1 /* Libart_LGPL - library of basic graphic primitives
2 * Copyright (C) 1998 Raph Levien
4 * This library is free software; you can redistribute it and/or
5 * modify it under the terms of the GNU Library General Public
6 * License as published by the Free Software Foundation; either
7 * version 2 of the License, or (at your option) any later version.
9 * This library is distributed in the hope that it will be useful,
10 * but WITHOUT ANY WARRANTY; without even the implied warranty of
11 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
12 * Library General Public License for more details.
14 * You should have received a copy of the GNU Library General Public
15 * License along with this library; if not, write to the
16 * Free Software Foundation, Inc., 59 Temple Place - Suite 330,
17 * Boston, MA 02111-1307, USA.
20 /* Basic constructors and operations for bezier paths */
23 #include "art_vpath_bpath.h"
29 #include "art_bpath.h"
30 #include "art_vpath.h"
32 /* p must be allocated 2^level points. */
34 /* level must be >= 1 */
36 art_bezier_to_vec (double x0, double y0,
46 printf ("bezier_to_vec: %g,%g %g,%g %g,%g %g,%g %d\n",
47 x0, y0, x1, y1, x2, y2, x3, y3, level);
50 x_m = (x0 + 3 * (x1 + x2) + x3) * 0.125;
51 y_m = (y0 + 3 * (y1 + y2) + y3) * 0.125;
59 printf ("-> (%g, %g) -> (%g, %g)\n", x_m, y_m, x3, y3);
67 xa1 = (x0 + x1) * 0.5;
68 ya1 = (y0 + y1) * 0.5;
69 xa2 = (x0 + 2 * x1 + x2) * 0.25;
70 ya2 = (y0 + 2 * y1 + y2) * 0.25;
71 xb1 = (x1 + 2 * x2 + x3) * 0.25;
72 yb1 = (y1 + 2 * y2 + y3) * 0.25;
73 xb2 = (x2 + x3) * 0.5;
74 yb2 = (y2 + y3) * 0.5;
75 x_m = (xa2 + xb1) * 0.5;
76 y_m = (ya2 + yb1) * 0.5;
78 printf ("%g,%g %g,%g %g,%g %g,%g\n", xa1, ya1, xa2, ya2,
81 p = art_bezier_to_vec (x0, y0, xa1, ya1, xa2, ya2, x_m, y_m, p, level - 1);
82 p = art_bezier_to_vec (x_m, y_m, xb1, yb1, xb2, yb2, x3, y3, p, level - 1);
87 #define RENDER_LEVEL 4
88 #define RENDER_SIZE (1 << (RENDER_LEVEL))
91 * art_vpath_render_bez: Render a bezier segment into the vpath.
92 * @p_vpath: Where the pointer to the #ArtVpath structure is stored.
93 * @pn_points: Pointer to the number of points in *@p_vpath.
94 * @pn_points_max: Pointer to the number of points allocated.
95 * @x0: X coordinate of starting bezier point.
96 * @y0: Y coordinate of starting bezier point.
97 * @x1: X coordinate of first bezier control point.
98 * @y1: Y coordinate of first bezier control point.
99 * @x2: X coordinate of second bezier control point.
100 * @y2: Y coordinate of second bezier control point.
101 * @x3: X coordinate of ending bezier point.
102 * @y3: Y coordinate of ending bezier point.
103 * @flatness: Flatness control.
105 * Renders a bezier segment into the vector path, reallocating and
106 * updating *@p_vpath and *@pn_vpath_max as necessary. *@pn_vpath is
107 * incremented by the number of vector points added.
109 * This step includes (@x0, @y0) but not (@x3, @y3).
111 * The @flatness argument guides the amount of subdivision. The Adobe
112 * PostScript reference manual defines flatness as the maximum
113 * deviation between the any point on the vpath approximation and the
114 * corresponding point on the "true" curve, and we follow this
115 * definition here. A value of 0.25 should ensure high quality for aa
119 art_vpath_render_bez (ArtVpath **p_vpath, int *pn, int *pn_max,
120 double x0, double y0,
121 double x1, double y1,
122 double x2, double y2,
123 double x3, double y3,
128 double z1_dot, z2_dot;
129 double z1_perp, z2_perp;
138 /* It's possible to optimize this routine a fair amount.
140 First, once the _dot conditions are met, they will also be met in
141 all further subdivisions. So we might recurse to a different
142 routine that only checks the _perp conditions.
144 Second, the distance _should_ decrease according to fairly
145 predictable rules (a factor of 4 with each subdivision). So it might
146 be possible to note that the distance is within a factor of 4 of
147 acceptable, and subdivide once. But proving this might be hard.
149 Third, at the last subdivision, x_m and y_m can be computed more
150 expeditiously (as in the routine above).
152 Finally, if we were able to subdivide by, say 2 or 3, this would
153 allow considerably finer-grain control, i.e. fewer points for the
154 same flatness tolerance. This would speed things up downstream.
156 In any case, this routine is unlikely to be the bottleneck. It's
157 just that I have this undying quest for more speed...
164 /* z3_0_dot is dist z0-z3 squared */
165 z3_0_dot = x3_0 * x3_0 + y3_0 * y3_0;
167 if (z3_0_dot < 0.001)
169 /* if start and end point are almost identical, the flatness tests
170 * don't work properly, so fall back on testing whether both of
171 * the other two control points are the same as the start point,
174 if (hypot(x1 - x0, y1 - y0) < 0.001
175 && hypot(x2 - x0, y2 - y0) < 0.001)
181 /* we can avoid subdivision if:
183 z1 has distance no more than flatness from the z0-z3 line
185 z1 is no more z0'ward than flatness past z0-z3
187 z1 is more z0'ward than z3'ward on the line traversing z0-z3
189 and correspondingly for z2 */
191 /* perp is distance from line, multiplied by dist z0-z3 */
192 max_perp_sq = flatness * flatness * z3_0_dot;
194 z1_perp = (y1 - y0) * x3_0 - (x1 - x0) * y3_0;
195 if (z1_perp * z1_perp > max_perp_sq)
198 z2_perp = (y3 - y2) * x3_0 - (x3 - x2) * y3_0;
199 if (z2_perp * z2_perp > max_perp_sq)
202 z1_dot = (x1 - x0) * x3_0 + (y1 - y0) * y3_0;
203 if (z1_dot < 0 && z1_dot * z1_dot > max_perp_sq)
206 z2_dot = (x3 - x2) * x3_0 + (y3 - y2) * y3_0;
207 if (z2_dot < 0 && z2_dot * z2_dot > max_perp_sq)
210 if (z1_dot + z1_dot > z3_0_dot)
213 if (z2_dot + z2_dot > z3_0_dot)
218 /* don't subdivide */
219 art_vpath_add_point (p_vpath, pn, pn_max,
225 xa1 = (x0 + x1) * 0.5;
226 ya1 = (y0 + y1) * 0.5;
227 xa2 = (x0 + 2 * x1 + x2) * 0.25;
228 ya2 = (y0 + 2 * y1 + y2) * 0.25;
229 xb1 = (x1 + 2 * x2 + x3) * 0.25;
230 yb1 = (y1 + 2 * y2 + y3) * 0.25;
231 xb2 = (x2 + x3) * 0.5;
232 yb2 = (y2 + y3) * 0.5;
233 x_m = (xa2 + xb1) * 0.5;
234 y_m = (ya2 + yb1) * 0.5;
236 printf ("%g,%g %g,%g %g,%g %g,%g\n", xa1, ya1, xa2, ya2,
239 art_vpath_render_bez (p_vpath, pn, pn_max,
240 x0, y0, xa1, ya1, xa2, ya2, x_m, y_m, flatness);
241 art_vpath_render_bez (p_vpath, pn, pn_max,
242 x_m, y_m, xb1, yb1, xb2, yb2, x3, y3, flatness);
246 * art_bez_path_to_vec: Create vpath from bezier path.
248 * @flatness: Flatness control.
250 * Creates a vector path closely approximating the bezier path defined by
251 * @bez. The @flatness argument controls the amount of subdivision. In
252 * general, the resulting vpath deviates by at most @flatness pixels
253 * from the "ideal" path described by @bez.
255 * Return value: Newly allocated vpath.
258 art_bez_path_to_vec (const ArtBpath *bez, double flatness)
261 int vec_n, vec_n_max;
266 vec_n_max = RENDER_SIZE;
267 vec = art_new (ArtVpath, vec_n_max);
269 /* Initialization is unnecessary because of the precondition that the
270 bezier path does not begin with LINETO or CURVETO, but is here
271 to make the code warning-free. */
279 printf ("%s %g %g\n",
280 bez[bez_index].code == ART_CURVETO ? "curveto" :
281 bez[bez_index].code == ART_LINETO ? "lineto" :
282 bez[bez_index].code == ART_MOVETO ? "moveto" :
283 bez[bez_index].code == ART_MOVETO_OPEN ? "moveto-open" :
284 "end", bez[bez_index].x3, bez[bez_index].y3);
286 /* make sure space for at least one more code */
287 if (vec_n >= vec_n_max)
288 art_expand (vec, ArtVpath, vec_n_max);
289 switch (bez[bez_index].code)
291 case ART_MOVETO_OPEN:
294 x = bez[bez_index].x3;
295 y = bez[bez_index].y3;
296 vec[vec_n].code = bez[bez_index].code;
302 vec[vec_n].code = bez[bez_index].code;
309 printf ("%g,%g %g,%g %g,%g %g,%g\n", x, y,
310 bez[bez_index].x1, bez[bez_index].y1,
311 bez[bez_index].x2, bez[bez_index].y2,
312 bez[bez_index].x3, bez[bez_index].y3);
314 art_vpath_render_bez (&vec, &vec_n, &vec_n_max,
316 bez[bez_index].x1, bez[bez_index].y1,
317 bez[bez_index].x2, bez[bez_index].y2,
318 bez[bez_index].x3, bez[bez_index].y3,
320 x = bez[bez_index].x3;
321 y = bez[bez_index].y3;
325 while (bez[bez_index++].code != ART_END);