+++ /dev/null
-/* Libart_LGPL - library of basic graphic primitives
- * Copyright (C) 1998 Raph Levien
- *
- * This library is free software; you can redistribute it and/or
- * modify it under the terms of the GNU Library General Public
- * License as published by the Free Software Foundation; either
- * version 2 of the License, or (at your option) any later version.
- *
- * This library is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- * Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with this library; if not, write to the
- * Free Software Foundation, Inc., 59 Temple Place - Suite 330,
- * Boston, MA 02111-1307, USA.
- */
-
-/* Basic constructors and operations for bezier paths */
-
-#include <math.h>
-
-#include "art_misc.h"
-
-#include "art_bpath.h"
-#include "art_vpath.h"
-#include "art_vpath_bpath.h"
-
-/* p must be allocated 2^level points. */
-
-/* level must be >= 1 */
-ArtPoint *
-art_bezier_to_vec (double x0, double y0,
- double x1, double y1,
- double x2, double y2,
- double x3, double y3,
- ArtPoint *p,
- int level)
-{
- double x_m, y_m;
-
-#ifdef VERBOSE
- printf ("bezier_to_vec: %g,%g %g,%g %g,%g %g,%g %d\n",
- x0, y0, x1, y1, x2, y2, x3, y3, level);
-#endif
- if (level == 1) {
- x_m = (x0 + 3 * (x1 + x2) + x3) * 0.125;
- y_m = (y0 + 3 * (y1 + y2) + y3) * 0.125;
- p->x = x_m;
- p->y = y_m;
- p++;
- p->x = x3;
- p->y = y3;
- p++;
-#ifdef VERBOSE
- printf ("-> (%g, %g) -> (%g, %g)\n", x_m, y_m, x3, y3);
-#endif
- } else {
- double xa1, ya1;
- double xa2, ya2;
- double xb1, yb1;
- double xb2, yb2;
-
- xa1 = (x0 + x1) * 0.5;
- ya1 = (y0 + y1) * 0.5;
- xa2 = (x0 + 2 * x1 + x2) * 0.25;
- ya2 = (y0 + 2 * y1 + y2) * 0.25;
- xb1 = (x1 + 2 * x2 + x3) * 0.25;
- yb1 = (y1 + 2 * y2 + y3) * 0.25;
- xb2 = (x2 + x3) * 0.5;
- yb2 = (y2 + y3) * 0.5;
- x_m = (xa2 + xb1) * 0.5;
- y_m = (ya2 + yb1) * 0.5;
-#ifdef VERBOSE
- printf ("%g,%g %g,%g %g,%g %g,%g\n", xa1, ya1, xa2, ya2,
- xb1, yb1, xb2, yb2);
-#endif
- p = art_bezier_to_vec (x0, y0, xa1, ya1, xa2, ya2, x_m, y_m, p, level - 1);
- p = art_bezier_to_vec (x_m, y_m, xb1, yb1, xb2, yb2, x3, y3, p, level - 1);
- }
- return p;
-}
-
-#define RENDER_LEVEL 4
-#define RENDER_SIZE (1 << (RENDER_LEVEL))
-
-/**
- * art_vpath_render_bez: Render a bezier segment into the vpath.
- * @p_vpath: Where the pointer to the #ArtVpath structure is stored.
- * @pn_points: Pointer to the number of points in *@p_vpath.
- * @pn_points_max: Pointer to the number of points allocated.
- * @x0: X coordinate of starting bezier point.
- * @y0: Y coordinate of starting bezier point.
- * @x1: X coordinate of first bezier control point.
- * @y1: Y coordinate of first bezier control point.
- * @x2: X coordinate of second bezier control point.
- * @y2: Y coordinate of second bezier control point.
- * @x3: X coordinate of ending bezier point.
- * @y3: Y coordinate of ending bezier point.
- * @flatness: Flatness control.
- *
- * Renders a bezier segment into the vector path, reallocating and
- * updating *@p_vpath and *@pn_vpath_max as necessary. *@pn_vpath is
- * incremented by the number of vector points added.
- *
- * This step includes (@x0, @y0) but not (@x3, @y3).
- *
- * The @flatness argument guides the amount of subdivision. The Adobe
- * PostScript reference manual defines flatness as the maximum
- * deviation between the any point on the vpath approximation and the
- * corresponding point on the "true" curve, and we follow this
- * definition here. A value of 0.25 should ensure high quality for aa
- * rendering.
-**/
-static void
-art_vpath_render_bez (ArtVpath **p_vpath, int *pn, int *pn_max,
- double x0, double y0,
- double x1, double y1,
- double x2, double y2,
- double x3, double y3,
- double flatness)
-{
- double x3_0, y3_0;
- double z3_0_dot;
- double z1_dot, z2_dot;
- double z1_perp, z2_perp;
- double max_perp_sq;
-
- double x_m, y_m;
- double xa1, ya1;
- double xa2, ya2;
- double xb1, yb1;
- double xb2, yb2;
-
- /* It's possible to optimize this routine a fair amount.
-
- First, once the _dot conditions are met, they will also be met in
- all further subdivisions. So we might recurse to a different
- routine that only checks the _perp conditions.
-
- Second, the distance _should_ decrease according to fairly
- predictable rules (a factor of 4 with each subdivision). So it might
- be possible to note that the distance is within a factor of 4 of
- acceptable, and subdivide once. But proving this might be hard.
-
- Third, at the last subdivision, x_m and y_m can be computed more
- expeditiously (as in the routine above).
-
- Finally, if we were able to subdivide by, say 2 or 3, this would
- allow considerably finer-grain control, i.e. fewer points for the
- same flatness tolerance. This would speed things up downstream.
-
- In any case, this routine is unlikely to be the bottleneck. It's
- just that I have this undying quest for more speed...
-
- */
-
- x3_0 = x3 - x0;
- y3_0 = y3 - y0;
-
- /* z3_0_dot is dist z0-z3 squared */
- z3_0_dot = x3_0 * x3_0 + y3_0 * y3_0;
-
- /* todo: this test is far from satisfactory. */
- if (z3_0_dot < 0.001)
- goto nosubdivide;
-
- /* we can avoid subdivision if:
-
- z1 has distance no more than flatness from the z0-z3 line
-
- z1 is no more z0'ward than flatness past z0-z3
-
- z1 is more z0'ward than z3'ward on the line traversing z0-z3
-
- and correspondingly for z2 */
-
- /* perp is distance from line, multiplied by dist z0-z3 */
- max_perp_sq = flatness * flatness * z3_0_dot;
-
- z1_perp = (y1 - y0) * x3_0 - (x1 - x0) * y3_0;
- if (z1_perp * z1_perp > max_perp_sq)
- goto subdivide;
-
- z2_perp = (y3 - y2) * x3_0 - (x3 - x2) * y3_0;
- if (z2_perp * z2_perp > max_perp_sq)
- goto subdivide;
-
- z1_dot = (x1 - x0) * x3_0 + (y1 - y0) * y3_0;
- if (z1_dot < 0 && z1_dot * z1_dot > max_perp_sq)
- goto subdivide;
-
- z2_dot = (x3 - x2) * x3_0 + (y3 - y2) * y3_0;
- if (z2_dot < 0 && z2_dot * z2_dot > max_perp_sq)
- goto subdivide;
-
- if (z1_dot + z1_dot > z3_0_dot)
- goto subdivide;
-
- if (z2_dot + z2_dot > z3_0_dot)
- goto subdivide;
-
- nosubdivide:
- /* don't subdivide */
- art_vpath_add_point (p_vpath, pn, pn_max,
- ART_LINETO, x3, y3);
- return;
-
- subdivide:
-
- xa1 = (x0 + x1) * 0.5;
- ya1 = (y0 + y1) * 0.5;
- xa2 = (x0 + 2 * x1 + x2) * 0.25;
- ya2 = (y0 + 2 * y1 + y2) * 0.25;
- xb1 = (x1 + 2 * x2 + x3) * 0.25;
- yb1 = (y1 + 2 * y2 + y3) * 0.25;
- xb2 = (x2 + x3) * 0.5;
- yb2 = (y2 + y3) * 0.5;
- x_m = (xa2 + xb1) * 0.5;
- y_m = (ya2 + yb1) * 0.5;
-#ifdef VERBOSE
- printf ("%g,%g %g,%g %g,%g %g,%g\n", xa1, ya1, xa2, ya2,
- xb1, yb1, xb2, yb2);
-#endif
- art_vpath_render_bez (p_vpath, pn, pn_max,
- x0, y0, xa1, ya1, xa2, ya2, x_m, y_m, flatness);
- art_vpath_render_bez (p_vpath, pn, pn_max,
- x_m, y_m, xb1, yb1, xb2, yb2, x3, y3, flatness);
-}
-
-/**
- * art_bez_path_to_vec: Create vpath from bezier path.
- * @bez: Bezier path.
- * @flatness: Flatness control.
- *
- * Creates a vector path closely approximating the bezier path defined by
- * @bez. The @flatness argument controls the amount of subdivision. In
- * general, the resulting vpath deviates by at most @flatness pixels
- * from the "ideal" path described by @bez.
- *
- * Return value: Newly allocated vpath.
- **/
-ArtVpath *
-art_bez_path_to_vec (const ArtBpath *bez, double flatness)
-{
- ArtVpath *vec;
- int vec_n, vec_n_max;
- int bez_index;
- double x, y;
-
- vec_n = 0;
- vec_n_max = RENDER_SIZE;
- vec = art_new (ArtVpath, vec_n_max);
-
- /* Initialization is unnecessary because of the precondition that the
- bezier path does not begin with LINETO or CURVETO, but is here
- to make the code warning-free. */
- x = 0;
- y = 0;
-
- bez_index = 0;
- do
- {
-#ifdef VERBOSE
- printf ("%s %g %g\n",
- bez[bez_index].code == ART_CURVETO ? "curveto" :
- bez[bez_index].code == ART_LINETO ? "lineto" :
- bez[bez_index].code == ART_MOVETO ? "moveto" :
- bez[bez_index].code == ART_MOVETO_OPEN ? "moveto-open" :
- "end", bez[bez_index].x3, bez[bez_index].y3);
-#endif
- /* make sure space for at least one more code */
- if (vec_n >= vec_n_max)
- art_expand (vec, ArtVpath, vec_n_max);
- switch (bez[bez_index].code)
- {
- case ART_MOVETO_OPEN:
- case ART_MOVETO:
- case ART_LINETO:
- x = bez[bez_index].x3;
- y = bez[bez_index].y3;
- vec[vec_n].code = bez[bez_index].code;
- vec[vec_n].x = x;
- vec[vec_n].y = y;
- vec_n++;
- break;
- case ART_END:
- vec[vec_n].code = bez[bez_index].code;
- vec[vec_n].x = 0;
- vec[vec_n].y = 0;
- vec_n++;
- break;
- case ART_CURVETO:
-#ifdef VERBOSE
- printf ("%g,%g %g,%g %g,%g %g,%g\n", x, y,
- bez[bez_index].x1, bez[bez_index].y1,
- bez[bez_index].x2, bez[bez_index].y2,
- bez[bez_index].x3, bez[bez_index].y3);
-#endif
- art_vpath_render_bez (&vec, &vec_n, &vec_n_max,
- x, y,
- bez[bez_index].x1, bez[bez_index].y1,
- bez[bez_index].x2, bez[bez_index].y2,
- bez[bez_index].x3, bez[bez_index].y3,
- flatness);
- x = bez[bez_index].x3;
- y = bez[bez_index].y3;
- break;
- }
- }
- while (bez[bez_index++].code != ART_END);
- return vec;
-}
-
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