/* gb_math.h - v0.06a - public domain C math library - no warranty implied; use at your own risk A C math library geared towards game development use '#define GB_MATH_IMPLEMENTATION' before including to create the implementation in _ONE_ file Version History: 0.06a - Implement rough versions of mod, remainder, copy_sign 0.06 - Windows GCC Support and C90-ish Support 0.05 - Less/no dependencies or CRT 0.04d - License Update 0.04c - Use 64-bit murmur64 version on WIN64 0.04b - Fix strict aliasing in gb_quake_rsqrt 0.04a - Minor bug fixes 0.04 - Namespace everything with gb 0.03 - Complete Replacement 0.01 - Initial Version LICENSE This software is dual-licensed to the public domain and under the following license: you are granted a perpetual, irrevocable license to copy, modify, publish, and distribute this file as you see fit. WARNING - This library is _slightly_ experimental and features may not work as expected. - This also means that many functions are not documented. CONTENTS - Common Macros - Types - gbVec(2,3,4) - gbMat(2,3,4) - gbFloat(2,3,4) - gbQuat - gbRect(2,3) - gbAabb(2,3) - gbHalf (16-bit floating point) (storage only) - Operations - Functions - Type Functions - Random - Hash */ #ifndef GB_MATH_INCLUDE_GB_MATH_H #define GB_MATH_INCLUDE_GB_MATH_H #include #if !defined(GB_MATH_NO_MATH_H) #include #else #include #endif #ifndef GB_MATH_DEF #ifdef GB_MATH_STATIC #define GB_MATH_DEF static #else #define GB_MATH_DEF extern #endif #endif typedef union gbVec2 { struct { float x, y; }; float e[2]; } gbVec2; typedef union gbVec3 { struct { float x, y, z; }; struct { float r, g, b; }; gbVec2 xy; float e[2]; } gbVec3; typedef union gbVec4 { struct { float x, y, z, w; }; struct { float r, g, b, a; }; struct { gbVec2 xy, zw; }; gbVec3 xyz; gbVec3 rgb; float e[4]; } gbVec4; typedef union gbMat2 { struct { gbVec2 x, y; }; gbVec4 col[2]; float e[4]; } gbMat2; typedef union gbMat3 { struct { gbVec3 x, y, z; }; gbVec3 col[3]; float e[9]; } gbMat3; typedef union gbMat4 { struct { gbVec4 x, y, z, w; }; gbVec4 col[4]; float e[16]; } gbMat4; typedef union gbQuat { struct { float x, y, z, w; }; gbVec4 xyzw; gbVec3 xyz; float e[4]; } gbQuat; typedef float gbFloat2[2]; typedef float gbFloat3[3]; typedef float gbFloat4[4]; typedef struct gbRect2 { gbVec2 pos, dim; } gbRect2; typedef struct gbRect3 { gbVec3 pos, dim; } gbRect3; typedef struct gbAabb2 { gbVec2 centre, half_size; } gbAabb2; typedef struct gbAabb3 { gbVec3 centre, half_size; } gbAabb3; #if defined(_MSC_VER) typedef unsigned __int32 gb_math_u32; typedef unsigned __int64 gb_math_u64; #else #if defined(GB_USE_STDINT) #include typedef uint32_t gb_math_u32; typedef uint64_t gb_math_u64; #else typedef unsigned int gb_math_u32; typedef unsigned long long gb_math_u64; #endif #endif typedef short gbHalf; #ifndef GB_MATH_CONSTANTS #define GB_MATH_CONSTANTS #define GB_MATH_EPSILON 1.19209290e-7f #define GB_MATH_ZERO 0.0f #define GB_MATH_ONE 1.0f #define GB_MATH_TWO_THIRDS 0.666666666666666666666666666666666666667f #define GB_MATH_TAU 6.28318530717958647692528676655900576f #define GB_MATH_PI 3.14159265358979323846264338327950288f #define GB_MATH_ONE_OVER_TAU 0.636619772367581343075535053490057448f #define GB_MATH_ONE_OVER_PI 0.159154943091895335768883763372514362f #define GB_MATH_TAU_OVER_2 3.14159265358979323846264338327950288f #define GB_MATH_TAU_OVER_4 1.570796326794896619231321691639751442f #define GB_MATH_TAU_OVER_8 0.785398163397448309615660845819875721f #define GB_MATH_E 2.71828182845904523536f #define GB_MATH_SQRT_TWO 1.41421356237309504880168872420969808f #define GB_MATH_SQRT_THREE 1.73205080756887729352744634150587236f #define GB_MATH_SQRT_FIVE 2.23606797749978969640917366873127623f #define GB_MATH_LOG_TWO 0.693147180559945309417232121458176568f #define GB_MATH_LOG_TEN 2.30258509299404568401799145468436421f #endif #if defined(__cplusplus) extern "C" { #endif #ifndef gb_clamp #define gb_clamp(x, lower, upper) (gb_min(gb_max(x, (lower)), (upper))) #endif #ifndef gb_clamp01 #define gb_clamp01(x) gb_clamp(x, 0, 1) #endif #ifndef gb_square #define gb_square(x) ((x)*(x)) #endif #ifndef gb_cube #define gb_cube(x) ((x)*(x)*(x)) #endif #ifndef gb_abs #define gb_abs(x) ((x) > 0 ? (x) : -(x)) #endif #ifndef gb_sign #define gb_sign(x) ((x) >= 0 ? 1 : -1) #endif GB_MATH_DEF float gb_to_radians(float degrees); GB_MATH_DEF float gb_to_degrees(float radians); /* NOTE(bill): Because to interpolate angles */ GB_MATH_DEF float gb_angle_diff(float radians_a, float radians_b); #ifndef gb_min #define gb_min(a, b) ((a) < (b) ? (a) : (b)) #endif #ifndef gb_max #define gb_max(a, b) ((a) > (b) ? (a) : (b)) #endif GB_MATH_DEF float gb_copy_sign(float x, float y); GB_MATH_DEF float gb_remainder(float x, float y); GB_MATH_DEF float gb_mod(float x, float y); GB_MATH_DEF float gb_sqrt(float a); GB_MATH_DEF float gb_rsqrt(float a); GB_MATH_DEF float gb_quake_rsqrt(float a); /* NOTE(bill): It's probably better to use 1.0f/gb_sqrt(a) * And for simd, there is usually isqrt functions too! */ GB_MATH_DEF float gb_sin(float radians); GB_MATH_DEF float gb_cos(float radians); GB_MATH_DEF float gb_tan(float radians); GB_MATH_DEF float gb_arcsin(float a); GB_MATH_DEF float gb_arccos(float a); GB_MATH_DEF float gb_arctan(float a); GB_MATH_DEF float gb_arctan2(float y, float x); GB_MATH_DEF float gb_exp(float x); GB_MATH_DEF float gb_exp2(float x); GB_MATH_DEF float gb_log(float x); GB_MATH_DEF float gb_log2(float x); GB_MATH_DEF float gb_fast_exp(float x); /* NOTE(bill): Only valid from -1 <= x <= +1 */ GB_MATH_DEF float gb_fast_exp2(float x); /* NOTE(bill): Only valid from -1 <= x <= +1 */ GB_MATH_DEF float gb_pow(float x, float y); /* x^y */ GB_MATH_DEF float gb_round(float x); GB_MATH_DEF float gb_floor(float x); GB_MATH_DEF float gb_ceil(float x); GB_MATH_DEF float gb_half_to_float(gbHalf value); GB_MATH_DEF gbHalf gb_float_to_half(float value); GB_MATH_DEF gbVec2 gb_vec2_zero(void); GB_MATH_DEF gbVec2 gb_vec2(float x, float y); GB_MATH_DEF gbVec2 gb_vec2v(float x[2]); GB_MATH_DEF gbVec3 gb_vec3_zero(void); GB_MATH_DEF gbVec3 gb_vec3(float x, float y, float z); GB_MATH_DEF gbVec3 gb_vec3v(float x[3]); GB_MATH_DEF gbVec4 gb_vec4_zero(void); GB_MATH_DEF gbVec4 gb_vec4(float x, float y, float z, float w); GB_MATH_DEF gbVec4 gb_vec4v(float x[4]); GB_MATH_DEF void gb_vec2_add(gbVec2 *d, gbVec2 v0, gbVec2 v1); GB_MATH_DEF void gb_vec2_sub(gbVec2 *d, gbVec2 v0, gbVec2 v1); GB_MATH_DEF void gb_vec2_mul(gbVec2 *d, gbVec2 v, float s); GB_MATH_DEF void gb_vec2_div(gbVec2 *d, gbVec2 v, float s); GB_MATH_DEF void gb_vec3_add(gbVec3 *d, gbVec3 v0, gbVec3 v1); GB_MATH_DEF void gb_vec3_sub(gbVec3 *d, gbVec3 v0, gbVec3 v1); GB_MATH_DEF void gb_vec3_mul(gbVec3 *d, gbVec3 v, float s); GB_MATH_DEF void gb_vec3_div(gbVec3 *d, gbVec3 v, float s); GB_MATH_DEF void gb_vec4_add(gbVec4 *d, gbVec4 v0, gbVec4 v1); GB_MATH_DEF void gb_vec4_sub(gbVec4 *d, gbVec4 v0, gbVec4 v1); GB_MATH_DEF void gb_vec4_mul(gbVec4 *d, gbVec4 v, float s); GB_MATH_DEF void gb_vec4_div(gbVec4 *d, gbVec4 v, float s); GB_MATH_DEF void gb_vec2_addeq(gbVec2 *d, gbVec2 v); GB_MATH_DEF void gb_vec2_subeq(gbVec2 *d, gbVec2 v); GB_MATH_DEF void gb_vec2_muleq(gbVec2 *d, float s); GB_MATH_DEF void gb_vec2_diveq(gbVec2 *d, float s); GB_MATH_DEF void gb_vec3_addeq(gbVec3 *d, gbVec3 v); GB_MATH_DEF void gb_vec3_subeq(gbVec3 *d, gbVec3 v); GB_MATH_DEF void gb_vec3_muleq(gbVec3 *d, float s); GB_MATH_DEF void gb_vec3_diveq(gbVec3 *d, float s); GB_MATH_DEF void gb_vec4_addeq(gbVec4 *d, gbVec4 v); GB_MATH_DEF void gb_vec4_subeq(gbVec4 *d, gbVec4 v); GB_MATH_DEF void gb_vec4_muleq(gbVec4 *d, float s); GB_MATH_DEF void gb_vec4_diveq(gbVec4 *d, float s); GB_MATH_DEF float gb_vec2_dot(gbVec2 v0, gbVec2 v1); GB_MATH_DEF float gb_vec3_dot(gbVec3 v0, gbVec3 v1); GB_MATH_DEF float gb_vec4_dot(gbVec4 v0, gbVec4 v1); GB_MATH_DEF void gb_vec2_cross(float *d, gbVec2 v0, gbVec2 v1); GB_MATH_DEF void gb_vec3_cross(gbVec3 *d, gbVec3 v0, gbVec3 v1); GB_MATH_DEF float gb_vec2_mag2(gbVec2 v); GB_MATH_DEF float gb_vec3_mag2(gbVec3 v); GB_MATH_DEF float gb_vec4_mag2(gbVec4 v); GB_MATH_DEF float gb_vec2_mag(gbVec2 v); GB_MATH_DEF float gb_vec3_mag(gbVec3 v); GB_MATH_DEF float gb_vec4_mag(gbVec4 v); GB_MATH_DEF void gb_vec2_norm(gbVec2 *d, gbVec2 v); GB_MATH_DEF void gb_vec3_norm(gbVec3 *d, gbVec3 v); GB_MATH_DEF void gb_vec4_norm(gbVec4 *d, gbVec4 v); GB_MATH_DEF void gb_vec2_norm0(gbVec2 *d, gbVec2 v); GB_MATH_DEF void gb_vec3_norm0(gbVec3 *d, gbVec3 v); GB_MATH_DEF void gb_vec4_norm0(gbVec4 *d, gbVec4 v); GB_MATH_DEF void gb_vec2_reflect(gbVec2 *d, gbVec2 i, gbVec2 n); GB_MATH_DEF void gb_vec3_reflect(gbVec3 *d, gbVec3 i, gbVec3 n); GB_MATH_DEF void gb_vec2_refract(gbVec2 *d, gbVec2 i, gbVec2 n, float eta); GB_MATH_DEF void gb_vec3_refract(gbVec3 *d, gbVec3 i, gbVec3 n, float eta); GB_MATH_DEF float gb_vec2_aspect_ratio(gbVec2 v); GB_MATH_DEF void gb_mat2_identity(gbMat2 *m); GB_MATH_DEF void gb_float22_identity(float m[2][2]); GB_MATH_DEF void gb_mat2_transpose(gbMat2 *m); GB_MATH_DEF void gb_mat2_mul(gbMat2 *out, gbMat2 *m1, gbMat2 *m2); GB_MATH_DEF void gb_mat2_mul_vec2(gbVec2 *out, gbMat2 *m, gbVec2 in); GB_MATH_DEF gbMat2 *gb_mat2_v(gbVec2 m[2]); GB_MATH_DEF gbMat2 *gb_mat2_f(float m[2][2]); GB_MATH_DEF gbFloat2 *gb_float22_m(gbMat2 *m); GB_MATH_DEF gbFloat2 *gb_float22_v(gbVec2 m[2]); GB_MATH_DEF gbFloat2 *gb_float22_4(float m[4]); GB_MATH_DEF void gb_float22_transpose(float (*vec)[2]); GB_MATH_DEF void gb_float22_mul(float (*out)[2], float (*mat1)[2], float (*mat2)[2]); GB_MATH_DEF void gb_float22_mul_vec2(gbVec2 *out, float m[2][2], gbVec2 in); GB_MATH_DEF void gb_mat3_identity(gbMat3 *m); GB_MATH_DEF void gb_float33_identity(float m[3][3]); GB_MATH_DEF void gb_mat3_transpose(gbMat3 *m); GB_MATH_DEF void gb_mat3_mul(gbMat3 *out, gbMat3 *m1, gbMat3 *m2); GB_MATH_DEF void gb_mat3_mul_vec3(gbVec3 *out, gbMat3 *m, gbVec3 in); GB_MATH_DEF gbMat3 *gb_mat3_v(gbVec3 m[3]); GB_MATH_DEF gbMat3 *gb_mat3_f(float m[3][3]); GB_MATH_DEF gbFloat3 *gb_float33_m(gbMat3 *m); GB_MATH_DEF gbFloat3 *gb_float33_v(gbVec3 m[3]); GB_MATH_DEF gbFloat3 *gb_float33_9(float m[9]); GB_MATH_DEF void gb_float33_transpose(float (*vec)[3]); GB_MATH_DEF void gb_float33_mul(float (*out)[3], float (*mat1)[3], float (*mat2)[3]); GB_MATH_DEF void gb_float33_mul_vec3(gbVec3 *out, float m[3][3], gbVec3 in); GB_MATH_DEF void gb_mat4_identity(gbMat4 *m); GB_MATH_DEF void gb_float44_identity(float m[4][4]); GB_MATH_DEF void gb_mat4_transpose(gbMat4 *m); GB_MATH_DEF void gb_mat4_mul(gbMat4 *out, gbMat4 *m1, gbMat4 *m2); GB_MATH_DEF void gb_mat4_mul_vec4(gbVec4 *out, gbMat4 *m, gbVec4 in); GB_MATH_DEF gbMat4 *gb_mat4_v(gbVec4 m[4]); GB_MATH_DEF gbMat4 *gb_mat4_f(float m[4][4]); GB_MATH_DEF gbFloat4 *gb_float44_m(gbMat4 *m); GB_MATH_DEF gbFloat4 *gb_float44_v(gbVec4 m[4]); GB_MATH_DEF gbFloat4 *gb_float44_16(float m[16]); GB_MATH_DEF void gb_float44_transpose(float (*vec)[4]); GB_MATH_DEF void gb_float44_mul(float (*out)[4], float (*mat1)[4], float (*mat2)[4]); GB_MATH_DEF void gb_float44_mul_vec4(gbVec4 *out, float m[4][4], gbVec4 in); GB_MATH_DEF void gb_mat4_translate(gbMat4 *out, gbVec3 v); GB_MATH_DEF void gb_mat4_rotate(gbMat4 *out, gbVec3 v, float angle_radians); GB_MATH_DEF void gb_mat4_scale(gbMat4 *out, gbVec3 v); GB_MATH_DEF void gb_mat4_scalef(gbMat4 *out, float s); GB_MATH_DEF void gb_mat4_ortho2d(gbMat4 *out, float left, float right, float bottom, float top); GB_MATH_DEF void gb_mat4_ortho3d(gbMat4 *out, float left, float right, float bottom, float top, float z_near, float z_far); GB_MATH_DEF void gb_mat4_perspective(gbMat4 *out, float fovy, float aspect, float z_near, float z_far); GB_MATH_DEF void gb_mat4_infinite_perspective(gbMat4 *out, float fovy, float aspect, float z_near); GB_MATH_DEF void gb_mat4_look_at(gbMat4 *out, gbVec3 eye, gbVec3 centre, gbVec3 up); GB_MATH_DEF gbQuat gb_quat(float x, float y, float z, float w); GB_MATH_DEF gbQuat gb_quatv(float e[4]); GB_MATH_DEF gbQuat gb_quat_axis_angle(gbVec3 axis, float angle_radians); GB_MATH_DEF gbQuat gb_quat_euler_angles(float pitch, float yaw, float roll); GB_MATH_DEF gbQuat gb_quat_identity(void); GB_MATH_DEF void gb_quat_add(gbQuat *d, gbQuat q0, gbQuat q1); GB_MATH_DEF void gb_quat_sub(gbQuat *d, gbQuat q0, gbQuat q1); GB_MATH_DEF void gb_quat_mul(gbQuat *d, gbQuat q0, gbQuat q1); GB_MATH_DEF void gb_quat_div(gbQuat *d, gbQuat q0, gbQuat q1); GB_MATH_DEF void gb_quat_mulf(gbQuat *d, gbQuat q, float s); GB_MATH_DEF void gb_quat_divf(gbQuat *d, gbQuat q, float s); GB_MATH_DEF void gb_quat_addeq(gbQuat *d, gbQuat q); GB_MATH_DEF void gb_quat_subeq(gbQuat *d, gbQuat q); GB_MATH_DEF void gb_quat_muleq(gbQuat *d, gbQuat q); GB_MATH_DEF void gb_quat_diveq(gbQuat *d, gbQuat q); GB_MATH_DEF void gb_quat_muleqf(gbQuat *d, float s); GB_MATH_DEF void gb_quat_diveqf(gbQuat *d, float s); GB_MATH_DEF float gb_quat_dot(gbQuat q0, gbQuat q1); GB_MATH_DEF float gb_quat_mag(gbQuat q); GB_MATH_DEF void gb_quat_norm(gbQuat *d, gbQuat q); GB_MATH_DEF void gb_quat_conj(gbQuat *d, gbQuat q); GB_MATH_DEF void gb_quat_inverse(gbQuat *d, gbQuat q); GB_MATH_DEF void gb_quat_axis(gbVec3 *axis, gbQuat q); GB_MATH_DEF float gb_quat_angle(gbQuat q); GB_MATH_DEF float gb_quat_pitch(gbQuat q); GB_MATH_DEF float gb_quat_yaw(gbQuat q); GB_MATH_DEF float gb_quat_roll(gbQuat q); /* NOTE(bill): Rotate v by q */ GB_MATH_DEF void gb_quat_rotate_vec3(gbVec3 *d, gbQuat q, gbVec3 v); GB_MATH_DEF void gb_mat4_from_quat(gbMat4 *out, gbQuat q); GB_MATH_DEF void gb_quat_from_mat4(gbQuat *out, gbMat4 *m); /* Interpolations */ GB_MATH_DEF float gb_lerp(float a, float b, float t); GB_MATH_DEF float gb_smooth_step(float a, float b, float t); GB_MATH_DEF float gb_smoother_step(float a, float b, float t); GB_MATH_DEF void gb_vec2_lerp(gbVec2 *d, gbVec2 a, gbVec2 b, float t); GB_MATH_DEF void gb_vec3_lerp(gbVec3 *d, gbVec3 a, gbVec3 b, float t); GB_MATH_DEF void gb_vec4_lerp(gbVec4 *d, gbVec4 a, gbVec4 b, float t); GB_MATH_DEF void gb_quat_lerp(gbQuat *d, gbQuat a, gbQuat b, float t); GB_MATH_DEF void gb_quat_nlerp(gbQuat *d, gbQuat a, gbQuat b, float t); GB_MATH_DEF void gb_quat_slerp(gbQuat *d, gbQuat a, gbQuat b, float t); GB_MATH_DEF void gb_quat_slerp_approx(gbQuat *d, gbQuat a, gbQuat b, float t); GB_MATH_DEF void gb_quat_nquad(gbQuat *d, gbQuat p, gbQuat a, gbQuat b, gbQuat q, float t); GB_MATH_DEF void gb_quat_squad(gbQuat *d, gbQuat p, gbQuat a, gbQuat b, gbQuat q, float t); GB_MATH_DEF void gb_quat_squad_approx(gbQuat *d, gbQuat p, gbQuat a, gbQuat b, gbQuat q, float t); /* Rects */ GB_MATH_DEF gbRect2 gb_rect2(gbVec2 pos, gbVec2 dim); GB_MATH_DEF gbRect3 gb_rect3(gbVec3 pos, gbVec3 dim); GB_MATH_DEF int gb_rect2_contains(gbRect2 a, float x, float y); GB_MATH_DEF int gb_rect2_contains_vec2(gbRect2 a, gbVec2 p); GB_MATH_DEF int gb_rect2_intersects(gbRect2 a, gbRect2 b); GB_MATH_DEF int gb_rect2_intersection_result(gbRect2 a, gbRect2 b, gbRect2 *intersection); #ifndef GB_MURMUR64_DEFAULT_SEED #define GB_MURMUR64_DEFAULT_SEED 0x9747b28c #endif /* Hashing */ GB_MATH_DEF gb_math_u64 gb_hash_murmur64(void const *key, size_t num_bytes, gb_math_u64 seed); /* Random */ /* TODO(bill): Use a generator for the random numbers */ GB_MATH_DEF float gb_random_range_float(float min_inc, float max_inc); GB_MATH_DEF int gb_random_range_int(int min_inc, int max_inc); #if defined(__cplusplus) } #endif #if defined(__cplusplus) && defined(GB_MATH_USE_OPERATOR_OVERLOADS) bool operator==(gbVec2 a, gbVec2 b) { return (a.x == b.x) && (a.y == b.y); } bool operator!=(gbVec2 a, gbVec2 b) { return !operator==(a, b); } gbVec2 operator+(gbVec2 a) { return a; } gbVec2 operator-(gbVec2 a) { gbVec2 r = {-a.x, -a.y}; return r; } gbVec2 operator+(gbVec2 a, gbVec2 b) { gbVec2 r; gb_vec2_add(&r, a, b); return r; } gbVec2 operator-(gbVec2 a, gbVec2 b) { gbVec2 r; gb_vec2_sub(&r, a, b); return r; } gbVec2 operator*(gbVec2 a, float scalar) { gbVec2 r; gb_vec2_mul(&r, a, scalar); return r; } gbVec2 operator*(float scalar, gbVec2 a) { return operator*(a, scalar); } gbVec2 operator/(gbVec2 a, float scalar) { return operator*(a, 1.0f/scalar); } /* Hadamard Product */ gbVec2 operator*(gbVec2 a, gbVec2 b) { gbVec2 r = {a.x*b.x, a.y*b.y}; return r; } gbVec2 operator/(gbVec2 a, gbVec2 b) { gbVec2 r = {a.x/b.x, a.y/b.y}; return r; } gbVec2 &operator+=(gbVec2 &a, gbVec2 b) { return (a = a + b); } gbVec2 &operator-=(gbVec2 &a, gbVec2 b) { return (a = a - b); } gbVec2 &operator*=(gbVec2 &a, float scalar) { return (a = a * scalar); } gbVec2 &operator/=(gbVec2 &a, float scalar) { return (a = a / scalar); } bool operator==(gbVec3 a, gbVec3 b) { return (a.x == b.x) && (a.y == b.y) && (a.z == b.z); } bool operator!=(gbVec3 a, gbVec3 b) { return !operator==(a, b); } gbVec3 operator+(gbVec3 a) { return a; } gbVec3 operator-(gbVec3 a) { gbVec3 r = {-a.x, -a.y, -a.z}; return r; } gbVec3 operator+(gbVec3 a, gbVec3 b) { gbVec3 r; gb_vec3_add(&r, a, b); return r; } gbVec3 operator-(gbVec3 a, gbVec3 b) { gbVec3 r; gb_vec3_sub(&r, a, b); return r; } gbVec3 operator*(gbVec3 a, float scalar) { gbVec3 r; gb_vec3_mul(&r, a, scalar); return r; } gbVec3 operator*(float scalar, gbVec3 a) { return operator*(a, scalar); } gbVec3 operator/(gbVec3 a, float scalar) { return operator*(a, 1.0f/scalar); } /* Hadamard Product */ gbVec3 operator*(gbVec3 a, gbVec3 b) { gbVec3 r = {a.x*b.x, a.y*b.y, a.z*b.z}; return r; } gbVec3 operator/(gbVec3 a, gbVec3 b) { gbVec3 r = {a.x/b.x, a.y/b.y, a.z/b.z}; return r; } gbVec3 &operator+=(gbVec3 &a, gbVec3 b) { return (a = a + b); } gbVec3 &operator-=(gbVec3 &a, gbVec3 b) { return (a = a - b); } gbVec3 &operator*=(gbVec3 &a, float scalar) { return (a = a * scalar); } gbVec3 &operator/=(gbVec3 &a, float scalar) { return (a = a / scalar); } bool operator==(gbVec4 a, gbVec4 b) { return (a.x == b.x) && (a.y == b.y) && (a.z == b.z) && (a.w == b.w); } bool operator!=(gbVec4 a, gbVec4 b) { return !operator==(a, b); } gbVec4 operator+(gbVec4 a) { return a; } gbVec4 operator-(gbVec4 a) { gbVec4 r = {-a.x, -a.y, -a.z, -a.w}; return r; } gbVec4 operator+(gbVec4 a, gbVec4 b) { gbVec4 r; gb_vec4_add(&r, a, b); return r; } gbVec4 operator-(gbVec4 a, gbVec4 b) { gbVec4 r; gb_vec4_sub(&r, a, b); return r; } gbVec4 operator*(gbVec4 a, float scalar) { gbVec4 r; gb_vec4_mul(&r, a, scalar); return r; } gbVec4 operator*(float scalar, gbVec4 a) { return operator*(a, scalar); } gbVec4 operator/(gbVec4 a, float scalar) { return operator*(a, 1.0f/scalar); } /* Hadamard Product */ gbVec4 operator*(gbVec4 a, gbVec4 b) { gbVec4 r = {a.x*b.x, a.y*b.y, a.z*b.z, a.w*b.w}; return r; } gbVec4 operator/(gbVec4 a, gbVec4 b) { gbVec4 r = {a.x/b.x, a.y/b.y, a.z/b.z, a.w/b.w}; return r; } gbVec4 &operator+=(gbVec4 &a, gbVec4 b) { return (a = a + b); } gbVec4 &operator-=(gbVec4 &a, gbVec4 b) { return (a = a - b); } gbVec4 &operator*=(gbVec4 &a, float scalar) { return (a = a * scalar); } gbVec4 &operator/=(gbVec4 &a, float scalar) { return (a = a / scalar); } gbMat2 operator+(gbMat2 const &a, gbMat2 const &b) { int i, j; gbMat2 r = {0}; for (j = 0; j < 2; j++) { for (i = 0; i < 2; i++) r.e[2*j+i] = a.e[2*j+i] + b.e[2*j+i]; } return r; } gbMat2 operator-(gbMat2 const &a, gbMat2 const &b) { int i, j; gbMat2 r = {0}; for (j = 0; j < 2; j++) { for (i = 0; i < 2; i++) r.e[2*j+i] = a.e[2*j+i] - b.e[2*j+i]; } return r; } gbMat2 operator*(gbMat2 const &a, gbMat2 const &b) { gbMat2 r; gb_mat2_mul(&r, (gbMat2 *)&a, (gbMat2 *)&b); return r; } gbVec2 operator*(gbMat2 const &a, gbVec2 v) { gbVec2 r; gb_mat2_mul_vec2(&r, (gbMat2 *)&a, v); return r; } gbMat2 operator*(gbMat2 const &a, float scalar) { gbMat2 r = {0}; int i; for (i = 0; i < 2*2; i++) r.e[i] = a.e[i] * scalar; return r; } gbMat2 operator*(float scalar, gbMat2 const &a) { return operator*(a, scalar); } gbMat2 operator/(gbMat2 const &a, float scalar) { return operator*(a, 1.0f/scalar); } gbMat2& operator+=(gbMat2& a, gbMat2 const &b) { return (a = a + b); } gbMat2& operator-=(gbMat2& a, gbMat2 const &b) { return (a = a - b); } gbMat2& operator*=(gbMat2& a, gbMat2 const &b) { return (a = a * b); } gbMat3 operator+(gbMat3 const &a, gbMat3 const &b) { int i, j; gbMat3 r = {0}; for (j = 0; j < 3; j++) { for (i = 0; i < 3; i++) r.e[3*j+i] = a.e[3*j+i] + b.e[3*j+i]; } return r; } gbMat3 operator-(gbMat3 const &a, gbMat3 const &b) { int i, j; gbMat3 r = {0}; for (j = 0; j < 3; j++) { for (i = 0; i < 3; i++) r.e[3*j+i] = a.e[3*j+i] - b.e[3*j+i]; } return r; } gbMat3 operator*(gbMat3 const &a, gbMat3 const &b) { gbMat3 r; gb_mat3_mul(&r, (gbMat3 *)&a, (gbMat3 *)&b); return r; } gbVec3 operator*(gbMat3 const &a, gbVec3 v) { gbVec3 r; gb_mat3_mul_vec3(&r, (gbMat3 *)&a, v); return r; } gbMat3 operator*(gbMat3 const &a, float scalar) { gbMat3 r = {0}; int i; for (i = 0; i < 3*3; i++) r.e[i] = a.e[i] * scalar; return r; } gbMat3 operator*(float scalar, gbMat3 const &a) { return operator*(a, scalar); } gbMat3 operator/(gbMat3 const &a, float scalar) { return operator*(a, 1.0f/scalar); } gbMat3& operator+=(gbMat3& a, gbMat3 const &b) { return (a = a + b); } gbMat3& operator-=(gbMat3& a, gbMat3 const &b) { return (a = a - b); } gbMat3& operator*=(gbMat3& a, gbMat3 const &b) { return (a = a * b); } gbMat4 operator+(gbMat4 const &a, gbMat4 const &b) { int i, j; gbMat4 r = {0}; for (j = 0; j < 4; j++) { for (i = 0; i < 4; i++) r.e[4*j+i] = a.e[4*j+i] + b.e[4*j+i]; } return r; } gbMat4 operator-(gbMat4 const &a, gbMat4 const &b) { int i, j; gbMat4 r = {0}; for (j = 0; j < 4; j++) { for (i = 0; i < 4; i++) r.e[4*j+i] = a.e[4*j+i] - b.e[4*j+i]; } return r; } gbMat4 operator*(gbMat4 const &a, gbMat4 const &b) { gbMat4 r; gb_mat4_mul(&r, (gbMat4 *)&a, (gbMat4 *)&b); return r; } gbVec4 operator*(gbMat4 const &a, gbVec4 v) { gbVec4 r; gb_mat4_mul_vec4(&r, (gbMat4 *)&a, v); return r; } gbMat4 operator*(gbMat4 const &a, float scalar) { gbMat4 r = {0}; int i; for (i = 0; i < 4*4; i++) r.e[i] = a.e[i] * scalar; return r; } gbMat4 operator*(float scalar, gbMat4 const &a) { return operator*(a, scalar); } gbMat4 operator/(gbMat4 const &a, float scalar) { return operator*(a, 1.0f/scalar); } gbMat4& operator+=(gbMat4 &a, gbMat4 const &b) { return (a = a + b); } gbMat4& operator-=(gbMat4 &a, gbMat4 const &b) { return (a = a - b); } gbMat4& operator*=(gbMat4 &a, gbMat4 const &b) { return (a = a * b); } bool operator==(gbQuat a, gbQuat b) { return a.xyzw == b.xyzw; } bool operator!=(gbQuat a, gbQuat b) { return !operator==(a, b); } gbQuat operator+(gbQuat q) { return q; } gbQuat operator-(gbQuat q) { return gb_quat(-q.x, -q.y, -q.z, -q.w); } gbQuat operator+(gbQuat a, gbQuat b) { gbQuat r; gb_quat_add(&r, a, b); return r; } gbQuat operator-(gbQuat a, gbQuat b) { gbQuat r; gb_quat_sub(&r, a, b); return r; } gbQuat operator*(gbQuat a, gbQuat b) { gbQuat r; gb_quat_mul(&r, a, b); return r; } gbQuat operator*(gbQuat q, float s) { gbQuat r; gb_quat_mulf(&r, q, s); return r; } gbQuat operator*(float s, gbQuat q) { return operator*(q, s); } gbQuat operator/(gbQuat q, float s) { gbQuat r; gb_quat_divf(&r, q, s); return r; } gbQuat &operator+=(gbQuat &a, gbQuat b) { gb_quat_addeq(&a, b); return a; } gbQuat &operator-=(gbQuat &a, gbQuat b) { gb_quat_subeq(&a, b); return a; } gbQuat &operator*=(gbQuat &a, gbQuat b) { gb_quat_muleq(&a, b); return a; } gbQuat &operator/=(gbQuat &a, gbQuat b) { gb_quat_diveq(&a, b); return a; } gbQuat &operator*=(gbQuat &a, float b) { gb_quat_muleqf(&a, b); return a; } gbQuat &operator/=(gbQuat &a, float b) { gb_quat_diveqf(&a, b); return a; } /* Rotate v by a */ gbVec3 operator*(gbQuat q, gbVec3 v) { gbVec3 r; gb_quat_rotate_vec3(&r, q, v); return r; } #endif #endif /* GB_MATH_INCLUDE_GB_MATH_H */ /**************************************************************** * * * * * * * * * * * * * * * * * * Implementation * * * * * * * * * * * * * * * * /****************************************************************/ #if defined(GB_MATH_IMPLEMENTATION) && !defined(GB_MATH_IMPLEMENTATION_DONE) #define GB_MATH_IMPLEMENTATION_DONE static void gb__memcpy_4byte(void *dest, void const *src, size_t size) { size_t i; unsigned int *d, *s; d = (unsigned int *)dest; s = (unsigned int *)src; for (i = 0; i < size/4; i++) { *d++ = *s++; } } static void gb__memzero_byte4(void *dest, size_t size) { int *d = (int *)dest; int i; for (i = 0; i < size/4; i++) *d++ = 0; } float gb_to_radians(float degrees) { return degrees * GB_MATH_TAU / 360.0f; } float gb_to_degrees(float radians) { return radians * 360.0f / GB_MATH_TAU; } float gb_angle_diff(float radians_a, float radians_b) { float delta = gb_mod(radians_b-radians_a, GB_MATH_TAU); delta = gb_mod(delta + 1.5f*GB_MATH_TAU, GB_MATH_TAU); delta -= 0.5f*GB_MATH_TAU; return delta; } float gb_copy_sign(float x, float y) { int ix, iy; ix = *(int *)&x; iy = *(int *)&y; ix &= 0x7fffffff; ix |= iy & 0x80000000; return *(float *)ix; } float gb_remainder(float x, float y) { return x - (gb_round(x/y)*y); } float gb_mod(float x, float y) { float result; y = gb_abs(y); result = gb_remainder(gb_abs(x), (y = gb_abs(y))); if (gb_sign(result)) result += y; return gb_copy_sign(result, x); } float gb_quake_rsqrt(float a) { union { int i; float f; } t; float x2; float const three_halfs = 1.5f; x2 = a * 0.5f; t.f = a; t.i = 0x5f375a86 - (t.i >> 1); /* What the fuck? */ t.f = t.f * (three_halfs - (x2 * t.f * t.f)); /* 1st iteration */ t.f = t.f * (three_halfs - (x2 * t.f * t.f)); /* 2nd iteration, this can be removed */ return t.f; } #if defined(GB_MATH_NO_MATH_H) #if defined(_MSC_VER) float gb_rsqrt(float a) { return _mm_cvtss_f32(_mm_rsqrt_ss(_mm_set_ss(a))); } float gb_sqrt(float a) { return _mm_cvtss_f32(_mm_sqrt_ss(_mm_set_ss(a))); }; float gb_sin(float a) { static float const a0 = +1.91059300966915117e-31f; static float const a1 = +1.00086760103908896f; static float const a2 = -1.21276126894734565e-2f; static float const a3 = -1.38078780785773762e-1f; static float const a4 = -2.67353392911981221e-2f; static float const a5 = +2.08026600266304389e-2f; static float const a6 = -3.03996055049204407e-3f; static float const a7 = +1.38235642404333740e-4f; return a0 + a*(a1 + a*(a2 + a*(a3 + a*(a4 + a*(a5 + a*(a6 + a*a7)))))); } float gb_cos(float a) { static float const a0 = +1.00238601909309722f; static float const a1 = -3.81919947353040024e-2f; static float const a2 = -3.94382342128062756e-1f; static float const a3 = -1.18134036025221444e-1f; static float const a4 = +1.07123798512170878e-1f; static float const a5 = -1.86637164165180873e-2f; static float const a6 = +9.90140908664079833e-4f; static float const a7 = -5.23022132118824778e-14f; return a0 + a*(a1 + a*(a2 + a*(a3 + a*(a4 + a*(a5 + a*(a6 + a*a7)))))); } float gb_tan(float radians) { float rr = radians*radians; float a = 9.5168091e-03f; a *= rr; a += 2.900525e-03f; a *= rr; a += 2.45650893e-02f; a *= rr; a += 5.33740603e-02f; a *= rr; a += 1.333923995e-01f; a *= rr; a += 3.333314036e-01f; a *= rr; a += 1.0f; a *= radians; return a; } float gb_arcsin(float a) { return gb_arctan2(a, gb_sqrt((1.0f + a) * (1.0f - a))); } float gb_arccos(float a) { return gb_arctan2(gb_sqrt((1.0f + a) * (1.0 - a)), a); } float gb_arctan(float a) { float u = a*a; float u2 = u*u; float u3 = u2*u; float u4 = u3*u; float f = 1.0f+0.33288950512027f*u-0.08467922817644f*u2+0.03252232640125f*u3-0.00749305860992f*u4; return a/f; } float gb_arctan2(float y, float x) { if (gb_abs(x) > gb_abs(y)) { float a = gb_arctan(y/x); if (x > 0.0f) return a; else return y > 0.0f ? a+GB_MATH_TAU_OVER_2:a-GB_MATH_TAU_OVER_2; } else { float a = gb_arctan(x/y); if (x > 0.0f) return y > 0.0f ? GB_MATH_TAU_OVER_4-a:-GB_MATH_TAU_OVER_4-a; else return y > 0.0f ? GB_MATH_TAU_OVER_4+a:-GB_MATH_TAU_OVER_4+a; } } float gb_exp(float a) { union { float f; int i; } u, v; u.i = (int)(6051102 * a + 1056478197); v.i = (int)(1056478197 - 6051102 * a); return u.f / v.f; } float gb_log(float a) { union { float f; int i; } u = {a}; return (u.i - 1064866805) * 8.262958405176314e-8f; /* 1 / 12102203.0; */ } float gb_pow(float a, float b) { int flipped = 0, e; float f, r = 1.0f; if (b < 0) { flipped = 1; b = -b; } e = (int)b; f = gb_exp(b - e); while (e) { if (e & 1) r *= a; a *= a; e >>= 1; } r *= f; return flipped ? 1.0f/r : r; } #else float gb_rsqrt(float a) { return 1.0f/__builtin_sqrt(a); } float gb_sqrt(float a) { return __builtin_sqrt(a); } float gb_sin(float radians) { return __builtin_sinf(radians); } float gb_cos(float radians) { return __builtin_cosf(radians); } float gb_tan(float radians) { return __builtin_tanf(radians); } float gb_arcsin(float a) { return __builtin_asinf(a); } float gb_arccos(float a) { return __builtin_acosf(a); } float gb_arctan(float a) { return __builtin_atanf(a); } float gb_arctan2(float y, float x) { return __builtin_atan2f(y, x); } float gb_exp(float x) { return __builtin_expf(x); } float gb_log(float x) { return __builtin_logf(x); } // TODO(bill): Should this be gb_exp(y * gb_log(x)) ??? float gb_pow(float x, float y) { return __builtin_powf(x, y); } #endif #else float gb_rsqrt(float a) { return 1.0f/sqrtf(a); } float gb_sqrt(float a) { return sqrtf(a); }; float gb_sin(float radians) { return sinf(radians); }; float gb_cos(float radians) { return cosf(radians); }; float gb_tan(float radians) { return tanf(radians); }; float gb_arcsin(float a) { return asinf(a); }; float gb_arccos(float a) { return acosf(a); }; float gb_arctan(float a) { return atanf(a); }; float gb_arctan2(float y, float x) { return atan2f(y, x); }; float gb_exp(float x) { return expf(x); } float gb_log(float x) { return logf(x); } float gb_pow(float x, float y) { return powf(x, y); } #endif float gb_exp2(float x) { return gb_exp(GB_MATH_LOG_TWO * x); } float gb_log2(float x) { return gb_log(x) / GB_MATH_LOG_TWO; } float gb_fast_exp(float x) { /* NOTE(bill): Only works in the range -1 <= x <= +1 */ float e = 1.0f + x*(1.0f + x*0.5f*(1.0f + x*0.3333333333f*(1.0f + x*0.25*(1.0f + x*0.2f)))); return e; } float gb_fast_exp2(float x) { return gb_fast_exp(GB_MATH_LOG_TWO * x); } float gb_round(float x) { return (x >= 0.0f) ? gb_floor(x + 0.5f) : gb_ceil(x - 0.5f); } float gb_floor(float x) { return (x >= 0.0f) ? (int)x : (int)(x-0.9999999999999999f); } float gb_ceil(float x) { return (x < 0) ? (int)x : ((int)x)+1; } typedef union { unsigned int i; float f; } gb_uif32; float gb_half_to_float(gbHalf value) { gb_uif32 result; int s = (value >> 15) & 0x001; int e = (value >> 10) & 0x01f; int m = value & 0x3ff; if (e == 0) { if (m == 0) { /* Plus or minus zero */ result.i = (unsigned int)(s << 31); return result.f; } else { /* Denormalized number */ while (!(m & 0x00000400)) { m <<= 1; e -= 1; } e += 1; m &= ~0x00000400; } } else if (e == 31) { if (m == 0) { /* Positive or negative infinity */ result.i = (unsigned int)((s << 31) | 0x7f800000); return result.f; } else { /* Nan */ result.i = (unsigned int)((s << 31) | 0x7f800000 | (m << 13)); return result.f; } } e = e + (127 - 15); m = m << 13; result.i = (unsigned int)((s << 31) | (e << 23) | m); return result.f; } gbHalf gb_float_to_half(float value) { gb_uif32 v; int i, s, e, m; v.f = value; i = (int)v.i; s = (i >> 16) & 0x00008000; e = ((i >> 23) & 0x000000ff) - (127 - 15); m = i & 0x007fffff; if (e <= 0) { if (e < -10) return (gbHalf)s; m = (m | 0x00800000) >> (1 - e); if (m & 0x00001000) m += 0x00002000; return (gbHalf)(s | (m >> 13)); } else if (e == 0xff - (127 - 15)) { if (m == 0) { return (gbHalf)(s | 0x7c00); /* NOTE(bill): infinity */ } else { /* NOTE(bill): NAN */ m >>= 13; return (gbHalf)(s | 0x7c00 | m | (m == 0)); } } else { if (m & 0x00001000) { m += 0x00002000; if (m & 0x00800000) { m = 0; e += 1; } } if (e > 30) { float volatile f = 1e12f; int j; for (j = 0; j < 10; j++) f *= f; /* NOTE(bill): Cause overflow */ return (gbHalf)(s | 0x7c00); } return (gbHalf)(s | (e << 10) | (m >> 13)); } } #define GB_VEC2_2OP(a,c,post) \ a->x = c.x post; \ a->y = c.y post; #define GB_VEC2_3OP(a,b,op,c,post) \ a->x = b.x op c.x post; \ a->y = b.y op c.y post; #define GB_VEC3_2OP(a,c,post) \ a->x = c.x post; \ a->y = c.y post; \ a->z = c.z post; #define GB_VEC3_3OP(a,b,op,c,post) \ a->x = b.x op c.x post; \ a->y = b.y op c.y post; \ a->z = b.z op c.z post; #define GB_VEC4_2OP(a,c,post) \ a->x = c.x post; \ a->y = c.y post; \ a->z = c.z post; \ a->w = c.w post; #define GB_VEC4_3OP(a,b,op,c,post) \ a->x = b.x op c.x post; \ a->y = b.y op c.y post; \ a->z = b.z op c.z post; \ a->w = b.w op c.w post; gbVec2 gb_vec2_zero(void) { gbVec2 v = {0, 0}; return v; } gbVec2 gb_vec2(float x, float y) { gbVec2 v = {x, y}; return v; } gbVec2 gb_vec2v(float x[2]) { gbVec2 v = {x[0], x[1]}; return v; } gbVec3 gb_vec3_zero(void) { gbVec3 v = {0, 0, 0}; return v; } gbVec3 gb_vec3(float x, float y, float z) { gbVec3 v = {x, y, z}; return v; } gbVec3 gb_vec3v(float x[3]) { gbVec3 v = {x[0], x[1], x[2]}; return v; } gbVec4 gb_vec4_zero(void) { gbVec4 v = {0, 0, 0, 0}; return v; } gbVec4 gb_vec4(float x, float y, float z, float w) { gbVec4 v = {x, y, z, w}; return v; } gbVec4 gb_vec4v(float x[4]) { gbVec4 v = {x[0], x[1], x[2], x[3]}; return v; } void gb_vec2_add(gbVec2 *d, gbVec2 v0, gbVec2 v1) { GB_VEC2_3OP(d,v0,+,v1,+0); } void gb_vec2_sub(gbVec2 *d, gbVec2 v0, gbVec2 v1) { GB_VEC2_3OP(d,v0,-,v1,+0); } void gb_vec2_mul(gbVec2 *d, gbVec2 v, float s) { GB_VEC2_2OP(d,v,* s); } void gb_vec2_div(gbVec2 *d, gbVec2 v, float s) { GB_VEC2_2OP(d,v,/ s); } void gb_vec3_add(gbVec3 *d, gbVec3 v0, gbVec3 v1) { GB_VEC3_3OP(d,v0,+,v1,+0); } void gb_vec3_sub(gbVec3 *d, gbVec3 v0, gbVec3 v1) { GB_VEC3_3OP(d,v0,-,v1,+0); } void gb_vec3_mul(gbVec3 *d, gbVec3 v, float s) { GB_VEC3_2OP(d,v,* s); } void gb_vec3_div(gbVec3 *d, gbVec3 v, float s) { GB_VEC3_2OP(d,v,/ s); } void gb_vec4_add(gbVec4 *d, gbVec4 v0, gbVec4 v1) { GB_VEC4_3OP(d,v0,+,v1,+0); } void gb_vec4_sub(gbVec4 *d, gbVec4 v0, gbVec4 v1) { GB_VEC4_3OP(d,v0,-,v1,+0); } void gb_vec4_mul(gbVec4 *d, gbVec4 v, float s) { GB_VEC4_2OP(d,v,* s); } void gb_vec4_div(gbVec4 *d, gbVec4 v, float s) { GB_VEC4_2OP(d,v,/ s); } void gb_vec2_addeq(gbVec2 *d, gbVec2 v) { GB_VEC2_3OP(d,(*d),+,v,+0); } void gb_vec2_subeq(gbVec2 *d, gbVec2 v) { GB_VEC2_3OP(d,(*d),-,v,+0); } void gb_vec2_muleq(gbVec2 *d, float s) { GB_VEC2_2OP(d,(*d),* s); } void gb_vec2_diveq(gbVec2 *d, float s) { GB_VEC2_2OP(d,(*d),/ s); } void gb_vec3_addeq(gbVec3 *d, gbVec3 v) { GB_VEC3_3OP(d,(*d),+,v,+0); } void gb_vec3_subeq(gbVec3 *d, gbVec3 v) { GB_VEC3_3OP(d,(*d),-,v,+0); } void gb_vec3_muleq(gbVec3 *d, float s) { GB_VEC3_2OP(d,(*d),* s); } void gb_vec3_diveq(gbVec3 *d, float s) { GB_VEC3_2OP(d,(*d),/ s); } void gb_vec4_addeq(gbVec4 *d, gbVec4 v) { GB_VEC4_3OP(d,(*d),+,v,+0); } void gb_vec4_subeq(gbVec4 *d, gbVec4 v) { GB_VEC4_3OP(d,(*d),-,v,+0); } void gb_vec4_muleq(gbVec4 *d, float s) { GB_VEC4_2OP(d,(*d),* s); } void gb_vec4_diveq(gbVec4 *d, float s) { GB_VEC4_2OP(d,(*d),/ s); } #undef GB_VEC2_2OP #undef GB_VEC2_3OP #undef GB_VEC3_3OP #undef GB_VEC3_2OP #undef GB_VEC4_2OP #undef GB_VEC4_3OP float gb_vec2_dot(gbVec2 v0, gbVec2 v1) { return v0.x*v1.x + v0.y*v1.y; } float gb_vec3_dot(gbVec3 v0, gbVec3 v1) { return v0.x*v1.x + v0.y*v1.y + v0.z*v1.z; } float gb_vec4_dot(gbVec4 v0, gbVec4 v1) { return v0.x*v1.x + v0.y*v1.y + v0.z*v1.z + v0.w*v1.w; } void gb_vec2_cross(float *d, gbVec2 v0, gbVec2 v1) { *d = v0.x*v1.y - v1.x*v0.y; } void gb_vec3_cross(gbVec3 *d, gbVec3 v0, gbVec3 v1) { d->x = v0.y*v1.z - v0.z*v1.y; d->y = v0.z*v1.x - v0.x*v1.z; d->z = v0.x*v1.y - v0.y*v1.x; } float gb_vec2_mag2(gbVec2 v) { return gb_vec2_dot(v, v); } float gb_vec3_mag2(gbVec3 v) { return gb_vec3_dot(v, v); } float gb_vec4_mag2(gbVec4 v) { return gb_vec4_dot(v, v); } /* TODO(bill): Create custom sqrt function */ float gb_vec2_mag(gbVec2 v) { return gb_sqrt(gb_vec2_dot(v, v)); } float gb_vec3_mag(gbVec3 v) { return gb_sqrt(gb_vec3_dot(v, v)); } float gb_vec4_mag(gbVec4 v) { return gb_sqrt(gb_vec4_dot(v, v)); } void gb_vec2_norm(gbVec2 *d, gbVec2 v) { float inv_mag = gb_rsqrt(gb_vec2_dot(v, v)); gb_vec2_mul(d, v, inv_mag); } void gb_vec3_norm(gbVec3 *d, gbVec3 v) { float mag = gb_vec3_mag(v); gb_vec3_div(d, v, mag); } void gb_vec4_norm(gbVec4 *d, gbVec4 v) { float mag = gb_vec4_mag(v); gb_vec4_div(d, v, mag); } void gb_vec2_norm0(gbVec2 *d, gbVec2 v) { float mag = gb_vec2_mag(v); if (mag > 0) gb_vec2_div(d, v, mag); else *d = gb_vec2_zero(); } void gb_vec3_norm0(gbVec3 *d, gbVec3 v) { float mag = gb_vec3_mag(v); if (mag > 0) gb_vec3_div(d, v, mag); else *d = gb_vec3_zero(); } void gb_vec4_norm0(gbVec4 *d, gbVec4 v) { float mag = gb_vec4_mag(v); if (mag > 0) gb_vec4_div(d, v, mag); else *d = gb_vec4_zero(); } void gb_vec2_reflect(gbVec2 *d, gbVec2 i, gbVec2 n) { gbVec2 b = n; gb_vec2_muleq(&b, 2.0f*gb_vec2_dot(n, i)); gb_vec2_sub(d, i, b); } void gb_vec3_reflect(gbVec3 *d, gbVec3 i, gbVec3 n) { gbVec3 b = n; gb_vec3_muleq(&b, 2.0f*gb_vec3_dot(n, i)); gb_vec3_sub(d, i, b); } void gb_vec2_refract(gbVec2 *d, gbVec2 i, gbVec2 n, float eta) { gbVec2 a, b; float dv, k; dv = gb_vec2_dot(n, i); k = 1.0f - eta*eta * (1.0f - dv*dv); gb_vec2_mul(&a, i, eta); gb_vec2_mul(&b, n, eta*dv*gb_sqrt(k)); gb_vec2_sub(d, a, b); gb_vec2_muleq(d, (float)(k >= 0.0f)); } void gb_vec3_refract(gbVec3 *d, gbVec3 i, gbVec3 n, float eta) { gbVec3 a, b; float dv, k; dv = gb_vec3_dot(n, i); k = 1.0f - eta*eta * (1.0f - dv*dv); gb_vec3_mul(&a, i, eta); gb_vec3_mul(&b, n, eta*dv*gb_sqrt(k)); gb_vec3_sub(d, a, b); gb_vec3_muleq(d, (float)(k >= 0.0f)); } float gb_vec2_aspect_ratio(gbVec2 v) { return (v.y < 0.0001f) ? 0.0f : v.x/v.y; } void gb_mat2_transpose(gbMat2 *m) { gb_float22_transpose(gb_float22_m(m)); } void gb_mat2_identity(gbMat2 *m) { gb_float22_identity(gb_float22_m(m)); } void gb_mat2_mul(gbMat2 *out, gbMat2 *m1, gbMat2 *m2) { gb_float22_mul(gb_float22_m(out), gb_float22_m(m1), gb_float22_m(m2)); } void gb_float22_identity(float m[2][2]) { m[0][0] = 1; m[0][1] = 0; m[1][0] = 0; m[1][1] = 1; } void gb_mat2_mul_vec2(gbVec2 *out, gbMat2 *m, gbVec2 in) { gb_float22_mul_vec2(out, gb_float22_m(m), in); } gbMat2 *gb_mat2_v(gbVec2 m[2]) { return (gbMat2 *)m; } gbMat2 *gb_mat2_f(float m[2][2]) { return (gbMat2 *)m; } gbFloat2 *gb_float22_m(gbMat2 *m) { return (gbFloat2 *)m; } gbFloat2 *gb_float22_v(gbVec2 m[2]) { return (gbFloat2 *)m; } gbFloat2 *gb_float22_4(float m[4]) { return (gbFloat2 *)m; } void gb_float22_transpose(float (*vec)[2]) { int i, j; for (j = 0; j < 2; j++) { for (i = j + 1; i < 2; i++) { float t = vec[i][j]; vec[i][j] = vec[j][i]; vec[j][i] = t; } } } void gb_float22_mul(float (*out)[2], float (*mat1)[2], float (*mat2)[2]) { int i, j; float temp1[2][2], temp2[2][2]; if (mat1 == out) { gb__memcpy_4byte(temp1, mat1, sizeof(temp1)); mat1 = temp1; } if (mat2 == out) { gb__memcpy_4byte(temp2, mat2, sizeof(temp2)); mat2 = temp2; } for (j = 0; j < 2; j++) { for (i = 0; i < 2; i++) { out[j][i] = mat1[0][i]*mat2[j][0] + mat1[1][i]*mat2[j][1]; } } } void gb_float22_mul_vec2(gbVec2 *out, float m[2][2], gbVec2 v) { out->x = m[0][0]*v.x + m[0][1]*v.y; out->y = m[1][0]*v.x + m[1][1]*v.y; } void gb_mat3_transpose(gbMat3 *m) { gb_float33_transpose(gb_float33_m(m)); } void gb_mat3_identity(gbMat3 *m) { gb_float33_identity(gb_float33_m(m)); } void gb_mat3_mul(gbMat3 *out, gbMat3 *m1, gbMat3 *m2) { gb_float33_mul(gb_float33_m(out), gb_float33_m(m1), gb_float33_m(m2)); } void gb_float33_identity(float m[3][3]) { m[0][0] = 1; m[0][1] = 0; m[0][2] = 0; m[1][0] = 0; m[1][1] = 1; m[1][2] = 0; m[2][0] = 0; m[2][1] = 0; m[2][2] = 1; } void gb_mat3_mul_vec3(gbVec3 *out, gbMat3 *m, gbVec3 in) { gb_float33_mul_vec3(out, gb_float33_m(m), in); } gbMat3 *gb_mat3_v(gbVec3 m[3]) { return (gbMat3 *)m; } gbMat3 *gb_mat3_f(float m[3][3]) { return (gbMat3 *)m; } gbFloat3 *gb_float33_m(gbMat3 *m) { return (gbFloat3 *)m; } gbFloat3 *gb_float33_v(gbVec3 m[3]) { return (gbFloat3 *)m; } gbFloat3 *gb_float33_16(float m[9]) { return (gbFloat3 *)m; } void gb_float33_transpose(float (*vec)[3]) { int i, j; for (j = 0; j < 3; j++) { for (i = j + 1; i < 3; i++) { float t = vec[i][j]; vec[i][j] = vec[j][i]; vec[j][i] = t; } } } void gb_float33_mul(float (*out)[3], float (*mat1)[3], float (*mat2)[3]) { int i, j; float temp1[3][3], temp2[3][3]; if (mat1 == out) { gb__memcpy_4byte(temp1, mat1, sizeof(temp1)); mat1 = temp1; } if (mat2 == out) { gb__memcpy_4byte(temp2, mat2, sizeof(temp2)); mat2 = temp2; } for (j = 0; j < 3; j++) { for (i = 0; i < 3; i++) { out[j][i] = mat1[0][i]*mat2[j][0] + mat1[1][i]*mat2[j][1] + mat1[2][i]*mat2[j][2]; } } } void gb_float33_mul_vec3(gbVec3 *out, float m[3][3], gbVec3 v) { out->x = m[0][0]*v.x + m[0][1]*v.y + m[0][2]*v.z; out->y = m[1][0]*v.x + m[1][1]*v.y + m[1][2]*v.z; out->z = m[2][0]*v.x + m[2][1]*v.y + m[2][2]*v.z; } void gb_mat4_transpose(gbMat4 *m) { gb_float44_transpose(gb_float44_m(m)); } void gb_mat4_identity(gbMat4 *m) { gb_float44_identity(gb_float44_m(m)); } void gb_mat4_mul(gbMat4 *out, gbMat4 *m1, gbMat4 *m2) { gb_float44_mul(gb_float44_m(out), gb_float44_m(m1), gb_float44_m(m2)); } void gb_float44_identity(float m[4][4]) { m[0][0] = 1; m[0][1] = 0; m[0][2] = 0; m[0][3] = 0; m[1][0] = 0; m[1][1] = 1; m[1][2] = 0; m[1][3] = 0; m[2][0] = 0; m[2][1] = 0; m[2][2] = 1; m[2][3] = 0; m[3][0] = 0; m[3][1] = 0; m[3][2] = 0; m[3][3] = 1; } void gb_mat4_mul_vec4(gbVec4 *out, gbMat4 *m, gbVec4 in) { gb_float44_mul_vec4(out, gb_float44_m(m), in); } gbMat4 *gb_mat4_v(gbVec4 m[4]) { return (gbMat4 *)m; } gbMat4 *gb_mat4_f(float m[4][4]) { return (gbMat4 *)m; } gbFloat4 *gb_float44_m(gbMat4 *m) { return (gbFloat4 *)m; } gbFloat4 *gb_float44_v(gbVec4 m[4]) { return (gbFloat4 *)m; } gbFloat4 *gb_float44_16(float m[16]) { return (gbFloat4 *)m; } void gb_float44_transpose(float (*vec)[4]) { int i, j; for (j = 0; j < 4; j++) { for (i = j + 1; i < 4; i++) { float t = vec[i][j]; vec[i][j] = vec[j][i]; vec[j][i] = t; } } } void gb_float44_mul(float (*out)[4], float (*mat1)[4], float (*mat2)[4]) { int i, j; float temp1[4][4], temp2[4][4]; if (mat1 == out) { gb__memcpy_4byte(temp1, mat1, sizeof(temp1)); mat1 = temp1; } if (mat2 == out) { gb__memcpy_4byte(temp2, mat2, sizeof(temp2)); mat2 = temp2; } for (j = 0; j < 4; j++) { for (i = 0; i < 4; i++) { out[j][i] = mat1[0][i]*mat2[j][0] + mat1[1][i]*mat2[j][1] + mat1[2][i]*mat2[j][2] + mat1[3][i]*mat2[j][3]; } } } void gb_float44_mul_vec4(gbVec4 *out, float m[4][4], gbVec4 v) { out->x = m[0][0]*v.x + m[0][1]*v.y + m[0][2]*v.z + m[0][3]*v.w; out->y = m[1][0]*v.x + m[1][1]*v.y + m[1][2]*v.z + m[1][3]*v.w; out->z = m[2][0]*v.x + m[2][1]*v.y + m[2][2]*v.z + m[2][3]*v.w; out->w = m[3][0]*v.x + m[3][1]*v.y + m[3][2]*v.z + m[3][3]*v.w; } void gb_mat4_translate(gbMat4 *out, gbVec3 v) { gb_mat4_identity(out); out->col[3].xyz = v; out->col[3].w = 1; } void gb_mat4_rotate(gbMat4 *out, gbVec3 v, float angle_radians) { float c, s; gbVec3 axis, t; gbFloat4 *rot; c = gb_cos(angle_radians); s = gb_sin(angle_radians); gb_vec3_norm(&axis, v); gb_vec3_mul(&t, axis, 1.0f-c); gb_mat4_identity(out); rot = gb_float44_m(out); rot[0][0] = c + t.x*axis.x; rot[0][1] = 0 + t.x*axis.y + s*axis.z; rot[0][2] = 0 + t.x*axis.z - s*axis.y; rot[0][3] = 0; rot[1][0] = 0 + t.y*axis.x - s*axis.z; rot[1][1] = c + t.y*axis.y; rot[1][2] = 0 + t.y*axis.z + s*axis.x; rot[1][3] = 0; rot[2][0] = 0 + t.z*axis.x + s*axis.y; rot[2][1] = 0 + t.z*axis.y - s*axis.x; rot[2][2] = c + t.z*axis.z; rot[2][3] = 0; } void gb_mat4_scale(gbMat4 *out, gbVec3 v) { gb_mat4_identity(out); out->e[0] = v.x; out->e[5] = v.y; out->e[10] = v.z; } void gb_mat4_scalef(gbMat4 *out, float s) { gb_mat4_identity(out); out->e[0] = s; out->e[5] = s; out->e[10] = s; } void gb_mat4_ortho2d(gbMat4 *out, float left, float right, float bottom, float top) { gbFloat4 *m; gb_mat4_identity(out); m = gb_float44_m(out); m[0][0] = 2.0f / (right - left); m[1][1] = 2.0f / (top - bottom); m[2][2] = -1.0f; m[3][0] = -(right + left) / (right - left); m[3][1] = -(top + bottom) / (top - bottom); } void gb_mat4_ortho3d(gbMat4 *out, float left, float right, float bottom, float top, float z_near, float z_far) { gbFloat4 *m; gb_mat4_identity(out); m = gb_float44_m(out); m[0][0] = +2.0f / (right - left); m[1][1] = +2.0f / (top - bottom); m[2][2] = -2.0f / (z_far - z_near); m[3][0] = -(right + left) / (right - left); m[3][1] = -(top + bottom) / (top - bottom); m[3][2] = -(z_far + z_near) / (z_far - z_near); } void gb_mat4_perspective(gbMat4 *out, float fovy, float aspect, float z_near, float z_far) { float tan_half_fovy = gb_tan(0.5f * fovy); gbFloat4 *m = gb_float44_m(out); gb__memzero_byte4(m, sizeof(gbMat4)); m[0][0] = 1.0f / (aspect*tan_half_fovy); m[1][1] = 1.0f / (tan_half_fovy); m[2][2] = -(z_far + z_near) / (z_far - z_near); m[2][3] = -1.0f; m[3][2] = -2.0f*z_far*z_near / (z_far - z_near); } void gb_mat4_infinite_perspective(gbMat4 *out, float fovy, float aspect, float z_near) { float range = gb_tan(0.5f * fovy) * z_near; float left = -range * aspect; float right = range * aspect; float bottom = -range; float top = range; gbFloat4 *m = gb_float44_m(out); gb__memzero_byte4(m, sizeof(gbMat4)); m[0][0] = (2.0f*z_near) / (right - left); m[1][1] = (2.0f*z_near) / (top - bottom); m[2][2] = -1.0f; m[2][3] = -1.0f; m[3][2] = -2.0f*z_near; } void gb_mat4_look_at(gbMat4 *out, gbVec3 eye, gbVec3 centre, gbVec3 up) { gbVec3 f, s, u; gbFloat4 *m; gb_vec3_sub(&f, centre, eye); gb_vec3_norm(&f, f); gb_vec3_cross(&s, f, up); gb_vec3_norm(&s, s); gb_vec3_cross(&u, s, f); gb_mat4_identity(out); m = gb_float44_m(out); m[0][0] = +s.x; m[1][0] = +s.y; m[2][0] = +s.z; m[0][1] = +u.x; m[1][1] = +u.y; m[2][1] = +u.z; m[0][2] = -f.x; m[1][2] = -f.y; m[2][2] = -f.z; m[3][0] = gb_vec3_dot(s, eye); m[3][1] = gb_vec3_dot(u, eye); m[3][2] = gb_vec3_dot(f, eye); } gbQuat gb_quat(float x, float y, float z, float w) { gbQuat q = {x, y, z, w}; return q; } gbQuat gb_quatv(float e[4]) { gbQuat q = {e[0], e[1], e[2], e[3]}; return q; } gbQuat gb_quat_axis_angle(gbVec3 axis, float angle_radians) { gbQuat q; gb_vec3_norm(&q.xyz, axis); gb_vec3_muleq(&q.xyz, gb_sin(0.5f*angle_radians)); q.w = gb_cos(0.5f*angle_radians); return q; } gbQuat gb_quat_euler_angles(float pitch, float yaw, float roll) { /* TODO(bill): Do without multiplication, i.e. make it faster */ gbQuat q, p, y, r; p = gb_quat_axis_angle(gb_vec3(1, 0, 0), pitch); y = gb_quat_axis_angle(gb_vec3(0, 1, 0), yaw); r = gb_quat_axis_angle(gb_vec3(0, 0, 1), roll); gb_quat_mul(&q, y, p); gb_quat_muleq(&q, r); return q; } gbQuat gb_quat_identity(void) { gbQuat q = {0, 0, 0, 1}; return q; } void gb_quat_add(gbQuat *d, gbQuat q0, gbQuat q1) { gb_vec4_add(&d->xyzw, q0.xyzw, q1.xyzw); } void gb_quat_sub(gbQuat *d, gbQuat q0, gbQuat q1) { gb_vec4_sub(&d->xyzw, q0.xyzw, q1.xyzw); } void gb_quat_mul(gbQuat *d, gbQuat q0, gbQuat q1) { d->x = q0.w * q1.x + q0.x * q1.w + q0.y * q1.z - q0.z * q1.y; d->y = q0.w * q1.y - q0.x * q1.z + q0.y * q1.w + q0.z * q1.x; d->z = q0.w * q1.z + q0.x * q1.y - q0.y * q1.x + q0.z * q1.w; d->w = q0.w * q1.w - q0.x * q1.x - q0.y * q1.y - q0.z * q1.z; } void gb_quat_div(gbQuat *d, gbQuat q0, gbQuat q1){ gbQuat iq1; gb_quat_inverse(&iq1, q1); gb_quat_mul(d, q0, iq1); } void gb_quat_mulf(gbQuat *d, gbQuat q0, float s) { gb_vec4_mul(&d->xyzw, q0.xyzw, s); } void gb_quat_divf(gbQuat *d, gbQuat q0, float s) { gb_vec4_div(&d->xyzw, q0.xyzw, s); } void gb_quat_addeq(gbQuat *d, gbQuat q) { gb_vec4_addeq(&d->xyzw, q.xyzw); } void gb_quat_subeq(gbQuat *d, gbQuat q) { gb_vec4_subeq(&d->xyzw, q.xyzw); } void gb_quat_muleq(gbQuat *d, gbQuat q) { gb_quat_mul(d, *d, q); } void gb_quat_diveq(gbQuat *d, gbQuat q) { gb_quat_div(d, *d, q); } void gb_quat_muleqf(gbQuat *d, float s) { gb_vec4_muleq(&d->xyzw, s); } void gb_quat_diveqf(gbQuat *d, float s) { gb_vec4_diveq(&d->xyzw, s); } float gb_quat_dot(gbQuat q0, gbQuat q1) { float r = gb_vec3_dot(q0.xyz, q1.xyz) + q0.w*q1.w; return r; } float gb_quat_mag(gbQuat q) { float r = gb_sqrt(gb_quat_dot(q, q)); return r; } void gb_quat_norm(gbQuat *d, gbQuat q) { gb_quat_divf(d, q, gb_quat_mag(q)); } void gb_quat_conj(gbQuat *d, gbQuat q) { d->xyz = gb_vec3(-q.x, -q.y, -q.z); d->w = q.w; } void gb_quat_inverse(gbQuat *d, gbQuat q) { gb_quat_conj(d, q); gb_quat_diveqf(d, gb_quat_dot(q, q)); } void gb_quat_axis(gbVec3 *axis, gbQuat q) { gbQuat n; gb_quat_norm(&n, q); gb_vec3_div(axis, n.xyz, gb_sin(gb_arccos(q.w))); } float gb_quat_angle(gbQuat q) { float mag = gb_quat_mag(q); float c = q.w * (1.0f/mag); float angle = 2.0f*gb_arccos(c); return angle; } float gb_quat_roll(gbQuat q) { return gb_arctan2(2.0f*q.x*q.y + q.z*q.w, q.x*q.x + q.w*q.w - q.y*q.y - q.z*q.z); } float gb_quat_pitch(gbQuat q) { return gb_arctan2(2.0f*q.y*q.z + q.w*q.x, q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z); } float gb_quat_yaw(gbQuat q) { return gb_arcsin(-2.0f*(q.x*q.z - q.w*q.y)); } void gb_quat_rotate_vec3(gbVec3 *d, gbQuat q, gbVec3 v) { /* gbVec3 t = 2.0f * cross(q.xyz, v); * *d = q.w*t + v + cross(q.xyz, t); */ gbVec3 t, p; gb_vec3_cross(&t, q.xyz, v); gb_vec3_muleq(&t, 2.0f); gb_vec3_cross(&p, q.xyz, t); gb_vec3_mul(d, t, q.w); gb_vec3_addeq(d, v); gb_vec3_addeq(d, p); } void gb_mat4_from_quat(gbMat4 *out, gbQuat q) { gbFloat4 *m; gbQuat a; float xx, yy, zz, xy, xz, yz, wx, wy, wz; gb_quat_norm(&a, q); xx = a.x*a.x; yy = a.y*a.y; zz = a.z*a.z; xy = a.x*a.y; xz = a.x*a.z; yz = a.y*a.z; wx = a.w*a.x; wy = a.w*a.y; wz = a.w*a.z; gb_mat4_identity(out); m = gb_float44_m(out); m[0][0] = 1.0f - 2.0f*(yy + zz); m[0][1] = 2.0f*(xy + wz); m[0][2] = 2.0f*(xz - wy); m[1][0] = 2.0f*(xy - wz); m[1][1] = 1.0f - 2.0f*(xx + zz); m[1][2] = 2.0f*(yz + wx); m[2][0] = 2.0f*(xz + wy); m[2][1] = 2.0f*(yz - wx); m[2][2] = 1.0f - 2.0f*(xx + yy); } void gb_quat_from_mat4(gbQuat *out, gbMat4 *mat) { gbFloat4 *m; float four_x_squared_minus_1, four_y_squared_minus_1, four_z_squared_minus_1, four_w_squared_minus_1, four_biggest_squared_minus_1; int biggest_index = 0; float biggest_value, mult; m = gb_float44_m(mat); four_x_squared_minus_1 = m[0][0] - m[1][1] - m[2][2]; four_y_squared_minus_1 = m[1][1] - m[0][0] - m[2][2]; four_z_squared_minus_1 = m[2][2] - m[0][0] - m[1][1]; four_w_squared_minus_1 = m[0][0] + m[1][1] + m[2][2]; four_biggest_squared_minus_1 = four_w_squared_minus_1; if (four_x_squared_minus_1 > four_biggest_squared_minus_1) { four_biggest_squared_minus_1 = four_x_squared_minus_1; biggest_index = 1; } if (four_y_squared_minus_1 > four_biggest_squared_minus_1) { four_biggest_squared_minus_1 = four_y_squared_minus_1; biggest_index = 2; } if (four_z_squared_minus_1 > four_biggest_squared_minus_1) { four_biggest_squared_minus_1 = four_z_squared_minus_1; biggest_index = 3; } biggest_value = gb_sqrt(four_biggest_squared_minus_1 + 1.0f) * 0.5f; mult = 0.25f / biggest_value; switch (biggest_index) { case 0: out->w = biggest_value; out->x = (m[1][2] - m[2][1]) * mult; out->y = (m[2][0] - m[0][2]) * mult; out->z = (m[0][1] - m[1][0]) * mult; break; case 1: out->w = (m[1][2] - m[2][1]) * mult; out->x = biggest_value; out->y = (m[0][1] + m[1][0]) * mult; out->z = (m[2][0] + m[0][2]) * mult; break; case 2: out->w = (m[2][0] - m[0][2]) * mult; out->x = (m[0][1] + m[1][0]) * mult; out->y = biggest_value; out->z = (m[1][2] + m[2][1]) * mult; break; case 3: out->w = (m[0][1] - m[1][0]) * mult; out->x = (m[2][0] + m[0][2]) * mult; out->y = (m[1][2] + m[2][1]) * mult; out->z = biggest_value; break; default: /* NOTE(bill): This shouldn't fucking happen!!! */ break; } } float gb_lerp(float a, float b, float t) { return a*(1.0f-t) + b*t; } float gb_smooth_step(float a, float b, float t) { float x = (t - a)/(b - a); return x*x*(3.0f - 2.0f*x); } float gb_smoother_step(float a, float b, float t) { float x = (t - a)/(b - a); return x*x*x*(x*(6.0f*x - 15.0f) + 10.0f); } #define GB_VEC_LERPN(N, d, a, b, t) \ gbVec##N db; \ gb_vec##N##_sub(&db, b, a); \ gb_vec##N##_muleq(&db, t); \ gb_vec##N##_add(d, a, db) void gb_vec2_lerp(gbVec2 *d, gbVec2 a, gbVec2 b, float t) { GB_VEC_LERPN(2, d, a, b, t); } void gb_vec3_lerp(gbVec3 *d, gbVec3 a, gbVec3 b, float t) { GB_VEC_LERPN(3, d, a, b, t); } void gb_vec4_lerp(gbVec4 *d, gbVec4 a, gbVec4 b, float t) { GB_VEC_LERPN(4, d, a, b, t); } #undef GB_VEC_LERPN void gb_quat_lerp(gbQuat *d, gbQuat a, gbQuat b, float t) { gb_vec4_lerp(&d->xyzw, a.xyzw, b.xyzw, t); } void gb_quat_nlerp(gbQuat *d, gbQuat a, gbQuat b, float t) { gb_quat_lerp(d, a, b, t); gb_quat_norm(d, *d); } void gb_quat_slerp(gbQuat *d, gbQuat a, gbQuat b, float t) { gbQuat x, y, z; float cos_theta, angle; float s1, s0, is; z = b; cos_theta = gb_quat_dot(a, b); if (cos_theta < 0.0f) { z = gb_quat(-b.x, -b.y, -b.z, -b.w); cos_theta = -cos_theta; } if (cos_theta > 1.0f) { /* NOTE(bill): Use lerp not nlerp as it's not a real angle or they are not normalized */ gb_quat_lerp(d, a, b, t); } angle = gb_arccos(cos_theta); s1 = gb_sin(1.0f - t*angle); s0 = gb_sin(t*angle); is = 1.0f/gb_sin(angle); gb_quat_mulf(&x, z, s1); gb_quat_mulf(&y, z, s0); gb_quat_add(d, x, y); gb_quat_muleqf(d, is); } void gb_quat_slerp_approx(gbQuat *d, gbQuat a, gbQuat b, float t) { /* NOTE(bill): Derived by taylor expanding the geometric interpolation equation * Even works okay for nearly anti-parallel versors!!! */ /* NOTE(bill): Extra interations cannot be used as they require angle^4 which is not worth it to approximate */ float tp = t + (1.0f - gb_quat_dot(a, b))/3.0f * t*(-2.0f*t*t + 3.0f*t - 1.0f); gb_quat_nlerp(d, a, b, tp); } void gb_quat_nquad(gbQuat *d, gbQuat p, gbQuat a, gbQuat b, gbQuat q, float t) { gbQuat x, y; gb_quat_nlerp(&x, p, q, t); gb_quat_nlerp(&y, a, b, t); gb_quat_nlerp(d, x, y, 2.0f*t*(1.0f-t)); } void gb_quat_squad(gbQuat *d, gbQuat p, gbQuat a, gbQuat b, gbQuat q, float t) { gbQuat x, y; gb_quat_slerp(&x, p, q, t); gb_quat_slerp(&y, a, b, t); gb_quat_slerp(d, x, y, 2.0f*t*(1.0f-t)); } void gb_quat_squad_approx(gbQuat *d, gbQuat p, gbQuat a, gbQuat b, gbQuat q, float t) { gbQuat x, y; gb_quat_slerp_approx(&x, p, q, t); gb_quat_slerp_approx(&y, a, b, t); gb_quat_slerp_approx(d, x, y, 2.0f*t*(1.0f-t)); } gbRect2 gb_rect2(gbVec2 pos, gbVec2 dim) { gbRect2 r; r.pos = pos; r.dim = dim; return r; } gbRect3 gb_rect3(gbVec3 pos, gbVec3 dim) { gbRect3 r; r.pos = pos; r.dim = dim; return r; } int gb_rect2_contains(gbRect2 a, float x, float y) { float min_x = gb_min(a.pos.x, a.pos.x+a.dim.x); float max_x = gb_max(a.pos.x, a.pos.x+a.dim.x); float min_y = gb_min(a.pos.y, a.pos.y+a.dim.y); float max_y = gb_max(a.pos.y, a.pos.y+a.dim.y); int result = (x >= min_x) & (x < max_x) & (y >= min_y) & (y < max_y); return result; } int gb_rect2_contains_vec2(gbRect2 a, gbVec2 p) { return gb_rect2_contains(a, p.x, p.y); } int gb_rect2_intersects(gbRect2 a, gbRect2 b) { gbRect2 r = {0}; return gb_rect2_intersection_result(a, b, &r); } int gb_rect2_intersection_result(gbRect2 a, gbRect2 b, gbRect2 *intersection) { float a_min_x = gb_min(a.pos.x, a.pos.x+a.dim.x); float a_max_x = gb_max(a.pos.x, a.pos.x+a.dim.x); float a_min_y = gb_min(a.pos.y, a.pos.y+a.dim.y); float a_max_y = gb_max(a.pos.y, a.pos.y+a.dim.y); float b_min_x = gb_min(b.pos.x, b.pos.x+b.dim.x); float b_max_x = gb_max(b.pos.x, b.pos.x+b.dim.x); float b_min_y = gb_min(b.pos.y, b.pos.y+b.dim.y); float b_max_y = gb_max(b.pos.y, b.pos.y+b.dim.y); float x0 = gb_max(a_min_x, b_min_x); float y0 = gb_max(a_min_y, b_min_y); float x1 = gb_min(a_max_x, b_max_x); float y1 = gb_min(a_max_y, b_max_y); if ((x0 < x1) && (y0 < y1)) { gbRect2 r = gb_rect2(gb_vec2(x0, y0), gb_vec2(x1-x0, y1-y0)); *intersection = r; return 1; } else { gbRect2 r = {0}; *intersection = r; return 0; } } #if defined(_WIN64) || defined(__x86_64__) || defined(__ppc64__) gb_math_u64 gb_hash_murmur64(void const *key, size_t num_bytes, gb_math_u64 seed) { gb_math_u64 const m = 0xc6a4a7935bd1e995ULL; gb_math_u64 const r = 47; gb_math_u64 h = seed ^ (num_bytes * m); gb_math_u64 *data = (gb_math_u64 *)(key); gb_math_u64 *end = data + (num_bytes / 8); unsigned char *data2; while (data != end) { gb_math_u64 k = *data++; k *= m; k ^= k >> r; k *= m; h ^= k; h *= m; } data2 = (unsigned char *)data; switch (num_bytes & 7) { case 7: h ^= (gb_math_u64)data2[6] << 48; case 6: h ^= (gb_math_u64)data2[5] << 40; case 5: h ^= (gb_math_u64)data2[4] << 32; case 4: h ^= (gb_math_u64)data2[3] << 24; case 3: h ^= (gb_math_u64)data2[2] << 16; case 2: h ^= (gb_math_u64)data2[1] << 8; case 1: h ^= (gb_math_u64)data2[0]; h *= m; }; h ^= h >> r; h *= m; h ^= h >> r; return h; } #else gb_math_u64 gb_hash_murmur64(void const *key, size_t num_bytes, gb_math_u64 seed) { gb_math_u32 const m = 0x5bd1e995; gb_math_u32 const r = 24; gb_math_u64 h = 0; gb_math_u32 h1 = (gb_math_u32)seed ^ (gb_math_u32)num_bytes; gb_math_u32 h2 = (gb_math_u32)((gb_math_u64)seed >> 32); gb_math_u32 *data = (gb_math_u32 *)key; while (num_bytes >= 8) { gb_math_u32 k1, k2; k1 = *data++; k1 *= m; k1 ^= k1 >> r; k1 *= m; h1 *= m; h1 ^= k1; num_bytes -= 4; k2 = *data++; k2 *= m; k2 ^= k2 >> r; k2 *= m; h2 *= m; h2 ^= k2; num_bytes -= 4; } if (num_bytes >= 4) { gb_math_u32 k1 = *data++; k1 *= m; k1 ^= k1 >> r; k1 *= m; h1 *= m; h1 ^= k1; num_bytes -= 4; } switch (num_bytes) { gb_math_u32 a, b, c; case 3: c = data[2]; h2 ^= c << 16; case 2: b = data[1]; h2 ^= b << 8; case 1: a = data[0]; h2 ^= a << 0; h2 *= m; }; h1 ^= h2 >> 18; h1 *= m; h2 ^= h1 >> 22; h2 *= m; h1 ^= h2 >> 17; h1 *= m; h2 ^= h1 >> 19; h2 *= m; h = (gb_math_u64)(h << 32) | (gb_math_u64)h2; return h; } #endif /* TODO(bill): Make better random number generators */ float gb_random_range_float(float min_inc, float max_inc) { int int_result = gb_random_range_int(0, 2147483646); /* Prevent integer overflow */ float result = int_result/(float)2147483646; result *= max_inc - min_inc; result += min_inc; return result; } int gb_random_range_int(int min_inc, int max_inc) { static int random_value = 0xdeadbeef; /* Random Value */ int diff, result; random_value = random_value * 2147001325 + 715136305; /* BCPL generator */ diff = max_inc - min_inc + 1; result = random_value % diff; result += min_inc; return result; } #endif /* GB_MATH_IMPLEMENTATION */