kicad/potrace/render.cpp

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/* Copyright (C) 2001-2017 Peter Selinger.
* This file is part of Potrace. It is free software and it is covered
* by the GNU General Public License. See the file COPYING for details. */
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "auxiliary.h"
#include "greymap.h"
#include "render.h"
/* ---------------------------------------------------------------------- */
/* routines for anti-aliased rendering of curves */
/* we use the following method. Given a point (x,y) (with real-valued
* coordinates) in the plane, let (xi,yi) be the integer part of the
* coordinates, i.e., xi=floor(x), yi=floor(y). Define a path from
* (x,y) to infinity as follows: path(x,y) =
* (x,y)--(xi+1,y)--(xi+1,yi)--(+infty,yi). Now as the point (x,y)
* moves smoothly across the plane, the path path(x,y) sweeps
* (non-smoothly) across a certain area. We proportionately blacken
* the area as the path moves "downward", and we whiten the area as
* the path moves "upward". This way, after the point has traversed a
* closed curve, the interior of the curve has been darkened
* (counterclockwise movement) or lightened (clockwise movement). (The
* "grey shift" is actually proportional to the winding number). By
* choosing the above path with mostly integer coordinates, we achieve
* that only pixels close to (x,y) receive grey values and are subject
* to round-off errors. The grey value of pixels far away from (x,y)
* is always in "integer" (where 0=black, 1=white). As a special
* trick, we keep an accumulator rm->a1, which holds a double value to
* be added to the grey value to be added to the current pixel
* (xi,yi). Only when changing "current" pixels, we convert this
* double value to an integer. This way we avoid round-off errors at
* the meeting points of line segments. Another speedup measure is
* that we sometimes use the rm->incrow_buf array to postpone
* incrementing or decrementing an entire row. If incrow_buf[y]=x+1!=0,
* then all the pixels (x,y),(x+1,y),(x+2,y),... are scheduled to be
* incremented/decremented (which one is the case will be clear from
* context). This keeps the greymap operations reasonably local. */
/* allocate a new rendering state */
render_t* render_new( greymap_t* gm )
{
render_t* rm;
rm = (render_t*) malloc( sizeof( render_t ) );
if( !rm )
{
return NULL;
}
memset( rm, 0, sizeof( render_t ) );
rm->gm = gm;
rm->incrow_buf = (int*) calloc( gm->h, sizeof( int ) );
if( !rm->incrow_buf )
{
free( rm );
return NULL;
}
return rm;
}
/* free a given rendering state. Note: this does not free the
* underlying greymap. */
void render_free( render_t* rm )
{
free( rm->incrow_buf );
free( rm );
}
/* close path */
void render_close( render_t* rm )
{
if( rm->x0 != rm->x1 || rm->y0 != rm->y1 )
{
render_lineto( rm, rm->x0, rm->y0 );
}
GM_INC( rm->gm, rm->x0i, rm->y0i, ( rm->a0 + rm->a1 ) * 255 );
/* assert (rm->x0i != rm->x1i || rm->y0i != rm->y1i); */
/* the persistent state is now undefined */
}
/* move point */
void render_moveto( render_t* rm, double x, double y )
{
/* close the previous path */
render_close( rm );
rm->x0 = rm->x1 = x;
rm->y0 = rm->y1 = y;
rm->x0i = (int) floor( rm->x0 );
rm->x1i = (int) floor( rm->x1 );
rm->y0i = (int) floor( rm->y0 );
rm->y1i = (int) floor( rm->y1 );
rm->a0 = rm->a1 = 0;
}
/* add b to pixels (x,y) and all pixels to the right of it. However,
* use rm->incrow_buf as a buffer to economize on multiple calls */
static void incrow( render_t* rm, int x, int y, int b )
{
int i, x0;
if( y < 0 || y >= rm->gm->h )
{
return;
}
if( x < 0 )
{
x = 0;
}
else if( x > rm->gm->w )
{
x = rm->gm->w;
}
if( rm->incrow_buf[y] == 0 )
{
rm->incrow_buf[y] = x + 1; /* store x+1 so that we can use 0 for "vacant" */
return;
}
x0 = rm->incrow_buf[y] - 1;
rm->incrow_buf[y] = 0;
if( x0 < x )
{
for( i = x0; i < x; i++ )
{
GM_INC( rm->gm, i, y, -b );
}
}
else
{
for( i = x; i < x0; i++ )
{
GM_INC( rm->gm, i, y, b );
}
}
}
/* render a straight line */
void render_lineto( render_t* rm, double x2, double y2 )
{
int x2i, y2i;
double t0 = 2, s0 = 2;
int sn, tn;
double ss = 2, ts = 2;
double r0, r1;
int i, j;
int rxi, ryi;
int s;
x2i = (int) floor( x2 );
y2i = (int) floor( y2 );
sn = abs( x2i - rm->x1i );
tn = abs( y2i - rm->y1i );
if( sn )
{
s0 = ( ( x2 > rm->x1 ? rm->x1i + 1 : rm->x1i ) - rm->x1 ) / ( x2 - rm->x1 );
ss = fabs( 1.0 / ( x2 - rm->x1 ) );
}
if( tn )
{
t0 = ( ( y2 > rm->y1 ? rm->y1i + 1 : rm->y1i ) - rm->y1 ) / ( y2 - rm->y1 );
ts = fabs( 1.0 / ( y2 - rm->y1 ) );
}
r0 = 0;
i = 0;
j = 0;
rxi = rm->x1i;
ryi = rm->y1i;
while( i < sn || j < tn )
{
if( j >= tn || ( i < sn && s0 + i * ss < t0 + j * ts ) )
{
r1 = s0 + i * ss;
i++;
s = 1;
}
else
{
r1 = t0 + j * ts;
j++;
s = 0;
}
/* render line from r0 to r1 segment of (rm->x1,rm->y1)..(x2,y2) */
/* move point to r1 */
rm->a1 += ( r1 - r0 ) * ( y2 - rm->y1 )
* ( rxi + 1 - ( ( r0 + r1 ) / 2.0 * ( x2 - rm->x1 ) + rm->x1 ) );
/* move point across pixel boundary */
if( s && x2 > rm->x1 )
{
GM_INC( rm->gm, rxi, ryi, rm->a1 * 255 );
rm->a1 = 0;
rxi++;
rm->a1 += rm->y1 + r1 * ( y2 - rm->y1 ) - ryi;
}
else if( !s && y2 > rm->y1 )
{
GM_INC( rm->gm, rxi, ryi, rm->a1 * 255 );
rm->a1 = 0;
incrow( rm, rxi + 1, ryi, 255 );
ryi++;
}
else if( s && x2 <= rm->x1 )
{
rm->a1 -= rm->y1 + r1 * ( y2 - rm->y1 ) - ryi;
GM_INC( rm->gm, rxi, ryi, rm->a1 * 255 );
rm->a1 = 0;
rxi--;
}
else if( !s && y2 <= rm->y1 )
{
GM_INC( rm->gm, rxi, ryi, rm->a1 * 255 );
rm->a1 = 0;
ryi--;
incrow( rm, rxi + 1, ryi, -255 );
}
r0 = r1;
}
/* move point to (x2,y2) */
r1 = 1;
rm->a1 += ( r1 - r0 ) * ( y2 - rm->y1 )
* ( rxi + 1 - ( ( r0 + r1 ) / 2.0 * ( x2 - rm->x1 ) + rm->x1 ) );
rm->x1i = x2i;
rm->y1i = y2i;
rm->x1 = x2;
rm->y1 = y2;
/* assert (rxi != rm->x1i || ryi != rm->y1i); */
}
/* render a Bezier curve. */
void render_curveto( render_t* rm, double x2, double y2, double x3, double y3, double x4,
double y4 )
{
double x1, y1, dd0, dd1, dd, delta, e2, epsilon, t;
x1 = rm->x1; /* starting point */
y1 = rm->y1;
/* we approximate the curve by small line segments. The interval
* size, epsilon, is determined on the fly so that the distance
* between the true curve and its approximation does not exceed the
* desired accuracy delta. */
delta = .1; /* desired accuracy, in pixels */
/* let dd = maximal value of 2nd derivative over curve - this must
* occur at an endpoint. */
dd0 = sq( x1 - 2 * x2 + x3 ) + sq( y1 - 2 * y2 + y3 );
dd1 = sq( x2 - 2 * x3 + x4 ) + sq( y2 - 2 * y3 + y4 );
dd = 6 * sqrt( max( dd0, dd1 ) );
e2 = 8 * delta <= dd ? 8 * delta / dd : 1;
epsilon = sqrt( e2 ); /* necessary interval size */
for( t = epsilon; t < 1; t += epsilon )
{
render_lineto( rm, x1 * cu( 1 - t ) + 3 * x2 * sq( 1 - t ) * t
+ 3 * x3 * ( 1 - t ) * sq( t ) + x4 * cu( t ),
y1 * cu( 1 - t ) + 3 * y2 * sq( 1 - t ) * t + 3 * y3 * ( 1 - t ) * sq( t )
+ y4 * cu( t ) );
}
render_lineto( rm, x4, y4 );
}