--- /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 "config.h"
+#include "art_vpath_bpath.h"
+
+#include <math.h>
+
+#include "art_misc.h"
+
+#include "art_bpath.h"
+#include "art_vpath.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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