1 /* gph-cmath - C graphics math library
2 * Copyright (C) 2018 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.
45 typedef enum cgm_euler_mode {
64 /* --- operations on cgm_vec3 --- */
65 static inline void cgm_vcons(cgm_vec3 *v, float x, float y, float z);
67 static inline void cgm_vadd(cgm_vec3 *a, const cgm_vec3 *b);
68 static inline void cgm_vadd_scaled(cgm_vec3 *a, const cgm_vec3 *b, float s); /* a+b*s */
69 static inline void cgm_vsub(cgm_vec3 *a, const cgm_vec3 *b);
70 static inline void cgm_vsub_scaled(cgm_vec3 *a, const cgm_vec3 *b, float s); /* a-b*s */
71 static inline void cgm_vmul(cgm_vec3 *a, const cgm_vec3 *b);
72 static inline void cgm_vscale(cgm_vec3 *v, float s);
73 static inline void cgm_vmul_m4v3(cgm_vec3 *v, const float *m); /* m4x4 * v */
74 static inline void cgm_vmul_v3m4(cgm_vec3 *v, const float *m); /* v * m4x4 */
75 static inline void cgm_vmul_m3v3(cgm_vec3 *v, const float *m); /* m3x3 * v (m still 16 floats) */
76 static inline void cgm_vmul_v3m3(cgm_vec3 *v, const float *m); /* v * m3x3 (m still 16 floats) */
78 static inline float cgm_vdot(const cgm_vec3 *a, const cgm_vec3 *b);
79 static inline void cgm_vcross(cgm_vec3 *res, const cgm_vec3 *a, const cgm_vec3 *b);
80 static inline float cgm_vlength(const cgm_vec3 *v);
81 static inline float cgm_vlength_sq(const cgm_vec3 *v);
82 static inline float cgm_vdist(const cgm_vec3 *a, const cgm_vec3 *b);
83 static inline float cgm_vdist_sq(const cgm_vec3 *a, const cgm_vec3 *b);
84 static inline void cgm_vnormalize(cgm_vec3 *v);
86 static inline void cgm_vreflect(cgm_vec3 *v, const cgm_vec3 *n);
87 static inline int cgm_vrefract(cgm_vec3 *v, const cgm_vec3 *n, float ior);
89 static inline void cgm_vrotate_quat(cgm_vec3 *v, const cgm_quat *q);
90 static inline void cgm_vrotate_axis(cgm_vec3 *v, int axis, float angle);
91 static inline void cgm_vrotate(cgm_vec3 *v, float angle, float x, float y, float z);
92 static inline void cgm_vrotate_euler(cgm_vec3 *v, float a, float b, float c, enum cgm_euler_mode mode);
94 static inline void cgm_vlerp(cgm_vec3 *res, const cgm_vec3 *a, const cgm_vec3 *b, float t);
96 #define cgm_velem(vptr, idx) ((&(vptr)->x)[idx])
98 /* --- operations on cgm_vec4 --- */
99 static inline void cgm_wcons(cgm_vec4 *v, float x, float y, float z, float w);
101 static inline void cgm_wadd(cgm_vec4 *a, const cgm_vec4 *b);
102 static inline void cgm_wsub(cgm_vec4 *a, const cgm_vec4 *b);
103 static inline void cgm_wmul(cgm_vec4 *a, const cgm_vec4 *b);
104 static inline void cgm_wscale(cgm_vec4 *v, float s);
106 static inline void cgm_wmul_m4v4(cgm_vec4 *v, const float *m);
107 static inline void cgm_wmul_v4m4(cgm_vec4 *v, const float *m);
108 static inline void cgm_wmul_m34v4(cgm_vec4 *v, const float *m); /* doesn't affect w */
109 static inline void cgm_wmul_v4m43(cgm_vec4 *v, const float *m); /* doesn't affect w */
110 static inline void cgm_wmul_m3v4(cgm_vec4 *v, const float *m); /* (m still 16 floats) */
111 static inline void cgm_wmul_v4m3(cgm_vec4 *v, const float *m); /* (m still 16 floats) */
113 static inline float cgm_wdot(const cgm_vec4 *a, const cgm_vec4 *b);
115 static inline float cgm_wlength(const cgm_vec4 *v);
116 static inline float cgm_wlength_sq(const cgm_vec4 *v);
117 static inline float cgm_wdist(const cgm_vec4 *a, const cgm_vec4 *b);
118 static inline float cgm_wdist_sq(const cgm_vec4 *a, const cgm_vec4 *b);
119 static inline void cgm_wnormalize(cgm_vec4 *v);
121 static inline void cgm_wlerp(cgm_vec4 *res, const cgm_vec4 *a, const cgm_vec4 *b, float t);
123 #define cgm_welem(vptr, idx) ((&(vptr)->x)[idx])
125 /* --- operations on quaternions --- */
126 static inline void cgm_qcons(cgm_quat *q, float x, float y, float z, float w);
128 static inline void cgm_qneg(cgm_quat *q);
129 static inline void cgm_qadd(cgm_quat *a, const cgm_quat *b);
130 static inline void cgm_qsub(cgm_quat *a, const cgm_quat *b);
131 static inline void cgm_qmul(cgm_quat *a, const cgm_quat *b);
133 static inline float cgm_qlength(const cgm_quat *q);
134 static inline float cgm_qlength_sq(const cgm_quat *q);
135 static inline void cgm_qnormalize(cgm_quat *q);
136 static inline void cgm_qconjugate(cgm_quat *q);
137 static inline void cgm_qinvert(cgm_quat *q);
139 static inline void cgm_qrotation(cgm_quat *q, float angle, float x, float y, float z);
140 static inline void cgm_qrotate(cgm_quat *q, float angle, float x, float y, float z);
142 static inline void cgm_qslerp(cgm_quat *res, const cgm_quat *a, const cgm_quat *b, float t);
143 static inline void cgm_qlerp(cgm_quat *res, const cgm_quat *a, const cgm_quat *b, float t);
145 #define cgm_qelem(qptr, idx) ((&(qptr)->x)[idx])
147 /* --- operations on matrices --- */
148 static inline void cgm_mcopy(float *dest, const float *src);
149 static inline void cgm_mzero(float *m);
150 static inline void cgm_midentity(float *m);
152 static inline void cgm_mmul(float *a, const float *b);
153 static inline void cgm_mpremul(float *a, const float *b);
155 static inline void cgm_msubmatrix(float *m, int row, int col);
156 static inline void cgm_mupper3(float *m);
157 static inline float cgm_msubdet(const float *m, int row, int col);
158 static inline float cgm_mcofactor(const float *m, int row, int col);
159 static inline float cgm_mdet(const float *m);
160 static inline void cgm_mtranspose(float *m);
161 static inline void cgm_mcofmatrix(float *m);
162 static inline int cgm_minverse(float *m); /* returns 0 on success, -1 for singular */
164 static inline void cgm_mtranslation(float *m, float x, float y, float z);
165 static inline void cgm_mscaling(float *m, float sx, float sy, float sz);
166 static inline void cgm_mrotation_x(float *m, float angle);
167 static inline void cgm_mrotation_y(float *m, float angle);
168 static inline void cgm_mrotation_z(float *m, float angle);
169 static inline void cgm_mrotation_axis(float *m, int idx, float angle);
170 static inline void cgm_mrotation(float *m, float angle, float x, float y, float z);
171 static inline void cgm_mrotation_euler(float *m, float a, float b, float c, int mode);
172 static inline void cgm_mrotation_quat(float *m, const cgm_quat *q);
174 static inline void cgm_mtranslate(float *m, float x, float y, float z);
175 static inline void cgm_mscale(float *m, float sx, float sy, float sz);
176 static inline void cgm_mrotate_x(float *m, float angle);
177 static inline void cgm_mrotate_y(float *m, float angle);
178 static inline void cgm_mrotate_z(float *m, float angle);
179 static inline void cgm_mrotate_axis(float *m, int idx, float angle);
180 static inline void cgm_mrotate(float *m, float angle, float x, float y, float z);
181 static inline void cgm_mrotate_euler(float *m, float a, float b, float c, int mode);
182 static inline void cgm_mrotate_quat(float *m, const cgm_quat *q);
184 static inline void cgm_mpretranslate(float *m, float x, float y, float z);
185 static inline void cgm_mprescale(float *m, float sx, float sy, float sz);
186 static inline void cgm_mprerotate_x(float *m, float angle);
187 static inline void cgm_mprerotate_y(float *m, float angle);
188 static inline void cgm_mprerotate_z(float *m, float angle);
189 static inline void cgm_mprerotate_axis(float *m, int idx, float angle);
190 static inline void cgm_mprerotate(float *m, float angle, float x, float y, float z);
191 static inline void cgm_mprerotate_euler(float *m, float a, float b, float c, int mode);
192 static inline void cgm_mprerotate_quat(float *m, const cgm_quat *q);
194 static inline void cgm_mget_translation(const float *m, cgm_vec3 *res);
195 static inline void cgm_mget_rotation(const float *m, cgm_quat *res);
196 static inline void cgm_mget_scaling(const float *m, cgm_vec3 *res);
197 static inline void cgm_mget_frustum_plane(const float *m, int p, cgm_vec4 *res);
199 static inline void cgm_mlookat(float *m, const cgm_vec3 *pos, const cgm_vec3 *targ,
201 static inline void cgm_minv_lookat(float *m, const cgm_vec3 *pos, const cgm_vec3 *targ,
203 static inline void cgm_mortho(float *m, float left, float right, float bot, float top,
204 float znear, float zfar);
205 static inline void cgm_mfrustum(float *m, float left, float right, float bot, float top,
206 float znear, float zfar);
207 static inline void cgm_mperspective(float *m, float vfov, float aspect, float znear, float zfar);
209 static inline void cgm_mmirror(float *m, float a, float b, float c, float d);
211 /* --- operations on rays --- */
212 static inline void cgm_rcons(cgm_ray *r, float x, float y, float z, float dx, float dy, float dz);
214 static inline void cgm_rmul_mr(cgm_ray *ray, const float *m); /* m4x4 * ray */
215 static inline void cgm_rmul_rm(cgm_ray *ray, const float *m); /* ray * m4x4 */
217 static inline void cgm_rreflect(cgm_ray *ray, const cgm_vec3 *n);
218 static inline void cgm_rrefract(cgm_ray *ray, const cgm_vec3 *n, float ior);
220 /* --- miscellaneous utility functions --- */
221 static inline float cgm_deg_to_rad(float deg);
222 static inline float cgm_rad_to_deg(float rad);
224 static inline float cgm_smoothstep(float a, float b, float x);
225 static inline float cgm_lerp(float a, float b, float t);
226 static inline float cgm_bezier(float a, float b, float c, float d, float t);
227 static inline float cgm_bspline(float a, float b, float c, float d, float t);
228 static inline float cgm_spline(float a, float b, float c, float d, float t);
230 static inline void cgm_discrand(cgm_vec3 *v, float rad);
231 static inline void cgm_sphrand(cgm_vec3 *v, float rad);
233 static inline void cgm_unproject(cgm_vec3 *res, const cgm_vec3 *norm_scrpos,
234 const float *inv_viewproj);
235 static inline void cgm_glu_unproject(float winx, float winy, float winz,
236 const float *view, const float *proj, const int *vp,
237 float *objx, float *objy, float *objz);
239 static inline void cgm_pick_ray(cgm_ray *ray, float nx, float ny,
240 const float *viewmat, const float *projmat);
242 static inline void cgm_raypos(cgm_vec3 *p, const cgm_ray *ray, float t);
244 /* calculate barycentric coordinates of point pt in triangle (a, b, c) */
245 static inline void cgm_bary(cgm_vec3 *bary, const cgm_vec3 *a,
246 const cgm_vec3 *b, const cgm_vec3 *c, const cgm_vec3 *pt);
248 /* convert between unit vectors and spherical coordinates */
249 static inline void cgm_uvec_to_sph(float *theta, float *phi, const cgm_vec3 *v);
250 static inline void cgm_sph_to_uvec(cgm_vec3 *v, float theta, float phi);
252 #include "cgmvec3.inl"
253 #include "cgmvec4.inl"
254 #include "cgmquat.inl"
255 #include "cgmmat.inl"
256 #include "cgmray.inl"
257 #include "cgmmisc.inl"
263 #endif /* CGMATH_H_ */