1 /****************************************************************************
2  *
3  * ftstroke.c
4  *
5  *   FreeType path stroker (body).
6  *
7  * Copyright (C) 2002-2021 by
8  * David Turner, Robert Wilhelm, and Werner Lemberg.
9  *
10  * This file is part of the FreeType project, and may only be used,
11  * modified, and distributed under the terms of the FreeType project
12  * license, LICENSE.TXT.  By continuing to use, modify, or distribute
13  * this file you indicate that you have read the license and
14  * understand and accept it fully.
15  *
16  */
17 
18 
19 #include <freetype/ftstroke.h>
20 #include <freetype/fttrigon.h>
21 #include <freetype/ftoutln.h>
22 #include <freetype/internal/ftmemory.h>
23 #include <freetype/internal/ftdebug.h>
24 #include <freetype/internal/ftobjs.h>
25 
26 
27   /* declare an extern to access `ft_outline_glyph_class' globally */
28   /* allocated  in `ftglyph.c'                                     */
29   FT_CALLBACK_TABLE const FT_Glyph_Class  ft_outline_glyph_class;
30 
31 
32   /* documentation is in ftstroke.h */
33 
34   FT_EXPORT_DEF( FT_StrokerBorder )
FT_Outline_GetInsideBorder(FT_Outline * outline)35   FT_Outline_GetInsideBorder( FT_Outline*  outline )
36   {
37     FT_Orientation  o = FT_Outline_Get_Orientation( outline );
38 
39 
40     return o == FT_ORIENTATION_TRUETYPE ? FT_STROKER_BORDER_RIGHT
41                                         : FT_STROKER_BORDER_LEFT;
42   }
43 
44 
45   /* documentation is in ftstroke.h */
46 
47   FT_EXPORT_DEF( FT_StrokerBorder )
FT_Outline_GetOutsideBorder(FT_Outline * outline)48   FT_Outline_GetOutsideBorder( FT_Outline*  outline )
49   {
50     FT_Orientation  o = FT_Outline_Get_Orientation( outline );
51 
52 
53     return o == FT_ORIENTATION_TRUETYPE ? FT_STROKER_BORDER_LEFT
54                                         : FT_STROKER_BORDER_RIGHT;
55   }
56 
57 
58   /*************************************************************************/
59   /*************************************************************************/
60   /*****                                                               *****/
61   /*****                      BEZIER COMPUTATIONS                      *****/
62   /*****                                                               *****/
63   /*************************************************************************/
64   /*************************************************************************/
65 
66 #define FT_SMALL_CONIC_THRESHOLD  ( FT_ANGLE_PI / 6 )
67 #define FT_SMALL_CUBIC_THRESHOLD  ( FT_ANGLE_PI / 8 )
68 
69 #define FT_EPSILON  2
70 
71 #define FT_IS_SMALL( x )  ( (x) > -FT_EPSILON && (x) < FT_EPSILON )
72 
73 
74   static FT_Pos
ft_pos_abs(FT_Pos x)75   ft_pos_abs( FT_Pos  x )
76   {
77     return x >= 0 ? x : -x;
78   }
79 
80 
81   static void
ft_conic_split(FT_Vector * base)82   ft_conic_split( FT_Vector*  base )
83   {
84     FT_Pos  a, b;
85 
86 
87     base[4].x = base[2].x;
88     a = base[0].x + base[1].x;
89     b = base[1].x + base[2].x;
90     base[3].x = b >> 1;
91     base[2].x = ( a + b ) >> 2;
92     base[1].x = a >> 1;
93 
94     base[4].y = base[2].y;
95     a = base[0].y + base[1].y;
96     b = base[1].y + base[2].y;
97     base[3].y = b >> 1;
98     base[2].y = ( a + b ) >> 2;
99     base[1].y = a >> 1;
100   }
101 
102 
103   static FT_Bool
ft_conic_is_small_enough(FT_Vector * base,FT_Angle * angle_in,FT_Angle * angle_out)104   ft_conic_is_small_enough( FT_Vector*  base,
105                             FT_Angle   *angle_in,
106                             FT_Angle   *angle_out )
107   {
108     FT_Vector  d1, d2;
109     FT_Angle   theta;
110     FT_Int     close1, close2;
111 
112 
113     d1.x = base[1].x - base[2].x;
114     d1.y = base[1].y - base[2].y;
115     d2.x = base[0].x - base[1].x;
116     d2.y = base[0].y - base[1].y;
117 
118     close1 = FT_IS_SMALL( d1.x ) && FT_IS_SMALL( d1.y );
119     close2 = FT_IS_SMALL( d2.x ) && FT_IS_SMALL( d2.y );
120 
121     if ( close1 )
122     {
123       if ( close2 )
124       {
125         /* basically a point;                      */
126         /* do nothing to retain original direction */
127       }
128       else
129       {
130         *angle_in  =
131         *angle_out = FT_Atan2( d2.x, d2.y );
132       }
133     }
134     else /* !close1 */
135     {
136       if ( close2 )
137       {
138         *angle_in  =
139         *angle_out = FT_Atan2( d1.x, d1.y );
140       }
141       else
142       {
143         *angle_in  = FT_Atan2( d1.x, d1.y );
144         *angle_out = FT_Atan2( d2.x, d2.y );
145       }
146     }
147 
148     theta = ft_pos_abs( FT_Angle_Diff( *angle_in, *angle_out ) );
149 
150     return FT_BOOL( theta < FT_SMALL_CONIC_THRESHOLD );
151   }
152 
153 
154   static void
ft_cubic_split(FT_Vector * base)155   ft_cubic_split( FT_Vector*  base )
156   {
157     FT_Pos  a, b, c;
158 
159 
160     base[6].x = base[3].x;
161     a = base[0].x + base[1].x;
162     b = base[1].x + base[2].x;
163     c = base[2].x + base[3].x;
164     base[5].x = c >> 1;
165     c += b;
166     base[4].x = c >> 2;
167     base[1].x = a >> 1;
168     a += b;
169     base[2].x = a >> 2;
170     base[3].x = ( a + c ) >> 3;
171 
172     base[6].y = base[3].y;
173     a = base[0].y + base[1].y;
174     b = base[1].y + base[2].y;
175     c = base[2].y + base[3].y;
176     base[5].y = c >> 1;
177     c += b;
178     base[4].y = c >> 2;
179     base[1].y = a >> 1;
180     a += b;
181     base[2].y = a >> 2;
182     base[3].y = ( a + c ) >> 3;
183   }
184 
185 
186   /* Return the average of `angle1' and `angle2'.            */
187   /* This gives correct result even if `angle1' and `angle2' */
188   /* have opposite signs.                                    */
189   static FT_Angle
ft_angle_mean(FT_Angle angle1,FT_Angle angle2)190   ft_angle_mean( FT_Angle  angle1,
191                  FT_Angle  angle2 )
192   {
193     return angle1 + FT_Angle_Diff( angle1, angle2 ) / 2;
194   }
195 
196 
197   static FT_Bool
ft_cubic_is_small_enough(FT_Vector * base,FT_Angle * angle_in,FT_Angle * angle_mid,FT_Angle * angle_out)198   ft_cubic_is_small_enough( FT_Vector*  base,
199                             FT_Angle   *angle_in,
200                             FT_Angle   *angle_mid,
201                             FT_Angle   *angle_out )
202   {
203     FT_Vector  d1, d2, d3;
204     FT_Angle   theta1, theta2;
205     FT_Int     close1, close2, close3;
206 
207 
208     d1.x = base[2].x - base[3].x;
209     d1.y = base[2].y - base[3].y;
210     d2.x = base[1].x - base[2].x;
211     d2.y = base[1].y - base[2].y;
212     d3.x = base[0].x - base[1].x;
213     d3.y = base[0].y - base[1].y;
214 
215     close1 = FT_IS_SMALL( d1.x ) && FT_IS_SMALL( d1.y );
216     close2 = FT_IS_SMALL( d2.x ) && FT_IS_SMALL( d2.y );
217     close3 = FT_IS_SMALL( d3.x ) && FT_IS_SMALL( d3.y );
218 
219     if ( close1 )
220     {
221       if ( close2 )
222       {
223         if ( close3 )
224         {
225           /* basically a point;                      */
226           /* do nothing to retain original direction */
227         }
228         else /* !close3 */
229         {
230           *angle_in  =
231           *angle_mid =
232           *angle_out = FT_Atan2( d3.x, d3.y );
233         }
234       }
235       else /* !close2 */
236       {
237         if ( close3 )
238         {
239           *angle_in  =
240           *angle_mid =
241           *angle_out = FT_Atan2( d2.x, d2.y );
242         }
243         else /* !close3 */
244         {
245           *angle_in  =
246           *angle_mid = FT_Atan2( d2.x, d2.y );
247           *angle_out = FT_Atan2( d3.x, d3.y );
248         }
249       }
250     }
251     else /* !close1 */
252     {
253       if ( close2 )
254       {
255         if ( close3 )
256         {
257           *angle_in  =
258           *angle_mid =
259           *angle_out = FT_Atan2( d1.x, d1.y );
260         }
261         else /* !close3 */
262         {
263           *angle_in  = FT_Atan2( d1.x, d1.y );
264           *angle_out = FT_Atan2( d3.x, d3.y );
265           *angle_mid = ft_angle_mean( *angle_in, *angle_out );
266         }
267       }
268       else /* !close2 */
269       {
270         if ( close3 )
271         {
272           *angle_in  = FT_Atan2( d1.x, d1.y );
273           *angle_mid =
274           *angle_out = FT_Atan2( d2.x, d2.y );
275         }
276         else /* !close3 */
277         {
278           *angle_in  = FT_Atan2( d1.x, d1.y );
279           *angle_mid = FT_Atan2( d2.x, d2.y );
280           *angle_out = FT_Atan2( d3.x, d3.y );
281         }
282       }
283     }
284 
285     theta1 = ft_pos_abs( FT_Angle_Diff( *angle_in,  *angle_mid ) );
286     theta2 = ft_pos_abs( FT_Angle_Diff( *angle_mid, *angle_out ) );
287 
288     return FT_BOOL( theta1 < FT_SMALL_CUBIC_THRESHOLD &&
289                     theta2 < FT_SMALL_CUBIC_THRESHOLD );
290   }
291 
292 
293   /*************************************************************************/
294   /*************************************************************************/
295   /*****                                                               *****/
296   /*****                       STROKE BORDERS                          *****/
297   /*****                                                               *****/
298   /*************************************************************************/
299   /*************************************************************************/
300 
301   typedef enum  FT_StrokeTags_
302   {
303     FT_STROKE_TAG_ON    = 1,   /* on-curve point  */
304     FT_STROKE_TAG_CUBIC = 2,   /* cubic off-point */
305     FT_STROKE_TAG_BEGIN = 4,   /* sub-path start  */
306     FT_STROKE_TAG_END   = 8    /* sub-path end    */
307 
308   } FT_StrokeTags;
309 
310 #define  FT_STROKE_TAG_BEGIN_END  ( FT_STROKE_TAG_BEGIN | FT_STROKE_TAG_END )
311 
312   typedef struct  FT_StrokeBorderRec_
313   {
314     FT_UInt     num_points;
315     FT_UInt     max_points;
316     FT_Vector*  points;
317     FT_Byte*    tags;
318     FT_Bool     movable;  /* TRUE for ends of lineto borders */
319     FT_Int      start;    /* index of current sub-path start point */
320     FT_Memory   memory;
321     FT_Bool     valid;
322 
323   } FT_StrokeBorderRec, *FT_StrokeBorder;
324 
325 
326   static FT_Error
ft_stroke_border_grow(FT_StrokeBorder border,FT_UInt new_points)327   ft_stroke_border_grow( FT_StrokeBorder  border,
328                          FT_UInt          new_points )
329   {
330     FT_UInt   old_max = border->max_points;
331     FT_UInt   new_max = border->num_points + new_points;
332     FT_Error  error   = FT_Err_Ok;
333 
334 
335     if ( new_max > old_max )
336     {
337       FT_UInt    cur_max = old_max;
338       FT_Memory  memory  = border->memory;
339 
340 
341       while ( cur_max < new_max )
342         cur_max += ( cur_max >> 1 ) + 16;
343 
344       if ( FT_RENEW_ARRAY( border->points, old_max, cur_max ) ||
345            FT_RENEW_ARRAY( border->tags,   old_max, cur_max ) )
346         goto Exit;
347 
348       border->max_points = cur_max;
349     }
350 
351   Exit:
352     return error;
353   }
354 
355 
356   static void
ft_stroke_border_close(FT_StrokeBorder border,FT_Bool reverse)357   ft_stroke_border_close( FT_StrokeBorder  border,
358                           FT_Bool          reverse )
359   {
360     FT_UInt  start = (FT_UInt)border->start;
361     FT_UInt  count = border->num_points;
362 
363 
364     FT_ASSERT( border->start >= 0 );
365 
366     /* don't record empty paths! */
367     if ( count <= start + 1U )
368       border->num_points = start;
369     else
370     {
371       /* copy the last point to the start of this sub-path, since */
372       /* it contains the `adjusted' starting coordinates          */
373       border->num_points    = --count;
374       border->points[start] = border->points[count];
375       border->tags[start]   = border->tags[count];
376 
377       if ( reverse )
378       {
379         /* reverse the points */
380         {
381           FT_Vector*  vec1 = border->points + start + 1;
382           FT_Vector*  vec2 = border->points + count - 1;
383 
384 
385           for ( ; vec1 < vec2; vec1++, vec2-- )
386           {
387             FT_Vector  tmp;
388 
389 
390             tmp   = *vec1;
391             *vec1 = *vec2;
392             *vec2 = tmp;
393           }
394         }
395 
396         /* then the tags */
397         {
398           FT_Byte*  tag1 = border->tags + start + 1;
399           FT_Byte*  tag2 = border->tags + count - 1;
400 
401 
402           for ( ; tag1 < tag2; tag1++, tag2-- )
403           {
404             FT_Byte  tmp;
405 
406 
407             tmp   = *tag1;
408             *tag1 = *tag2;
409             *tag2 = tmp;
410           }
411         }
412       }
413 
414       border->tags[start    ] |= FT_STROKE_TAG_BEGIN;
415       border->tags[count - 1] |= FT_STROKE_TAG_END;
416     }
417 
418     border->start   = -1;
419     border->movable = FALSE;
420   }
421 
422 
423   static FT_Error
ft_stroke_border_lineto(FT_StrokeBorder border,FT_Vector * to,FT_Bool movable)424   ft_stroke_border_lineto( FT_StrokeBorder  border,
425                            FT_Vector*       to,
426                            FT_Bool          movable )
427   {
428     FT_Error  error = FT_Err_Ok;
429 
430 
431     FT_ASSERT( border->start >= 0 );
432 
433     if ( border->movable )
434     {
435       /* move last point */
436       border->points[border->num_points - 1] = *to;
437     }
438     else
439     {
440       /* don't add zero-length lineto, but always add moveto */
441       if ( border->num_points > (FT_UInt)border->start                     &&
442            FT_IS_SMALL( border->points[border->num_points - 1].x - to->x ) &&
443            FT_IS_SMALL( border->points[border->num_points - 1].y - to->y ) )
444         return error;
445 
446       /* add one point */
447       error = ft_stroke_border_grow( border, 1 );
448       if ( !error )
449       {
450         FT_Vector*  vec = border->points + border->num_points;
451         FT_Byte*    tag = border->tags   + border->num_points;
452 
453 
454         vec[0] = *to;
455         tag[0] = FT_STROKE_TAG_ON;
456 
457         border->num_points += 1;
458       }
459     }
460     border->movable = movable;
461     return error;
462   }
463 
464 
465   static FT_Error
ft_stroke_border_conicto(FT_StrokeBorder border,FT_Vector * control,FT_Vector * to)466   ft_stroke_border_conicto( FT_StrokeBorder  border,
467                             FT_Vector*       control,
468                             FT_Vector*       to )
469   {
470     FT_Error  error;
471 
472 
473     FT_ASSERT( border->start >= 0 );
474 
475     error = ft_stroke_border_grow( border, 2 );
476     if ( !error )
477     {
478       FT_Vector*  vec = border->points + border->num_points;
479       FT_Byte*    tag = border->tags   + border->num_points;
480 
481 
482       vec[0] = *control;
483       vec[1] = *to;
484 
485       tag[0] = 0;
486       tag[1] = FT_STROKE_TAG_ON;
487 
488       border->num_points += 2;
489     }
490 
491     border->movable = FALSE;
492 
493     return error;
494   }
495 
496 
497   static FT_Error
ft_stroke_border_cubicto(FT_StrokeBorder border,FT_Vector * control1,FT_Vector * control2,FT_Vector * to)498   ft_stroke_border_cubicto( FT_StrokeBorder  border,
499                             FT_Vector*       control1,
500                             FT_Vector*       control2,
501                             FT_Vector*       to )
502   {
503     FT_Error  error;
504 
505 
506     FT_ASSERT( border->start >= 0 );
507 
508     error = ft_stroke_border_grow( border, 3 );
509     if ( !error )
510     {
511       FT_Vector*  vec = border->points + border->num_points;
512       FT_Byte*    tag = border->tags   + border->num_points;
513 
514 
515       vec[0] = *control1;
516       vec[1] = *control2;
517       vec[2] = *to;
518 
519       tag[0] = FT_STROKE_TAG_CUBIC;
520       tag[1] = FT_STROKE_TAG_CUBIC;
521       tag[2] = FT_STROKE_TAG_ON;
522 
523       border->num_points += 3;
524     }
525 
526     border->movable = FALSE;
527 
528     return error;
529   }
530 
531 
532 #define FT_ARC_CUBIC_ANGLE  ( FT_ANGLE_PI / 2 )
533 
534 
535   static FT_Error
ft_stroke_border_arcto(FT_StrokeBorder border,FT_Vector * center,FT_Fixed radius,FT_Angle angle_start,FT_Angle angle_diff)536   ft_stroke_border_arcto( FT_StrokeBorder  border,
537                           FT_Vector*       center,
538                           FT_Fixed         radius,
539                           FT_Angle         angle_start,
540                           FT_Angle         angle_diff )
541   {
542     FT_Fixed   coef;
543     FT_Vector  a0, a1, a2, a3;
544     FT_Int     i, arcs = 1;
545     FT_Error   error = FT_Err_Ok;
546 
547 
548     /* number of cubic arcs to draw */
549     while (  angle_diff > FT_ARC_CUBIC_ANGLE * arcs ||
550             -angle_diff > FT_ARC_CUBIC_ANGLE * arcs )
551       arcs++;
552 
553     /* control tangents */
554     coef  = FT_Tan( angle_diff / ( 4 * arcs ) );
555     coef += coef / 3;
556 
557     /* compute start and first control point */
558     FT_Vector_From_Polar( &a0, radius, angle_start );
559     a1.x = FT_MulFix( -a0.y, coef );
560     a1.y = FT_MulFix(  a0.x, coef );
561 
562     a0.x += center->x;
563     a0.y += center->y;
564     a1.x += a0.x;
565     a1.y += a0.y;
566 
567     for ( i = 1; i <= arcs; i++ )
568     {
569       /* compute end and second control point */
570       FT_Vector_From_Polar( &a3, radius,
571                             angle_start + i * angle_diff / arcs );
572       a2.x = FT_MulFix(  a3.y, coef );
573       a2.y = FT_MulFix( -a3.x, coef );
574 
575       a3.x += center->x;
576       a3.y += center->y;
577       a2.x += a3.x;
578       a2.y += a3.y;
579 
580       /* add cubic arc */
581       error = ft_stroke_border_cubicto( border, &a1, &a2, &a3 );
582       if ( error )
583         break;
584 
585       /* a0 = a3; */
586       a1.x = a3.x - a2.x + a3.x;
587       a1.y = a3.y - a2.y + a3.y;
588     }
589 
590     return error;
591   }
592 
593 
594   static FT_Error
ft_stroke_border_moveto(FT_StrokeBorder border,FT_Vector * to)595   ft_stroke_border_moveto( FT_StrokeBorder  border,
596                            FT_Vector*       to )
597   {
598     /* close current open path if any ? */
599     if ( border->start >= 0 )
600       ft_stroke_border_close( border, FALSE );
601 
602     border->start = (FT_Int)border->num_points;
603     border->movable = FALSE;
604 
605     return ft_stroke_border_lineto( border, to, FALSE );
606   }
607 
608 
609   static void
ft_stroke_border_init(FT_StrokeBorder border,FT_Memory memory)610   ft_stroke_border_init( FT_StrokeBorder  border,
611                          FT_Memory        memory )
612   {
613     border->memory = memory;
614     border->points = NULL;
615     border->tags   = NULL;
616 
617     border->num_points = 0;
618     border->max_points = 0;
619     border->start      = -1;
620     border->valid      = FALSE;
621   }
622 
623 
624   static void
ft_stroke_border_reset(FT_StrokeBorder border)625   ft_stroke_border_reset( FT_StrokeBorder  border )
626   {
627     border->num_points = 0;
628     border->start      = -1;
629     border->valid      = FALSE;
630   }
631 
632 
633   static void
ft_stroke_border_done(FT_StrokeBorder border)634   ft_stroke_border_done( FT_StrokeBorder  border )
635   {
636     FT_Memory  memory = border->memory;
637 
638 
639     FT_FREE( border->points );
640     FT_FREE( border->tags );
641 
642     border->num_points = 0;
643     border->max_points = 0;
644     border->start      = -1;
645     border->valid      = FALSE;
646   }
647 
648 
649   static FT_Error
ft_stroke_border_get_counts(FT_StrokeBorder border,FT_UInt * anum_points,FT_UInt * anum_contours)650   ft_stroke_border_get_counts( FT_StrokeBorder  border,
651                                FT_UInt         *anum_points,
652                                FT_UInt         *anum_contours )
653   {
654     FT_Error  error        = FT_Err_Ok;
655     FT_UInt   num_points   = 0;
656     FT_UInt   num_contours = 0;
657 
658     FT_UInt     count      = border->num_points;
659     FT_Vector*  point      = border->points;
660     FT_Byte*    tags       = border->tags;
661     FT_Int      in_contour = 0;
662 
663 
664     for ( ; count > 0; count--, num_points++, point++, tags++ )
665     {
666       if ( tags[0] & FT_STROKE_TAG_BEGIN )
667       {
668         if ( in_contour != 0 )
669           goto Fail;
670 
671         in_contour = 1;
672       }
673       else if ( in_contour == 0 )
674         goto Fail;
675 
676       if ( tags[0] & FT_STROKE_TAG_END )
677       {
678         in_contour = 0;
679         num_contours++;
680       }
681     }
682 
683     if ( in_contour != 0 )
684       goto Fail;
685 
686     border->valid = TRUE;
687 
688   Exit:
689     *anum_points   = num_points;
690     *anum_contours = num_contours;
691     return error;
692 
693   Fail:
694     num_points   = 0;
695     num_contours = 0;
696     goto Exit;
697   }
698 
699 
700   static void
ft_stroke_border_export(FT_StrokeBorder border,FT_Outline * outline)701   ft_stroke_border_export( FT_StrokeBorder  border,
702                            FT_Outline*      outline )
703   {
704     /* copy point locations */
705     if ( border->num_points )
706       FT_ARRAY_COPY( outline->points + outline->n_points,
707                      border->points,
708                      border->num_points );
709 
710     /* copy tags */
711     {
712       FT_UInt   count = border->num_points;
713       FT_Byte*  read  = border->tags;
714       FT_Byte*  write = (FT_Byte*)outline->tags + outline->n_points;
715 
716 
717       for ( ; count > 0; count--, read++, write++ )
718       {
719         if ( *read & FT_STROKE_TAG_ON )
720           *write = FT_CURVE_TAG_ON;
721         else if ( *read & FT_STROKE_TAG_CUBIC )
722           *write = FT_CURVE_TAG_CUBIC;
723         else
724           *write = FT_CURVE_TAG_CONIC;
725       }
726     }
727 
728     /* copy contours */
729     {
730       FT_UInt    count = border->num_points;
731       FT_Byte*   tags  = border->tags;
732       FT_Short*  write = outline->contours + outline->n_contours;
733       FT_Short   idx   = (FT_Short)outline->n_points;
734 
735 
736       for ( ; count > 0; count--, tags++, idx++ )
737       {
738         if ( *tags & FT_STROKE_TAG_END )
739         {
740           *write++ = idx;
741           outline->n_contours++;
742         }
743       }
744     }
745 
746     outline->n_points += (short)border->num_points;
747 
748     FT_ASSERT( FT_Outline_Check( outline ) == 0 );
749   }
750 
751 
752   /*************************************************************************/
753   /*************************************************************************/
754   /*****                                                               *****/
755   /*****                           STROKER                             *****/
756   /*****                                                               *****/
757   /*************************************************************************/
758   /*************************************************************************/
759 
760 #define FT_SIDE_TO_ROTATE( s )   ( FT_ANGLE_PI2 - (s) * FT_ANGLE_PI )
761 
762   typedef struct  FT_StrokerRec_
763   {
764     FT_Angle             angle_in;             /* direction into curr join */
765     FT_Angle             angle_out;            /* direction out of join  */
766     FT_Vector            center;               /* current position */
767     FT_Fixed             line_length;          /* length of last lineto */
768     FT_Bool              first_point;          /* is this the start? */
769     FT_Bool              subpath_open;         /* is the subpath open? */
770     FT_Angle             subpath_angle;        /* subpath start direction */
771     FT_Vector            subpath_start;        /* subpath start position */
772     FT_Fixed             subpath_line_length;  /* subpath start lineto len */
773     FT_Bool              handle_wide_strokes;  /* use wide strokes logic? */
774 
775     FT_Stroker_LineCap   line_cap;
776     FT_Stroker_LineJoin  line_join;
777     FT_Stroker_LineJoin  line_join_saved;
778     FT_Fixed             miter_limit;
779     FT_Fixed             radius;
780 
781     FT_StrokeBorderRec   borders[2];
782     FT_Library           library;
783 
784   } FT_StrokerRec;
785 
786 
787   /* documentation is in ftstroke.h */
788 
789   FT_EXPORT_DEF( FT_Error )
FT_Stroker_New(FT_Library library,FT_Stroker * astroker)790   FT_Stroker_New( FT_Library   library,
791                   FT_Stroker  *astroker )
792   {
793     FT_Error    error;           /* assigned in FT_NEW */
794     FT_Memory   memory;
795     FT_Stroker  stroker = NULL;
796 
797 
798     if ( !library )
799       return FT_THROW( Invalid_Library_Handle );
800 
801     if ( !astroker )
802       return FT_THROW( Invalid_Argument );
803 
804     memory = library->memory;
805 
806     if ( !FT_NEW( stroker ) )
807     {
808       stroker->library = library;
809 
810       ft_stroke_border_init( &stroker->borders[0], memory );
811       ft_stroke_border_init( &stroker->borders[1], memory );
812     }
813 
814     *astroker = stroker;
815 
816     return error;
817   }
818 
819 
820   /* documentation is in ftstroke.h */
821 
822   FT_EXPORT_DEF( void )
FT_Stroker_Set(FT_Stroker stroker,FT_Fixed radius,FT_Stroker_LineCap line_cap,FT_Stroker_LineJoin line_join,FT_Fixed miter_limit)823   FT_Stroker_Set( FT_Stroker           stroker,
824                   FT_Fixed             radius,
825                   FT_Stroker_LineCap   line_cap,
826                   FT_Stroker_LineJoin  line_join,
827                   FT_Fixed             miter_limit )
828   {
829     if ( !stroker )
830       return;
831 
832     stroker->radius      = radius;
833     stroker->line_cap    = line_cap;
834     stroker->line_join   = line_join;
835     stroker->miter_limit = miter_limit;
836 
837     /* ensure miter limit has sensible value */
838     if ( stroker->miter_limit < 0x10000L )
839       stroker->miter_limit = 0x10000L;
840 
841     /* save line join style:                                           */
842     /* line join style can be temporarily changed when stroking curves */
843     stroker->line_join_saved = line_join;
844 
845     FT_Stroker_Rewind( stroker );
846   }
847 
848 
849   /* documentation is in ftstroke.h */
850 
851   FT_EXPORT_DEF( void )
FT_Stroker_Rewind(FT_Stroker stroker)852   FT_Stroker_Rewind( FT_Stroker  stroker )
853   {
854     if ( stroker )
855     {
856       ft_stroke_border_reset( &stroker->borders[0] );
857       ft_stroke_border_reset( &stroker->borders[1] );
858     }
859   }
860 
861 
862   /* documentation is in ftstroke.h */
863 
864   FT_EXPORT_DEF( void )
FT_Stroker_Done(FT_Stroker stroker)865   FT_Stroker_Done( FT_Stroker  stroker )
866   {
867     if ( stroker )
868     {
869       FT_Memory  memory = stroker->library->memory;
870 
871 
872       ft_stroke_border_done( &stroker->borders[0] );
873       ft_stroke_border_done( &stroker->borders[1] );
874 
875       stroker->library = NULL;
876       FT_FREE( stroker );
877     }
878   }
879 
880 
881   /* create a circular arc at a corner or cap */
882   static FT_Error
ft_stroker_arcto(FT_Stroker stroker,FT_Int side)883   ft_stroker_arcto( FT_Stroker  stroker,
884                     FT_Int      side )
885   {
886     FT_Angle         total, rotate;
887     FT_Fixed         radius = stroker->radius;
888     FT_Error         error  = FT_Err_Ok;
889     FT_StrokeBorder  border = stroker->borders + side;
890 
891 
892     rotate = FT_SIDE_TO_ROTATE( side );
893 
894     total = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
895     if ( total == FT_ANGLE_PI )
896       total = -rotate * 2;
897 
898     error = ft_stroke_border_arcto( border,
899                                     &stroker->center,
900                                     radius,
901                                     stroker->angle_in + rotate,
902                                     total );
903     border->movable = FALSE;
904     return error;
905   }
906 
907 
908   /* add a cap at the end of an opened path */
909   static FT_Error
ft_stroker_cap(FT_Stroker stroker,FT_Angle angle,FT_Int side)910   ft_stroker_cap( FT_Stroker  stroker,
911                   FT_Angle    angle,
912                   FT_Int      side )
913   {
914     FT_Error  error = FT_Err_Ok;
915 
916 
917     if ( stroker->line_cap == FT_STROKER_LINECAP_ROUND )
918     {
919       /* add a round cap */
920       stroker->angle_in  = angle;
921       stroker->angle_out = angle + FT_ANGLE_PI;
922 
923       error = ft_stroker_arcto( stroker, side );
924     }
925     else
926     {
927       /* add a square or butt cap */
928       FT_Vector        middle, delta;
929       FT_Fixed         radius = stroker->radius;
930       FT_StrokeBorder  border = stroker->borders + side;
931 
932 
933       /* compute middle point and first angle point */
934       FT_Vector_From_Polar( &middle, radius, angle );
935       delta.x = side ?  middle.y : -middle.y;
936       delta.y = side ? -middle.x :  middle.x;
937 
938       if ( stroker->line_cap == FT_STROKER_LINECAP_SQUARE )
939       {
940         middle.x += stroker->center.x;
941         middle.y += stroker->center.y;
942       }
943       else  /* FT_STROKER_LINECAP_BUTT */
944       {
945         middle.x  = stroker->center.x;
946         middle.y  = stroker->center.y;
947       }
948 
949       delta.x  += middle.x;
950       delta.y  += middle.y;
951 
952       error = ft_stroke_border_lineto( border, &delta, FALSE );
953       if ( error )
954         goto Exit;
955 
956       /* compute second angle point */
957       delta.x = middle.x - delta.x + middle.x;
958       delta.y = middle.y - delta.y + middle.y;
959 
960       error = ft_stroke_border_lineto( border, &delta, FALSE );
961     }
962 
963   Exit:
964     return error;
965   }
966 
967 
968   /* process an inside corner, i.e. compute intersection */
969   static FT_Error
ft_stroker_inside(FT_Stroker stroker,FT_Int side,FT_Fixed line_length)970   ft_stroker_inside( FT_Stroker  stroker,
971                      FT_Int      side,
972                      FT_Fixed    line_length )
973   {
974     FT_StrokeBorder  border = stroker->borders + side;
975     FT_Angle         phi, theta, rotate;
976     FT_Fixed         length;
977     FT_Vector        sigma = { 0, 0 };
978     FT_Vector        delta;
979     FT_Error         error = FT_Err_Ok;
980     FT_Bool          intersect;          /* use intersection of lines? */
981 
982 
983     rotate = FT_SIDE_TO_ROTATE( side );
984 
985     theta = FT_Angle_Diff( stroker->angle_in, stroker->angle_out ) / 2;
986 
987     /* Only intersect borders if between two lineto's and both */
988     /* lines are long enough (line_length is zero for curves). */
989     /* Also avoid U-turns of nearly 180 degree.                */
990     if ( !border->movable || line_length == 0  ||
991          theta > 0x59C000 || theta < -0x59C000 )
992       intersect = FALSE;
993     else
994     {
995       /* compute minimum required length of lines */
996       FT_Fixed  min_length;
997 
998 
999       FT_Vector_Unit( &sigma, theta );
1000       min_length =
1001         ft_pos_abs( FT_MulDiv( stroker->radius, sigma.y, sigma.x ) );
1002 
1003       intersect = FT_BOOL( min_length                         &&
1004                            stroker->line_length >= min_length &&
1005                            line_length          >= min_length );
1006     }
1007 
1008     if ( !intersect )
1009     {
1010       FT_Vector_From_Polar( &delta, stroker->radius,
1011                             stroker->angle_out + rotate );
1012       delta.x += stroker->center.x;
1013       delta.y += stroker->center.y;
1014 
1015       border->movable = FALSE;
1016     }
1017     else
1018     {
1019       /* compute median angle */
1020       phi = stroker->angle_in + theta + rotate;
1021 
1022       length = FT_DivFix( stroker->radius, sigma.x );
1023 
1024       FT_Vector_From_Polar( &delta, length, phi );
1025       delta.x += stroker->center.x;
1026       delta.y += stroker->center.y;
1027     }
1028 
1029     error = ft_stroke_border_lineto( border, &delta, FALSE );
1030 
1031     return error;
1032   }
1033 
1034 
1035   /* process an outside corner, i.e. compute bevel/miter/round */
1036   static FT_Error
ft_stroker_outside(FT_Stroker stroker,FT_Int side,FT_Fixed line_length)1037   ft_stroker_outside( FT_Stroker  stroker,
1038                       FT_Int      side,
1039                       FT_Fixed    line_length )
1040   {
1041     FT_StrokeBorder  border = stroker->borders + side;
1042     FT_Error         error;
1043     FT_Angle         rotate;
1044 
1045 
1046     if ( stroker->line_join == FT_STROKER_LINEJOIN_ROUND )
1047       error = ft_stroker_arcto( stroker, side );
1048     else
1049     {
1050       /* this is a mitered (pointed) or beveled (truncated) corner */
1051       FT_Fixed   radius = stroker->radius;
1052       FT_Vector  sigma = { 0, 0 };
1053       FT_Angle   theta = 0, phi = 0;
1054       FT_Bool    bevel, fixed_bevel;
1055 
1056 
1057       rotate = FT_SIDE_TO_ROTATE( side );
1058 
1059       bevel =
1060         FT_BOOL( stroker->line_join == FT_STROKER_LINEJOIN_BEVEL );
1061 
1062       fixed_bevel =
1063         FT_BOOL( stroker->line_join != FT_STROKER_LINEJOIN_MITER_VARIABLE );
1064 
1065       /* check miter limit first */
1066       if ( !bevel )
1067       {
1068         theta = FT_Angle_Diff( stroker->angle_in, stroker->angle_out ) / 2;
1069 
1070         if ( theta == FT_ANGLE_PI2 )
1071           theta = -rotate;
1072 
1073         phi    = stroker->angle_in + theta + rotate;
1074 
1075         FT_Vector_From_Polar( &sigma, stroker->miter_limit, theta );
1076 
1077         /* is miter limit exceeded? */
1078         if ( sigma.x < 0x10000L )
1079         {
1080           /* don't create variable bevels for very small deviations; */
1081           /* FT_Sin(x) = 0 for x <= 57                               */
1082           if ( fixed_bevel || ft_pos_abs( theta ) > 57 )
1083             bevel = TRUE;
1084         }
1085       }
1086 
1087       if ( bevel )  /* this is a bevel (broken angle) */
1088       {
1089         if ( fixed_bevel )
1090         {
1091           /* the outer corners are simply joined together */
1092           FT_Vector  delta;
1093 
1094 
1095           /* add bevel */
1096           FT_Vector_From_Polar( &delta,
1097                                 radius,
1098                                 stroker->angle_out + rotate );
1099           delta.x += stroker->center.x;
1100           delta.y += stroker->center.y;
1101 
1102           border->movable = FALSE;
1103           error = ft_stroke_border_lineto( border, &delta, FALSE );
1104         }
1105         else /* variable bevel or clipped miter */
1106         {
1107           /* the miter is truncated */
1108           FT_Vector  middle, delta;
1109           FT_Fixed   coef;
1110 
1111 
1112           /* compute middle point and first angle point */
1113           FT_Vector_From_Polar( &middle,
1114                                 FT_MulFix( radius, stroker->miter_limit ),
1115                                 phi );
1116 
1117           coef    = FT_DivFix(  0x10000L - sigma.x, sigma.y );
1118           delta.x = FT_MulFix(  middle.y, coef );
1119           delta.y = FT_MulFix( -middle.x, coef );
1120 
1121           middle.x += stroker->center.x;
1122           middle.y += stroker->center.y;
1123           delta.x  += middle.x;
1124           delta.y  += middle.y;
1125 
1126           error = ft_stroke_border_lineto( border, &delta, FALSE );
1127           if ( error )
1128             goto Exit;
1129 
1130           /* compute second angle point */
1131           delta.x = middle.x - delta.x + middle.x;
1132           delta.y = middle.y - delta.y + middle.y;
1133 
1134           error = ft_stroke_border_lineto( border, &delta, FALSE );
1135           if ( error )
1136             goto Exit;
1137 
1138           /* finally, add an end point; only needed if not lineto */
1139           /* (line_length is zero for curves)                     */
1140           if ( line_length == 0 )
1141           {
1142             FT_Vector_From_Polar( &delta,
1143                                   radius,
1144                                   stroker->angle_out + rotate );
1145 
1146             delta.x += stroker->center.x;
1147             delta.y += stroker->center.y;
1148 
1149             error = ft_stroke_border_lineto( border, &delta, FALSE );
1150           }
1151         }
1152       }
1153       else /* this is a miter (intersection) */
1154       {
1155         FT_Fixed   length;
1156         FT_Vector  delta;
1157 
1158 
1159         length = FT_MulDiv( stroker->radius, stroker->miter_limit, sigma.x );
1160 
1161         FT_Vector_From_Polar( &delta, length, phi );
1162         delta.x += stroker->center.x;
1163         delta.y += stroker->center.y;
1164 
1165         error = ft_stroke_border_lineto( border, &delta, FALSE );
1166         if ( error )
1167           goto Exit;
1168 
1169         /* now add an end point; only needed if not lineto */
1170         /* (line_length is zero for curves)                */
1171         if ( line_length == 0 )
1172         {
1173           FT_Vector_From_Polar( &delta,
1174                                 stroker->radius,
1175                                 stroker->angle_out + rotate );
1176           delta.x += stroker->center.x;
1177           delta.y += stroker->center.y;
1178 
1179           error = ft_stroke_border_lineto( border, &delta, FALSE );
1180         }
1181       }
1182     }
1183 
1184   Exit:
1185     return error;
1186   }
1187 
1188 
1189   static FT_Error
ft_stroker_process_corner(FT_Stroker stroker,FT_Fixed line_length)1190   ft_stroker_process_corner( FT_Stroker  stroker,
1191                              FT_Fixed    line_length )
1192   {
1193     FT_Error  error = FT_Err_Ok;
1194     FT_Angle  turn;
1195     FT_Int    inside_side;
1196 
1197 
1198     turn = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
1199 
1200     /* no specific corner processing is required if the turn is 0 */
1201     if ( turn == 0 )
1202       goto Exit;
1203 
1204     /* when we turn to the right, the inside side is 0 */
1205     /* otherwise, the inside side is 1 */
1206     inside_side = ( turn < 0 );
1207 
1208     /* process the inside side */
1209     error = ft_stroker_inside( stroker, inside_side, line_length );
1210     if ( error )
1211       goto Exit;
1212 
1213     /* process the outside side */
1214     error = ft_stroker_outside( stroker, !inside_side, line_length );
1215 
1216   Exit:
1217     return error;
1218   }
1219 
1220 
1221   /* add two points to the left and right borders corresponding to the */
1222   /* start of the subpath                                              */
1223   static FT_Error
ft_stroker_subpath_start(FT_Stroker stroker,FT_Angle start_angle,FT_Fixed line_length)1224   ft_stroker_subpath_start( FT_Stroker  stroker,
1225                             FT_Angle    start_angle,
1226                             FT_Fixed    line_length )
1227   {
1228     FT_Vector        delta;
1229     FT_Vector        point;
1230     FT_Error         error;
1231     FT_StrokeBorder  border;
1232 
1233 
1234     FT_Vector_From_Polar( &delta, stroker->radius,
1235                           start_angle + FT_ANGLE_PI2 );
1236 
1237     point.x = stroker->center.x + delta.x;
1238     point.y = stroker->center.y + delta.y;
1239 
1240     border = stroker->borders;
1241     error = ft_stroke_border_moveto( border, &point );
1242     if ( error )
1243       goto Exit;
1244 
1245     point.x = stroker->center.x - delta.x;
1246     point.y = stroker->center.y - delta.y;
1247 
1248     border++;
1249     error = ft_stroke_border_moveto( border, &point );
1250 
1251     /* save angle, position, and line length for last join */
1252     /* (line_length is zero for curves)                    */
1253     stroker->subpath_angle       = start_angle;
1254     stroker->first_point         = FALSE;
1255     stroker->subpath_line_length = line_length;
1256 
1257   Exit:
1258     return error;
1259   }
1260 
1261 
1262   /* documentation is in ftstroke.h */
1263 
1264   FT_EXPORT_DEF( FT_Error )
FT_Stroker_LineTo(FT_Stroker stroker,FT_Vector * to)1265   FT_Stroker_LineTo( FT_Stroker  stroker,
1266                      FT_Vector*  to )
1267   {
1268     FT_Error         error = FT_Err_Ok;
1269     FT_StrokeBorder  border;
1270     FT_Vector        delta;
1271     FT_Angle         angle;
1272     FT_Int           side;
1273     FT_Fixed         line_length;
1274 
1275 
1276     if ( !stroker || !to )
1277       return FT_THROW( Invalid_Argument );
1278 
1279     delta.x = to->x - stroker->center.x;
1280     delta.y = to->y - stroker->center.y;
1281 
1282     /* a zero-length lineto is a no-op; avoid creating a spurious corner */
1283     if ( delta.x == 0 && delta.y == 0 )
1284        goto Exit;
1285 
1286     /* compute length of line */
1287     line_length = FT_Vector_Length( &delta );
1288 
1289     angle = FT_Atan2( delta.x, delta.y );
1290     FT_Vector_From_Polar( &delta, stroker->radius, angle + FT_ANGLE_PI2 );
1291 
1292     /* process corner if necessary */
1293     if ( stroker->first_point )
1294     {
1295       /* This is the first segment of a subpath.  We need to     */
1296       /* add a point to each border at their respective starting */
1297       /* point locations.                                        */
1298       error = ft_stroker_subpath_start( stroker, angle, line_length );
1299       if ( error )
1300         goto Exit;
1301     }
1302     else
1303     {
1304       /* process the current corner */
1305       stroker->angle_out = angle;
1306       error = ft_stroker_process_corner( stroker, line_length );
1307       if ( error )
1308         goto Exit;
1309     }
1310 
1311     /* now add a line segment to both the `inside' and `outside' paths */
1312     for ( border = stroker->borders, side = 1; side >= 0; side--, border++ )
1313     {
1314       FT_Vector  point;
1315 
1316 
1317       point.x = to->x + delta.x;
1318       point.y = to->y + delta.y;
1319 
1320       /* the ends of lineto borders are movable */
1321       error = ft_stroke_border_lineto( border, &point, TRUE );
1322       if ( error )
1323         goto Exit;
1324 
1325       delta.x = -delta.x;
1326       delta.y = -delta.y;
1327     }
1328 
1329     stroker->angle_in    = angle;
1330     stroker->center      = *to;
1331     stroker->line_length = line_length;
1332 
1333   Exit:
1334     return error;
1335   }
1336 
1337 
1338   /* documentation is in ftstroke.h */
1339 
1340   FT_EXPORT_DEF( FT_Error )
FT_Stroker_ConicTo(FT_Stroker stroker,FT_Vector * control,FT_Vector * to)1341   FT_Stroker_ConicTo( FT_Stroker  stroker,
1342                       FT_Vector*  control,
1343                       FT_Vector*  to )
1344   {
1345     FT_Error    error = FT_Err_Ok;
1346     FT_Vector   bez_stack[34];
1347     FT_Vector*  arc;
1348     FT_Vector*  limit = bez_stack + 30;
1349     FT_Bool     first_arc = TRUE;
1350 
1351 
1352     if ( !stroker || !control || !to )
1353     {
1354       error = FT_THROW( Invalid_Argument );
1355       goto Exit;
1356     }
1357 
1358     /* if all control points are coincident, this is a no-op; */
1359     /* avoid creating a spurious corner                       */
1360     if ( FT_IS_SMALL( stroker->center.x - control->x ) &&
1361          FT_IS_SMALL( stroker->center.y - control->y ) &&
1362          FT_IS_SMALL( control->x        - to->x      ) &&
1363          FT_IS_SMALL( control->y        - to->y      ) )
1364     {
1365        stroker->center = *to;
1366        goto Exit;
1367     }
1368 
1369     arc    = bez_stack;
1370     arc[0] = *to;
1371     arc[1] = *control;
1372     arc[2] = stroker->center;
1373 
1374     while ( arc >= bez_stack )
1375     {
1376       FT_Angle  angle_in, angle_out;
1377 
1378 
1379       /* initialize with current direction */
1380       angle_in = angle_out = stroker->angle_in;
1381 
1382       if ( arc < limit                                             &&
1383            !ft_conic_is_small_enough( arc, &angle_in, &angle_out ) )
1384       {
1385         if ( stroker->first_point )
1386           stroker->angle_in = angle_in;
1387 
1388         ft_conic_split( arc );
1389         arc += 2;
1390         continue;
1391       }
1392 
1393       if ( first_arc )
1394       {
1395         first_arc = FALSE;
1396 
1397         /* process corner if necessary */
1398         if ( stroker->first_point )
1399           error = ft_stroker_subpath_start( stroker, angle_in, 0 );
1400         else
1401         {
1402           stroker->angle_out = angle_in;
1403           error = ft_stroker_process_corner( stroker, 0 );
1404         }
1405       }
1406       else if ( ft_pos_abs( FT_Angle_Diff( stroker->angle_in, angle_in ) ) >
1407                   FT_SMALL_CONIC_THRESHOLD / 4                             )
1408       {
1409         /* if the deviation from one arc to the next is too great, */
1410         /* add a round corner                                      */
1411         stroker->center    = arc[2];
1412         stroker->angle_out = angle_in;
1413         stroker->line_join = FT_STROKER_LINEJOIN_ROUND;
1414 
1415         error = ft_stroker_process_corner( stroker, 0 );
1416 
1417         /* reinstate line join style */
1418         stroker->line_join = stroker->line_join_saved;
1419       }
1420 
1421       if ( error )
1422         goto Exit;
1423 
1424       /* the arc's angle is small enough; we can add it directly to each */
1425       /* border                                                          */
1426       {
1427         FT_Vector        ctrl, end;
1428         FT_Angle         theta, phi, rotate, alpha0 = 0;
1429         FT_Fixed         length;
1430         FT_StrokeBorder  border;
1431         FT_Int           side;
1432 
1433 
1434         theta  = FT_Angle_Diff( angle_in, angle_out ) / 2;
1435         phi    = angle_in + theta;
1436         length = FT_DivFix( stroker->radius, FT_Cos( theta ) );
1437 
1438         /* compute direction of original arc */
1439         if ( stroker->handle_wide_strokes )
1440           alpha0 = FT_Atan2( arc[0].x - arc[2].x, arc[0].y - arc[2].y );
1441 
1442         for ( border = stroker->borders, side = 0;
1443               side <= 1;
1444               side++, border++ )
1445         {
1446           rotate = FT_SIDE_TO_ROTATE( side );
1447 
1448           /* compute control point */
1449           FT_Vector_From_Polar( &ctrl, length, phi + rotate );
1450           ctrl.x += arc[1].x;
1451           ctrl.y += arc[1].y;
1452 
1453           /* compute end point */
1454           FT_Vector_From_Polar( &end, stroker->radius, angle_out + rotate );
1455           end.x += arc[0].x;
1456           end.y += arc[0].y;
1457 
1458           if ( stroker->handle_wide_strokes )
1459           {
1460             FT_Vector  start;
1461             FT_Angle   alpha1;
1462 
1463 
1464             /* determine whether the border radius is greater than the */
1465             /* radius of curvature of the original arc                 */
1466             start = border->points[border->num_points - 1];
1467 
1468             alpha1 = FT_Atan2( end.x - start.x, end.y - start.y );
1469 
1470             /* is the direction of the border arc opposite to */
1471             /* that of the original arc? */
1472             if ( ft_pos_abs( FT_Angle_Diff( alpha0, alpha1 ) ) >
1473                    FT_ANGLE_PI / 2                             )
1474             {
1475               FT_Angle   beta, gamma;
1476               FT_Vector  bvec, delta;
1477               FT_Fixed   blen, sinA, sinB, alen;
1478 
1479 
1480               /* use the sine rule to find the intersection point */
1481               beta  = FT_Atan2( arc[2].x - start.x, arc[2].y - start.y );
1482               gamma = FT_Atan2( arc[0].x - end.x,   arc[0].y - end.y );
1483 
1484               bvec.x = end.x - start.x;
1485               bvec.y = end.y - start.y;
1486 
1487               blen = FT_Vector_Length( &bvec );
1488 
1489               sinA = ft_pos_abs( FT_Sin( alpha1 - gamma ) );
1490               sinB = ft_pos_abs( FT_Sin( beta - gamma ) );
1491 
1492               alen = FT_MulDiv( blen, sinA, sinB );
1493 
1494               FT_Vector_From_Polar( &delta, alen, beta );
1495               delta.x += start.x;
1496               delta.y += start.y;
1497 
1498               /* circumnavigate the negative sector backwards */
1499               border->movable = FALSE;
1500               error = ft_stroke_border_lineto( border, &delta, FALSE );
1501               if ( error )
1502                 goto Exit;
1503               error = ft_stroke_border_lineto( border, &end, FALSE );
1504               if ( error )
1505                 goto Exit;
1506               error = ft_stroke_border_conicto( border, &ctrl, &start );
1507               if ( error )
1508                 goto Exit;
1509               /* and then move to the endpoint */
1510               error = ft_stroke_border_lineto( border, &end, FALSE );
1511               if ( error )
1512                 goto Exit;
1513 
1514               continue;
1515             }
1516 
1517             /* else fall through */
1518           }
1519 
1520           /* simply add an arc */
1521           error = ft_stroke_border_conicto( border, &ctrl, &end );
1522           if ( error )
1523             goto Exit;
1524         }
1525       }
1526 
1527       arc -= 2;
1528 
1529       stroker->angle_in = angle_out;
1530     }
1531 
1532     stroker->center      = *to;
1533     stroker->line_length = 0;
1534 
1535   Exit:
1536     return error;
1537   }
1538 
1539 
1540   /* documentation is in ftstroke.h */
1541 
1542   FT_EXPORT_DEF( FT_Error )
FT_Stroker_CubicTo(FT_Stroker stroker,FT_Vector * control1,FT_Vector * control2,FT_Vector * to)1543   FT_Stroker_CubicTo( FT_Stroker  stroker,
1544                       FT_Vector*  control1,
1545                       FT_Vector*  control2,
1546                       FT_Vector*  to )
1547   {
1548     FT_Error    error = FT_Err_Ok;
1549     FT_Vector   bez_stack[37];
1550     FT_Vector*  arc;
1551     FT_Vector*  limit = bez_stack + 32;
1552     FT_Bool     first_arc = TRUE;
1553 
1554 
1555     if ( !stroker || !control1 || !control2 || !to )
1556     {
1557       error = FT_THROW( Invalid_Argument );
1558       goto Exit;
1559     }
1560 
1561     /* if all control points are coincident, this is a no-op; */
1562     /* avoid creating a spurious corner */
1563     if ( FT_IS_SMALL( stroker->center.x - control1->x ) &&
1564          FT_IS_SMALL( stroker->center.y - control1->y ) &&
1565          FT_IS_SMALL( control1->x       - control2->x ) &&
1566          FT_IS_SMALL( control1->y       - control2->y ) &&
1567          FT_IS_SMALL( control2->x       - to->x       ) &&
1568          FT_IS_SMALL( control2->y       - to->y       ) )
1569     {
1570        stroker->center = *to;
1571        goto Exit;
1572     }
1573 
1574     arc    = bez_stack;
1575     arc[0] = *to;
1576     arc[1] = *control2;
1577     arc[2] = *control1;
1578     arc[3] = stroker->center;
1579 
1580     while ( arc >= bez_stack )
1581     {
1582       FT_Angle  angle_in, angle_mid, angle_out;
1583 
1584 
1585       /* initialize with current direction */
1586       angle_in = angle_out = angle_mid = stroker->angle_in;
1587 
1588       if ( arc < limit                                         &&
1589            !ft_cubic_is_small_enough( arc, &angle_in,
1590                                       &angle_mid, &angle_out ) )
1591       {
1592         if ( stroker->first_point )
1593           stroker->angle_in = angle_in;
1594 
1595         ft_cubic_split( arc );
1596         arc += 3;
1597         continue;
1598       }
1599 
1600       if ( first_arc )
1601       {
1602         first_arc = FALSE;
1603 
1604         /* process corner if necessary */
1605         if ( stroker->first_point )
1606           error = ft_stroker_subpath_start( stroker, angle_in, 0 );
1607         else
1608         {
1609           stroker->angle_out = angle_in;
1610           error = ft_stroker_process_corner( stroker, 0 );
1611         }
1612       }
1613       else if ( ft_pos_abs( FT_Angle_Diff( stroker->angle_in, angle_in ) ) >
1614                   FT_SMALL_CUBIC_THRESHOLD / 4                             )
1615       {
1616         /* if the deviation from one arc to the next is too great, */
1617         /* add a round corner                                      */
1618         stroker->center    = arc[3];
1619         stroker->angle_out = angle_in;
1620         stroker->line_join = FT_STROKER_LINEJOIN_ROUND;
1621 
1622         error = ft_stroker_process_corner( stroker, 0 );
1623 
1624         /* reinstate line join style */
1625         stroker->line_join = stroker->line_join_saved;
1626       }
1627 
1628       if ( error )
1629         goto Exit;
1630 
1631       /* the arc's angle is small enough; we can add it directly to each */
1632       /* border                                                          */
1633       {
1634         FT_Vector        ctrl1, ctrl2, end;
1635         FT_Angle         theta1, phi1, theta2, phi2, rotate, alpha0 = 0;
1636         FT_Fixed         length1, length2;
1637         FT_StrokeBorder  border;
1638         FT_Int           side;
1639 
1640 
1641         theta1  = FT_Angle_Diff( angle_in,  angle_mid ) / 2;
1642         theta2  = FT_Angle_Diff( angle_mid, angle_out ) / 2;
1643         phi1    = ft_angle_mean( angle_in,  angle_mid );
1644         phi2    = ft_angle_mean( angle_mid, angle_out );
1645         length1 = FT_DivFix( stroker->radius, FT_Cos( theta1 ) );
1646         length2 = FT_DivFix( stroker->radius, FT_Cos( theta2 ) );
1647 
1648         /* compute direction of original arc */
1649         if ( stroker->handle_wide_strokes )
1650           alpha0 = FT_Atan2( arc[0].x - arc[3].x, arc[0].y - arc[3].y );
1651 
1652         for ( border = stroker->borders, side = 0;
1653               side <= 1;
1654               side++, border++ )
1655         {
1656           rotate = FT_SIDE_TO_ROTATE( side );
1657 
1658           /* compute control points */
1659           FT_Vector_From_Polar( &ctrl1, length1, phi1 + rotate );
1660           ctrl1.x += arc[2].x;
1661           ctrl1.y += arc[2].y;
1662 
1663           FT_Vector_From_Polar( &ctrl2, length2, phi2 + rotate );
1664           ctrl2.x += arc[1].x;
1665           ctrl2.y += arc[1].y;
1666 
1667           /* compute end point */
1668           FT_Vector_From_Polar( &end, stroker->radius, angle_out + rotate );
1669           end.x += arc[0].x;
1670           end.y += arc[0].y;
1671 
1672           if ( stroker->handle_wide_strokes )
1673           {
1674             FT_Vector  start;
1675             FT_Angle   alpha1;
1676 
1677 
1678             /* determine whether the border radius is greater than the */
1679             /* radius of curvature of the original arc                 */
1680             start = border->points[border->num_points - 1];
1681 
1682             alpha1 = FT_Atan2( end.x - start.x, end.y - start.y );
1683 
1684             /* is the direction of the border arc opposite to */
1685             /* that of the original arc? */
1686             if ( ft_pos_abs( FT_Angle_Diff( alpha0, alpha1 ) ) >
1687                    FT_ANGLE_PI / 2                             )
1688             {
1689               FT_Angle   beta, gamma;
1690               FT_Vector  bvec, delta;
1691               FT_Fixed   blen, sinA, sinB, alen;
1692 
1693 
1694               /* use the sine rule to find the intersection point */
1695               beta  = FT_Atan2( arc[3].x - start.x, arc[3].y - start.y );
1696               gamma = FT_Atan2( arc[0].x - end.x,   arc[0].y - end.y );
1697 
1698               bvec.x = end.x - start.x;
1699               bvec.y = end.y - start.y;
1700 
1701               blen = FT_Vector_Length( &bvec );
1702 
1703               sinA = ft_pos_abs( FT_Sin( alpha1 - gamma ) );
1704               sinB = ft_pos_abs( FT_Sin( beta - gamma ) );
1705 
1706               alen = FT_MulDiv( blen, sinA, sinB );
1707 
1708               FT_Vector_From_Polar( &delta, alen, beta );
1709               delta.x += start.x;
1710               delta.y += start.y;
1711 
1712               /* circumnavigate the negative sector backwards */
1713               border->movable = FALSE;
1714               error = ft_stroke_border_lineto( border, &delta, FALSE );
1715               if ( error )
1716                 goto Exit;
1717               error = ft_stroke_border_lineto( border, &end, FALSE );
1718               if ( error )
1719                 goto Exit;
1720               error = ft_stroke_border_cubicto( border,
1721                                                 &ctrl2,
1722                                                 &ctrl1,
1723                                                 &start );
1724               if ( error )
1725                 goto Exit;
1726               /* and then move to the endpoint */
1727               error = ft_stroke_border_lineto( border, &end, FALSE );
1728               if ( error )
1729                 goto Exit;
1730 
1731               continue;
1732             }
1733 
1734             /* else fall through */
1735           }
1736 
1737           /* simply add an arc */
1738           error = ft_stroke_border_cubicto( border, &ctrl1, &ctrl2, &end );
1739           if ( error )
1740             goto Exit;
1741         }
1742       }
1743 
1744       arc -= 3;
1745 
1746       stroker->angle_in = angle_out;
1747     }
1748 
1749     stroker->center      = *to;
1750     stroker->line_length = 0;
1751 
1752   Exit:
1753     return error;
1754   }
1755 
1756 
1757   /* documentation is in ftstroke.h */
1758 
1759   FT_EXPORT_DEF( FT_Error )
FT_Stroker_BeginSubPath(FT_Stroker stroker,FT_Vector * to,FT_Bool open)1760   FT_Stroker_BeginSubPath( FT_Stroker  stroker,
1761                            FT_Vector*  to,
1762                            FT_Bool     open )
1763   {
1764     if ( !stroker || !to )
1765       return FT_THROW( Invalid_Argument );
1766 
1767     /* We cannot process the first point, because there is not enough      */
1768     /* information regarding its corner/cap.  The latter will be processed */
1769     /* in the `FT_Stroker_EndSubPath' routine.                             */
1770     /*                                                                     */
1771     stroker->first_point  = TRUE;
1772     stroker->center       = *to;
1773     stroker->subpath_open = open;
1774 
1775     /* Determine if we need to check whether the border radius is greater */
1776     /* than the radius of curvature of a curve, to handle this case       */
1777     /* specially.  This is only required if bevel joins or butt caps may  */
1778     /* be created, because round & miter joins and round & square caps    */
1779     /* cover the negative sector created with wide strokes.               */
1780     stroker->handle_wide_strokes =
1781       FT_BOOL( stroker->line_join != FT_STROKER_LINEJOIN_ROUND  ||
1782                ( stroker->subpath_open                        &&
1783                  stroker->line_cap == FT_STROKER_LINECAP_BUTT ) );
1784 
1785     /* record the subpath start point for each border */
1786     stroker->subpath_start = *to;
1787 
1788     stroker->angle_in = 0;
1789 
1790     return FT_Err_Ok;
1791   }
1792 
1793 
1794   static FT_Error
ft_stroker_add_reverse_left(FT_Stroker stroker,FT_Bool open)1795   ft_stroker_add_reverse_left( FT_Stroker  stroker,
1796                                FT_Bool     open )
1797   {
1798     FT_StrokeBorder  right = stroker->borders + 0;
1799     FT_StrokeBorder  left  = stroker->borders + 1;
1800     FT_Int           new_points;
1801     FT_Error         error = FT_Err_Ok;
1802 
1803 
1804     FT_ASSERT( left->start >= 0 );
1805 
1806     new_points = (FT_Int)left->num_points - left->start;
1807     if ( new_points > 0 )
1808     {
1809       error = ft_stroke_border_grow( right, (FT_UInt)new_points );
1810       if ( error )
1811         goto Exit;
1812 
1813       {
1814         FT_Vector*  dst_point = right->points + right->num_points;
1815         FT_Byte*    dst_tag   = right->tags   + right->num_points;
1816         FT_Vector*  src_point = left->points  + left->num_points - 1;
1817         FT_Byte*    src_tag   = left->tags    + left->num_points - 1;
1818 
1819 
1820         while ( src_point >= left->points + left->start )
1821         {
1822           *dst_point = *src_point;
1823           *dst_tag   = *src_tag;
1824 
1825           if ( open )
1826             dst_tag[0] &= ~FT_STROKE_TAG_BEGIN_END;
1827           else
1828           {
1829             FT_Byte  ttag =
1830                        (FT_Byte)( dst_tag[0] & FT_STROKE_TAG_BEGIN_END );
1831 
1832 
1833             /* switch begin/end tags if necessary */
1834             if ( ttag == FT_STROKE_TAG_BEGIN ||
1835                  ttag == FT_STROKE_TAG_END   )
1836               dst_tag[0] ^= FT_STROKE_TAG_BEGIN_END;
1837           }
1838 
1839           src_point--;
1840           src_tag--;
1841           dst_point++;
1842           dst_tag++;
1843         }
1844       }
1845 
1846       left->num_points   = (FT_UInt)left->start;
1847       right->num_points += (FT_UInt)new_points;
1848 
1849       right->movable = FALSE;
1850       left->movable  = FALSE;
1851     }
1852 
1853   Exit:
1854     return error;
1855   }
1856 
1857 
1858   /* documentation is in ftstroke.h */
1859 
1860   /* there's a lot of magic in this function! */
1861   FT_EXPORT_DEF( FT_Error )
FT_Stroker_EndSubPath(FT_Stroker stroker)1862   FT_Stroker_EndSubPath( FT_Stroker  stroker )
1863   {
1864     FT_Error  error = FT_Err_Ok;
1865 
1866 
1867     if ( !stroker )
1868     {
1869       error = FT_THROW( Invalid_Argument );
1870       goto Exit;
1871     }
1872 
1873     if ( stroker->subpath_open )
1874     {
1875       FT_StrokeBorder  right = stroker->borders;
1876 
1877 
1878       /* All right, this is an opened path, we need to add a cap between */
1879       /* right & left, add the reverse of left, then add a final cap     */
1880       /* between left & right.                                           */
1881       error = ft_stroker_cap( stroker, stroker->angle_in, 0 );
1882       if ( error )
1883         goto Exit;
1884 
1885       /* add reversed points from `left' to `right' */
1886       error = ft_stroker_add_reverse_left( stroker, TRUE );
1887       if ( error )
1888         goto Exit;
1889 
1890       /* now add the final cap */
1891       stroker->center = stroker->subpath_start;
1892       error = ft_stroker_cap( stroker,
1893                               stroker->subpath_angle + FT_ANGLE_PI, 0 );
1894       if ( error )
1895         goto Exit;
1896 
1897       /* Now end the right subpath accordingly.  The left one is */
1898       /* rewind and doesn't need further processing.             */
1899       ft_stroke_border_close( right, FALSE );
1900     }
1901     else
1902     {
1903       /* close the path if needed */
1904       if ( !FT_IS_SMALL( stroker->center.x - stroker->subpath_start.x ) ||
1905            !FT_IS_SMALL( stroker->center.y - stroker->subpath_start.y ) )
1906       {
1907          error = FT_Stroker_LineTo( stroker, &stroker->subpath_start );
1908          if ( error )
1909            goto Exit;
1910       }
1911 
1912       /* process the corner */
1913       stroker->angle_out = stroker->subpath_angle;
1914 
1915       error = ft_stroker_process_corner( stroker,
1916                                          stroker->subpath_line_length );
1917       if ( error )
1918         goto Exit;
1919 
1920       /* then end our two subpaths */
1921       ft_stroke_border_close( stroker->borders + 0, FALSE );
1922       ft_stroke_border_close( stroker->borders + 1, TRUE );
1923     }
1924 
1925   Exit:
1926     return error;
1927   }
1928 
1929 
1930   /* documentation is in ftstroke.h */
1931 
1932   FT_EXPORT_DEF( FT_Error )
FT_Stroker_GetBorderCounts(FT_Stroker stroker,FT_StrokerBorder border,FT_UInt * anum_points,FT_UInt * anum_contours)1933   FT_Stroker_GetBorderCounts( FT_Stroker        stroker,
1934                               FT_StrokerBorder  border,
1935                               FT_UInt          *anum_points,
1936                               FT_UInt          *anum_contours )
1937   {
1938     FT_UInt   num_points = 0, num_contours = 0;
1939     FT_Error  error;
1940 
1941 
1942     if ( !stroker || border > 1 )
1943     {
1944       error = FT_THROW( Invalid_Argument );
1945       goto Exit;
1946     }
1947 
1948     error = ft_stroke_border_get_counts( stroker->borders + border,
1949                                          &num_points, &num_contours );
1950   Exit:
1951     if ( anum_points )
1952       *anum_points = num_points;
1953 
1954     if ( anum_contours )
1955       *anum_contours = num_contours;
1956 
1957     return error;
1958   }
1959 
1960 
1961   /* documentation is in ftstroke.h */
1962 
1963   FT_EXPORT_DEF( FT_Error )
FT_Stroker_GetCounts(FT_Stroker stroker,FT_UInt * anum_points,FT_UInt * anum_contours)1964   FT_Stroker_GetCounts( FT_Stroker  stroker,
1965                         FT_UInt    *anum_points,
1966                         FT_UInt    *anum_contours )
1967   {
1968     FT_UInt   count1, count2, num_points   = 0;
1969     FT_UInt   count3, count4, num_contours = 0;
1970     FT_Error  error;
1971 
1972 
1973     if ( !stroker )
1974     {
1975       error = FT_THROW( Invalid_Argument );
1976       goto Exit;
1977     }
1978 
1979     error = ft_stroke_border_get_counts( stroker->borders + 0,
1980                                          &count1, &count2 );
1981     if ( error )
1982       goto Exit;
1983 
1984     error = ft_stroke_border_get_counts( stroker->borders + 1,
1985                                          &count3, &count4 );
1986     if ( error )
1987       goto Exit;
1988 
1989     num_points   = count1 + count3;
1990     num_contours = count2 + count4;
1991 
1992   Exit:
1993     if ( anum_points )
1994       *anum_points   = num_points;
1995 
1996     if ( anum_contours )
1997       *anum_contours = num_contours;
1998 
1999     return error;
2000   }
2001 
2002 
2003   /* documentation is in ftstroke.h */
2004 
2005   FT_EXPORT_DEF( void )
FT_Stroker_ExportBorder(FT_Stroker stroker,FT_StrokerBorder border,FT_Outline * outline)2006   FT_Stroker_ExportBorder( FT_Stroker        stroker,
2007                            FT_StrokerBorder  border,
2008                            FT_Outline*       outline )
2009   {
2010     if ( !stroker || !outline )
2011       return;
2012 
2013     if ( border == FT_STROKER_BORDER_LEFT  ||
2014          border == FT_STROKER_BORDER_RIGHT )
2015     {
2016       FT_StrokeBorder  sborder = & stroker->borders[border];
2017 
2018 
2019       if ( sborder->valid )
2020         ft_stroke_border_export( sborder, outline );
2021     }
2022   }
2023 
2024 
2025   /* documentation is in ftstroke.h */
2026 
2027   FT_EXPORT_DEF( void )
FT_Stroker_Export(FT_Stroker stroker,FT_Outline * outline)2028   FT_Stroker_Export( FT_Stroker   stroker,
2029                      FT_Outline*  outline )
2030   {
2031     FT_Stroker_ExportBorder( stroker, FT_STROKER_BORDER_LEFT, outline );
2032     FT_Stroker_ExportBorder( stroker, FT_STROKER_BORDER_RIGHT, outline );
2033   }
2034 
2035 
2036   /* documentation is in ftstroke.h */
2037 
2038   /*
2039    * The following is very similar to FT_Outline_Decompose, except
2040    * that we do support opened paths, and do not scale the outline.
2041    */
2042   FT_EXPORT_DEF( FT_Error )
FT_Stroker_ParseOutline(FT_Stroker stroker,FT_Outline * outline,FT_Bool opened)2043   FT_Stroker_ParseOutline( FT_Stroker   stroker,
2044                            FT_Outline*  outline,
2045                            FT_Bool      opened )
2046   {
2047     FT_Vector   v_last;
2048     FT_Vector   v_control;
2049     FT_Vector   v_start;
2050 
2051     FT_Vector*  point;
2052     FT_Vector*  limit;
2053     char*       tags;
2054 
2055     FT_Error    error;
2056 
2057     FT_Int      n;         /* index of contour in outline     */
2058     FT_UInt     first;     /* index of first point in contour */
2059     FT_Int      tag;       /* current point's state           */
2060 
2061 
2062     if ( !outline )
2063       return FT_THROW( Invalid_Outline );
2064 
2065     if ( !stroker )
2066       return FT_THROW( Invalid_Argument );
2067 
2068     FT_Stroker_Rewind( stroker );
2069 
2070     first = 0;
2071 
2072     for ( n = 0; n < outline->n_contours; n++ )
2073     {
2074       FT_UInt  last;  /* index of last point in contour */
2075 
2076 
2077       last  = (FT_UInt)outline->contours[n];
2078       limit = outline->points + last;
2079 
2080       /* skip empty points; we don't stroke these */
2081       if ( last <= first )
2082       {
2083         first = last + 1;
2084         continue;
2085       }
2086 
2087       v_start = outline->points[first];
2088       v_last  = outline->points[last];
2089 
2090       v_control = v_start;
2091 
2092       point = outline->points + first;
2093       tags  = outline->tags   + first;
2094       tag   = FT_CURVE_TAG( tags[0] );
2095 
2096       /* A contour cannot start with a cubic control point! */
2097       if ( tag == FT_CURVE_TAG_CUBIC )
2098         goto Invalid_Outline;
2099 
2100       /* check first point to determine origin */
2101       if ( tag == FT_CURVE_TAG_CONIC )
2102       {
2103         /* First point is conic control.  Yes, this happens. */
2104         if ( FT_CURVE_TAG( outline->tags[last] ) == FT_CURVE_TAG_ON )
2105         {
2106           /* start at last point if it is on the curve */
2107           v_start = v_last;
2108           limit--;
2109         }
2110         else
2111         {
2112           /* if both first and last points are conic, */
2113           /* start at their middle                    */
2114           v_start.x = ( v_start.x + v_last.x ) / 2;
2115           v_start.y = ( v_start.y + v_last.y ) / 2;
2116         }
2117         point--;
2118         tags--;
2119       }
2120 
2121       error = FT_Stroker_BeginSubPath( stroker, &v_start, opened );
2122       if ( error )
2123         goto Exit;
2124 
2125       while ( point < limit )
2126       {
2127         point++;
2128         tags++;
2129 
2130         tag = FT_CURVE_TAG( tags[0] );
2131         switch ( tag )
2132         {
2133         case FT_CURVE_TAG_ON:  /* emit a single line_to */
2134           {
2135             FT_Vector  vec;
2136 
2137 
2138             vec.x = point->x;
2139             vec.y = point->y;
2140 
2141             error = FT_Stroker_LineTo( stroker, &vec );
2142             if ( error )
2143               goto Exit;
2144             continue;
2145           }
2146 
2147         case FT_CURVE_TAG_CONIC:  /* consume conic arcs */
2148           v_control.x = point->x;
2149           v_control.y = point->y;
2150 
2151         Do_Conic:
2152           if ( point < limit )
2153           {
2154             FT_Vector  vec;
2155             FT_Vector  v_middle;
2156 
2157 
2158             point++;
2159             tags++;
2160             tag = FT_CURVE_TAG( tags[0] );
2161 
2162             vec = point[0];
2163 
2164             if ( tag == FT_CURVE_TAG_ON )
2165             {
2166               error = FT_Stroker_ConicTo( stroker, &v_control, &vec );
2167               if ( error )
2168                 goto Exit;
2169               continue;
2170             }
2171 
2172             if ( tag != FT_CURVE_TAG_CONIC )
2173               goto Invalid_Outline;
2174 
2175             v_middle.x = ( v_control.x + vec.x ) / 2;
2176             v_middle.y = ( v_control.y + vec.y ) / 2;
2177 
2178             error = FT_Stroker_ConicTo( stroker, &v_control, &v_middle );
2179             if ( error )
2180               goto Exit;
2181 
2182             v_control = vec;
2183             goto Do_Conic;
2184           }
2185 
2186           error = FT_Stroker_ConicTo( stroker, &v_control, &v_start );
2187           goto Close;
2188 
2189         default:  /* FT_CURVE_TAG_CUBIC */
2190           {
2191             FT_Vector  vec1, vec2;
2192 
2193 
2194             if ( point + 1 > limit                             ||
2195                  FT_CURVE_TAG( tags[1] ) != FT_CURVE_TAG_CUBIC )
2196               goto Invalid_Outline;
2197 
2198             point += 2;
2199             tags  += 2;
2200 
2201             vec1 = point[-2];
2202             vec2 = point[-1];
2203 
2204             if ( point <= limit )
2205             {
2206               FT_Vector  vec;
2207 
2208 
2209               vec = point[0];
2210 
2211               error = FT_Stroker_CubicTo( stroker, &vec1, &vec2, &vec );
2212               if ( error )
2213                 goto Exit;
2214               continue;
2215             }
2216 
2217             error = FT_Stroker_CubicTo( stroker, &vec1, &vec2, &v_start );
2218             goto Close;
2219           }
2220         }
2221       }
2222 
2223     Close:
2224       if ( error )
2225         goto Exit;
2226 
2227       /* don't try to end the path if no segments have been generated */
2228       if ( !stroker->first_point )
2229       {
2230         error = FT_Stroker_EndSubPath( stroker );
2231         if ( error )
2232           goto Exit;
2233       }
2234 
2235       first = last + 1;
2236     }
2237 
2238     return FT_Err_Ok;
2239 
2240   Exit:
2241     return error;
2242 
2243   Invalid_Outline:
2244     return FT_THROW( Invalid_Outline );
2245   }
2246 
2247 
2248   /* documentation is in ftstroke.h */
2249 
2250   FT_EXPORT_DEF( FT_Error )
FT_Glyph_Stroke(FT_Glyph * pglyph,FT_Stroker stroker,FT_Bool destroy)2251   FT_Glyph_Stroke( FT_Glyph    *pglyph,
2252                    FT_Stroker   stroker,
2253                    FT_Bool      destroy )
2254   {
2255     FT_Error  error = FT_ERR( Invalid_Argument );
2256     FT_Glyph  glyph = NULL;
2257 
2258 
2259     if ( !pglyph )
2260       goto Exit;
2261 
2262     glyph = *pglyph;
2263     if ( !glyph || glyph->clazz != &ft_outline_glyph_class )
2264       goto Exit;
2265 
2266     {
2267       FT_Glyph  copy;
2268 
2269 
2270       error = FT_Glyph_Copy( glyph, &copy );
2271       if ( error )
2272         goto Exit;
2273 
2274       glyph = copy;
2275     }
2276 
2277     {
2278       FT_OutlineGlyph  oglyph  = (FT_OutlineGlyph)glyph;
2279       FT_Outline*      outline = &oglyph->outline;
2280       FT_UInt          num_points, num_contours;
2281 
2282 
2283       error = FT_Stroker_ParseOutline( stroker, outline, FALSE );
2284       if ( error )
2285         goto Fail;
2286 
2287       FT_Stroker_GetCounts( stroker, &num_points, &num_contours );
2288 
2289       FT_Outline_Done( glyph->library, outline );
2290 
2291       error = FT_Outline_New( glyph->library,
2292                               num_points,
2293                               (FT_Int)num_contours,
2294                               outline );
2295       if ( error )
2296         goto Fail;
2297 
2298       outline->n_points   = 0;
2299       outline->n_contours = 0;
2300 
2301       FT_Stroker_Export( stroker, outline );
2302     }
2303 
2304     if ( destroy )
2305       FT_Done_Glyph( *pglyph );
2306 
2307     *pglyph = glyph;
2308     goto Exit;
2309 
2310   Fail:
2311     FT_Done_Glyph( glyph );
2312     glyph = NULL;
2313 
2314     if ( !destroy )
2315       *pglyph = NULL;
2316 
2317   Exit:
2318     return error;
2319   }
2320 
2321 
2322   /* documentation is in ftstroke.h */
2323 
2324   FT_EXPORT_DEF( FT_Error )
FT_Glyph_StrokeBorder(FT_Glyph * pglyph,FT_Stroker stroker,FT_Bool inside,FT_Bool destroy)2325   FT_Glyph_StrokeBorder( FT_Glyph    *pglyph,
2326                          FT_Stroker   stroker,
2327                          FT_Bool      inside,
2328                          FT_Bool      destroy )
2329   {
2330     FT_Error  error = FT_ERR( Invalid_Argument );
2331     FT_Glyph  glyph = NULL;
2332 
2333 
2334     if ( !pglyph )
2335       goto Exit;
2336 
2337     glyph = *pglyph;
2338     if ( !glyph || glyph->clazz != &ft_outline_glyph_class )
2339       goto Exit;
2340 
2341     {
2342       FT_Glyph  copy;
2343 
2344 
2345       error = FT_Glyph_Copy( glyph, &copy );
2346       if ( error )
2347         goto Exit;
2348 
2349       glyph = copy;
2350     }
2351 
2352     {
2353       FT_OutlineGlyph   oglyph  = (FT_OutlineGlyph)glyph;
2354       FT_StrokerBorder  border;
2355       FT_Outline*       outline = &oglyph->outline;
2356       FT_UInt           num_points, num_contours;
2357 
2358 
2359       border = FT_Outline_GetOutsideBorder( outline );
2360       if ( inside )
2361       {
2362         if ( border == FT_STROKER_BORDER_LEFT )
2363           border = FT_STROKER_BORDER_RIGHT;
2364         else
2365           border = FT_STROKER_BORDER_LEFT;
2366       }
2367 
2368       error = FT_Stroker_ParseOutline( stroker, outline, FALSE );
2369       if ( error )
2370         goto Fail;
2371 
2372       FT_Stroker_GetBorderCounts( stroker, border,
2373                                   &num_points, &num_contours );
2374 
2375       FT_Outline_Done( glyph->library, outline );
2376 
2377       error = FT_Outline_New( glyph->library,
2378                               num_points,
2379                               (FT_Int)num_contours,
2380                               outline );
2381       if ( error )
2382         goto Fail;
2383 
2384       outline->n_points   = 0;
2385       outline->n_contours = 0;
2386 
2387       FT_Stroker_ExportBorder( stroker, border, outline );
2388     }
2389 
2390     if ( destroy )
2391       FT_Done_Glyph( *pglyph );
2392 
2393     *pglyph = glyph;
2394     goto Exit;
2395 
2396   Fail:
2397     FT_Done_Glyph( glyph );
2398     glyph = NULL;
2399 
2400     if ( !destroy )
2401       *pglyph = NULL;
2402 
2403   Exit:
2404     return error;
2405   }
2406 
2407 
2408 /* END */
2409