1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
|
#ifndef VECMATH_H
#define VECMATH_H
#include <string.h>
#include <math.h>
#include <stdbool.h>
#include <stdio.h>
#define MATH_FUNC static inline
#define DEFINE_VECTOR(SIZE) \
typedef float vec##SIZE[SIZE];\
MATH_FUNC void vec##SIZE##_dup(vec##SIZE r, vec##SIZE const a)\
{\
for(int i = 0; i < SIZE; i++)\
r[i] = a[i];\
}\
\
MATH_FUNC void vec##SIZE##_add(vec##SIZE r, vec##SIZE const a, vec##SIZE const b)\
{\
for(int i = 0; i < SIZE; i++) \
r[i] = a[i] + b[i];\
}\
\
MATH_FUNC void vec##SIZE##_mul(vec##SIZE r, vec##SIZE const a, vec##SIZE const b)\
{\
for(int i = 0; i < SIZE; i++) \
r[i] = a[i] * b[i];\
}\
\
MATH_FUNC void vec##SIZE##_sub(vec##SIZE r, vec##SIZE const a, vec##SIZE const b)\
{\
for(int i = 0; i < SIZE; i++) \
r[i] = a[i] - b[i];\
}\
\
MATH_FUNC void vec##SIZE##_div(vec##SIZE r, vec##SIZE const a, vec##SIZE const b)\
{\
for(int i = 0; i < SIZE; i++) \
r[i] = a[i] / b[i];\
}\
\
MATH_FUNC void vec##SIZE##_add_scaled(vec##SIZE r, vec##SIZE const a, vec##SIZE const b, float scale)\
{\
for(int i = 0; i < SIZE; i++) \
r[i] = a[i] + b[i] * scale;\
}\
\
MATH_FUNC void vec##SIZE##_sub_scaled(vec##SIZE r, vec##SIZE const a, vec##SIZE const b, float scale)\
{\
for(int i = 0; i < SIZE; i++) \
r[i] = a[i] - b[i] * scale;\
}\
\
MATH_FUNC float vec##SIZE##_dot(vec##SIZE const a, vec##SIZE const b) \
{\
float r = 0.0;\
for(int i = 0; i < SIZE; i++) {\
r += a[i] * b[i];\
}\
return r;\
}\
\
MATH_FUNC void vec##SIZE##_normalize(vec##SIZE r, vec##SIZE const a)\
{\
float distr = 1.0/sqrtf(vec##SIZE##_dot(a, a));\
for(int i = 0; i < SIZE; i++) {\
r[i] = a[i] * distr;\
}\
}\
\
MATH_FUNC void vec##SIZE##_reflect(vec##SIZE r, vec##SIZE const incid, vec##SIZE const normal)\
{\
float dot = vec##SIZE##_dot(incid, normal);\
for(int i = 0; i < SIZE; i++) {\
r[i] = incid[i] - 2 * dot * normal[i];\
}\
}\
MATH_FUNC void vec##SIZE##_print(vec##SIZE r)\
{\
for(int i = 0; i < SIZE; i++) {\
printf("%f ", r[i]);\
}\
printf("\n");\
}\
MATH_FUNC void vec##SIZE##_floor(vec##SIZE r, vec##SIZE const a)\
{\
for(int i = 0; i < SIZE; i++) {\
r[i] = floorf(a[i]); \
}\
}\
MATH_FUNC void vec##SIZE##_ceil(vec##SIZE r, vec##SIZE const a)\
{\
for(int i = 0; i < SIZE; i++) {\
r[i] = ceilf(a[i]); \
}\
}\
MATH_FUNC void vec##SIZE##_round(vec##SIZE r, vec##SIZE const a)\
{\
for(int i = 0; i < SIZE; i++) {\
r[i] = roundf(a[i]); \
}\
}\
#define VEC2_DUP(v) (vec2){ v[0], v[1] }
#define VEC3_DUP(v) (vec3){ v[0], v[1], v[2] }
#define VEC4_DUP(v) (vec4){ v[0], v[1], v[2], v[3] }
DEFINE_VECTOR(2)
DEFINE_VECTOR(3)
DEFINE_VECTOR(4)
MATH_FUNC void vec3_cross(vec3 r, vec3 const a, vec3 const b)
{
r[0] = a[1] * b[2] - a[2] * b[1];
r[1] = a[2] * b[0] - a[0] * b[2];
r[2] = a[0] * b[1] - a[1] * b[0];
}
#define DEFINE_MATRIX(SIZE)\
typedef float mat##SIZE[SIZE][SIZE];\
\
MATH_FUNC void mat##SIZE##_add(mat##SIZE r, mat##SIZE a, mat##SIZE b)\
{\
for(int y = 0; y < SIZE; y++)\
for(int x = 0; x < SIZE; x++)\
r[y][x] = a[y][x] + b[y][x];\
}\
\
MATH_FUNC void mat##SIZE##_sub(mat##SIZE r, mat##SIZE a, mat##SIZE b)\
{\
for(int y = 0; y < SIZE; y++)\
for(int x = 0; x < SIZE; x++)\
r[y][x] = a[y][x] - b[y][x];\
}\
\
MATH_FUNC void mat##SIZE##_mul(mat##SIZE r, mat##SIZE a, mat##SIZE b)\
{\
mat##SIZE result = {0};\
for(int y = 0; y < SIZE; y++)\
for(int x = 0; x < SIZE; x++) {\
for(int i = 0; i < SIZE; i++) {\
result[x][y] += a[i][y] * b[x][i];\
}\
}\
memcpy(r, result, sizeof(result));\
}\
\
MATH_FUNC void mat##SIZE##_ident(mat##SIZE r)\
{\
for(int y = 0; y < SIZE; y++)\
for(int x = 0; x < SIZE; x++) {\
r[x][y] = x == y ? 1.0 : 0.0;\
}\
}\
MATH_FUNC void mat##SIZE##_mul_vec##SIZE(vec##SIZE r, mat##SIZE m, vec##SIZE v)\
{\
vec##SIZE result = {0};\
for(int i = 0; i < SIZE; i++) {\
for(int y = 0; y < SIZE; y++) {\
result[i] += m[i][y] * v[i];\
}\
}\
memcpy(r, result, sizeof(result));\
}\
MATH_FUNC void mat##SIZE##_print(mat##SIZE r)\
{\
float *f = &r[0][0];\
for(int i = 0; i < SIZE * SIZE; i++) {\
if(i % SIZE == 0)\
printf("\n");\
printf("%f ", f[i]);\
}\
printf("\n-----------\n");\
}\
DEFINE_MATRIX(2)
DEFINE_MATRIX(3)
DEFINE_MATRIX(4)
MATH_FUNC void affine2d_rotate(mat4 r, float angle)
{
const float sinv = sinf(angle),
cosv = cosf(angle);
mat4 trans = {
{ cosv, -sinv, 0, 0 },
{ sinv, cosv, 0, 0 },
{ 0, 0, 1, 0 },
{ 0, 0, 0, 1 }
};
mat4_mul(r, trans, r);
}
MATH_FUNC void affine2d_translate(mat4 r, vec2 pos)
{
mat4 trans = {
{ 1, 0, 0, 0 },
{ 0, 1, 0, 0 },
{ 0, 0, 1, 0 },
{ pos[0], pos[1], 0, 1 }
};
mat4_mul(r, trans, r);
}
MATH_FUNC void affine2d_scale(mat4 r, vec2 s)
{
mat4 trans = {
{ s[0], 0, 0, 0 },
{ 0, s[1], 0, 0 },
{ 0, 0, 1, 0 },
{ 0, 0, 0, 1 }
};
mat4_mul(r, trans, r);
}
MATH_FUNC void affine2d_setup_ortho_window(mat4 r, const float w, const float h)
{
r[0][0] = 2.0 / w;
r[1][1] = -2.0 / h;
r[2][2] = -1.0;
r[3][0] = -1.0;
r[3][1] = 1.0;
r[3][2] = 0.0;
r[3][3] = 1.0;
}
typedef struct Rectangle {
vec2 position;
vec2 half_size;
} Rectangle;
static inline Rectangle rect_from_boundaries(vec2 min, vec2 max)
{
Rectangle rect;
rect.half_size[0] = (max[0] - min[0]) / 2.0;
rect.half_size[1] = (max[1] - min[1]) / 2.0;
rect.position[0] = rect.half_size[0] + min[0];
rect.position[1] = rect.half_size[1] + min[1];
return rect;
}
static inline void rect_boundaries(vec2 out_min, vec2 out_max, Rectangle *rect)
{
vec2_sub(out_min, rect->position, rect->half_size);
vec2_add(out_max, rect->position, rect->half_size);
}
static inline void rect_intersect(Rectangle *rect_out, Rectangle *rect1, Rectangle *rect2)
{
vec2 min1, max1;
vec2 min2, max2;
vec2 itsc_min, itsc_max;
rect_boundaries(min1, max1, rect1);
rect_boundaries(min2, max2, rect2);
itsc_min[0] = min1[0] > min2[0] ? min1[0] : min2[0];
itsc_min[1] = min1[1] > min2[1] ? min1[1] : min2[1];
itsc_max[0] = max1[0] < max2[0] ? max1[0] : max2[0];
itsc_max[1] = max1[1] < max2[1] ? max1[1] : max2[1];
*rect_out = rect_from_boundaries(itsc_min, itsc_max);
}
static inline bool rect_contains_point(Rectangle *rect, vec2 point)
{
vec2 min, max;
vec2_add(max, rect->position, rect->half_size);
vec2_sub(min, rect->position, rect->half_size);
bool x_contains = point[0] > min[0] && point[0] < max[0];
bool y_contains = point[1] > min[1] && point[1] < max[1];
return x_contains && y_contains;
}
static inline bool rect_contains_rect(Rectangle *outer, Rectangle *inner)
{
vec2 min1, max1;
vec2 min2, max2;
rect_boundaries(min1, max1, outer);
rect_boundaries(min2, max2, inner);
return min1[0] <= min2[0] &&
min1[1] <= min2[1] &&
max1[0] >= max2[0] &&
max1[1] >= max2[1];
}
static inline void rect_accomodate(Rectangle *rect_out, Rectangle *rparent, Rectangle *rchild)
{
vec2 min1, max1;
vec2 min2, max2;
vec2 itsc_min, itsc_max;
rect_boundaries(min1, max1, rparent);
rect_boundaries(min2, max2, rchild);
itsc_min[0] = min1[0] < min2[0] ? min1[0] : min2[0];
itsc_min[1] = min1[1] < min2[1] ? min1[1] : min2[1];
itsc_max[0] = max1[0] > max2[0] ? max1[0] : max2[0];
itsc_max[1] = max1[1] > max2[1] ? max1[1] : max2[1];
*rect_out = rect_from_boundaries(itsc_min, itsc_max);
}
#undef MATH_FUNC
#endif
|
