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 */
26 #include "art_bpath.h"
27 #include "art_vpath.h"
28 #include "art_vpath_bpath.h"
30 /* p must be allocated 2^level points. */
32 /* level must be >= 1 */
34 art_bezier_to_vec (double x0, double y0,
44 printf ("bezier_to_vec: %g,%g %g,%g %g,%g %g,%g %d\n",
45 x0, y0, x1, y1, x2, y2, x3, y3, level);
48 x_m = (x0 + 3 * (x1 + x2) + x3) * 0.125;
49 y_m = (y0 + 3 * (y1 + y2) + y3) * 0.125;
57 printf ("-> (%g, %g) -> (%g, %g)\n", x_m, y_m, x3, y3);
65 xa1 = (x0 + x1) * 0.5;
66 ya1 = (y0 + y1) * 0.5;
67 xa2 = (x0 + 2 * x1 + x2) * 0.25;
68 ya2 = (y0 + 2 * y1 + y2) * 0.25;
69 xb1 = (x1 + 2 * x2 + x3) * 0.25;
70 yb1 = (y1 + 2 * y2 + y3) * 0.25;
71 xb2 = (x2 + x3) * 0.5;
72 yb2 = (y2 + y3) * 0.5;
73 x_m = (xa2 + xb1) * 0.5;
74 y_m = (ya2 + yb1) * 0.5;
76 printf ("%g,%g %g,%g %g,%g %g,%g\n", xa1, ya1, xa2, ya2,
79 p = art_bezier_to_vec (x0, y0, xa1, ya1, xa2, ya2, x_m, y_m, p, level - 1);
80 p = art_bezier_to_vec (x_m, y_m, xb1, yb1, xb2, yb2, x3, y3, p, level - 1);
85 #define RENDER_LEVEL 4
86 #define RENDER_SIZE (1 << (RENDER_LEVEL))
89 * art_vpath_render_bez: Render a bezier segment into the vpath.
90 * @p_vpath: Where the pointer to the #ArtVpath structure is stored.
91 * @pn_points: Pointer to the number of points in *@p_vpath.
92 * @pn_points_max: Pointer to the number of points allocated.
93 * @x0: X coordinate of starting bezier point.
94 * @y0: Y coordinate of starting bezier point.
95 * @x1: X coordinate of first bezier control point.
96 * @y1: Y coordinate of first bezier control point.
97 * @x2: X coordinate of second bezier control point.
98 * @y2: Y coordinate of second bezier control point.
99 * @x3: X coordinate of ending bezier point.
100 * @y3: Y coordinate of ending bezier point.
101 * @flatness: Flatness control.
103 * Renders a bezier segment into the vector path, reallocating and
104 * updating *@p_vpath and *@pn_vpath_max as necessary. *@pn_vpath is
105 * incremented by the number of vector points added.
107 * This step includes (@x0, @y0) but not (@x3, @y3).
109 * The @flatness argument guides the amount of subdivision. The Adobe
110 * PostScript reference manual defines flatness as the maximum
111 * deviation between the any point on the vpath approximation and the
112 * corresponding point on the "true" curve, and we follow this
113 * definition here. A value of 0.25 should ensure high quality for aa
117 art_vpath_render_bez (ArtVpath **p_vpath, int *pn, int *pn_max,
118 double x0, double y0,
119 double x1, double y1,
120 double x2, double y2,
121 double x3, double y3,
126 double z1_dot, z2_dot;
127 double z1_perp, z2_perp;
136 /* It's possible to optimize this routine a fair amount.
138 First, once the _dot conditions are met, they will also be met in
139 all further subdivisions. So we might recurse to a different
140 routine that only checks the _perp conditions.
142 Second, the distance _should_ decrease according to fairly
143 predictable rules (a factor of 4 with each subdivision). So it might
144 be possible to note that the distance is within a factor of 4 of
145 acceptable, and subdivide once. But proving this might be hard.
147 Third, at the last subdivision, x_m and y_m can be computed more
148 expeditiously (as in the routine above).
150 Finally, if we were able to subdivide by, say 2 or 3, this would
151 allow considerably finer-grain control, i.e. fewer points for the
152 same flatness tolerance. This would speed things up downstream.
154 In any case, this routine is unlikely to be the bottleneck. It's
155 just that I have this undying quest for more speed...
162 /* z3_0_dot is dist z0-z3 squared */
163 z3_0_dot = x3_0 * x3_0 + y3_0 * y3_0;
165 /* todo: this test is far from satisfactory. */
166 if (z3_0_dot < 0.001)
169 /* we can avoid subdivision if:
171 z1 has distance no more than flatness from the z0-z3 line
173 z1 is no more z0'ward than flatness past z0-z3
175 z1 is more z0'ward than z3'ward on the line traversing z0-z3
177 and correspondingly for z2 */
179 /* perp is distance from line, multiplied by dist z0-z3 */
180 max_perp_sq = flatness * flatness * z3_0_dot;
182 z1_perp = (y1 - y0) * x3_0 - (x1 - x0) * y3_0;
183 if (z1_perp * z1_perp > max_perp_sq)
186 z2_perp = (y3 - y2) * x3_0 - (x3 - x2) * y3_0;
187 if (z2_perp * z2_perp > max_perp_sq)
190 z1_dot = (x1 - x0) * x3_0 + (y1 - y0) * y3_0;
191 if (z1_dot < 0 && z1_dot * z1_dot > max_perp_sq)
194 z2_dot = (x3 - x2) * x3_0 + (y3 - y2) * y3_0;
195 if (z2_dot < 0 && z2_dot * z2_dot > max_perp_sq)
198 if (z1_dot + z1_dot > z3_0_dot)
201 if (z2_dot + z2_dot > z3_0_dot)
205 /* don't subdivide */
206 art_vpath_add_point (p_vpath, pn, pn_max,
212 xa1 = (x0 + x1) * 0.5;
213 ya1 = (y0 + y1) * 0.5;
214 xa2 = (x0 + 2 * x1 + x2) * 0.25;
215 ya2 = (y0 + 2 * y1 + y2) * 0.25;
216 xb1 = (x1 + 2 * x2 + x3) * 0.25;
217 yb1 = (y1 + 2 * y2 + y3) * 0.25;
218 xb2 = (x2 + x3) * 0.5;
219 yb2 = (y2 + y3) * 0.5;
220 x_m = (xa2 + xb1) * 0.5;
221 y_m = (ya2 + yb1) * 0.5;
223 printf ("%g,%g %g,%g %g,%g %g,%g\n", xa1, ya1, xa2, ya2,
226 art_vpath_render_bez (p_vpath, pn, pn_max,
227 x0, y0, xa1, ya1, xa2, ya2, x_m, y_m, flatness);
228 art_vpath_render_bez (p_vpath, pn, pn_max,
229 x_m, y_m, xb1, yb1, xb2, yb2, x3, y3, flatness);
233 * art_bez_path_to_vec: Create vpath from bezier path.
235 * @flatness: Flatness control.
237 * Creates a vector path closely approximating the bezier path defined by
238 * @bez. The @flatness argument controls the amount of subdivision. In
239 * general, the resulting vpath deviates by at most @flatness pixels
240 * from the "ideal" path described by @bez.
242 * Return value: Newly allocated vpath.
245 art_bez_path_to_vec (const ArtBpath *bez, double flatness)
248 int vec_n, vec_n_max;
253 vec_n_max = RENDER_SIZE;
254 vec = art_new (ArtVpath, vec_n_max);
256 /* Initialization is unnecessary because of the precondition that the
257 bezier path does not begin with LINETO or CURVETO, but is here
258 to make the code warning-free. */
266 printf ("%s %g %g\n",
267 bez[bez_index].code == ART_CURVETO ? "curveto" :
268 bez[bez_index].code == ART_LINETO ? "lineto" :
269 bez[bez_index].code == ART_MOVETO ? "moveto" :
270 bez[bez_index].code == ART_MOVETO_OPEN ? "moveto-open" :
271 "end", bez[bez_index].x3, bez[bez_index].y3);
273 /* make sure space for at least one more code */
274 if (vec_n >= vec_n_max)
275 art_expand (vec, ArtVpath, vec_n_max);
276 switch (bez[bez_index].code)
278 case ART_MOVETO_OPEN:
281 x = bez[bez_index].x3;
282 y = bez[bez_index].y3;
283 vec[vec_n].code = bez[bez_index].code;
289 vec[vec_n].code = bez[bez_index].code;
296 printf ("%g,%g %g,%g %g,%g %g,%g\n", x, y,
297 bez[bez_index].x1, bez[bez_index].y1,
298 bez[bez_index].x2, bez[bez_index].y2,
299 bez[bez_index].x3, bez[bez_index].y3);
301 art_vpath_render_bez (&vec, &vec_n, &vec_n_max,
303 bez[bez_index].x1, bez[bez_index].y1,
304 bez[bez_index].x2, bez[bez_index].y2,
305 bez[bez_index].x3, bez[bez_index].y3,
307 x = bez[bez_index].x3;
308 y = bez[bez_index].y3;
312 while (bez[bez_index++].code != ART_END);