quat_normalize beforehand if needed.

◆ bj_quat_rotate_vec4()

bj_vec4 bj_quat_rotate_vec4	(	bj_quat	q,
		bj_vec4	v )

inlinestatic

Rotate a 4D vector by a quaternion, preserving w.

Parameters

q	Rotation quaternion. Expected to be unit length for pure rotation.
v	Vector to rotate. Its `w` component is passed through unchanged.

Returns: Rotated vector with original w.

◆ bj_quat_slerp()

bj_quat bj_quat_slerp	(	bj_quat	a,
		bj_quat	b,
		bj_real	t )

inlinestatic

Spherical linear interpolation between two orientations.

Interpolates along the shortest arc on S^3. If inputs are nearly parallel, falls back to normalized linear interpolation to avoid divide-by-zero.

Parameters

a	Start quaternion.
b	End quaternion.
t	Interpolation factor in [0,1].

Returns: Interpolated quaternion.

Note: Inputs need not be normalized; the result is normalized.

◆ bj_quat_to_mat4()

void bj_quat_to_mat4	(	bj_mat4 *restrict	M,
		bj_quat	q )

inlinestatic

Fill a 4×4 rotation matrix from a quaternion.

Parameters

[out]	M	Destination matrix (column-major).
[in]	q	Input quaternion. It is normalized internally.

Note: The resulting matrix has the last row and column set to form a proper rigid transform rotation block with bottom-right element equal to 1.

◆ bj_real_cmp()

int bj_real_cmp	(	bj_real	a,
		bj_real	b )

inlinestatic

Three-way compare using absolute epsilon.

Parameters

a	First value
b	Second value

Returns: -1 if a < b, 1 if a > b, 0 otherwise

◆ bj_real_cmp_rel()

int bj_real_cmp_rel	(	bj_real	a,
		bj_real	b )

inlinestatic

Three-way compare using relative epsilon.

Parameters

a	First value
b	Second value

Returns: -1 if a < b, 1 if a > b, 0 otherwise

◆ bj_real_eq()

int bj_real_eq	(	bj_real	a,
		bj_real	b )

inlinestatic

Equality within absolute epsilon.

Parameters

a	First value
b	Second value

Returns: Non-zero if |a - b| <= BJ_EPSILON

◆ bj_real_eq_rel()

int bj_real_eq_rel	(	bj_real	a,
		bj_real	b )

inlinestatic

Equality within relative epsilon.

Parameters

a	First value
b	Second value

Returns: Non-zero if |a - b| <= BJ_EPSILON * max(1, |a|, |b|)

◆ bj_real_gt()

int bj_real_gt	(	bj_real	a,
		bj_real	b )

inlinestatic

a > b by more than absolute epsilon.

Parameters

a	First value
b	Second value

Returns: Non-zero if (a - b) > BJ_EPSILON

◆ bj_real_gt_rel()

int bj_real_gt_rel	(	bj_real	a,
		bj_real	b )

inlinestatic

a > b by more than relative epsilon.

Parameters

a	First value
b	Second value

Returns: Non-zero if (a - b) > BJ_EPSILON * max(1, |a|, |b|)

◆ bj_real_gte()

int bj_real_gte	(	bj_real	a,
		bj_real	b )

inlinestatic

a >= b within absolute epsilon.

Parameters

a	First value
b	Second value

Returns: Non-zero if a >= b within tolerance

◆ bj_real_gte_rel()

int bj_real_gte_rel	(	bj_real	a,
		bj_real	b )

inlinestatic

a >= b within relative epsilon.

Parameters

a	First value
b	Second value

Returns: Non-zero if a >= b within tolerance

◆ bj_real_is_zero()

int bj_real_is_zero ( bj_real x )

inlinestatic

Absolute-zero test.

Parameters

x	Input value

Returns: Non-zero if |x| <= BJ_EPSILON

◆ bj_real_is_zero_scaled()

int bj_real_is_zero_scaled	(	bj_real	x,
		bj_real	scale )

inlinestatic

Scaled zero test using max(1, |scale|).

Parameters

x	Input value
scale	Scale reference

Returns: Non-zero if |x| <= BJ_EPSILON * max(1, |scale|)

◆ bj_real_lt()

int bj_real_lt	(	bj_real	a,
		bj_real	b )

inlinestatic

a < b by more than absolute epsilon.

Parameters

a	First value
b	Second value

Returns: Non-zero if (b - a) > BJ_EPSILON

◆ bj_real_lt_rel()

int bj_real_lt_rel	(	bj_real	a,
		bj_real	b )

inlinestatic

a < b by more than relative epsilon.

Parameters

a	First value
b	Second value

Returns: Non-zero if (b - a) > BJ_EPSILON * max(1, |a|, |b|)

◆ bj_real_lte()

int bj_real_lte	(	bj_real	a,
		bj_real	b )

inlinestatic

a <= b within absolute epsilon.

Parameters

a	First value
b	Second value

Returns: Non-zero if a <= b within tolerance

◆ bj_real_lte_rel()

int bj_real_lte_rel	(	bj_real	a,
		bj_real	b )

inlinestatic

a <= b within relative epsilon.

Parameters

a	First value
b	Second value

Returns: Non-zero if a <= b within tolerance

◆ bj_real_neq()

int bj_real_neq	(	bj_real	a,
		bj_real	b )

inlinestatic

Inequality within absolute epsilon.

Parameters

a	First value
b	Second value

Returns: Non-zero if not equal within absolute epsilon

◆ bj_real_neq_rel()

int bj_real_neq_rel	(	bj_real	a,
		bj_real	b )

inlinestatic

Inequality within relative epsilon.

Parameters

a	First value
b	Second value

Returns: Non-zero if not equal within relative epsilon

◆ bj_real_relative_scale()

bj_real bj_real_relative_scale	(	bj_real	a,
		bj_real	b )

inlinestatic

Internal scale helper max(1, |a|, |b|).

Parameters

a	First value
b	Second value

Returns: Scale factor s >= 1

◆ bj_real_snap_zero()

bj_real bj_real_snap_zero ( bj_real x )

inlinestatic

Snap to exact zero under absolute epsilon.

Parameters

x	Input value

Returns: 0 if |x| <= BJ_EPSILON, else x

◆ bj_real_snorm_safe()

bj_real bj_real_snorm_safe	(	bj_real	x,
		bj_real	len )

inlinestatic

Safe scalar normalization.

Parameters

x	Numerator
len	Denominator magnitude

Returns: 0 if len is zero, else x / len

◆ bj_rect_intersection()

bj_bool bj_rect_intersection	(	const bj_rect *	p_rect_a,
		const bj_rect *	p_rect_b,
		bj_rect *	p_result )

Computes the intersection of two bj_rect.

Parameters

p_rect_a	Pointer to the first rectangle. Must not be 0.
p_rect_b	Pointer to the second rectangle. Must not be 0.
p_result	Pointer to the rectangle where the result will be stored. Can be 0 if only checking intersection presence.

Returns: BJ_TRUE if the rectangles intersect and neither input is 0, BJ_FALSE.

Note: Both input rectangles must be valid and properly initialized. If either p_rect_a or p_rect_b is 0, the function returns 0. If p_result is 0, the function only checks for intersection presence and does not compute the intersection rectangle.

Example usage:

bj_rect rect_a = {0, 0, 10, 10};
bj_rect rect_b = {5, 5, 15, 15};
bj_rect result;
if (bj_rect_intersection(&rect_a, &rect_b, 0)) {
    // There is an intersection between rect_a and rect_b.
}

◆ bj_smoothstep()

bj_real bj_smoothstep	(	bj_real	e0,
		bj_real	e1,
		bj_real	x )

inlinestatic

Smooth Hermite step between e0 and e1.

Clamps t to [0,1].

Parameters

e0	Start edge
e1	End edge
x	Input value

Returns: Interpolant in [0,1]

◆ bj_step()

bj_real bj_step	(	bj_real	edge,
		bj_real	x )

inlinestatic

Step function.

Parameters

edge	Threshold edge
x	Input value

Returns: 0 if x < edge, else 1

◆ bj_vec2_add()

bj_vec2 bj_vec2_add	(	bj_vec2	lhs,
		bj_vec2	rhs )

inlinestatic

Component-wise addition of two 2D vectors: res = lhs + rhs.

Parameters

lhs	Left-hand input vector.
rhs	Right-hand input vector.

Returns: Sum of lhs and rhs.

◆ bj_vec2_add_scaled()

bj_vec2 bj_vec2_add_scaled	(	bj_vec2	lhs,
		bj_vec2	rhs,
		bj_real	s )

inlinestatic

Add a scaled vector: res = a + s * b.

Parameters

lhs	Input component or vector a.
rhs	Input component or vector b.
s	Scalar factor.

Returns: Sum of lhs and rhs * s.

◆ bj_vec2_distance()

bj_real bj_vec2_distance	(	const bj_vec2	a,
		const bj_vec2	b )

inlinestatic

Euclidean distance between two 2D vectors.

Parameters

a	Input vector a.
b	Input vector b.

Returns: The Euclidean distance ||a - b||.

◆ bj_vec2_distance_sq()

bj_real bj_vec2_distance_sq	(	bj_vec2	a,
		bj_vec2	b )

inlinestatic

Squared Euclidean distance between two 2D vectors.

Parameters

a	Input vector a.
b	Input vector b.

Returns: The squared distance ||a - b||^2.

◆ bj_vec2_dot()

bj_real bj_vec2_dot	(	bj_vec2	a,
		bj_vec2	b )

inlinestatic

Dot product of two 2D vectors.

Parameters

a	Input component or vector a.
b	Input component or vector b.

Returns: The scalar dot product.

◆ bj_vec2_len()

bj_real bj_vec2_len ( bj_vec2 v )

inlinestatic

Euclidean length (L2 norm) of a 2D vector.

Parameters

v	Input vector.

Returns: The Euclidean norm.

◆ bj_vec2_map()

bj_vec2 bj_vec2_map	(	bj_vec2	a,
		bj_real(*	f )(bj_real) )

inlinestatic

◆ bj_vec2_max()

bj_vec2 bj_vec2_max	(	bj_vec2	a,
		bj_vec2	b )

inlinestatic

Component-wise maximum of two 2D vectors.

Parameters

res	Output 2D vector.
a	Input component or vector a.
b	Input component or vector b.

◆ bj_vec2_min()

bj_vec2 bj_vec2_min	(	bj_vec2	a,
		bj_vec2	b )

inlinestatic

Component-wise minimum of two 2D vectors.

Parameters

res	Output 2D vector.
a	Input component or vector a.
b	Input component or vector b.

◆ bj_vec2_mul_comp()

bj_vec2 bj_vec2_mul_comp	(	const bj_vec2	v,
		const bj_vec2	s )

inlinestatic

Per-component scaling: res[i] = v[i] * s[i].

Parameters

v	Input vector.
s	Scalar factor.

Returns: The result of v * s

◆ bj_vec2_normalize()

bj_vec2 bj_vec2_normalize ( bj_vec2 v )

inlinestatic

Normalize a 2D vector to unit length (safe).

Computes v / ||v||. If the squared length is zero according to bj_real_is_zero, returns the zero vector to avoid division by zero. Uses a single square root.

Parameters

v	Input vector.

Returns: Unit-length copy of v, or {0,0} if ||v|| == 0 by bj_real_is_zero.

Warning: Zero-detection follows bj_real_is_zero semantics and tolerance.

See also: bj_vec2_normalize_unsafe, bj_real_is_zero

◆ bj_vec2_normalize_unsafe()

bj_vec2 bj_vec2_normalize_unsafe ( bj_vec2 v )

inlinestatic

Normalize a 2D vector to unit length (unsafe).

Computes v / ||v|| without any zero-length check. Faster on hot paths where nonzero length is guaranteed.

Parameters

v	Input vector (must be nonzero).

Returns: Unit-length copy of v.

Precondition: ||v|| > 0 (caller guarantees).

Warning: Undefined results if ||v|| == 0. Consider bj_vec2_normalize instead.

See also: bj_vec2_normalize

◆ bj_vec2_perp_dot()

bj_real bj_vec2_perp_dot	(	bj_vec2	a,
		bj_vec2	b )

inlinestatic

2D "cross product" (perp dot): returns scalar a.x*b.y - a.y*b.x.

Useful for orientation tests, signed area, segment intersection.

◆ bj_vec2_scale()

bj_vec2 bj_vec2_scale	(	bj_vec2	v,
		bj_real	s )

inlinestatic

Uniform scaling by scalar: res = v * s.

Parameters

v	Input vector.
s	Scalar factor.

Returns: The result of v * s

◆ bj_vec2_scale_to_len()

bj_vec2 bj_vec2_scale_to_len	(	bj_vec2	v,
		bj_real	L )

inlinestatic

Scale a 2D vector to a given length.

Parameters

res	Output 2D vector.
v	Input vector.
target_len	Desired length of the result.

Warning: Undefined if the input vector has zero length.

◆ bj_vec2_sub()

bj_vec2 bj_vec2_sub	(	const bj_vec2	lhs,
		const bj_vec2	rhs )

inlinestatic

Component-wise subtraction of two 2D vectors: res = lhs - rhs.

Parameters

lhs	Left-hand input vector.
rhs	Right-hand input vector.

Returns: lhs - rhs

◆ bj_vec3_add()

bj_vec3 bj_vec3_add	(	bj_vec3	lhs,
		bj_vec3	rhs )

inlinestatic

Component-wise addition of two 3D vectors: res = lhs + rhs.

Parameters

res	Output 3D vector.
lhs	Left-hand input vector.
rhs	Right-hand input vector.

◆ bj_vec3_add_scaled()

bj_vec3 bj_vec3_add_scaled	(	bj_vec3	lhs,
		bj_vec3	rhs,
		bj_real	s )

inlinestatic

Add a scaled vector: res = a + s * b.

Parameters

lhs	Input component or vector a.
rhs	Input component or vector b.
s	Scalar factor.

Returns: Sum of lhs and rhs * s.

◆ bj_vec3_cross()

bj_vec3 bj_vec3_cross	(	bj_vec3	l,
		bj_vec3	r )

inlinestatic

3D cross product: res = l × r (right-hand rule).

Parameters

l	Left-hand input vector.
r	Right-hand input vector.

Returns: Resulting cross product.

◆ bj_vec3_distance()

bj_real bj_vec3_distance	(	bj_vec3	a,
		bj_vec3	b )

inlinestatic

Euclidean distance between two 3D vectors.

Parameters

a	Input vector a.
b	Input vector b.

Returns: The Euclidean distance ||a - b||.

◆ bj_vec3_distance_sq()

bj_real bj_vec3_distance_sq	(	bj_vec3	a,
		bj_vec3	b )

inlinestatic

Squared Euclidean distance between two 3D vectors.

Parameters

a	Input vector a.
b	Input vector b.

Returns: The squared distance ||a - b||^2.

◆ bj_vec3_dot()

bj_real bj_vec3_dot	(	bj_vec3	a,
		bj_vec3	b )

inlinestatic

Dot product of two 3D vectors.

Parameters

a	Input component or vector a.
b	Input component or vector b.

Returns: The scalar dot product.

◆ bj_vec3_len()

bj_real bj_vec3_len ( bj_vec3 v )

inlinestatic

Euclidean length (L2 norm) of a 3D vector.

Parameters

v	Input vector.

Returns: The Euclidean norm.

◆ bj_vec3_map()

bj_vec3 bj_vec3_map	(	bj_vec3	a,
		bj_real(*	f )(bj_real) )

inlinestatic

◆ bj_vec3_max()

bj_vec3 bj_vec3_max	(	bj_vec3	a,
		bj_vec3	b )

inlinestatic

Component-wise maximum of two 3D vectors.

Parameters

res	Output 3D vector.
a	Input component or vector a.
b	Input component or vector b.

◆ bj_vec3_min()

bj_vec3 bj_vec3_min	(	bj_vec3	a,
		bj_vec3	b )

inlinestatic

Component-wise minimum of two 3D vectors.

Parameters

res	Output 3D vector.
a	Input component or vector a.
b	Input component or vector b.

◆ bj_vec3_normalize()

bj_vec3 bj_vec3_normalize ( bj_vec3 v )

inlinestatic

Normalize a 3D vector to unit length (safe).

Computes v / ||v||. Returns {0,0,0} if ||v|| is zero by bj_real_is_zero. Uses one square root.

Parameters

v	Input vector.

Returns: Unit-length copy of v, or {0,0,0} if ||v|| == 0 by bj_real_is_zero.

Warning: Zero-detection follows bj_real_is_zero semantics and tolerance.

See also: bj_vec3_normalize_unsafe, bj_real_is_zero

◆ bj_vec3_normalize_unsafe()

bj_vec3 bj_vec3_normalize_unsafe ( bj_vec3 v )

inlinestatic

Normalize a 3D vector to unit length (unsafe).

Computes v / ||v|| without any zero-length check.

Parameters

v	Input vector (must be nonzero).

Returns: Unit-length copy of v.

Precondition: ||v|| > 0 (caller guarantees).

Warning: Undefined results if ||v|| == 0. Consider bj_vec3_normalize instead.

See also: bj_vec3_normalize

◆ bj_vec3_reflect()

bj_vec3 bj_vec3_reflect	(	bj_vec3	v,
		bj_vec3	n )

inlinestatic

Reflect a vector about a normal: res = v - 2*dot(v, n)*n.

Parameters

v	Input vector.
n	Surface normal (expected normalized). \reutrn Resulting reflect vector.

Note: The normal n should be normalized for a true reflection.

◆ bj_vec3_scale()

bj_vec3 bj_vec3_scale	(	bj_vec3	v,
		bj_real	s )

inlinestatic

Uniform scaling by scalar: res = v * s.

Parameters

v	Input vector.
s	Scalar factor.

Returns: The result of v * s

◆ bj_vec3_scale_to_len()

bj_vec3 bj_vec3_scale_to_len	(	bj_vec3	v,
		bj_real	L )

inlinestatic

Scale a 3D vector to a given length.

Parameters

res	Output 3D vector.
v	Input vector.
target_len	Desired length of the result.

Warning: Undefined if the input vector has zero length.

◆ bj_vec3_sub()

bj_vec3 bj_vec3_sub	(	bj_vec3	lhs,
		bj_vec3	rhs )

inlinestatic

Component-wise subtraction of two 3D vectors: res = lhs - rhs.

Parameters

lhs	Left-hand input vector.
rhs	Right-hand input vector.

Returns: lhs - rhs

◆ bj_vec4_add()

bj_vec4 bj_vec4_add	(	bj_vec4	lhs,
		bj_vec4	rhs )

inlinestatic

Component-wise addition of two 4D vectors: res = lhs + rhs.

Parameters

lhs	Left-hand input vector.
rhs	Right-hand input vector.

Returns: Result of lhs + rhs

◆ bj_vec4_add_scaled()

bj_vec4 bj_vec4_add_scaled	(	bj_vec4	lhs,
		bj_vec4	rhs,
		bj_real	s )

inlinestatic

Add a scaled vector: res = a + s * b.

Parameters

lhs	Input component or vector a.
rhs	Input component or vector b.
s	Scalar factor.

Returns: Sum of lhs and rhs * s.

◆ bj_vec4_cross_xyz()

bj_vec4 bj_vec4_cross_xyz	(	bj_vec4	l,
		bj_vec4	r )

inlinestatic

Cross product using xyz components; w is set to 1.

Parameters

res	Output 4D vector.
l	Left-hand input vector.
r	Right-hand input vector.

Note: Uses only xyz components; the result w component is set to 1.0.

◆ bj_vec4_dot()

bj_real bj_vec4_dot	(	bj_vec4	a,
		bj_vec4	b )

inlinestatic

Dot product of two 4D vectors.

Parameters

a	Input component or vector a.
b	Input component or vector b.

Returns: The scalar dot product.

◆ bj_vec4_len()

bj_real bj_vec4_len ( bj_vec4 v )

inlinestatic

Euclidean length (L2 norm) of a 4D vector.

Parameters

v	Input vector.

Returns: The Euclidean norm.

◆ bj_vec4_map()

bj_vec4 bj_vec4_map	(	bj_vec4	a,
		bj_real(*	f )(bj_real) )

inlinestatic

◆ bj_vec4_max()

bj_vec4 bj_vec4_max	(	bj_vec4	a,
		bj_vec4	b )

inlinestatic

Component-wise maximum of two 4D vectors.

Parameters

res	Output 4D vector.
a	Input component or vector a.
b	Input component or vector b.

◆ bj_vec4_min()

bj_vec4 bj_vec4_min	(	bj_vec4	a,
		bj_vec4	b )

inlinestatic

Component-wise minimum of two 4D vectors.

Parameters

res	Output 4D vector.
a	Input component or vector a.
b	Input component or vector b.

◆ bj_vec4_normalize()

bj_vec4 bj_vec4_normalize ( bj_vec4 v )

inlinestatic

Normalize a 4D vector to unit length (safe).

Computes v / ||v||. Returns {0,0,0,0} if ||v|| is zero by bj_real_is_zero. Uses one square root.

Parameters

v	Input vector.

Returns: Unit-length copy of v, or {0,0,0,0} if ||v|| == 0 by bj_real_is_zero.

Warning: Zero-detection follows bj_real_is_zero semantics and tolerance.

See also: bj_vec4_normalize_unsafe, bj_real_is_zero

◆ bj_vec4_normalize_unsafe()

bj_vec4 bj_vec4_normalize_unsafe ( bj_vec4 v )

inlinestatic

Normalize a 4D vector to unit length (unsafe).

Computes v / ||v|| without any zero-length check.

Parameters

v	Input vector (must be nonzero).

Returns: Unit-length copy of v.

Precondition: ||v|| > 0 (caller guarantees).

Warning: Undefined results if ||v|| == 0. Consider bj_vec4_normalize instead.

See also: bj_vec4_normalize

◆ bj_vec4_reflect()

bj_vec4 bj_vec4_reflect	(	bj_vec4	v,
		bj_vec4	n )

inlinestatic

Reflect a vector about a normal: res = v - 2*dot(v, n)*n.

Parameters

res	Output 4D vector.
v	Input vector.
n	Surface normal (expected normalized).

Note: The normal n should be normalized for a true reflection.

◆ bj_vec4_scale()

bj_vec4 bj_vec4_scale	(	bj_vec4	v,
		bj_real	s )

inlinestatic

Uniform scaling by scalar: res = v * s.

Parameters

v	Input vector.
s	Scalar factor.

Returns: The result of v * s

◆ bj_vec4_sub()

bj_vec4 bj_vec4_sub	(	bj_vec4	lhs,
		bj_vec4	rhs )

inlinestatic

Component-wise subtraction of two 4D vectors: res = lhs - rhs.

Parameters

lhs	Left-hand input vector.
rhs	Right-hand input vector.

Returns: lhs - rhs

Topics

Data Structures

Macros

Typedefs

Functions

Real type selection and helpers

Scalar utilities

Absolute-epsilon comparisons

Relative-epsilon comparisons

Zero tests and helpers

Circle constants

Typed wrappers (float)

Typed wrappers (double)

Typed wrappers (long double)

Precision-dispatch to match bj_real

Detailed Description

Data Structure Documentation

◆ bj_mat3x3_t

◆ bj_mat3x2_t

◆ bj_mat4x4_t

◆ bj_mat4x3_t

◆ bj_rect_t

◆ bj_vec2_t

◆ bj_vec3_t

◆ bj_vec4_t

Macro Definition Documentation

◆ bj_abs

◆ bj_absd

◆ bj_absf

◆ bj_absl

◆ bj_acos

◆ bj_acosd

◆ bj_acosf

◆ bj_acosl

◆ bj_atan2

◆ bj_atan2d

◆ bj_atan2f

◆ bj_atan2l

◆ bj_copysign

◆ bj_copysignd

◆ bj_copysignf

◆ bj_copysignl

◆ bj_cos

◆ bj_cosd

◆ bj_cosf

◆ bj_cosl

◆ BJ_EPSILON

◆ bj_exp

◆ bj_expd

◆ bj_expf

◆ bj_expl

◆ BJ_F

◆ BJ_FI

◆ bj_floor

◆ bj_floord

◆ bj_floorf

◆ bj_floorl

◆ bj_fmod

◆ bj_fmodd

◆ bj_fmodf

◆ bj_fmodl

◆ BJ_FZERO

◆ bj_log

◆ bj_logd

◆ bj_logf

◆ bj_logl

◆ BJ_M3

◆ BJ_M32

◆ BJ_M4

◆ BJ_M43

◆ bj_max

◆ bj_maxd

◆ bj_maxf

◆ bj_maxl

◆ bj_min

◆ bj_mind

◆ bj_minf

◆ bj_minl

◆ BJ_PI

◆ BJ_PI_D