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294 lines
8.1 KiB
294 lines
8.1 KiB
/* Copyright (C) 2001-2007 Peter Selinger.
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* This file is part of Potrace. It is free software and it is covered
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* by the GNU General Public License. See the file COPYING for details. */
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/* $Id: render.c 147 2007-04-09 00:44:09Z selinger $ */
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#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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#include <string.h>
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#include "render.h"
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#include "greymap.h"
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#include "auxiliary.h"
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/* ---------------------------------------------------------------------- */
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/* routines for anti-aliased rendering of curves */
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/* we use the following method. Given a point (x,y) (with real-valued
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* coordinates) in the plane, let (xi,yi) be the integer part of the
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* coordinates, i.e., xi=floor(x), yi=floor(y). Define a path from
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* (x,y) to infinity as follows: path(x,y) =
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* (x,y)--(xi+1,y)--(xi+1,yi)--(+infty,yi). Now as the point (x,y)
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* moves smoothly across the plane, the path path(x,y) sweeps
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* (non-smoothly) across a certain area. We proportionately blacken
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* the area as the path moves "downward", and we whiten the area as
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* the path moves "upward". This way, after the point has traversed a
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* closed curve, the interior of the curve has been darkened
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* (counterclockwise movement) or lightened (clockwise movement). (The
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* "grey shift" is actually proportional to the winding number). By
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* choosing the above path with mostly integer coordinates, we achieve
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* that only pixels close to (x,y) receive grey values and are subject
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* to round-off errors. The grey value of pixels far away from (x,y)
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* is always in "integer" (where 0=black, 1=white). As a special
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* trick, we keep an accumulator rm->a1, which holds a double value to
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* be added to the grey value to be added to the current pixel
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* (xi,yi). Only when changing "current" pixels, we convert this
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* double value to an integer. This way we avoid round-off errors at
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* the meeting points of line segments. Another speedup measure is
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* that we sometimes use the rm->incrow_buf array to postpone
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* incrementing or decrementing an entire row. If incrow_buf[y]=x+1!=0,
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* then all the pixels (x,y),(x+1,y),(x+2,y),... are scheduled to be
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* incremented/decremented (which one is the case will be clear from
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* context). This keeps the greymap operations reasonably local. */
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/* allocate a new rendering state */
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render_t* render_new( greymap_t* gm )
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{
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render_t* rm;
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rm = (render_t*) malloc( sizeof(render_t) );
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if( !rm )
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{
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return NULL;
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}
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memset( rm, 0, sizeof(render_t) );
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rm->gm = gm;
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rm->incrow_buf = (int*) malloc( gm->h * sizeof(int) );
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if( !rm->incrow_buf )
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{
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free( rm );
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return NULL;
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}
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memset( rm->incrow_buf, 0, gm->h * sizeof(int) );
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return rm;
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}
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/* free a given rendering state. Note: this does not free the
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* underlying greymap. */
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void render_free( render_t* rm )
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{
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free( rm->incrow_buf );
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free( rm );
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}
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/* close path */
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void render_close( render_t* rm )
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{
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if( rm->x0 != rm->x1 || rm->y0 != rm->y1 )
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{
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render_lineto( rm, rm->x0, rm->y0 );
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}
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GM_INC( rm->gm, rm->x0i, rm->y0i, (rm->a0 + rm->a1) * 255 );
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/* assert (rm->x0i != rm->x1i || rm->y0i != rm->y1i); */
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/* the persistent state is now undefined */
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}
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/* move point */
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void render_moveto( render_t* rm, double x, double y )
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{
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/* close the previous path */
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render_close( rm );
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rm->x0 = rm->x1 = x;
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rm->y0 = rm->y1 = y;
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rm->x0i = (int) floor( rm->x0 );
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rm->x1i = (int) floor( rm->x1 );
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rm->y0i = (int) floor( rm->y0 );
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rm->y1i = (int) floor( rm->y1 );
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rm->a0 = rm->a1 = 0;
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}
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/* add b to pixels (x,y) and all pixels to the right of it. However,
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* use rm->incrow_buf as a buffer to economize on multiple calls */
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static void incrow( render_t* rm, int x, int y, int b )
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{
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int i, x0;
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if( y < 0 || y >= rm->gm->h )
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{
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return;
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}
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if( x < 0 )
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{
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x = 0;
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}
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else if( x > rm->gm->w )
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{
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x = rm->gm->w;
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}
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if( rm->incrow_buf[y] == 0 )
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{
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rm->incrow_buf[y] = x + 1; /* store x+1 so that we can use 0 for "vacant" */
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return;
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}
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x0 = rm->incrow_buf[y] - 1;
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rm->incrow_buf[y] = 0;
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if( x0 < x )
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{
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for( i = x0; i<x; i++ )
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{
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GM_INC( rm->gm, i, y, -b );
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}
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}
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else
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{
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for( i = x; i<x0; i++ )
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{
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GM_INC( rm->gm, i, y, b );
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}
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}
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}
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/* render a straight line */
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void render_lineto( render_t* rm, double x2, double y2 )
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{
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int x2i, y2i;
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double t0 = 2, s0 = 2;
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int sn, tn;
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double ss = 2, ts = 2;
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double r0, r1;
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int i, j;
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int rxi, ryi;
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int s;
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x2i = (int) floor( x2 );
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y2i = (int) floor( y2 );
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sn = abs( x2i - rm->x1i );
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tn = abs( y2i - rm->y1i );
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if( sn )
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{
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s0 = ( (x2>rm->x1 ? rm->x1i + 1 : rm->x1i) - rm->x1 ) / (x2 - rm->x1);
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ss = fabs( 1.0 / (x2 - rm->x1) );
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}
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if( tn )
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{
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t0 = ( (y2>rm->y1 ? rm->y1i + 1 : rm->y1i) - rm->y1 ) / (y2 - rm->y1);
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ts = fabs( 1.0 / (y2 - rm->y1) );
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}
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r0 = 0;
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i = 0;
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j = 0;
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rxi = rm->x1i;
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ryi = rm->y1i;
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while( i<sn || j<tn )
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{
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if( j>=tn || (i<sn && s0 + i * ss < t0 + j * ts) )
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{
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r1 = s0 + i * ss;
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i++;
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s = 1;
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}
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else
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{
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r1 = t0 + j * ts;
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j++;
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s = 0;
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}
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/* render line from r0 to r1 segment of (rm->x1,rm->y1)..(x2,y2) */
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/* move point to r1 */
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rm->a1 +=
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(r1 - r0) * (y2 - rm->y1) * ( rxi + 1 - ( (r0 + r1) / 2.0 * (x2 - rm->x1) + rm->x1 ) );
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/* move point across pixel boundary */
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if( s && x2>rm->x1 )
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{
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GM_INC( rm->gm, rxi, ryi, rm->a1 * 255 );
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rm->a1 = 0;
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rxi++;
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rm->a1 += rm->y1 + r1 * (y2 - rm->y1) - ryi;
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}
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else if( !s && y2>rm->y1 )
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{
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GM_INC( rm->gm, rxi, ryi, rm->a1 * 255 );
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rm->a1 = 0;
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incrow( rm, rxi + 1, ryi, 255 );
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ryi++;
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}
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else if( s && x2<=rm->x1 )
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{
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rm->a1 -= rm->y1 + r1 * (y2 - rm->y1) - ryi;
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GM_INC( rm->gm, rxi, ryi, rm->a1 * 255 );
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rm->a1 = 0;
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rxi--;
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}
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else if( !s && y2<=rm->y1 )
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{
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GM_INC( rm->gm, rxi, ryi, rm->a1 * 255 );
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rm->a1 = 0;
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ryi--;
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incrow( rm, rxi + 1, ryi, -255 );
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}
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r0 = r1;
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}
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/* move point to (x2,y2) */
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r1 = 1;
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rm->a1 += (r1 - r0) * (y2 - rm->y1) * ( rxi + 1 - ( (r0 + r1) / 2.0 * (x2 - rm->x1) + rm->x1 ) );
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rm->x1i = x2i;
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rm->y1i = y2i;
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rm->x1 = x2;
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rm->y1 = y2;
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/* assert (rxi != rm->x1i || ryi != rm->y1i); */
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}
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/* render a Bezier curve. */
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void render_curveto( render_t* rm,
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double x2,
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double y2,
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double x3,
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double y3,
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double x4,
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double y4 )
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{
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double x1, y1, dd0, dd1, dd, delta, e2, epsilon, t;
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x1 = rm->x1; /* starting point */
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y1 = rm->y1;
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/* we approximate the curve by small line segments. The interval
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* size, epsilon, is determined on the fly so that the distance
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* between the true curve and its approximation does not exceed the
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* desired accuracy delta. */
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delta = .1; /* desired accuracy, in pixels */
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/* let dd = maximal value of 2nd derivative over curve - this must
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* occur at an endpoint. */
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dd0 = sq( x1 - 2 * x2 + x3 ) + sq( y1 - 2 * y2 + y3 );
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dd1 = sq( x2 - 2 * x3 + x4 ) + sq( y2 - 2 * y3 + y4 );
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dd = 6 * sqrt( fmax( dd0, dd1 ) );
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e2 = 8 * delta <= dd ? 8 * delta / dd : 1;
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epsilon = sqrt( e2 ); /* necessary interval size */
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for( t = epsilon; t<1; t += epsilon )
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{
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render_lineto( rm, x1 * cu( 1 - t ) + 3 * x2 * sq( 1 - t ) * t + 3 * x3 * (1 - t) * sq(
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t ) + x4 * cu( t ),
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y1 * cu( 1 - t ) + 3 * y2 * sq( 1 - t ) * t + 3 * y3 * (1 - t) * sq(
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t ) + y4 * cu( t ) );
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}
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render_lineto( rm, x4, y4 );
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}
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