Math

Collaboration diagram for Math:

Topics
	Geometry 2D

Data Structures
struct	bj_rect_t

Macros
#define	bj_quat_add   bj_vec4_add
#define	bj_quat_sub   bj_vec4_sub
#define	bj_quat_norm   bj_vec4_normalize
#define	bj_quat_scale   bj_vec4_scale
#define	bj_quat_dot   bj_vec4_dot

Typedefs
typedef bj_vec3	bj_mat3x3[3]
typedef bj_mat3x3	bj_mat3
typedef bj_vec2	bj_mat3x2[3]
typedef bj_vec4	bj_mat4x4[4]
typedef bj_mat4x4	bj_mat4
typedef bj_vec3	bj_mat4x3[4]
typedef bj_real	bj_quat[4]
typedef struct bj_rect_t	bj_rect
typedef bj_real	bj_vec2[2]
typedef bj_real	bj_vec3[3]
typedef bj_real	bj_vec4[4]

Functions
static void	bj_mat3_identity (bj_mat3x3 m)
static void	bj_mat3_copy (bj_mat3x3 to, const bj_mat3x3 from)
static void	bj_mat3_row (bj_vec3 res, const bj_mat3x3 m, int r)
static void	bj_mat3_col (bj_vec3 res, const bj_mat3x3 m, int c)
static void	bj_mat3_transpose (bj_mat3x3 res, const bj_mat3x3 m)
static void	bj_mat3_add (bj_mat3x3 res, const bj_mat3x3 a, const bj_mat3x3 b)
static void	bj_mat3_sub (bj_mat3x3 res, const bj_mat3x3 a, const bj_mat3x3 b)
static void	bj_mat3_scale (bj_mat3x3 res, const bj_mat3x3 m, bj_real k)
static void	bj_mat3_mul (bj_real res[restrict static(3)][3], const bj_real lhs[restrict static(3)][3], const bj_real rhs[restrict static(3)][3])
static void	bj_mat3_mul_vec3 (bj_real res[restrict static(3)], const bj_real m[restrict static(3)][3], const bj_real v[restrict static(3)])
static void	bj_mat3_mul_point (bj_vec2 res, const bj_mat3x3 m, const bj_vec2 p)
static void	bj_mat3_mul_vector2 (bj_vec2 res, const bj_mat3x3 m, const bj_vec2 v2)
static void	bj_mat3_translation (bj_mat3x3 res, bj_real tx, bj_real ty)
static void	bj_mat3_translation_inplace (bj_mat3x3 M, bj_real tx, bj_real ty)
static void	bj_mat3_scale_xy (bj_mat3x3 res, bj_real sx, bj_real sy)
static void	bj_mat3_shear (bj_mat3x3 res, bj_real shx, bj_real shy)
static void	bj_mat3_rotate (bj_mat3x3 res, bj_real angle)
static void	bj_mat3_inverse (bj_mat3x3 res, const bj_mat3x3 m)
static void	bj_mat3_ortho (bj_real omat[restrict static(3)][3], bj_real l, bj_real r, bj_real b, bj_real t)
static void	bj_mat3_viewport (bj_real vpmat[restrict static(3)][3], bj_real x, bj_real y, bj_real w, bj_real h)
static void	bj_mat3x2_identity (bj_real m[restrict static(3)][2])
static void	bj_mat3x2_translate (bj_real m[restrict static(3)][2], bj_real tx, bj_real ty)
static void	bj_mat3x2_scale (bj_real m[restrict static(3)][2], bj_real sx, bj_real sy)
static void	bj_mat3x2_rotate (bj_real m[restrict static(3)][2], bj_real angle)
static void	bj_mat3x2_mul (bj_real res[restrict static(3)][2], const bj_real A[restrict static(3)][2], const bj_real B[restrict static(3)][2])
static void	bj_mat3x2_mul_point (bj_real r[restrict static(2)], const bj_real m[restrict static(3)][2], const bj_real p[restrict static(2)])
static void	bj_mat3x2_mul_dir (bj_real r[restrict static(2)], const bj_real m[restrict static(3)][2], const bj_real v[restrict static(2)])
static void	bj_mat3_from_mat3x2 (bj_real out3x3[restrict static(3)][3], const bj_real a[restrict static(3)][2])
static void	bj_mat3x2_from_mat3 (bj_real out3x2[restrict static(3)][2], const bj_real m[restrict static(3)][3])
static void	bj_mat4_identity (bj_mat4x4 mat)
static void	bj_mat4_copy (bj_mat4x4 to, const bj_mat4x4 from)
static void	bj_mat4_row (bj_vec4 res, const bj_mat4x4 mat, int r)
static void	bj_mat4_col (bj_vec4 res, const bj_mat4x4 mat, int c)
static void	bj_mat4_transpose (bj_mat4x4 res, const bj_mat4x4 mat)
static void	bj_mat4_add (bj_mat4x4 res, const bj_mat4x4 lhs, const bj_mat4x4 rhs)
static void	bj_mat4_sub (bj_mat4x4 res, const bj_mat4x4 lhs, const bj_mat4x4 rhs)
static void	bj_mat4_scale (bj_mat4x4 res, const bj_mat4x4 lhs, bj_real k)
static void	bj_mat4_scale_xyz (bj_mat4x4 res, const bj_mat4x4 mat, bj_real x, bj_real y, bj_real z)
static void	bj_mat4_mul (bj_real res[restrict static(4)][4], const bj_real lhs[restrict static(4)][4], const bj_real rhs[restrict static(4)][4])
static void	bj_mat4_mul_vec4 (bj_real res[restrict static(4)], const bj_real mat[restrict static(4)][4], const bj_real v[restrict static(4)])
static void	bj_mat4_translation (bj_mat4x4 res, bj_real x, bj_real y, bj_real z)
static void	bj_mat4_translation_inplace (bj_mat4x4 M, bj_real x, bj_real y, bj_real z)
static void	bj_mat4_mul_outer (bj_mat4x4 res, const bj_vec3 a, const bj_vec3 b)
static void	bj_mat4_rotate (bj_mat4x4 res, const bj_mat4x4 mat, bj_real x, bj_real y, bj_real z, bj_real angle)
static void	bj_mat4_rotate_x (bj_mat4x4 res, const bj_mat4x4 mat, bj_real angle)
static void	bj_mat4_rotate_y (bj_mat4x4 res, const bj_mat4x4 mat, bj_real angle)
static void	bj_mat4_rotate_z (bj_mat4x4 res, const bj_mat4x4 mat, bj_real angle)
static void	bj_mat4_rotate_arcball (bj_mat4x4 R, const bj_mat4x4 M, bj_vec2 const _a, bj_vec2 const _b, bj_real s)
static void	bj_mat4_inverse (bj_mat4x4 res, const bj_mat4x4 mat)
static void	bj_mat4_orthonormalize (bj_mat4x4 res, const bj_mat4x4 mat)
static void	bj_mat4_frustum (bj_real fmat[restrict static(4)][4], bj_real l, bj_real r, bj_real b, bj_real t, bj_real n, bj_real f)
static void	bj_mat4_ortho (bj_real omat[restrict static(4)][4], bj_real l, bj_real r, bj_real b, bj_real t, bj_real n, bj_real f)
static void	bj_mat4_perspective (bj_real pmat[restrict static(4)][4], bj_real y_fov, bj_real aspect, bj_real n, bj_real f)
static void	bj_mat4_viewport (bj_real vpmat[restrict static(4)][4], bj_real x, bj_real y, bj_real w, bj_real h)
static void	bj_mat4_lookat (bj_real m[restrict static(4)][4], const bj_vec3 eye, const bj_vec3 center, const bj_vec3 up)
static void	bj_mat4x3_identity (bj_real m[restrict static(4)][3])
static void	bj_mat4x3_translate (bj_real m[restrict static(4)][3], bj_real tx, bj_real ty, bj_real tz)
static void	bj_mat4x3_scale (bj_real m[restrict static(4)][3], bj_real sx, bj_real sy, bj_real sz)
static void	bj_mat4x3_rotate_x (bj_real m[restrict static(4)][3], bj_real angle)
static void	bj_mat4x3_rotate_y (bj_real m[restrict static(4)][3], bj_real angle)
static void	bj_mat4x3_rotate_z (bj_real m[restrict static(4)][3], bj_real angle)
static void	bj_mat4x3_mul (bj_real res[restrict static(4)][3], const bj_real A[restrict static(4)][3], const bj_real B[restrict static(4)][3])
static void	bj_mat4x3_mul_point (bj_real r[restrict static(3)], const bj_real m[restrict static(4)][3], const bj_real p[restrict static(3)])
static void	bj_mat4x3_mul_dir (bj_real r[restrict static(3)], const bj_real m[restrict static(4)][3], const bj_real v[restrict static(3)])
static void	bj_mat4_from_mat4x3 (bj_mat4x4 out, const bj_real a[restrict static(4)][3])
static void	bj_mat4x3_from_mat4 (bj_real out43[restrict static(4)][3], const bj_mat4x4 m)
static void	bj_mat4x3_lookat (bj_real m[restrict static(4)][3], const bj_real eye[restrict static(3)], const bj_real center[restrict static(3)], const bj_real up[restrict static(3)])
static void	bj_quat_identity (bj_quat q)
static void	bj_quat_mul (bj_quat res, const bj_quat p, const bj_quat q)
static void	bj_quat_conjugate (bj_quat res, const bj_quat q)
static void	bj_quat_rotation (bj_quat res, bj_real angle, const bj_vec3 axis)
static void	bj_quat_mul_vec3 (bj_vec3 res, const bj_quat q, const bj_vec3 v)
static void	bj_mat4_from_quat (bj_mat4 res, const bj_quat q)
static void	bj_mat4_rotate_from_quat (bj_mat4 R, const bj_mat4 M, const bj_quat q)
static void	bj_quat_from_mat4 (bj_quat q, const bj_mat4 M)
bj_bool	bj_rect_intersection (const bj_rect *p_rect_a, const bj_rect *p_rect_b, bj_rect *p_result)
static void	bj_vec2_set (bj_vec2 res, bj_real a, bj_real b)
static void	bj_vec2_zero (bj_vec2 res)
static void	bj_vec2_apply (bj_vec2 res, const bj_vec2 a, bj_real(*f)(bj_real))
static void	bj_vec2_add (bj_vec2 res, const bj_vec2 lhs, const bj_vec2 rhs)
static void	bj_vec2_add_scaled (bj_vec2 res, const bj_vec2 a, const bj_vec2 b, bj_real s)
static void	bj_vec2_sub (bj_vec2 res, const bj_vec2 lhs, const bj_vec2 rhs)
static void	bj_vec2_scale (bj_vec2 res, const bj_vec2 v, bj_real s)
static void	bj_vec2_scale_each (bj_vec2 res, const bj_vec2 v, const bj_vec2 s)
static bj_real	bj_vec2_dot (const bj_vec2 a, const bj_vec2 b)
static bj_real	bj_vec2_cross (const bj_vec2 a, const bj_vec2 b)
static bj_real	bj_vec2_len (const bj_vec2 v)
static void	bj_vec2_set_len (bj_vec2 res, const bj_vec2 v, bj_real target_len)
static bj_real	bj_vec2_dist_squared (const bj_vec2 a, const bj_vec2 b)
static bj_real	bj_vec2_dist (const bj_vec2 a, const bj_vec2 b)
static void	bj_vec2_normalize (bj_vec2 res, const bj_vec2 v)
static void	bj_vec2_min (bj_vec2 res, const bj_vec2 a, const bj_vec2 b)
static void	bj_vec2_max (bj_vec2 res, const bj_vec2 a, const bj_vec2 b)
static void	bj_vec2_copy (bj_vec2 res, const bj_vec2 src)
static void	bj_vec3_set (bj_vec3 res, bj_real a, bj_real b, bj_real c)
static void	bj_vec3_zero (bj_vec3 res)
static void	bj_vec3_apply (bj_vec3 res, const bj_vec3 a, bj_real(*f)(bj_real))
static void	bj_vec3_add (bj_vec3 res, const bj_vec3 lhs, const bj_vec3 rhs)
static void	bj_vec3_add_scaled (bj_vec3 res, const bj_vec3 a, const bj_vec3 b, bj_real s)
static void	bj_vec3_sub (bj_vec3 res, const bj_vec3 lhs, const bj_vec3 rhs)
static void	bj_vec3_scale (bj_vec3 res, const bj_vec3 v, bj_real s)
static bj_real	bj_vec3_dot (const bj_vec3 a, const bj_vec3 b)
static bj_real	bj_vec3_len (const bj_vec3 v)
static void	bj_vec3_set_len (bj_vec3 res, const bj_vec3 v, bj_real target_len)
static bj_real	bj_vec3_dist_squared (const bj_vec3 a, const bj_vec3 b)
static bj_real	bj_vec3_dist (const bj_vec3 a, const bj_vec3 b)
static void	bj_vec3_normalize (bj_vec3 res, const bj_vec3 v)
static void	bj_vec3_min (bj_vec3 res, const bj_vec3 a, const bj_vec3 b)
static void	bj_vec3_max (bj_vec3 res, const bj_vec3 a, const bj_vec3 b)
static void	bj_vec3_copy (bj_vec3 res, const bj_vec3 src)
static void	bj_vec3_cross (bj_vec3 res, const bj_vec3 l, const bj_vec3 r)
static void	bj_vec3_reflect (bj_vec3 res, const bj_vec3 v, const bj_vec3 n)
static void	bj_vec4_set (bj_vec4 res, bj_real a, bj_real b, bj_real c, bj_real d)
static void	bj_vec4_apply (bj_vec4 res, const bj_vec4 a, bj_real(*f)(bj_real))
static void	bj_vec4_add (bj_vec4 res, const bj_vec4 lhs, const bj_vec4 rhs)
static void	bj_vec4_add_scaled (bj_vec4 res, const bj_vec4 a, const bj_vec4 b, bj_real s)
static void	bj_vec4_sub (bj_vec4 res, const bj_vec4 lhs, const bj_vec4 rhs)
static void	bj_vec4_scale (bj_vec4 res, const bj_vec4 v, bj_real s)
static bj_real	bj_vec4_dot (const bj_vec4 a, const bj_vec4 b)
static bj_real	bj_vec4_len (const bj_vec4 v)
static void	bj_vec4_normalize (bj_vec4 res, const bj_vec4 v)
static void	bj_vec4_min (bj_vec4 res, const bj_vec4 a, const bj_vec4 b)
static void	bj_vec4_max (bj_vec4 res, const bj_vec4 a, const bj_vec4 b)
static void	bj_vec4_copy (bj_vec4 res, const bj_vec4 src)
static void	bj_vec4_cross (bj_vec4 res, const bj_vec4 l, const bj_vec4 r)
static void	bj_vec4_reflect (bj_vec4 res, const bj_vec4 v, const 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_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.

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)

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_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_quat_add

#define bj_quat_add   bj_vec4_add

Alias to vector add (component-wise).

See also

bj_vec4_add

bj_quat_dot

#define bj_quat_dot   bj_vec4_dot

Alias to 4D dot product.

See also

bj_vec4_dot

bj_quat_norm

#define bj_quat_norm   bj_vec4_normalize

Alias to normalize quaternion (scales to unit length).

See also

bj_vec4_normalize

bj_quat_scale

#define bj_quat_scale   bj_vec4_scale

Alias to uniform scale all four components.

See also

bj_vec4_scale

bj_quat_sub

#define bj_quat_sub   bj_vec4_sub

Alias to vector subtract (component-wise).

See also

bj_vec4_sub

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).

Typedef Documentation

bj_mat3

typedef bj_mat3x3 bj_mat3

bj_mat3: Alias for bj_mat3x3

bj_mat3x2

typedef bj_vec2 bj_mat3x2[3]

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.

bj_mat3x3

typedef bj_vec3 bj_mat3x3[3]

bj_mat3x3: 3×3 column-major matrix backed by bj_vec3.

Columns are arrays of 3 components.

bj_mat4

typedef bj_mat4x4 bj_mat4

bj_mat4: Alias for bj_mat4x4

bj_mat4x3

typedef bj_vec3 bj_mat4x3[4]

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.

bj_mat4x4

typedef bj_vec4 bj_mat4x4[4]

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

Columns are arrays of 4 components.

bj_quat

typedef bj_real bj_quat[4]

bj_quat: Quaternion stored as {x, y, z, w} with bj_real components.

Multiplication composes rotations; unit quaternions represent pure rotations.

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 bj_real bj_vec2[2]

bj_vec2: 2D vector of bj_real values.

Intended for lightweight math operations and POD interop. Components are indexed as 0..1.

bj_vec3

typedef bj_real bj_vec3[3]

bj_vec3: 3D vector of bj_real values.

Intended for lightweight math operations and POD interop. Components are indexed as 0..2.

bj_vec4

typedef bj_real bj_vec4[4]

bj_vec4: 4D vector of bj_real values.

Intended for lightweight math operations and POD interop. Components are indexed as 0..3.

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_mat3x3 res, const bj_mat3x3 a, const bj_mat3x3 b )

inlinestatic

Component-wise addition: res = a + b.

bj_mat3_col()

void bj_mat3_col ( bj_vec3 res, const bj_mat3x3 m, int c )

inlinestatic

Extract a column as a vector (column index into first subscript).

Parameters

res	Output vector.
m	Input matrix.
c	Column index.

bj_mat3_copy()

void bj_mat3_copy ( bj_mat3x3 to, const bj_mat3x3 from )

inlinestatic

Copy matrix contents.

Parameters

to	Output matrix.
from	Input matrix.

bj_mat3_from_mat3x2()

void bj_mat3_from_mat3x2 ( bj_real out3x3[restrict static(3)][3], const bj_real a[restrict static(3)][2] )

inlinestatic

Promote 3×2 to 3×3 homogeneous.

bj_mat3_identity()

void bj_mat3_identity ( bj_mat3x3 m )

inlinestatic

Set to identity matrix.

Parameters

m	Output buffer.

bj_mat3_inverse()

void bj_mat3_inverse ( bj_mat3x3 res, const bj_mat3x3 m )

inlinestatic

Invert a 3×3.

bj_mat3_mul()

void bj_mat3_mul ( bj_real res[restrict static(3)][3], const bj_real lhs[restrict static(3)][3], const bj_real rhs[restrict static(3)][3] )

inlinestatic

Matrix multiplication: res = lhs * rhs (column-major).

Note

Column-major convention: res = lhs * rhs.

bj_mat3_mul_point()

void bj_mat3_mul_point ( bj_vec2 res, const bj_mat3x3 m, const bj_vec2 p )

inlinestatic

Transform a point (homogeneous w=1).

Note

Column-major convention: res = m * p.

bj_mat3_mul_vec3()

void bj_mat3_mul_vec3 ( bj_real res[restrict static(3)], const bj_real m[restrict static(3)][3], const bj_real v[restrict static(3)] )

inlinestatic

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

Note

Column-major convention: res = lhs * rhs.

bj_mat3_mul_vector2()

void bj_mat3_mul_vector2 ( bj_vec2 res, const bj_mat3x3 m, const bj_vec2 v2 )

inlinestatic

Transform a direction (w=0; ignores translation).

Note

Column-major convention: res = m * v2.

bj_mat3_ortho()

void bj_mat3_ortho ( bj_real omat[restrict static(3)][3], bj_real l, bj_real r, bj_real b, bj_real t )

inlinestatic

Orthographic projection matrix (3×3).

bj_mat3_rotate()

void bj_mat3_rotate ( bj_mat3x3 res, bj_real angle )

inlinestatic

Rotate 2D about Z.

bj_mat3_row()

void bj_mat3_row ( bj_vec3 res, const bj_mat3x3 m, int r )

inlinestatic

Extract a row as a vector (row index into second subscript).

Parameters

res	Output vector.
m	Input matrix.
r	Row index.

bj_mat3_scale()

void bj_mat3_scale ( bj_mat3x3 res, const bj_mat3x3 m, bj_real k )

inlinestatic

Uniformly scale all elements by scalar k.

bj_mat3_scale_xy()

void bj_mat3_scale_xy ( bj_mat3x3 res, bj_real sx, bj_real sy )

inlinestatic

Create 2D scaling matrix with independent X/Y scales.

bj_mat3_shear()

void bj_mat3_shear ( bj_mat3x3 res, bj_real shx, bj_real shy )

inlinestatic

Create 2D shear matrix.

bj_mat3_sub()

void bj_mat3_sub ( bj_mat3x3 res, const bj_mat3x3 a, const bj_mat3x3 b )

inlinestatic

Component-wise subtraction: res = a - b.

bj_mat3_translation()

void bj_mat3_translation ( bj_mat3x3 res, bj_real tx, bj_real ty )

inlinestatic

Create a translation matrix.

bj_mat3_translation_inplace()

void bj_mat3_translation_inplace ( bj_mat3x3 M, bj_real tx, bj_real ty )

inlinestatic

Apply a translation in-place.

bj_mat3_transpose()

void bj_mat3_transpose ( bj_mat3x3 res, const bj_mat3x3 m )

inlinestatic

Transpose the matrix.

Parameters

res	Output matrix.
m	Input matrix.

bj_mat3_viewport()

void bj_mat3_viewport ( bj_real vpmat[restrict static(3)][3], bj_real x, bj_real y, bj_real w, bj_real h )

inlinestatic

Viewport transform matrix (3×3).

bj_mat3x2_from_mat3()

void bj_mat3x2_from_mat3 ( bj_real out3x2[restrict static(3)][2], const bj_real m[restrict static(3)][3] )

inlinestatic

Extract 3×2 from 3×3.

bj_mat3x2_identity()

void bj_mat3x2_identity ( bj_real m[restrict static(3)][2] )

inlinestatic

Set 3×2 to identity.

bj_mat3x2_mul()

void bj_mat3x2_mul ( bj_real res[restrict static(3)][2], const bj_real A[restrict static(3)][2], const bj_real B[restrict static(3)][2] )

inlinestatic

3×2 multiplication: res = A * B.

bj_mat3x2_mul_dir()

void bj_mat3x2_mul_dir ( bj_real r[restrict static(2)], const bj_real m[restrict static(3)][2], const bj_real v[restrict static(2)] )

inlinestatic

3×2 transform direction (no translation).

bj_mat3x2_mul_point()

void bj_mat3x2_mul_point ( bj_real r[restrict static(2)], const bj_real m[restrict static(3)][2], const bj_real p[restrict static(2)] )

inlinestatic

3×2 transform point.

bj_mat3x2_rotate()

void bj_mat3x2_rotate ( bj_real m[restrict static(3)][2], bj_real angle )

inlinestatic

Build 3×2 rotation.

bj_mat3x2_scale()

void bj_mat3x2_scale ( bj_real m[restrict static(3)][2], bj_real sx, bj_real sy )

inlinestatic

Build 3×2 scale.

bj_mat3x2_translate()

void bj_mat3x2_translate ( bj_real m[restrict static(3)][2], bj_real tx, bj_real ty )

inlinestatic

Build 3×2 translation.

bj_mat4_add()

void bj_mat4_add ( bj_mat4x4 res, const bj_mat4x4 lhs, const bj_mat4x4 rhs )

inlinestatic

Add 4×4.

bj_mat4_col()

void bj_mat4_col ( bj_vec4 res, const bj_mat4x4 mat, int c )

inlinestatic

Extract 4×4 column.

bj_mat4_copy()

void bj_mat4_copy ( bj_mat4x4 to, const bj_mat4x4 from )

inlinestatic

Copy 4×4.

bj_mat4_from_mat4x3()

void bj_mat4_from_mat4x3 ( bj_mat4x4 out, const bj_real a[restrict static(4)][3] )

inlinestatic

Promote 4×3 to 4×4 homogeneous.

bj_mat4_from_quat()

void bj_mat4_from_quat ( bj_mat4 res, const bj_quat q )

inlinestatic

Convert unit quaternion to a 4×4 rotation matrix.

Parameters

res	Output quaternion.
q	Input quaternion.

Note

Assumes unit-length quaternions for pure rotations.

bj_mat4_frustum()

void bj_mat4_frustum ( bj_real fmat[restrict static(4)][4], bj_real l, bj_real r, bj_real b, bj_real t, bj_real n, bj_real f )

inlinestatic

Off-center perspective frustum (4×4).

bj_mat4_identity()

void bj_mat4_identity ( bj_mat4x4 mat )

inlinestatic

Set 4×4 to identity.

bj_mat4_inverse()

void bj_mat4_inverse ( bj_mat4x4 res, const bj_mat4x4 mat )

inlinestatic

Invert 4×4.

bj_mat4_lookat()

void bj_mat4_lookat ( bj_real m[restrict static(4)][4], const bj_vec3 eye, const bj_vec3 center, const bj_vec3 up )

inlinestatic

Look-at view matrix builder (4×4).

bj_mat4_mul()

void bj_mat4_mul ( bj_real res[restrict static(4)][4], const bj_real lhs[restrict static(4)][4], const bj_real rhs[restrict static(4)][4] )

inlinestatic

4×4 multiplication: res = lhs * rhs.

bj_mat4_mul_outer()

void bj_mat4_mul_outer ( bj_mat4x4 res, const bj_vec3 a, const bj_vec3 b )

inlinestatic

Outer product to upper-left 3×3 block of 4×4.

bj_mat4_mul_vec4()

void bj_mat4_mul_vec4 ( bj_real res[restrict static(4)], const bj_real mat[restrict static(4)][4], const bj_real v[restrict static(4)] )

inlinestatic

4×4 multiply by vec4.

bj_mat4_ortho()

void bj_mat4_ortho ( bj_real omat[restrict static(4)][4], bj_real l, bj_real r, bj_real b, bj_real t, bj_real n, bj_real f )

inlinestatic

Orthographic projection (4×4).

bj_mat4_orthonormalize()

void bj_mat4_orthonormalize ( bj_mat4x4 res, const bj_mat4x4 mat )

inlinestatic

Orthonormalize upper-left 3×3 of 4×4.

bj_mat4_perspective()

void bj_mat4_perspective ( bj_real pmat[restrict static(4)][4], bj_real y_fov, bj_real aspect, bj_real n, bj_real f )

inlinestatic

Symmetric perspective from FOV+aspect (4×4).

bj_mat4_rotate()

void bj_mat4_rotate ( bj_mat4x4 res, const bj_mat4x4 mat, bj_real x, bj_real y, bj_real z, bj_real angle )

inlinestatic

Rotate about axis, post-multiply.

bj_mat4_rotate_arcball()

void bj_mat4_rotate_arcball ( bj_mat4x4 R, const bj_mat4x4 M, bj_vec2 const _a, bj_vec2 const _b, bj_real s )

inlinestatic

Arcball rotation.

bj_mat4_rotate_from_quat()

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

inlinestatic

Post-multiply matrix by rotation from quaternion: R = M * rot(q).

Parameters

R	Output matrix.
M	Input 4×4 matrix.
q	Input quaternion.

Note

Assumes unit-length quaternions for pure rotations.

bj_mat4_rotate_x()

void bj_mat4_rotate_x ( bj_mat4x4 res, const bj_mat4x4 mat, bj_real angle )

inlinestatic

Rotate about X/Y/Z, post-multiply.

bj_mat4_rotate_y()

void bj_mat4_rotate_y ( bj_mat4x4 res, const bj_mat4x4 mat, bj_real angle )

inlinestatic

bj_mat4_rotate_z()

void bj_mat4_rotate_z ( bj_mat4x4 res, const bj_mat4x4 mat, bj_real angle )

inlinestatic

bj_mat4_row()

void bj_mat4_row ( bj_vec4 res, const bj_mat4x4 mat, int r )

inlinestatic

Extract 4×4 row.

bj_mat4_scale()

void bj_mat4_scale ( bj_mat4x4 res, const bj_mat4x4 lhs, bj_real k )

inlinestatic

Scale 4×4 by k.

bj_mat4_scale_xyz()

void bj_mat4_scale_xyz ( bj_mat4x4 res, const bj_mat4x4 mat, bj_real x, bj_real y, bj_real z )

inlinestatic

Scale basis vectors.

bj_mat4_sub()

void bj_mat4_sub ( bj_mat4x4 res, const bj_mat4x4 lhs, const bj_mat4x4 rhs )

inlinestatic

Sub 4×4.

bj_mat4_translation()

void bj_mat4_translation ( bj_mat4x4 res, bj_real x, bj_real y, bj_real z )

inlinestatic

Create 4×4 translation matrix.

bj_mat4_translation_inplace()

void bj_mat4_translation_inplace ( bj_mat4x4 M, bj_real x, bj_real y, bj_real z )

inlinestatic

Apply 4×4 translation in-place.

bj_mat4_transpose()

void bj_mat4_transpose ( bj_mat4x4 res, const bj_mat4x4 mat )

inlinestatic

Transpose 4×4.

bj_mat4_viewport()

void bj_mat4_viewport ( bj_real vpmat[restrict static(4)][4], bj_real x, bj_real y, bj_real w, bj_real h )

inlinestatic

Viewport transform (4×4).

bj_mat4x3_from_mat4()

void bj_mat4x3_from_mat4 ( bj_real out43[restrict static(4)][3], const bj_mat4x4 m )

inlinestatic

Extract 4×3 from 4×4.

bj_mat4x3_identity()

void bj_mat4x3_identity ( bj_real m[restrict static(4)][3] )

inlinestatic

Set 4×3 to identity.

bj_mat4x3_lookat()

void bj_mat4x3_lookat ( bj_real m[restrict static(4)][3], const bj_real eye[restrict static(3)], const bj_real center[restrict static(3)], const bj_real up[restrict static(3)] )

inlinestatic

Look-at builder for 4×3.

bj_mat4x3_mul()

void bj_mat4x3_mul ( bj_real res[restrict static(4)][3], const bj_real A[restrict static(4)][3], const bj_real B[restrict static(4)][3] )

inlinestatic

4×3 multiplication: res = A * B.

bj_mat4x3_mul_dir()

void bj_mat4x3_mul_dir ( bj_real r[restrict static(3)], const bj_real m[restrict static(4)][3], const bj_real v[restrict static(3)] )

inlinestatic

4×3 transform direction (no translation).

bj_mat4x3_mul_point()

void bj_mat4x3_mul_point ( bj_real r[restrict static(3)], const bj_real m[restrict static(4)][3], const bj_real p[restrict static(3)] )

inlinestatic

4×3 transform point.

bj_mat4x3_rotate_x()

void bj_mat4x3_rotate_x ( bj_real m[restrict static(4)][3], bj_real angle )

inlinestatic

4×3 rotate X/Y/Z.

bj_mat4x3_rotate_y()

void bj_mat4x3_rotate_y ( bj_real m[restrict static(4)][3], bj_real angle )

inlinestatic

bj_mat4x3_rotate_z()

void bj_mat4x3_rotate_z ( bj_real m[restrict static(4)][3], bj_real angle )

inlinestatic

bj_mat4x3_scale()

void bj_mat4x3_scale ( bj_real m[restrict static(4)][3], bj_real sx, bj_real sy, bj_real sz )

inlinestatic

4×3 scale.

bj_mat4x3_translate()

void bj_mat4x3_translate ( bj_real m[restrict static(4)][3], bj_real tx, bj_real ty, bj_real tz )

inlinestatic

4×3 translation.

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()

void bj_quat_conjugate ( bj_quat res, const bj_quat q )

inlinestatic

Conjugate quaternion: (x,y,z,w) -> (-x,-y,-z,w).

Parameters

res	Output quaternion.
q	Input quaternion.

bj_quat_from_mat4()

void bj_quat_from_mat4 ( bj_quat q, const bj_mat4 M )

inlinestatic

Extract a unit quaternion from a 4×4 rotation matrix.

Parameters

q	Input quaternion.
M	Input 4×4 matrix.

Note

Assumes unit-length quaternions for pure rotations.

Uses a numerically stable branch based on the dominant diagonal term.

bj_quat_identity()

void bj_quat_identity ( bj_quat q )

inlinestatic

Set quaternion to identity (no rotation).

Parameters

q	Input quaternion.

bj_quat_mul()

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

inlinestatic

Hamilton product: res = p * q.

Parameters

res	Output quaternion.
p	Input quaternion.
q	Input quaternion.

Note

Assumes unit-length quaternions for pure rotations.

bj_quat_mul_vec3()

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

inlinestatic

Rotate a 3D vector by a unit quaternion.

Parameters

res	Output quaternion.
q	Input quaternion.
v	3D vector.

Note

Assumes unit-length quaternions for pure rotations.

bj_quat_rotation()

void bj_quat_rotation ( bj_quat res, bj_real angle, const bj_vec3 axis )

inlinestatic

Build a unit quaternion from axis-angle.

Parameters

res	Output quaternion.
angle	Rotation angle in radians.
axis	3D vector.

Note

Assumes unit-length quaternions for pure rotations.

Warning

If axis is near zero length, the result is implementation-defined.

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()

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

inlinestatic

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

Parameters

res	Output 2D vector.
lhs	Left-hand input vector.
rhs	Right-hand input vector.

bj_vec2_add_scaled()

void bj_vec2_add_scaled ( bj_vec2 res, const bj_vec2 a, const bj_vec2 b, bj_real s )

inlinestatic

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

Parameters

res	Output 2D vector.
a	Input component or vector a.
b	Input component or vector b.
s	Scalar factor.

bj_vec2_apply()

void bj_vec2_apply ( bj_vec2 res, const bj_vec2 a, bj_real(* f )(bj_real) )

inlinestatic

bj_vec2_copy()

void bj_vec2_copy ( bj_vec2 res, const bj_vec2 src )

inlinestatic

Copy a 2D vector.

Parameters

res	Output 2D vector.
src	Source vector to copy from.

bj_vec2_cross()

bj_real bj_vec2_cross ( const bj_vec2 a, const 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_dist()

bj_real bj_vec2_dist ( 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_dist_squared()

bj_real bj_vec2_dist_squared ( const bj_vec2 a, const 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 ( const bj_vec2 a, const 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 ( const bj_vec2 v )

inlinestatic

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

Parameters

v	Input vector.

Returns

The Euclidean norm.

bj_vec2_max()

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

void bj_vec2_min ( bj_vec2 res, const bj_vec2 a, const 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_normalize()

void bj_vec2_normalize ( bj_vec2 res, const bj_vec2 v )

inlinestatic

Normalize a 2D vector to unit length.

Parameters

res	Output 2D vector.
v	Input vector.

Warning

Undefined if the input vector has zero length.

bj_vec2_scale()

void bj_vec2_scale ( bj_vec2 res, const bj_vec2 v, bj_real s )

inlinestatic

Uniform scaling by scalar: res = v * s.

Parameters

res	Output 2D vector.
v	Input vector.
s	Scalar factor.

bj_vec2_scale_each()

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

inlinestatic

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

Parameters

res	Output 2D vector.
v	Input vector.
s	Scalar factor.

bj_vec2_set()

void bj_vec2_set ( bj_vec2 res, bj_real a, bj_real b )

inlinestatic

Set a 2D vector from components (x, y).

Parameters

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

bj_vec2_set_len()

void bj_vec2_set_len ( bj_vec2 res, const bj_vec2 v, bj_real target_len )

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()

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

inlinestatic

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

Parameters

res	Output 2D vector.
lhs	Left-hand input vector.
rhs	Right-hand input vector.

bj_vec2_zero()

void bj_vec2_zero ( bj_vec2 res )

inlinestatic

bj_vec3_add()

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

void bj_vec3_add_scaled ( bj_vec3 res, const bj_vec3 a, const bj_vec3 b, bj_real s )

inlinestatic

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

Parameters

res	Output 3D vector.
a	Input component or vector a.
b	Input component or vector b.
s	Scalar factor.

bj_vec3_apply()

void bj_vec3_apply ( bj_vec3 res, const bj_vec3 a, bj_real(* f )(bj_real) )

inlinestatic

bj_vec3_copy()

void bj_vec3_copy ( bj_vec3 res, const bj_vec3 src )

inlinestatic

Copy a 3D vector.

Parameters

res	Output 3D vector.
src	Source vector to copy from.

bj_vec3_cross()

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

inlinestatic

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

Parameters

res	Output 3D vector.
l	Left-hand input vector.
r	Right-hand input vector.

bj_vec3_dist()

bj_real bj_vec3_dist ( const bj_vec3 a, const 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_dist_squared()

bj_real bj_vec3_dist_squared ( const bj_vec3 a, const 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 ( const bj_vec3 a, const 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 ( const bj_vec3 v )

inlinestatic

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

Parameters

v	Input vector.

Returns

The Euclidean norm.

bj_vec3_max()

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

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

void bj_vec3_normalize ( bj_vec3 res, const bj_vec3 v )

inlinestatic

Normalize a 3D vector to unit length.

Parameters

res	Output 3D vector.
v	Input vector.

Warning

Undefined if the input vector has zero length.

bj_vec3_reflect()

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

inlinestatic

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

Parameters

res	Output 3D vector.
v	Input vector.
n	Surface normal (expected normalized).

Note

The normal n should be normalized for a true reflection.

bj_vec3_scale()

void bj_vec3_scale ( bj_vec3 res, const bj_vec3 v, bj_real s )

inlinestatic

Uniform scaling by scalar: res = v * s.

Parameters

res	Output 3D vector.
v	Input vector.
s	Scalar factor.

bj_vec3_set()

void bj_vec3_set ( bj_vec3 res, bj_real a, bj_real b, bj_real c )

inlinestatic

Set a 3D vector from components (x, y, z).

Parameters

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

bj_vec3_set_len()

void bj_vec3_set_len ( bj_vec3 res, const bj_vec3 v, bj_real target_len )

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()

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

inlinestatic

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

Parameters

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

bj_vec3_zero()

void bj_vec3_zero ( bj_vec3 res )

inlinestatic

bj_vec4_add()

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

inlinestatic

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

Parameters

res	Output 4D vector.
lhs	Left-hand input vector.
rhs	Right-hand input vector.

bj_vec4_add_scaled()

void bj_vec4_add_scaled ( bj_vec4 res, const bj_vec4 a, const bj_vec4 b, bj_real s )

inlinestatic

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

Parameters

res	Output 4D vector.
a	Input component or vector a.
b	Input component or vector b.
s	Scalar factor.

bj_vec4_apply()

void bj_vec4_apply ( bj_vec4 res, const bj_vec4 a, bj_real(* f )(bj_real) )

inlinestatic

bj_vec4_copy()

void bj_vec4_copy ( bj_vec4 res, const bj_vec4 src )

inlinestatic

Copy a 4D vector.

Parameters

res	Output 4D vector.
src	Source vector to copy from.

bj_vec4_cross()

void bj_vec4_cross ( bj_vec4 res, const bj_vec4 l, const 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 ( const bj_vec4 a, const 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 ( const bj_vec4 v )

inlinestatic

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

Parameters

v	Input vector.

Returns

The Euclidean norm.

bj_vec4_max()

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

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

void bj_vec4_normalize ( bj_vec4 res, const bj_vec4 v )

inlinestatic

Normalize a 4D vector to unit length.

Parameters

res	Output 4D vector.
v	Input vector.

Warning

Undefined if the input vector has zero length.

bj_vec4_reflect()

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

void bj_vec4_scale ( bj_vec4 res, const bj_vec4 v, bj_real s )

inlinestatic

Uniform scaling by scalar: res = v * s.

Parameters

res	Output 4D vector.
v	Input vector.
s	Scalar factor.

bj_vec4_set()

void bj_vec4_set ( bj_vec4 res, bj_real a, bj_real b, bj_real c, bj_real d )

inlinestatic

Set a 4D vector from components (x, y, z, w).

Parameters

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

bj_vec4_sub()

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

inlinestatic

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

Parameters

res	Output 4D vector.
lhs	Left-hand input vector.
rhs	Right-hand input vector.