Skip to content
Navigation Menu
{{ message }}
-
-
Notifications
You must be signed in to change notification settings - Fork 646
Expand file tree
/
Copy pathtobj_tess.c
More file actions
279 lines (246 loc) · 9.39 KB
/
Copy pathtobj_tess.c
File metadata and controls
279 lines (246 loc) · 9.39 KB
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
/*
* tobj_tess.c -- robust polygon tessellation (see tobj_tess.h).
*
* Strategy: project the 3D ring to 2D (Newell normal, bbox fallback), then
* triangulate the 2D polygon with a convex fan fast-path or robust ear
* clipping. All 2D work is done in double precision regardless of the input
* real type. The ear-clip loop is monotone in the number of remaining
* vertices (an unconditional force-clip backstop), so it always terminates
* and always emits exactly n-2 triangles for n >= 3.
*
* SPDX-License-Identifier: MIT
*/
#include "tobj_tess.h"
/* Relative epsilon for the 2D "is zero area" test (scaled by polygon size). */
#define TOBJ_TESS_REL 1e-9
/* Newell-normal degeneracy threshold (relative to coord magnitude^4). */
#define TOBJ_TESS_REL_N 1e-18
/* Largest n handled with on-stack scratch when no buffer/allocator is given. */
#define TOBJ_TESS_STACK_N 64u
#define TOBJ_TESS_STACK_BYTES 2048u
/* ----------------------------------------------------------------------- */
/* scratch layout */
/* ----------------------------------------------------------------------- */
typedef struct {
double *p2d; /* 2*n */
uint32_t *nxt; /* n */
uint32_t *prv; /* n */
uint8_t *reflex; /* (n+7)/8 */
} tobj_tess_work;
static size_t tobj_tess_align(size_t x, size_t a) {
return (x + (a - 1)) & ~(a - 1);
}
size_t tobj_tess_scratch_size(uint32_t n) {
size_t sn = (size_t)n;
size_t a = tobj_tess_align(sn * 2u * sizeof(double), 16);
size_t b = tobj_tess_align(sn * sizeof(uint32_t), 16);
size_t c = tobj_tess_align(sn * sizeof(uint32_t), 16);
size_t d = tobj_tess_align((sn + 7u) / 8u, 16);
return a + b + c + d;
}
static int tobj_tess_work_bind(tobj_tess_work *w, void *scratch, size_t size,
uint32_t n) {
if (size < tobj_tess_scratch_size(n)) return 0;
unsigned char *base = (unsigned char *)scratch;
size_t sn = (size_t)n;
size_t off = 0;
w->p2d = (double *)(base + off);
off += tobj_tess_align(sn * 2u * sizeof(double), 16);
w->nxt = (uint32_t *)(base + off);
off += tobj_tess_align(sn * sizeof(uint32_t), 16);
w->prv = (uint32_t *)(base + off);
off += tobj_tess_align(sn * sizeof(uint32_t), 16);
w->reflex = (uint8_t *)(base + off);
return 1;
}
static void tobj_tess_set_reflex(tobj_tess_work *w, uint32_t i, int v) {
if (v)
w->reflex[i >> 3] |= (uint8_t)(1u << (i & 7u));
else
w->reflex[i >> 3] &= (uint8_t)~(1u << (i & 7u));
}
static int tobj_tess_is_reflex(tobj_tess_work *w, uint32_t i) {
return (w->reflex[i >> 3] >> (i & 7u)) & 1u;
}
/* ----------------------------------------------------------------------- */
/* 2D predicates */
/* ----------------------------------------------------------------------- */
static double tobj_orient2d(const double *a, const double *b, const double *c) {
return (b[0] - a[0]) * (c[1] - a[1]) - (b[1] - a[1]) * (c[0] - a[0]);
}
static double tobj_dabs(double x) { return x < 0 ? -x : x; }
static int tobj_is_finite(double x) { return x == x && tobj_dabs(x) < 1e308; }
/* Strictly-inside test for triangle (a,b,c) wound so that `wind` * area > 0. */
static int tobj_point_in_tri(const double *p, const double *a, const double *b,
const double *c, double wind, double eps) {
double d1 = wind * tobj_orient2d(a, b, p);
double d2 = wind * tobj_orient2d(b, c, p);
double d3 = wind * tobj_orient2d(c, a, p);
return d1 > eps && d2 > eps && d3 > eps;
}
/* ----------------------------------------------------------------------- */
/* 2D triangulation core (operates entirely on w->p2d) */
/* ----------------------------------------------------------------------- */
static void tobj_tess_emit(uint32_t *out, uint32_t *k, uint32_t a, uint32_t b,
uint32_t c) {
out[*k * 3u + 0u] = a;
out[*k * 3u + 1u] = b;
out[*k * 3u + 2u] = c;
(*k)++;
}
/* Fan from corner 0; always valid count, used for convex/forced cases. */
static void tobj_tess_fan(uint32_t n, uint32_t *out, uint32_t *kp) {
for (uint32_t k = 1; k + 1 < n; k++) tobj_tess_emit(out, kp, 0, k, k + 1);
}
static double tobj_tess_scale2d(const double *p2d, uint32_t n) {
double m = 0.0;
for (uint32_t i = 0; i < n; i++) {
double x = tobj_dabs(p2d[2 * i]);
double y = tobj_dabs(p2d[2 * i + 1]);
if (x > m) m = x;
if (y > m) m = y;
}
return m;
}
static double tobj_tess_signed_area(const double *p2d, uint32_t n) {
double a = 0.0;
for (uint32_t i = 0; i < n; i++) {
uint32_t j = (i + 1u) % n;
a += p2d[2 * i] * p2d[2 * j + 1] - p2d[2 * j] * p2d[2 * i + 1];
}
return 0.5 * a;
}
static const double *tobj_tess_pt(tobj_tess_work *w, uint32_t i) {
return &w->p2d[2 * i];
}
/* Recompute and store the reflex flag for active vertex `cur`. */
static void tobj_tess_update_reflex(tobj_tess_work *w, uint32_t cur,
double wind, double eps_a) {
uint32_t p = w->prv[cur], n = w->nxt[cur];
double o = wind * tobj_orient2d(tobj_tess_pt(w, p), tobj_tess_pt(w, cur),
tobj_tess_pt(w, n));
tobj_tess_set_reflex(w, cur, o < -eps_a ? 1 : 0);
}
/* Triangulate the ring (n>=5) already projected into w->p2d.
* Returns OK or DEGENERATE_BESTEFFORT. Always writes n-2 triangles. */
static tobj_tess_status tobj_tess_run2d(tobj_tess_work *w, uint32_t n,
uint32_t *out, uint32_t flags) {
uint32_t k = 0;
if (flags & (TOBJ_TESS_FLAG_FORCE_FAN | TOBJ_TESS_FLAG_ASSUME_CONVEX)) {
tobj_tess_fan(n, out, &k);
return (flags & TOBJ_TESS_FLAG_FORCE_FAN) ? TOBJ_TESS_DEGENERATE_BESTEFFORT
: TOBJ_TESS_OK;
}
double scale = tobj_tess_scale2d(w->p2d, n);
double eps_a = scale * scale * TOBJ_TESS_REL;
double area = tobj_tess_signed_area(w->p2d, n);
double wind = area < 0 ? -1.0 : 1.0;
/* Build ring + reflex flags; count reflex vertices. */
uint32_t reflex_count = 0;
for (uint32_t i = 0; i < n; i++) {
w->nxt[i] = (i + 1u) % n;
w->prv[i] = (i + n - 1u) % n;
}
for (uint32_t i = 0; i < n; i++) {
double o = wind * tobj_orient2d(tobj_tess_pt(w, w->prv[i]),
tobj_tess_pt(w, i),
tobj_tess_pt(w, w->nxt[i]));
int rfx = o < -eps_a ? 1 : 0;
tobj_tess_set_reflex(w, i, rfx);
reflex_count += (uint32_t)rfx;
}
/* Convex (and simple) -> fan fast path. */
if (reflex_count == 0) {
tobj_tess_fan(n, out, &k);
/* near-zero overall area means a degenerate (collinear) polygon */
return tobj_dabs(area) <= eps_a ? TOBJ_TESS_DEGENERATE_BESTEFFORT
: TOBJ_TESS_OK;
}
tobj_tess_status status = TOBJ_TESS_OK;
uint32_t remaining = n;
uint32_t cur = 0;
uint32_t guard = 0;
int relax = 0; /* 0,1,2 escalation level */
while (remaining > 3) {
uint32_t prev = w->prv[cur];
uint32_t next = w->nxt[cur];
const double *pp = tobj_tess_pt(w, prev);
const double *pc = tobj_tess_pt(w, cur);
const double *pn = tobj_tess_pt(w, next);
double raw = tobj_orient2d(pp, pc, pn);
double o = wind * raw;
double eps_scaled = eps_a * (relax == 0 ? 1.0 : (relax == 1 ? 1e3 : 1e12));
int clip = 0;
if (tobj_dabs(raw) <= eps_scaled) {
/* collinear / zero-area corner: removable degenerate ear */
clip = 1;
status = TOBJ_TESS_DEGENERATE_BESTEFFORT;
} else if (o > eps_scaled) {
/* convex corner: ensure no reflex active vertex lies inside */
int blocked = 0;
uint32_t r = w->nxt[next];
while (r != prev) {
if (tobj_tess_is_reflex(w, r) &&
tobj_point_in_tri(tobj_tess_pt(w, r), pp, pc, pn, wind,
eps_scaled)) {
blocked = 1;
break;
}
r = w->nxt[r];
}
if (!blocked) clip = 1;
}
if (clip) {
tobj_tess_emit(out, &k, prev, cur, next);
w->nxt[prev] = next;
w->prv[next] = prev;
remaining--;
tobj_tess_update_reflex(w, prev, wind, eps_a);
tobj_tess_update_reflex(w, next, wind, eps_a);
cur = next;
guard = 0;
relax = 0;
continue;
}
cur = next;
if (++guard > remaining) {
if (relax < 2) {
relax++;
guard = 0;
} else {
/* backstop: force-clip current corner to guarantee progress */
prev = w->prv[cur];
next = w->nxt[cur];
tobj_tess_emit(out, &k, prev, cur, next);
w->nxt[prev] = next;
w->prv[next] = prev;
remaining--;
tobj_tess_update_reflex(w, prev, wind, eps_a);
tobj_tess_update_reflex(w, next, wind, eps_a);
cur = next;
guard = 0;
relax = 0;
status = TOBJ_TESS_DEGENERATE_BESTEFFORT;
}
}
}
/* final triangle from the three survivors */
uint32_t a = cur;
uint32_t b = w->nxt[a];
uint32_t c = w->nxt[b];
tobj_tess_emit(out, &k, a, b, c);
return status;
}
/* ----------------------------------------------------------------------- */
/* per-precision wrappers (projection + dispatch) */
/* ----------------------------------------------------------------------- */
#define TOBJ_TESS_REAL float
#define TOBJ_TESS_SUF _f
#include "tobj_tess_impl.inc"
#undef TOBJ_TESS_REAL
#undef TOBJ_TESS_SUF
#define TOBJ_TESS_REAL double
#define TOBJ_TESS_SUF _d
#include "tobj_tess_impl.inc"
#undef TOBJ_TESS_REAL
#undef TOBJ_TESS_SUF
You can’t perform that action at this time.