render.cpp
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1 /* Copyright (C) 2001-2017 Peter Selinger.
2  * This file is part of Potrace. It is free software and it is covered
3  * by the GNU General Public License. See the file COPYING for details. */
4
5 #ifdef HAVE_CONFIG_H
6 #include <config.h>
7 #endif
8
9 #include <math.h>
10 #include <stdio.h>
11 #include <stdlib.h>
12 #include <string.h>
13
14 #include "auxiliary.h"
15 #include "greymap.h"
16 #include "render.h"
17
18 /* ---------------------------------------------------------------------- */
19 /* routines for anti-aliased rendering of curves */
20
21 /* we use the following method. Given a point (x,y) (with real-valued
22  * coordinates) in the plane, let (xi,yi) be the integer part of the
23  * coordinates, i.e., xi=floor(x), yi=floor(y). Define a path from
24  * (x,y) to infinity as follows: path(x,y) =
25  * (x,y)--(xi+1,y)--(xi+1,yi)--(+infty,yi). Now as the point (x,y)
26  * moves smoothly across the plane, the path path(x,y) sweeps
27  * (non-smoothly) across a certain area. We proportionately blacken
28  * the area as the path moves "downward", and we whiten the area as
29  * the path moves "upward". This way, after the point has traversed a
30  * closed curve, the interior of the curve has been darkened
31  * (counterclockwise movement) or lightened (clockwise movement). (The
32  * "grey shift" is actually proportional to the winding number). By
33  * choosing the above path with mostly integer coordinates, we achieve
34  * that only pixels close to (x,y) receive grey values and are subject
35  * to round-off errors. The grey value of pixels far away from (x,y)
36  * is always in "integer" (where 0=black, 1=white). As a special
37  * trick, we keep an accumulator rm->a1, which holds a double value to
38  * be added to the grey value to be added to the current pixel
39  * (xi,yi). Only when changing "current" pixels, we convert this
40  * double value to an integer. This way we avoid round-off errors at
41  * the meeting points of line segments. Another speedup measure is
42  * that we sometimes use the rm->incrow_buf array to postpone
43  * incrementing or decrementing an entire row. If incrow_buf[y]=x+1!=0,
44  * then all the pixels (x,y),(x+1,y),(x+2,y),... are scheduled to be
45  * incremented/decremented (which one is the case will be clear from
46  * context). This keeps the greymap operations reasonably local. */
47
48 /* allocate a new rendering state */
50 {
51  render_t* rm;
52
53  rm = (render_t*) malloc( sizeof( render_t ) );
54
55  if( !rm )
56  {
57  return NULL;
58  }
59
60  memset( rm, 0, sizeof( render_t ) );
61  rm->gm = gm;
62  rm->incrow_buf = (int*) calloc( gm->h, sizeof( int ) );
63
64  if( !rm->incrow_buf )
65  {
66  free( rm );
67  return NULL;
68  }
69
70  return rm;
71 }
72
73
74 /* free a given rendering state. Note: this does not free the
75  * underlying greymap. */
76 void render_free( render_t* rm )
77 {
78  free( rm->incrow_buf );
79  free( rm );
80 }
81
82
83 /* close path */
85 {
86  if( rm->x0 != rm->x1 || rm->y0 != rm->y1 )
87  {
88  render_lineto( rm, rm->x0, rm->y0 );
89  }
90
91  GM_INC( rm->gm, rm->x0i, rm->y0i, ( rm->a0 + rm->a1 ) * 255 );
92
93  /* assert (rm->x0i != rm->x1i || rm->y0i != rm->y1i); */
94
95  /* the persistent state is now undefined */
96 }
97
98
99 /* move point */
100 void render_moveto( render_t* rm, double x, double y )
101 {
102  /* close the previous path */
103  render_close( rm );
104
105  rm->x0 = rm->x1 = x;
106  rm->y0 = rm->y1 = y;
107  rm->x0i = (int) floor( rm->x0 );
108  rm->x1i = (int) floor( rm->x1 );
109  rm->y0i = (int) floor( rm->y0 );
110  rm->y1i = (int) floor( rm->y1 );
111  rm->a0 = rm->a1 = 0;
112 }
113
114
115 /* add b to pixels (x,y) and all pixels to the right of it. However,
116  * use rm->incrow_buf as a buffer to economize on multiple calls */
117 static void incrow( render_t* rm, int x, int y, int b )
118 {
119  int i, x0;
120
121  if( y < 0 || y >= rm->gm->h )
122  {
123  return;
124  }
125
126  if( x < 0 )
127  {
128  x = 0;
129  }
130  else if( x > rm->gm->w )
131  {
132  x = rm->gm->w;
133  }
134
135  if( rm->incrow_buf[y] == 0 )
136  {
137  rm->incrow_buf[y] = x + 1; /* store x+1 so that we can use 0 for "vacant" */
138  return;
139  }
140
141  x0 = rm->incrow_buf[y] - 1;
142  rm->incrow_buf[y] = 0;
143
144  if( x0 < x )
145  {
146  for( i = x0; i < x; i++ )
147  {
148  GM_INC( rm->gm, i, y, -b );
149  }
150  }
151  else
152  {
153  for( i = x; i < x0; i++ )
154  {
155  GM_INC( rm->gm, i, y, b );
156  }
157  }
158 }
159
160
161 /* render a straight line */
162 void render_lineto( render_t* rm, double x2, double y2 )
163 {
164  int x2i, y2i;
165  double t0 = 2, s0 = 2;
166  int sn, tn;
167  double ss = 2, ts = 2;
168  double r0, r1;
169  int i, j;
170  int rxi, ryi;
171  int s;
172
173  x2i = (int) floor( x2 );
174  y2i = (int) floor( y2 );
175
176  sn = abs( x2i - rm->x1i );
177  tn = abs( y2i - rm->y1i );
178
179  if( sn )
180  {
181  s0 = ( ( x2 > rm->x1 ? rm->x1i + 1 : rm->x1i ) - rm->x1 ) / ( x2 - rm->x1 );
182  ss = fabs( 1.0 / ( x2 - rm->x1 ) );
183  }
184
185  if( tn )
186  {
187  t0 = ( ( y2 > rm->y1 ? rm->y1i + 1 : rm->y1i ) - rm->y1 ) / ( y2 - rm->y1 );
188  ts = fabs( 1.0 / ( y2 - rm->y1 ) );
189  }
190
191  r0 = 0;
192
193  i = 0;
194  j = 0;
195
196  rxi = rm->x1i;
197  ryi = rm->y1i;
198
199  while( i < sn || j < tn )
200  {
201  if( j >= tn || ( i < sn && s0 + i * ss < t0 + j * ts ) )
202  {
203  r1 = s0 + i * ss;
204  i++;
205  s = 1;
206  }
207  else
208  {
209  r1 = t0 + j * ts;
210  j++;
211  s = 0;
212  }
213
214  /* render line from r0 to r1 segment of (rm->x1,rm->y1)..(x2,y2) */
215
216  /* move point to r1 */
217  rm->a1 += ( r1 - r0 ) * ( y2 - rm->y1 )
218  * ( rxi + 1 - ( ( r0 + r1 ) / 2.0 * ( x2 - rm->x1 ) + rm->x1 ) );
219
220  /* move point across pixel boundary */
221  if( s && x2 > rm->x1 )
222  {
223  GM_INC( rm->gm, rxi, ryi, rm->a1 * 255 );
224  rm->a1 = 0;
225  rxi++;
226  rm->a1 += rm->y1 + r1 * ( y2 - rm->y1 ) - ryi;
227  }
228  else if( !s && y2 > rm->y1 )
229  {
230  GM_INC( rm->gm, rxi, ryi, rm->a1 * 255 );
231  rm->a1 = 0;
232  incrow( rm, rxi + 1, ryi, 255 );
233  ryi++;
234  }
235  else if( s && x2 <= rm->x1 )
236  {
237  rm->a1 -= rm->y1 + r1 * ( y2 - rm->y1 ) - ryi;
238  GM_INC( rm->gm, rxi, ryi, rm->a1 * 255 );
239  rm->a1 = 0;
240  rxi--;
241  }
242  else if( !s && y2 <= rm->y1 )
243  {
244  GM_INC( rm->gm, rxi, ryi, rm->a1 * 255 );
245  rm->a1 = 0;
246  ryi--;
247  incrow( rm, rxi + 1, ryi, -255 );
248  }
249
250  r0 = r1;
251  }
252
253  /* move point to (x2,y2) */
254
255  r1 = 1;
256  rm->a1 += ( r1 - r0 ) * ( y2 - rm->y1 )
257  * ( rxi + 1 - ( ( r0 + r1 ) / 2.0 * ( x2 - rm->x1 ) + rm->x1 ) );
258
259  rm->x1i = x2i;
260  rm->y1i = y2i;
261  rm->x1 = x2;
262  rm->y1 = y2;
263
264  /* assert (rxi != rm->x1i || ryi != rm->y1i); */
265 }
266
267
268 /* render a Bezier curve. */
269 void render_curveto( render_t* rm, double x2, double y2, double x3, double y3, double x4,
270  double y4 )
271 {
272  double x1, y1, dd0, dd1, dd, delta, e2, epsilon, t;
273
274  x1 = rm->x1; /* starting point */
275  y1 = rm->y1;
276
277  /* we approximate the curve by small line segments. The interval
278  * size, epsilon, is determined on the fly so that the distance
279  * between the true curve and its approximation does not exceed the
280  * desired accuracy delta. */
281
282  delta = .1; /* desired accuracy, in pixels */
283
284  /* let dd = maximal value of 2nd derivative over curve - this must
285  * occur at an endpoint. */
286  dd0 = sq( x1 - 2 * x2 + x3 ) + sq( y1 - 2 * y2 + y3 );
287  dd1 = sq( x2 - 2 * x3 + x4 ) + sq( y2 - 2 * y3 + y4 );
288  dd = 6 * sqrt( max( dd0, dd1 ) );
289  e2 = 8 * delta <= dd ? 8 * delta / dd : 1;
290  epsilon = sqrt( e2 ); /* necessary interval size */
291
292  for( t = epsilon; t < 1; t += epsilon )
293  {
294  render_lineto( rm, x1 * cu( 1 - t ) + 3 * x2 * sq( 1 - t ) * t
295  + 3 * x3 * ( 1 - t ) * sq( t ) + x4 * cu( t ),
296  y1 * cu( 1 - t ) + 3 * y2 * sq( 1 - t ) * t + 3 * y3 * ( 1 - t ) * sq( t )
297  + y4 * cu( t ) );
298  }
299
300  render_lineto( rm, x4, y4 );
301 }
int h
Definition: greymap.h:21
#define GM_INC(gm, x, y, b)
Definition: greymap.h:42
render_t * render_new(greymap_t *gm)
Definition: render.cpp:49
int x0i
Definition: render.h:14
double a0
Definition: render.h:15
void render_free(render_t *rm)
Definition: render.cpp:76
static void incrow(render_t *rm, int x, int y, int b)
Definition: render.cpp:117
int * incrow_buf
Definition: render.h:16
void render_moveto(render_t *rm, double x, double y)
Definition: render.cpp:100
int w
Definition: greymap.h:20
void render_lineto(render_t *rm, double x2, double y2)
Definition: render.cpp:162
#define cu(a)
Definition: auxiliary.h:88
#define abs(a)
Definition: auxiliary.h:84
int y0i
Definition: render.h:14
int y1i
Definition: render.h:14
greymap_t * gm
Definition: render.h:12
double x0
Definition: render.h:13
double x1
Definition: render.h:13
double y1
Definition: render.h:13
double y0
Definition: render.h:13
#define max(a, b)
Definition: auxiliary.h:86
void render_curveto(render_t *rm, double x2, double y2, double x3, double y3, double x4, double y4)
Definition: render.cpp:269
double a1
Definition: render.h:15
size_t i
Definition: json11.cpp:597
#define sq(x)
int x1i
Definition: render.h:14
void render_close(render_t *rm)
Definition: render.cpp:84