1 #define __NR_PATH_C__
3 /*
4 * Pixel buffer rendering library
5 *
6 * Authors:
7 * Lauris Kaplinski <lauris@kaplinski.com>
8 *
9 * This code is in public domain
10 */
12 #include <glib/gmem.h>
13 #include "n-art-bpath.h"
14 #include "nr-rect.h"
15 #include "nr-path.h"
17 static void nr_curve_bbox (NR::Coord x000, NR::Coord y000, NR::Coord x001, NR::Coord y001, NR::Coord x011, NR::Coord y011, NR::Coord x111, NR::Coord y111, NRRect *bbox);
19 static void nr_curve_bbox(NR::Point const p000, NR::Point const p001,
20 NR::Point const p011, NR::Point const p111,
21 NRRect *bbox);
23 NRBPath *nr_path_duplicate_transform(NRBPath *d, NRBPath *s, NRMatrix const *transform)
24 {
25 int i;
27 if (!s->path) {
28 d->path = NULL;
29 return d;
30 }
32 i = 0;
33 while (s->path[i].code != NR_END) i += 1;
35 d->path = g_new (NArtBpath, i + 1);
37 i = 0;
38 while (s->path[i].code != NR_END) {
39 d->path[i].code = s->path[i].code;
40 if (s->path[i].code == NR_CURVETO) {
41 d->path[i].x1 = NR_MATRIX_DF_TRANSFORM_X (transform, s->path[i].x1, s->path[i].y1);
42 d->path[i].y1 = NR_MATRIX_DF_TRANSFORM_Y (transform, s->path[i].x1, s->path[i].y1);
43 d->path[i].x2 = NR_MATRIX_DF_TRANSFORM_X (transform, s->path[i].x2, s->path[i].y2);
44 d->path[i].y2 = NR_MATRIX_DF_TRANSFORM_Y (transform, s->path[i].x2, s->path[i].y2);
45 }
46 d->path[i].x3 = NR_MATRIX_DF_TRANSFORM_X (transform, s->path[i].x3, s->path[i].y3);
47 d->path[i].y3 = NR_MATRIX_DF_TRANSFORM_Y (transform, s->path[i].x3, s->path[i].y3);
48 i += 1;
49 }
50 d->path[i].code = NR_END;
52 return d;
53 }
55 NRBPath *nr_path_duplicate_transform(NRBPath *d, NRBPath *s, NR::Matrix const transform) {
56 NRMatrix tr = transform;
57 return nr_path_duplicate_transform(d, s, &tr);
58 }
60 NArtBpath* nr_artpath_affine(NArtBpath *s, NR::Matrix const &aff) {
61 NRBPath bp, abp;
62 bp.path = s;
63 nr_path_duplicate_transform(&abp, &bp, aff);
64 return abp.path;
65 }
67 static void
68 nr_line_wind_distance (NR::Coord x0, NR::Coord y0, NR::Coord x1, NR::Coord y1, NR::Point &pt, int *wind, NR::Coord *best)
69 {
70 NR::Coord Ax, Ay, Bx, By, Dx, Dy, s;
71 NR::Coord dist2;
73 /* Find distance */
74 Ax = x0;
75 Ay = y0;
76 Bx = x1;
77 By = y1;
78 Dx = x1 - x0;
79 Dy = y1 - y0;
80 const NR::Coord Px = pt[NR::X];
81 const NR::Coord Py = pt[NR::Y];
83 if (best) {
84 s = ((Px - Ax) * Dx + (Py - Ay) * Dy) / (Dx * Dx + Dy * Dy);
85 if (s <= 0.0) {
86 dist2 = (Px - Ax) * (Px - Ax) + (Py - Ay) * (Py - Ay);
87 } else if (s >= 1.0) {
88 dist2 = (Px - Bx) * (Px - Bx) + (Py - By) * (Py - By);
89 } else {
90 NR::Coord Qx, Qy;
91 Qx = Ax + s * Dx;
92 Qy = Ay + s * Dy;
93 dist2 = (Px - Qx) * (Px - Qx) + (Py - Qy) * (Py - Qy);
94 }
96 if (dist2 < (*best * *best)) *best = sqrt (dist2);
97 }
99 if (wind) {
100 /* Find wind */
101 if ((Ax >= Px) && (Bx >= Px)) return;
102 if ((Ay >= Py) && (By >= Py)) return;
103 if ((Ay < Py) && (By < Py)) return;
104 if (Ay == By) return;
105 /* Ctach upper y bound */
106 if (Ay == Py) {
107 if (Ax < Px) *wind -= 1;
108 return;
109 } else if (By == Py) {
110 if (Bx < Px) *wind += 1;
111 return;
112 } else {
113 NR::Coord Qx;
114 /* Have to calculate intersection */
115 Qx = Ax + Dx * (Py - Ay) / Dy;
116 if (Qx < Px) {
117 *wind += (Dy > 0.0) ? 1 : -1;
118 }
119 }
120 }
121 }
123 static void
124 nr_curve_bbox_wind_distance (NR::Coord x000, NR::Coord y000,
125 NR::Coord x001, NR::Coord y001,
126 NR::Coord x011, NR::Coord y011,
127 NR::Coord x111, NR::Coord y111,
128 NR::Point &pt,
129 NRRect *bbox, int *wind, NR::Coord *best,
130 NR::Coord tolerance)
131 {
132 NR::Coord x0, y0, x1, y1, len2;
133 int needdist, needwind, needline;
135 const NR::Coord Px = pt[NR::X];
136 const NR::Coord Py = pt[NR::Y];
138 needdist = 0;
139 needwind = 0;
140 needline = 0;
142 if (bbox) nr_curve_bbox (x000, y000, x001, y001, x011, y011, x111, y111, bbox);
144 x0 = MIN (x000, x001);
145 x0 = MIN (x0, x011);
146 x0 = MIN (x0, x111);
147 y0 = MIN (y000, y001);
148 y0 = MIN (y0, y011);
149 y0 = MIN (y0, y111);
150 x1 = MAX (x000, x001);
151 x1 = MAX (x1, x011);
152 x1 = MAX (x1, x111);
153 y1 = MAX (y000, y001);
154 y1 = MAX (y1, y011);
155 y1 = MAX (y1, y111);
157 if (best) {
158 /* Quicly adjust to endpoints */
159 len2 = (x000 - Px) * (x000 - Px) + (y000 - Py) * (y000 - Py);
160 if (len2 < (*best * *best)) *best = (NR::Coord) sqrt (len2);
161 len2 = (x111 - Px) * (x111 - Px) + (y111 - Py) * (y111 - Py);
162 if (len2 < (*best * *best)) *best = (NR::Coord) sqrt (len2);
164 if (((x0 - Px) < *best) && ((y0 - Py) < *best) && ((Px - x1) < *best) && ((Py - y1) < *best)) {
165 /* Point is inside sloppy bbox */
166 /* Now we have to decide, whether subdivide */
167 /* fixme: (Lauris) */
168 if (((y1 - y0) > 5.0) || ((x1 - x0) > 5.0)) {
169 needdist = 1;
170 } else {
171 needline = 1;
172 }
173 }
174 }
175 if (!needdist && wind) {
176 if ((y1 >= Py) && (y0 < Py) && (x0 < Px)) {
177 /* Possible intersection at the left */
178 /* Now we have to decide, whether subdivide */
179 /* fixme: (Lauris) */
180 if (((y1 - y0) > 5.0) || ((x1 - x0) > 5.0)) {
181 needwind = 1;
182 } else {
183 needline = 1;
184 }
185 }
186 }
188 if (needdist || needwind) {
189 NR::Coord x00t, x0tt, xttt, x1tt, x11t, x01t;
190 NR::Coord y00t, y0tt, yttt, y1tt, y11t, y01t;
191 NR::Coord s, t;
193 t = 0.5;
194 s = 1 - t;
196 x00t = s * x000 + t * x001;
197 x01t = s * x001 + t * x011;
198 x11t = s * x011 + t * x111;
199 x0tt = s * x00t + t * x01t;
200 x1tt = s * x01t + t * x11t;
201 xttt = s * x0tt + t * x1tt;
203 y00t = s * y000 + t * y001;
204 y01t = s * y001 + t * y011;
205 y11t = s * y011 + t * y111;
206 y0tt = s * y00t + t * y01t;
207 y1tt = s * y01t + t * y11t;
208 yttt = s * y0tt + t * y1tt;
210 nr_curve_bbox_wind_distance (x000, y000, x00t, y00t, x0tt, y0tt, xttt, yttt, pt, NULL, wind, best, tolerance);
211 nr_curve_bbox_wind_distance (xttt, yttt, x1tt, y1tt, x11t, y11t, x111, y111, pt, NULL, wind, best, tolerance);
212 } else if (1 || needline) {
213 nr_line_wind_distance (x000, y000, x111, y111, pt, wind, best);
214 }
215 }
217 void
218 nr_path_matrix_point_bbox_wind_distance (NRBPath *bpath, NR::Matrix const &m, NR::Point &pt,
219 NRRect *bbox, int *wind, NR::Coord *dist,
220 NR::Coord tolerance, NR::Rect *viewbox)
221 {
222 if (!bpath->path) {
223 if (wind) *wind = 0;
224 if (dist) *dist = NR_HUGE;
225 return;
226 }
228 NR::Coord x0 = 0;
229 NR::Coord y0 = 0;
230 NR::Coord x1 = 0;
231 NR::Coord y1 = 0;
232 NR::Coord x2 = 0;
233 NR::Coord y2 = 0;
234 NR::Coord x3 = 0;
235 NR::Coord y3 = 0;
237 // remembering the start of subpath
238 NR::Coord x_start = 0, y_start = 0; bool start_set = false;
239 NR::Rect swept;
241 for (const NArtBpath *p = bpath->path; p->code != NR_END; p+= 1) {
242 switch (p->code) {
243 case NR_MOVETO_OPEN:
244 case NR_MOVETO:
245 if (start_set) { // this is a new subpath
246 if (wind && (x0 != x_start || y0 != y_start)) // for correct fill picking, each subpath must be closed
247 nr_line_wind_distance (x0, y0, x_start, y_start, pt, wind, dist);
248 }
249 x0 = m[0] * p->x3 + m[2] * p->y3 + m[4];
250 y0 = m[1] * p->x3 + m[3] * p->y3 + m[5];
251 x_start = x0; y_start = y0; start_set = true;
252 if (bbox) {
253 bbox->x0 = (NR::Coord) MIN (bbox->x0, x0);
254 bbox->y0 = (NR::Coord) MIN (bbox->y0, y0);
255 bbox->x1 = (NR::Coord) MAX (bbox->x1, x0);
256 bbox->y1 = (NR::Coord) MAX (bbox->y1, y0);
257 }
258 break;
259 case NR_LINETO:
260 x3 = m[0] * p->x3 + m[2] * p->y3 + m[4];
261 y3 = m[1] * p->x3 + m[3] * p->y3 + m[5];
262 if (bbox) {
263 bbox->x0 = (NR::Coord) MIN (bbox->x0, x3);
264 bbox->y0 = (NR::Coord) MIN (bbox->y0, y3);
265 bbox->x1 = (NR::Coord) MAX (bbox->x1, x3);
266 bbox->y1 = (NR::Coord) MAX (bbox->y1, y3);
267 }
268 if (dist || wind) {
269 if (wind) { // we need to pick fill, so do what we're told
270 nr_line_wind_distance (x0, y0, x3, y3, pt, wind, dist);
271 } else { // only stroke is being picked; skip this segment if it's totally outside the viewbox
272 swept = NR::Rect(NR::Point(x0, y0), NR::Point(x3, y3));
273 //std::cout << "swept: " << swept;
274 //std::cout << "view: " << *viewbox;
275 //std::cout << "intersects? " << (swept.intersects(*viewbox)? "YES" : "NO") << "\n";
276 if (!viewbox || swept.intersects(*viewbox))
277 nr_line_wind_distance (x0, y0, x3, y3, pt, wind, dist);
278 }
279 }
280 x0 = x3;
281 y0 = y3;
282 break;
283 case NR_CURVETO:
284 {
285 x3 = m[0] * p->x3 + m[2] * p->y3 + m[4];
286 y3 = m[1] * p->x3 + m[3] * p->y3 + m[5];
287 x1 = m[0] * p->x1 + m[2] * p->y1 + m[4];
288 y1 = m[1] * p->x1 + m[3] * p->y1 + m[5];
289 x2 = m[0] * p->x2 + m[2] * p->y2 + m[4];
290 y2 = m[1] * p->x2 + m[3] * p->y2 + m[5];
292 swept = NR::Rect(NR::Point(x0, y0), NR::Point(x3, y3));
293 swept.expandTo(NR::Point(x1, y1));
294 swept.expandTo(NR::Point(x2, y2));
296 if (!viewbox || swept.intersects(*viewbox)) { // we see this segment, so do full processing
297 nr_curve_bbox_wind_distance (
298 x0, y0,
299 x1, y1,
300 x2, y2,
301 x3, y3,
302 pt,
303 bbox, wind, dist, tolerance);
304 } else {
305 if (wind) { // if we need fill, we can just pretend it's a straight line
306 nr_line_wind_distance (x0, y0, x3, y3, pt, wind, dist);
307 } else { // otherwise, skip it completely
308 }
309 }
310 x0 = x3;
311 y0 = y3;
312 }
313 break;
314 default:
315 break;
316 }
317 }
319 if (start_set) {
320 if (wind && (x0 != x_start || y0 != y_start)) // for correct picking, each subpath must be closed
321 nr_line_wind_distance (x0, y0, x_start, y_start, pt, wind, dist);
322 }
323 }
325 static void
326 nr_curve_bbox(NR::Point const p000, NR::Point const p001,
327 NR::Point const p011, NR::Point const p111,
328 NRRect *bbox)
329 {
330 using NR::X;
331 using NR::Y;
333 nr_curve_bbox(p000[X], p000[Y],
334 p001[X], p001[Y],
335 p011[X], p011[Y],
336 p111[X], p111[Y],
337 bbox);
338 }
340 /* Fast bbox calculation */
341 /* Thanks to Nathan Hurst for suggesting it */
343 static void
344 nr_curve_bbox (NR::Coord x000, NR::Coord y000, NR::Coord x001, NR::Coord y001, NR::Coord x011, NR::Coord y011, NR::Coord x111, NR::Coord y111, NRRect *bbox)
345 {
346 NR::Coord a, b, c, D;
348 bbox->x0 = (NR::Coord) MIN (bbox->x0, x111);
349 bbox->y0 = (NR::Coord) MIN (bbox->y0, y111);
350 bbox->x1 = (NR::Coord) MAX (bbox->x1, x111);
351 bbox->y1 = (NR::Coord) MAX (bbox->y1, y111);
353 /*
354 * xttt = s * (s * (s * x000 + t * x001) + t * (s * x001 + t * x011)) + t * (s * (s * x001 + t * x011) + t * (s * x011 + t * x111))
355 * xttt = s * (s2 * x000 + s * t * x001 + t * s * x001 + t2 * x011) + t * (s2 * x001 + s * t * x011 + t * s * x011 + t2 * x111)
356 * xttt = s * (s2 * x000 + 2 * st * x001 + t2 * x011) + t * (s2 * x001 + 2 * st * x011 + t2 * x111)
357 * xttt = s3 * x000 + 2 * s2t * x001 + st2 * x011 + s2t * x001 + 2st2 * x011 + t3 * x111
358 * xttt = s3 * x000 + 3s2t * x001 + 3st2 * x011 + t3 * x111
359 * xttt = s3 * x000 + (1 - s) 3s2 * x001 + (1 - s) * (1 - s) * 3s * x011 + (1 - s) * (1 - s) * (1 - s) * x111
360 * xttt = s3 * x000 + (3s2 - 3s3) * x001 + (3s - 6s2 + 3s3) * x011 + (1 - 2s + s2 - s + 2s2 - s3) * x111
361 * xttt = (x000 - 3 * x001 + 3 * x011 - x111) * s3 +
362 * ( 3 * x001 - 6 * x011 + 3 * x111) * s2 +
363 * ( 3 * x011 - 3 * x111) * s +
364 * ( x111)
365 * xttt' = (3 * x000 - 9 * x001 + 9 * x011 - 3 * x111) * s2 +
366 * ( 6 * x001 - 12 * x011 + 6 * x111) * s +
367 * ( 3 * x011 - 3 * x111)
368 */
370 a = 3 * x000 - 9 * x001 + 9 * x011 - 3 * x111;
371 b = 6 * x001 - 12 * x011 + 6 * x111;
372 c = 3 * x011 - 3 * x111;
374 /*
375 * s = (-b +/- sqrt (b * b - 4 * a * c)) / 2 * a;
376 */
377 if (fabs (a) < NR_EPSILON) {
378 /* s = -c / b */
379 if (fabs (b) > NR_EPSILON) {
380 double s, t, xttt;
381 s = -c / b;
382 if ((s > 0.0) && (s < 1.0)) {
383 t = 1.0 - s;
384 xttt = s * s * s * x000 + 3 * s * s * t * x001 + 3 * s * t * t * x011 + t * t * t * x111;
385 bbox->x0 = (float) MIN (bbox->x0, xttt);
386 bbox->x1 = (float) MAX (bbox->x1, xttt);
387 }
388 }
389 } else {
390 /* s = (-b +/- sqrt (b * b - 4 * a * c)) / 2 * a; */
391 D = b * b - 4 * a * c;
392 if (D >= 0.0) {
393 NR::Coord d, s, t, xttt;
394 /* Have solution */
395 d = sqrt (D);
396 s = (-b + d) / (2 * a);
397 if ((s > 0.0) && (s < 1.0)) {
398 t = 1.0 - s;
399 xttt = s * s * s * x000 + 3 * s * s * t * x001 + 3 * s * t * t * x011 + t * t * t * x111;
400 bbox->x0 = (NR::Coord) MIN (bbox->x0, xttt);
401 bbox->x1 = (NR::Coord) MAX (bbox->x1, xttt);
402 }
403 s = (-b - d) / (2 * a);
404 if ((s > 0.0) && (s < 1.0)) {
405 t = 1.0 - s;
406 xttt = s * s * s * x000 + 3 * s * s * t * x001 + 3 * s * t * t * x011 + t * t * t * x111;
407 bbox->x0 = (NR::Coord) MIN (bbox->x0, xttt);
408 bbox->x1 = (NR::Coord) MAX (bbox->x1, xttt);
409 }
410 }
411 }
413 a = 3 * y000 - 9 * y001 + 9 * y011 - 3 * y111;
414 b = 6 * y001 - 12 * y011 + 6 * y111;
415 c = 3 * y011 - 3 * y111;
417 if (fabs (a) < NR_EPSILON) {
418 /* s = -c / b */
419 if (fabs (b) > NR_EPSILON) {
420 double s, t, yttt;
421 s = -c / b;
422 if ((s > 0.0) && (s < 1.0)) {
423 t = 1.0 - s;
424 yttt = s * s * s * y000 + 3 * s * s * t * y001 + 3 * s * t * t * y011 + t * t * t * y111;
425 bbox->y0 = (float) MIN (bbox->y0, yttt);
426 bbox->y1 = (float) MAX (bbox->y1, yttt);
427 }
428 }
429 } else {
430 /* s = (-b +/- sqrt (b * b - 4 * a * c)) / 2 * a; */
431 D = b * b - 4 * a * c;
432 if (D >= 0.0) {
433 NR::Coord d, s, t, yttt;
434 /* Have solution */
435 d = sqrt (D);
436 s = (-b + d) / (2 * a);
437 if ((s > 0.0) && (s < 1.0)) {
438 t = 1.0 - s;
439 yttt = s * s * s * y000 + 3 * s * s * t * y001 + 3 * s * t * t * y011 + t * t * t * y111;
440 bbox->y0 = (NR::Coord) MIN (bbox->y0, yttt);
441 bbox->y1 = (NR::Coord) MAX (bbox->y1, yttt);
442 }
443 s = (-b - d) / (2 * a);
444 if ((s > 0.0) && (s < 1.0)) {
445 t = 1.0 - s;
446 yttt = s * s * s * y000 + 3 * s * s * t * y001 + 3 * s * t * t * y011 + t * t * t * y111;
447 bbox->y0 = (NR::Coord) MIN (bbox->y0, yttt);
448 bbox->y1 = (NR::Coord) MAX (bbox->y1, yttt);
449 }
450 }
451 }
452 }
454 void
455 nr_path_matrix_bbox_union(NRBPath const *bpath, NR::Matrix const &m,
456 NRRect *bbox)
457 {
458 using NR::X;
459 using NR::Y;
461 if (!bpath->path) {
462 return;
463 }
465 NR::Point prev0(0, 0);
466 for (NArtBpath const *p = bpath->path; p->code != NR_END; ++p) {
467 switch (p->code) {
468 case NR_MOVETO_OPEN:
469 case NR_MOVETO: {
470 NR::Point const c3(p->x3,
471 p->y3);
472 prev0 = c3 * m;
473 nr_rect_union_pt(bbox, prev0);
474 break;
475 }
477 case NR_LINETO: {
478 NR::Point const c3(p->x3,
479 p->y3);
480 NR::Point const endPt( c3 * m );
481 nr_rect_union_pt(bbox, endPt);
482 prev0 = endPt;
483 break;
484 }
486 case NR_CURVETO: {
487 NR::Point const c1(p->x1, p->y1);
488 NR::Point const c2(p->x2, p->y2);
489 NR::Point const c3(p->x3, p->y3);
490 NR::Point const endPt( c3 * m );
491 nr_curve_bbox(prev0,
492 c1 * m,
493 c2 * m,
494 endPt,
495 bbox);
496 prev0 = endPt;
497 break;
498 }
500 default:
501 break;
502 }
503 }
504 }