зеркало из https://github.com/mozilla/pjs.git
318 строки
9.1 KiB
C
318 строки
9.1 KiB
C
/* 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;
|
|
}
|
|
|