1 /* gph-cmath - C graphics math library
2 * Copyright (C) 2018-2023 John Tsiombikas <nuclear@member.fsf.org>
4 * This program is free software. Feel free to use, modify, and/or redistribute
5 * it under the terms of the MIT/X11 license. See LICENSE for details.
6 * If you intend to redistribute parts of the code without the LICENSE file
7 * replace this paragraph with the full contents of the LICENSE file.
9 * Function prefixes signify the data type of their operand(s):
10 * - cgm_v... functions are operations on cgm_vec3 vectors
11 * - cgm_w... functions are operations on cgm_vec4 vectors
12 * - cgm_q... functions are operations on cgm_quat quaternions (w + xi + yj + zk)
13 * - cgm_m... functions are operations on 4x4 matrices (stored as linear 16 float arrays)
14 * - cgm_r... functions are operations on cgm_ray rays
16 * NOTE: *ALL* matrix arguments are pointers to 16 floats. Even the functions
17 * which operate on 3x3 matrices, actually use the upper 3x3 of a 4x4 matrix,
18 * and still expect an array of 16 floats.
20 * NOTE: matrices are treated by all operations as column-major, to match OpenGL
21 * conventions, so everything is pretty much transposed.
29 #define CGM_PI 3.141592653589793
47 typedef enum cgm_euler_mode {
63 #define CGM_INLINE inline
68 #if (__STDC_VERSION__ >= 199901) || defined(__GNUC__)
69 #define CGM_INLINE inline
71 #define CGM_INLINE __inline
76 /* --- operations on cgm_vec3 --- */
77 static CGM_INLINE void cgm_vcons(cgm_vec3 *v, float x, float y, float z);
78 static CGM_INLINE cgm_vec3 cgm_vvec(float x, float y, float z);
80 static CGM_INLINE void cgm_vadd(cgm_vec3 *a, const cgm_vec3 *b);
81 static CGM_INLINE void cgm_vadd_scaled(cgm_vec3 *a, const cgm_vec3 *b, float s); /* a+b*s */
82 static CGM_INLINE void cgm_vsub(cgm_vec3 *a, const cgm_vec3 *b);
83 static CGM_INLINE void cgm_vsub_scaled(cgm_vec3 *a, const cgm_vec3 *b, float s); /* a-b*s */
84 static CGM_INLINE void cgm_vmul(cgm_vec3 *a, const cgm_vec3 *b);
85 static CGM_INLINE void cgm_vscale(cgm_vec3 *v, float s);
86 static CGM_INLINE void cgm_vmul_m4v3(cgm_vec3 *v, const float *m); /* m4x4 * v */
87 static CGM_INLINE void cgm_vmul_v3m4(cgm_vec3 *v, const float *m); /* v * m4x4 */
88 static CGM_INLINE void cgm_vmul_m3v3(cgm_vec3 *v, const float *m); /* m3x3 * v (m still 16 floats) */
89 static CGM_INLINE void cgm_vmul_v3m3(cgm_vec3 *v, const float *m); /* v * m3x3 (m still 16 floats) */
91 static CGM_INLINE float cgm_vdot(const cgm_vec3 *a, const cgm_vec3 *b);
92 static CGM_INLINE void cgm_vcross(cgm_vec3 *res, const cgm_vec3 *a, const cgm_vec3 *b);
93 static CGM_INLINE float cgm_vlength(const cgm_vec3 *v);
94 static CGM_INLINE float cgm_vlength_sq(const cgm_vec3 *v);
95 static CGM_INLINE float cgm_vdist(const cgm_vec3 *a, const cgm_vec3 *b);
96 static CGM_INLINE float cgm_vdist_sq(const cgm_vec3 *a, const cgm_vec3 *b);
97 static CGM_INLINE void cgm_vnormalize(cgm_vec3 *v);
99 static CGM_INLINE void cgm_vreflect(cgm_vec3 *v, const cgm_vec3 *n);
100 static CGM_INLINE void cgm_vrefract(cgm_vec3 *v, const cgm_vec3 *n, float ior);
102 static CGM_INLINE void cgm_vrotate_quat(cgm_vec3 *v, const cgm_quat *q);
103 static CGM_INLINE void cgm_vrotate_axis(cgm_vec3 *v, int axis, float angle);
104 static CGM_INLINE void cgm_vrotate(cgm_vec3 *v, float angle, float x, float y, float z);
105 static CGM_INLINE void cgm_vrotate_euler(cgm_vec3 *v, float a, float b, float c, enum cgm_euler_mode mode);
107 static CGM_INLINE void cgm_vlerp(cgm_vec3 *res, const cgm_vec3 *a, const cgm_vec3 *b, float t);
109 #define cgm_velem(vptr, idx) ((&(vptr)->x)[idx])
111 /* --- operations on cgm_vec4 --- */
112 static CGM_INLINE void cgm_wcons(cgm_vec4 *v, float x, float y, float z, float w);
113 static CGM_INLINE cgm_vec4 cgm_wvec(float x, float y, float z, float w);
115 static CGM_INLINE void cgm_wadd(cgm_vec4 *a, const cgm_vec4 *b);
116 static CGM_INLINE void cgm_wsub(cgm_vec4 *a, const cgm_vec4 *b);
117 static CGM_INLINE void cgm_wmul(cgm_vec4 *a, const cgm_vec4 *b);
118 static CGM_INLINE void cgm_wscale(cgm_vec4 *v, float s);
120 static CGM_INLINE void cgm_wmul_m4v4(cgm_vec4 *v, const float *m);
121 static CGM_INLINE void cgm_wmul_v4m4(cgm_vec4 *v, const float *m);
122 static CGM_INLINE void cgm_wmul_m34v4(cgm_vec4 *v, const float *m); /* doesn't affect w */
123 static CGM_INLINE void cgm_wmul_v4m43(cgm_vec4 *v, const float *m); /* doesn't affect w */
124 static CGM_INLINE void cgm_wmul_m3v4(cgm_vec4 *v, const float *m); /* (m still 16 floats) */
125 static CGM_INLINE void cgm_wmul_v4m3(cgm_vec4 *v, const float *m); /* (m still 16 floats) */
127 static CGM_INLINE float cgm_wdot(const cgm_vec4 *a, const cgm_vec4 *b);
129 static CGM_INLINE float cgm_wlength(const cgm_vec4 *v);
130 static CGM_INLINE float cgm_wlength_sq(const cgm_vec4 *v);
131 static CGM_INLINE float cgm_wdist(const cgm_vec4 *a, const cgm_vec4 *b);
132 static CGM_INLINE float cgm_wdist_sq(const cgm_vec4 *a, const cgm_vec4 *b);
133 static CGM_INLINE void cgm_wnormalize(cgm_vec4 *v);
135 static CGM_INLINE void cgm_wlerp(cgm_vec4 *res, const cgm_vec4 *a, const cgm_vec4 *b, float t);
137 #define cgm_welem(vptr, idx) ((&(vptr)->x)[idx])
139 /* --- operations on quaternions --- */
140 static CGM_INLINE void cgm_qcons(cgm_quat *q, float x, float y, float z, float w);
142 static CGM_INLINE void cgm_qneg(cgm_quat *q);
143 static CGM_INLINE void cgm_qadd(cgm_quat *a, const cgm_quat *b);
144 static CGM_INLINE void cgm_qsub(cgm_quat *a, const cgm_quat *b);
145 static CGM_INLINE void cgm_qmul(cgm_quat *a, const cgm_quat *b);
147 static CGM_INLINE float cgm_qlength(const cgm_quat *q);
148 static CGM_INLINE float cgm_qlength_sq(const cgm_quat *q);
149 static CGM_INLINE void cgm_qnormalize(cgm_quat *q);
150 static CGM_INLINE void cgm_qconjugate(cgm_quat *q);
151 static CGM_INLINE void cgm_qinvert(cgm_quat *q);
153 static CGM_INLINE void cgm_qrotation(cgm_quat *q, float angle, float x, float y, float z);
154 static CGM_INLINE void cgm_qrotate(cgm_quat *q, float angle, float x, float y, float z);
156 static CGM_INLINE void cgm_qslerp(cgm_quat *res, const cgm_quat *a, const cgm_quat *b, float t);
157 static CGM_INLINE void cgm_qlerp(cgm_quat *res, const cgm_quat *a, const cgm_quat *b, float t);
159 #define cgm_qelem(qptr, idx) ((&(qptr)->x)[idx])
161 /* --- operations on matrices --- */
162 static CGM_INLINE void cgm_mcopy(float *dest, const float *src);
163 static CGM_INLINE void cgm_mzero(float *m);
164 static CGM_INLINE void cgm_midentity(float *m);
166 static CGM_INLINE void cgm_mmul(float *a, const float *b);
167 static CGM_INLINE void cgm_mpremul(float *a, const float *b);
169 static CGM_INLINE void cgm_msubmatrix(float *m, int row, int col);
170 static CGM_INLINE void cgm_mupper3(float *m);
171 static CGM_INLINE float cgm_msubdet(const float *m, int row, int col);
172 static CGM_INLINE float cgm_mcofactor(const float *m, int row, int col);
173 static CGM_INLINE float cgm_mdet(const float *m);
174 static CGM_INLINE void cgm_mtranspose(float *m);
175 static CGM_INLINE void cgm_mcofmatrix(float *m);
176 static CGM_INLINE int cgm_minverse(float *m); /* returns 0 on success, -1 for singular */
178 static CGM_INLINE void cgm_mtranslation(float *m, float x, float y, float z);
179 static CGM_INLINE void cgm_mscaling(float *m, float sx, float sy, float sz);
180 static CGM_INLINE void cgm_mrotation_x(float *m, float angle);
181 static CGM_INLINE void cgm_mrotation_y(float *m, float angle);
182 static CGM_INLINE void cgm_mrotation_z(float *m, float angle);
183 static CGM_INLINE void cgm_mrotation_axis(float *m, int idx, float angle);
184 static CGM_INLINE void cgm_mrotation(float *m, float angle, float x, float y, float z);
185 static CGM_INLINE void cgm_mrotation_euler(float *m, float a, float b, float c, int mode);
186 static CGM_INLINE void cgm_mrotation_quat(float *m, const cgm_quat *q);
188 static CGM_INLINE void cgm_mtranslate(float *m, float x, float y, float z);
189 static CGM_INLINE void cgm_mscale(float *m, float sx, float sy, float sz);
190 static CGM_INLINE void cgm_mrotate_x(float *m, float angle);
191 static CGM_INLINE void cgm_mrotate_y(float *m, float angle);
192 static CGM_INLINE void cgm_mrotate_z(float *m, float angle);
193 static CGM_INLINE void cgm_mrotate_axis(float *m, int idx, float angle);
194 static CGM_INLINE void cgm_mrotate(float *m, float angle, float x, float y, float z);
195 static CGM_INLINE void cgm_mrotate_euler(float *m, float a, float b, float c, int mode);
196 static CGM_INLINE void cgm_mrotate_quat(float *m, const cgm_quat *q);
198 static CGM_INLINE void cgm_mpretranslate(float *m, float x, float y, float z);
199 static CGM_INLINE void cgm_mprescale(float *m, float sx, float sy, float sz);
200 static CGM_INLINE void cgm_mprerotate_x(float *m, float angle);
201 static CGM_INLINE void cgm_mprerotate_y(float *m, float angle);
202 static CGM_INLINE void cgm_mprerotate_z(float *m, float angle);
203 static CGM_INLINE void cgm_mprerotate_axis(float *m, int idx, float angle);
204 static CGM_INLINE void cgm_mprerotate(float *m, float angle, float x, float y, float z);
205 static CGM_INLINE void cgm_mprerotate_euler(float *m, float a, float b, float c, int mode);
206 static CGM_INLINE void cgm_mprerotate_quat(float *m, const cgm_quat *q);
208 static CGM_INLINE void cgm_mget_translation(const float *m, cgm_vec3 *res);
209 static CGM_INLINE void cgm_mget_rotation(const float *m, cgm_quat *res);
210 static CGM_INLINE void cgm_mget_scaling(const float *m, cgm_vec3 *res);
211 static CGM_INLINE void cgm_mget_frustum_plane(const float *m, int p, cgm_vec4 *res);
213 static CGM_INLINE void cgm_normalize_plane(cgm_vec4 *p);
215 static CGM_INLINE void cgm_mlookat(float *m, const cgm_vec3 *pos, const cgm_vec3 *targ,
217 static CGM_INLINE void cgm_minv_lookat(float *m, const cgm_vec3 *pos, const cgm_vec3 *targ,
219 static CGM_INLINE void cgm_mortho(float *m, float left, float right, float bot, float top,
220 float znear, float zfar);
221 static CGM_INLINE void cgm_mfrustum(float *m, float left, float right, float bot, float top,
222 float znear, float zfar);
223 static CGM_INLINE void cgm_mperspective(float *m, float vfov, float aspect, float znear, float zfar);
225 static CGM_INLINE void cgm_mmirror(float *m, float a, float b, float c, float d);
227 /* --- operations on rays --- */
228 static CGM_INLINE void cgm_rcons(cgm_ray *r, float x, float y, float z, float dx, float dy, float dz);
230 static CGM_INLINE void cgm_rmul_mr(cgm_ray *ray, const float *m); /* m4x4 * ray */
231 static CGM_INLINE void cgm_rmul_rm(cgm_ray *ray, const float *m); /* ray * m4x4 */
233 static CGM_INLINE void cgm_rreflect(cgm_ray *ray, const cgm_vec3 *n);
234 static CGM_INLINE void cgm_rrefract(cgm_ray *ray, const cgm_vec3 *n, float ior);
236 /* --- miscellaneous utility functions --- */
237 static CGM_INLINE float cgm_deg_to_rad(float deg);
238 static CGM_INLINE float cgm_rad_to_deg(float rad);
240 static CGM_INLINE float cgm_smoothstep(float a, float b, float x);
241 static CGM_INLINE float cgm_lerp(float a, float b, float t);
242 static CGM_INLINE float cgm_logerp(float a, float b, float t);
243 static CGM_INLINE float cgm_bezier(float a, float b, float c, float d, float t);
244 static CGM_INLINE float cgm_bspline(float a, float b, float c, float d, float t);
245 static CGM_INLINE float cgm_spline(float a, float b, float c, float d, float t);
247 static CGM_INLINE void cgm_discrand(cgm_vec3 *v, float rad);
248 static CGM_INLINE void cgm_sphrand(cgm_vec3 *v, float rad);
250 static CGM_INLINE void cgm_unproject(cgm_vec3 *res, const cgm_vec3 *norm_scrpos,
251 const float *inv_viewproj);
252 static CGM_INLINE void cgm_glu_unproject(float winx, float winy, float winz,
253 const float *view, const float *proj, const int *vp,
254 float *objx, float *objy, float *objz);
256 static CGM_INLINE void cgm_pick_ray(cgm_ray *ray, float nx, float ny,
257 const float *viewmat, const float *projmat);
259 static CGM_INLINE void cgm_raypos(cgm_vec3 *p, const cgm_ray *ray, float t);
261 /* calculate barycentric coordinates of point pt in triangle (a, b, c) */
262 static CGM_INLINE void cgm_bary(cgm_vec3 *bary, const cgm_vec3 *a,
263 const cgm_vec3 *b, const cgm_vec3 *c, const cgm_vec3 *pt);
265 /* convert between unit vectors and spherical coordinates */
266 static CGM_INLINE void cgm_uvec_to_sph(float *theta, float *phi, const cgm_vec3 *v);
267 static CGM_INLINE void cgm_sph_to_uvec(cgm_vec3 *v, float theta, float phi);
269 #include "cgmvec3.inl"
270 #include "cgmvec4.inl"
271 #include "cgmquat.inl"
272 #include "cgmmat.inl"
273 #include "cgmray.inl"
274 #include "cgmmisc.inl"
280 #endif /* CGMATH_H_ */