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