1 /***************************************************************************/
2 /*                                                                         */
3 /*  ftstroke.c                                                             */
4 /*                                                                         */
5 /*    FreeType path stroker (body).                                        */
6 /*                                                                         */
7 /*  Copyright 2002-2018 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 <ft2build.h>
20 #include FT_STROKER_H
21 #include FT_TRIGONOMETRY_H
22 #include FT_OUTLINE_H
23 #include FT_INTERNAL_MEMORY_H
24 #include FT_INTERNAL_DEBUG_H
25 #include FT_INTERNAL_OBJECTS_H
26 
27 #include "basepic.h"
28 
29 
30   /* declare an extern to access `ft_outline_glyph_class' globally     */
31   /* allocated  in `ftglyph.c', and use the FT_OUTLINE_GLYPH_CLASS_GET */
32   /* macro to access it when FT_CONFIG_OPTION_PIC is defined           */
33 #ifndef FT_CONFIG_OPTION_PIC
34   FT_CALLBACK_TABLE const FT_Glyph_Class  ft_outline_glyph_class;
35 #endif
36 
37 
38   /* documentation is in ftstroke.h */
39 
40   FT_EXPORT_DEF( FT_StrokerBorder )
FT_Outline_GetInsideBorder(FT_Outline * outline)41   FT_Outline_GetInsideBorder( FT_Outline*  outline )
42   {
43     FT_Orientation  o = FT_Outline_Get_Orientation( outline );
44 
45 
46     return o == FT_ORIENTATION_TRUETYPE ? FT_STROKER_BORDER_RIGHT
47                                         : FT_STROKER_BORDER_LEFT;
48   }
49 
50 
51   /* documentation is in ftstroke.h */
52 
53   FT_EXPORT_DEF( FT_StrokerBorder )
FT_Outline_GetOutsideBorder(FT_Outline * outline)54   FT_Outline_GetOutsideBorder( FT_Outline*  outline )
55   {
56     FT_Orientation  o = FT_Outline_Get_Orientation( outline );
57 
58 
59     return o == FT_ORIENTATION_TRUETYPE ? FT_STROKER_BORDER_LEFT
60                                         : FT_STROKER_BORDER_RIGHT;
61   }
62 
63 
64   /*************************************************************************/
65   /*************************************************************************/
66   /*****                                                               *****/
67   /*****                      BEZIER COMPUTATIONS                      *****/
68   /*****                                                               *****/
69   /*************************************************************************/
70   /*************************************************************************/
71 
72 #define FT_SMALL_CONIC_THRESHOLD  ( FT_ANGLE_PI / 6 )
73 #define FT_SMALL_CUBIC_THRESHOLD  ( FT_ANGLE_PI / 8 )
74 
75 #define FT_EPSILON  2
76 
77 #define FT_IS_SMALL( x )  ( (x) > -FT_EPSILON && (x) < FT_EPSILON )
78 
79 
80   static FT_Pos
ft_pos_abs(FT_Pos x)81   ft_pos_abs( FT_Pos  x )
82   {
83     return x >= 0 ? x : -x;
84   }
85 
86 
87   static void
ft_conic_split(FT_Vector * base)88   ft_conic_split( FT_Vector*  base )
89   {
90     FT_Pos  a, b;
91 
92 
93     base[4].x = base[2].x;
94     b = base[1].x;
95     a = base[3].x = ( base[2].x + b ) / 2;
96     b = base[1].x = ( base[0].x + b ) / 2;
97     base[2].x = ( a + b ) / 2;
98 
99     base[4].y = base[2].y;
100     b = base[1].y;
101     a = base[3].y = ( base[2].y + b ) / 2;
102     b = base[1].y = ( base[0].y + b ) / 2;
103     base[2].y = ( a + b ) / 2;
104   }
105 
106 
107   static FT_Bool
ft_conic_is_small_enough(FT_Vector * base,FT_Angle * angle_in,FT_Angle * angle_out)108   ft_conic_is_small_enough( FT_Vector*  base,
109                             FT_Angle   *angle_in,
110                             FT_Angle   *angle_out )
111   {
112     FT_Vector  d1, d2;
113     FT_Angle   theta;
114     FT_Int     close1, close2;
115 
116 
117     d1.x = base[1].x - base[2].x;
118     d1.y = base[1].y - base[2].y;
119     d2.x = base[0].x - base[1].x;
120     d2.y = base[0].y - base[1].y;
121 
122     close1 = FT_IS_SMALL( d1.x ) && FT_IS_SMALL( d1.y );
123     close2 = FT_IS_SMALL( d2.x ) && FT_IS_SMALL( d2.y );
124 
125     if ( close1 )
126     {
127       if ( close2 )
128       {
129         /* basically a point;                      */
130         /* do nothing to retain original direction */
131       }
132       else
133       {
134         *angle_in  =
135         *angle_out = FT_Atan2( d2.x, d2.y );
136       }
137     }
138     else /* !close1 */
139     {
140       if ( close2 )
141       {
142         *angle_in  =
143         *angle_out = FT_Atan2( d1.x, d1.y );
144       }
145       else
146       {
147         *angle_in  = FT_Atan2( d1.x, d1.y );
148         *angle_out = FT_Atan2( d2.x, d2.y );
149       }
150     }
151 
152     theta = ft_pos_abs( FT_Angle_Diff( *angle_in, *angle_out ) );
153 
154     return FT_BOOL( theta < FT_SMALL_CONIC_THRESHOLD );
155   }
156 
157 
158   static void
ft_cubic_split(FT_Vector * base)159   ft_cubic_split( FT_Vector*  base )
160   {
161     FT_Pos  a, b, c, d;
162 
163 
164     base[6].x = base[3].x;
165     c = base[1].x;
166     d = base[2].x;
167     base[1].x = a = ( base[0].x + c ) / 2;
168     base[5].x = b = ( base[3].x + d ) / 2;
169     c = ( c + d ) / 2;
170     base[2].x = a = ( a + c ) / 2;
171     base[4].x = b = ( b + c ) / 2;
172     base[3].x = ( a + b ) / 2;
173 
174     base[6].y = base[3].y;
175     c = base[1].y;
176     d = base[2].y;
177     base[1].y = a = ( base[0].y + c ) / 2;
178     base[5].y = b = ( base[3].y + d ) / 2;
179     c = ( c + d ) / 2;
180     base[2].y = a = ( a + c ) / 2;
181     base[4].y = b = ( b + c ) / 2;
182     base[3].y = ( a + b ) / 2;
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 
376       if ( reverse )
377       {
378         /* reverse the points */
379         {
380           FT_Vector*  vec1 = border->points + start + 1;
381           FT_Vector*  vec2 = border->points + count - 1;
382 
383 
384           for ( ; vec1 < vec2; vec1++, vec2-- )
385           {
386             FT_Vector  tmp;
387 
388 
389             tmp   = *vec1;
390             *vec1 = *vec2;
391             *vec2 = tmp;
392           }
393         }
394 
395         /* then the tags */
396         {
397           FT_Byte*  tag1 = border->tags + start + 1;
398           FT_Byte*  tag2 = border->tags + count - 1;
399 
400 
401           for ( ; tag1 < tag2; tag1++, tag2-- )
402           {
403             FT_Byte  tmp;
404 
405 
406             tmp   = *tag1;
407             *tag1 = *tag2;
408             *tag2 = tmp;
409           }
410         }
411       }
412 
413       border->tags[start    ] |= FT_STROKE_TAG_BEGIN;
414       border->tags[count - 1] |= FT_STROKE_TAG_END;
415     }
416 
417     border->start   = -1;
418     border->movable = FALSE;
419   }
420 
421 
422   static FT_Error
ft_stroke_border_lineto(FT_StrokeBorder border,FT_Vector * to,FT_Bool movable)423   ft_stroke_border_lineto( FT_StrokeBorder  border,
424                            FT_Vector*       to,
425                            FT_Bool          movable )
426   {
427     FT_Error  error = FT_Err_Ok;
428 
429 
430     FT_ASSERT( border->start >= 0 );
431 
432     if ( border->movable )
433     {
434       /* move last point */
435       border->points[border->num_points - 1] = *to;
436     }
437     else
438     {
439       /* don't add zero-length lineto */
440       if ( border->num_points > 0                                          &&
441            FT_IS_SMALL( border->points[border->num_points - 1].x - to->x ) &&
442            FT_IS_SMALL( border->points[border->num_points - 1].y - to->y ) )
443         return error;
444 
445       /* add one point */
446       error = ft_stroke_border_grow( border, 1 );
447       if ( !error )
448       {
449         FT_Vector*  vec = border->points + border->num_points;
450         FT_Byte*    tag = border->tags   + border->num_points;
451 
452 
453         vec[0] = *to;
454         tag[0] = FT_STROKE_TAG_ON;
455 
456         border->num_points += 1;
457       }
458     }
459     border->movable = movable;
460     return error;
461   }
462 
463 
464   static FT_Error
ft_stroke_border_conicto(FT_StrokeBorder border,FT_Vector * control,FT_Vector * to)465   ft_stroke_border_conicto( FT_StrokeBorder  border,
466                             FT_Vector*       control,
467                             FT_Vector*       to )
468   {
469     FT_Error  error;
470 
471 
472     FT_ASSERT( border->start >= 0 );
473 
474     error = ft_stroke_border_grow( border, 2 );
475     if ( !error )
476     {
477       FT_Vector*  vec = border->points + border->num_points;
478       FT_Byte*    tag = border->tags   + border->num_points;
479 
480 
481       vec[0] = *control;
482       vec[1] = *to;
483 
484       tag[0] = 0;
485       tag[1] = FT_STROKE_TAG_ON;
486 
487       border->num_points += 2;
488     }
489 
490     border->movable = FALSE;
491 
492     return error;
493   }
494 
495 
496   static FT_Error
ft_stroke_border_cubicto(FT_StrokeBorder border,FT_Vector * control1,FT_Vector * control2,FT_Vector * to)497   ft_stroke_border_cubicto( FT_StrokeBorder  border,
498                             FT_Vector*       control1,
499                             FT_Vector*       control2,
500                             FT_Vector*       to )
501   {
502     FT_Error  error;
503 
504 
505     FT_ASSERT( border->start >= 0 );
506 
507     error = ft_stroke_border_grow( border, 3 );
508     if ( !error )
509     {
510       FT_Vector*  vec = border->points + border->num_points;
511       FT_Byte*    tag = border->tags   + border->num_points;
512 
513 
514       vec[0] = *control1;
515       vec[1] = *control2;
516       vec[2] = *to;
517 
518       tag[0] = FT_STROKE_TAG_CUBIC;
519       tag[1] = FT_STROKE_TAG_CUBIC;
520       tag[2] = FT_STROKE_TAG_ON;
521 
522       border->num_points += 3;
523     }
524 
525     border->movable = FALSE;
526 
527     return error;
528   }
529 
530 
531 #define FT_ARC_CUBIC_ANGLE  ( FT_ANGLE_PI / 2 )
532 
533 
534   static FT_Error
ft_stroke_border_arcto(FT_StrokeBorder border,FT_Vector * center,FT_Fixed radius,FT_Angle angle_start,FT_Angle angle_diff)535   ft_stroke_border_arcto( FT_StrokeBorder  border,
536                           FT_Vector*       center,
537                           FT_Fixed         radius,
538                           FT_Angle         angle_start,
539                           FT_Angle         angle_diff )
540   {
541     FT_Angle   total, angle, step, rotate, next, theta;
542     FT_Vector  a, b, a2, b2;
543     FT_Fixed   length;
544     FT_Error   error = FT_Err_Ok;
545 
546 
547     /* compute start point */
548     FT_Vector_From_Polar( &a, radius, angle_start );
549     a.x += center->x;
550     a.y += center->y;
551 
552     total  = angle_diff;
553     angle  = angle_start;
554     rotate = ( angle_diff >= 0 ) ? FT_ANGLE_PI2 : -FT_ANGLE_PI2;
555 
556     while ( total != 0 )
557     {
558       step = total;
559       if ( step > FT_ARC_CUBIC_ANGLE )
560         step = FT_ARC_CUBIC_ANGLE;
561 
562       else if ( step < -FT_ARC_CUBIC_ANGLE )
563         step = -FT_ARC_CUBIC_ANGLE;
564 
565       next  = angle + step;
566       theta = step;
567       if ( theta < 0 )
568         theta = -theta;
569 
570       theta >>= 1;
571 
572       /* compute end point */
573       FT_Vector_From_Polar( &b, radius, next );
574       b.x += center->x;
575       b.y += center->y;
576 
577       /* compute first and second control points */
578       length = FT_MulDiv( radius, FT_Sin( theta ) * 4,
579                           ( 0x10000L + FT_Cos( theta ) ) * 3 );
580 
581       FT_Vector_From_Polar( &a2, length, angle + rotate );
582       a2.x += a.x;
583       a2.y += a.y;
584 
585       FT_Vector_From_Polar( &b2, length, next - rotate );
586       b2.x += b.x;
587       b2.y += b.y;
588 
589       /* add cubic arc */
590       error = ft_stroke_border_cubicto( border, &a2, &b2, &b );
591       if ( error )
592         break;
593 
594       /* process the rest of the arc ?? */
595       a      = b;
596       total -= step;
597       angle  = next;
598     }
599 
600     return error;
601   }
602 
603 
604   static FT_Error
ft_stroke_border_moveto(FT_StrokeBorder border,FT_Vector * to)605   ft_stroke_border_moveto( FT_StrokeBorder  border,
606                            FT_Vector*       to )
607   {
608     /* close current open path if any ? */
609     if ( border->start >= 0 )
610       ft_stroke_border_close( border, FALSE );
611 
612     border->start = (FT_Int)border->num_points;
613     border->movable = FALSE;
614 
615     return ft_stroke_border_lineto( border, to, FALSE );
616   }
617 
618 
619   static void
ft_stroke_border_init(FT_StrokeBorder border,FT_Memory memory)620   ft_stroke_border_init( FT_StrokeBorder  border,
621                          FT_Memory        memory )
622   {
623     border->memory = memory;
624     border->points = NULL;
625     border->tags   = NULL;
626 
627     border->num_points = 0;
628     border->max_points = 0;
629     border->start      = -1;
630     border->valid      = FALSE;
631   }
632 
633 
634   static void
ft_stroke_border_reset(FT_StrokeBorder border)635   ft_stroke_border_reset( FT_StrokeBorder  border )
636   {
637     border->num_points = 0;
638     border->start      = -1;
639     border->valid      = FALSE;
640   }
641 
642 
643   static void
ft_stroke_border_done(FT_StrokeBorder border)644   ft_stroke_border_done( FT_StrokeBorder  border )
645   {
646     FT_Memory  memory = border->memory;
647 
648 
649     FT_FREE( border->points );
650     FT_FREE( border->tags );
651 
652     border->num_points = 0;
653     border->max_points = 0;
654     border->start      = -1;
655     border->valid      = FALSE;
656   }
657 
658 
659   static FT_Error
ft_stroke_border_get_counts(FT_StrokeBorder border,FT_UInt * anum_points,FT_UInt * anum_contours)660   ft_stroke_border_get_counts( FT_StrokeBorder  border,
661                                FT_UInt         *anum_points,
662                                FT_UInt         *anum_contours )
663   {
664     FT_Error  error        = FT_Err_Ok;
665     FT_UInt   num_points   = 0;
666     FT_UInt   num_contours = 0;
667 
668     FT_UInt     count      = border->num_points;
669     FT_Vector*  point      = border->points;
670     FT_Byte*    tags       = border->tags;
671     FT_Int      in_contour = 0;
672 
673 
674     for ( ; count > 0; count--, num_points++, point++, tags++ )
675     {
676       if ( tags[0] & FT_STROKE_TAG_BEGIN )
677       {
678         if ( in_contour != 0 )
679           goto Fail;
680 
681         in_contour = 1;
682       }
683       else if ( in_contour == 0 )
684         goto Fail;
685 
686       if ( tags[0] & FT_STROKE_TAG_END )
687       {
688         in_contour = 0;
689         num_contours++;
690       }
691     }
692 
693     if ( in_contour != 0 )
694       goto Fail;
695 
696     border->valid = TRUE;
697 
698   Exit:
699     *anum_points   = num_points;
700     *anum_contours = num_contours;
701     return error;
702 
703   Fail:
704     num_points   = 0;
705     num_contours = 0;
706     goto Exit;
707   }
708 
709 
710   static void
ft_stroke_border_export(FT_StrokeBorder border,FT_Outline * outline)711   ft_stroke_border_export( FT_StrokeBorder  border,
712                            FT_Outline*      outline )
713   {
714     /* copy point locations */
715     if ( border->num_points )
716       FT_ARRAY_COPY( outline->points + outline->n_points,
717                      border->points,
718                      border->num_points );
719 
720     /* copy tags */
721     {
722       FT_UInt   count = border->num_points;
723       FT_Byte*  read  = border->tags;
724       FT_Byte*  write = (FT_Byte*)outline->tags + outline->n_points;
725 
726 
727       for ( ; count > 0; count--, read++, write++ )
728       {
729         if ( *read & FT_STROKE_TAG_ON )
730           *write = FT_CURVE_TAG_ON;
731         else if ( *read & FT_STROKE_TAG_CUBIC )
732           *write = FT_CURVE_TAG_CUBIC;
733         else
734           *write = FT_CURVE_TAG_CONIC;
735       }
736     }
737 
738     /* copy contours */
739     {
740       FT_UInt    count = border->num_points;
741       FT_Byte*   tags  = border->tags;
742       FT_Short*  write = outline->contours + outline->n_contours;
743       FT_Short   idx   = (FT_Short)outline->n_points;
744 
745 
746       for ( ; count > 0; count--, tags++, idx++ )
747       {
748         if ( *tags & FT_STROKE_TAG_END )
749         {
750           *write++ = idx;
751           outline->n_contours++;
752         }
753       }
754     }
755 
756     outline->n_points += (short)border->num_points;
757 
758     FT_ASSERT( FT_Outline_Check( outline ) == 0 );
759   }
760 
761 
762   /*************************************************************************/
763   /*************************************************************************/
764   /*****                                                               *****/
765   /*****                           STROKER                             *****/
766   /*****                                                               *****/
767   /*************************************************************************/
768   /*************************************************************************/
769 
770 #define FT_SIDE_TO_ROTATE( s )   ( FT_ANGLE_PI2 - (s) * FT_ANGLE_PI )
771 
772   typedef struct  FT_StrokerRec_
773   {
774     FT_Angle             angle_in;             /* direction into curr join */
775     FT_Angle             angle_out;            /* direction out of join  */
776     FT_Vector            center;               /* current position */
777     FT_Fixed             line_length;          /* length of last lineto */
778     FT_Bool              first_point;          /* is this the start? */
779     FT_Bool              subpath_open;         /* is the subpath open? */
780     FT_Angle             subpath_angle;        /* subpath start direction */
781     FT_Vector            subpath_start;        /* subpath start position */
782     FT_Fixed             subpath_line_length;  /* subpath start lineto len */
783     FT_Bool              handle_wide_strokes;  /* use wide strokes logic? */
784 
785     FT_Stroker_LineCap   line_cap;
786     FT_Stroker_LineJoin  line_join;
787     FT_Stroker_LineJoin  line_join_saved;
788     FT_Fixed             miter_limit;
789     FT_Fixed             radius;
790 
791     FT_StrokeBorderRec   borders[2];
792     FT_Library           library;
793 
794   } FT_StrokerRec;
795 
796 
797   /* documentation is in ftstroke.h */
798 
799   FT_EXPORT_DEF( FT_Error )
FT_Stroker_New(FT_Library library,FT_Stroker * astroker)800   FT_Stroker_New( FT_Library   library,
801                   FT_Stroker  *astroker )
802   {
803     FT_Error    error;           /* assigned in FT_NEW */
804     FT_Memory   memory;
805     FT_Stroker  stroker = NULL;
806 
807 
808     if ( !library )
809       return FT_THROW( Invalid_Library_Handle );
810 
811     if ( !astroker )
812       return FT_THROW( Invalid_Argument );
813 
814     memory = library->memory;
815 
816     if ( !FT_NEW( stroker ) )
817     {
818       stroker->library = library;
819 
820       ft_stroke_border_init( &stroker->borders[0], memory );
821       ft_stroke_border_init( &stroker->borders[1], memory );
822     }
823 
824     *astroker = stroker;
825 
826     return error;
827   }
828 
829 
830   /* documentation is in ftstroke.h */
831 
832   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)833   FT_Stroker_Set( FT_Stroker           stroker,
834                   FT_Fixed             radius,
835                   FT_Stroker_LineCap   line_cap,
836                   FT_Stroker_LineJoin  line_join,
837                   FT_Fixed             miter_limit )
838   {
839     if ( !stroker )
840       return;
841 
842     stroker->radius      = radius;
843     stroker->line_cap    = line_cap;
844     stroker->line_join   = line_join;
845     stroker->miter_limit = miter_limit;
846 
847     /* ensure miter limit has sensible value */
848     if ( stroker->miter_limit < 0x10000L )
849       stroker->miter_limit = 0x10000L;
850 
851     /* save line join style:                                           */
852     /* line join style can be temporarily changed when stroking curves */
853     stroker->line_join_saved = line_join;
854 
855     FT_Stroker_Rewind( stroker );
856   }
857 
858 
859   /* documentation is in ftstroke.h */
860 
861   FT_EXPORT_DEF( void )
FT_Stroker_Rewind(FT_Stroker stroker)862   FT_Stroker_Rewind( FT_Stroker  stroker )
863   {
864     if ( stroker )
865     {
866       ft_stroke_border_reset( &stroker->borders[0] );
867       ft_stroke_border_reset( &stroker->borders[1] );
868     }
869   }
870 
871 
872   /* documentation is in ftstroke.h */
873 
874   FT_EXPORT_DEF( void )
FT_Stroker_Done(FT_Stroker stroker)875   FT_Stroker_Done( FT_Stroker  stroker )
876   {
877     if ( stroker )
878     {
879       FT_Memory  memory = stroker->library->memory;
880 
881 
882       ft_stroke_border_done( &stroker->borders[0] );
883       ft_stroke_border_done( &stroker->borders[1] );
884 
885       stroker->library = NULL;
886       FT_FREE( stroker );
887     }
888   }
889 
890 
891   /* create a circular arc at a corner or cap */
892   static FT_Error
ft_stroker_arcto(FT_Stroker stroker,FT_Int side)893   ft_stroker_arcto( FT_Stroker  stroker,
894                     FT_Int      side )
895   {
896     FT_Angle         total, rotate;
897     FT_Fixed         radius = stroker->radius;
898     FT_Error         error  = FT_Err_Ok;
899     FT_StrokeBorder  border = stroker->borders + side;
900 
901 
902     rotate = FT_SIDE_TO_ROTATE( side );
903 
904     total = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
905     if ( total == FT_ANGLE_PI )
906       total = -rotate * 2;
907 
908     error = ft_stroke_border_arcto( border,
909                                     &stroker->center,
910                                     radius,
911                                     stroker->angle_in + rotate,
912                                     total );
913     border->movable = FALSE;
914     return error;
915   }
916 
917 
918   /* add a cap at the end of an opened path */
919   static FT_Error
ft_stroker_cap(FT_Stroker stroker,FT_Angle angle,FT_Int side)920   ft_stroker_cap( FT_Stroker  stroker,
921                   FT_Angle    angle,
922                   FT_Int      side )
923   {
924     FT_Error  error = FT_Err_Ok;
925 
926 
927     if ( stroker->line_cap == FT_STROKER_LINECAP_ROUND )
928     {
929       /* add a round cap */
930       stroker->angle_in  = angle;
931       stroker->angle_out = angle + FT_ANGLE_PI;
932 
933       error = ft_stroker_arcto( stroker, side );
934     }
935     else if ( stroker->line_cap == FT_STROKER_LINECAP_SQUARE )
936     {
937       /* add a square cap */
938       FT_Vector        delta, delta2;
939       FT_Angle         rotate = FT_SIDE_TO_ROTATE( side );
940       FT_Fixed         radius = stroker->radius;
941       FT_StrokeBorder  border = stroker->borders + side;
942 
943 
944       FT_Vector_From_Polar( &delta2, radius, angle + rotate );
945       FT_Vector_From_Polar( &delta,  radius, angle );
946 
947       delta.x += stroker->center.x + delta2.x;
948       delta.y += stroker->center.y + delta2.y;
949 
950       error = ft_stroke_border_lineto( border, &delta, FALSE );
951       if ( error )
952         goto Exit;
953 
954       FT_Vector_From_Polar( &delta2, radius, angle - rotate );
955       FT_Vector_From_Polar( &delta,  radius, angle );
956 
957       delta.x += delta2.x + stroker->center.x;
958       delta.y += delta2.y + stroker->center.y;
959 
960       error = ft_stroke_border_lineto( border, &delta, FALSE );
961     }
962     else if ( stroker->line_cap == FT_STROKER_LINECAP_BUTT )
963     {
964       /* add a butt ending */
965       FT_Vector        delta;
966       FT_Angle         rotate = FT_SIDE_TO_ROTATE( side );
967       FT_Fixed         radius = stroker->radius;
968       FT_StrokeBorder  border = stroker->borders + side;
969 
970 
971       FT_Vector_From_Polar( &delta, radius, angle + rotate );
972 
973       delta.x += stroker->center.x;
974       delta.y += stroker->center.y;
975 
976       error = ft_stroke_border_lineto( border, &delta, FALSE );
977       if ( error )
978         goto Exit;
979 
980       FT_Vector_From_Polar( &delta, radius, angle - rotate );
981 
982       delta.x += stroker->center.x;
983       delta.y += stroker->center.y;
984 
985       error = ft_stroke_border_lineto( border, &delta, FALSE );
986     }
987 
988   Exit:
989     return error;
990   }
991 
992 
993   /* process an inside corner, i.e. compute intersection */
994   static FT_Error
ft_stroker_inside(FT_Stroker stroker,FT_Int side,FT_Fixed line_length)995   ft_stroker_inside( FT_Stroker  stroker,
996                      FT_Int      side,
997                      FT_Fixed    line_length )
998   {
999     FT_StrokeBorder  border = stroker->borders + side;
1000     FT_Angle         phi, theta, rotate;
1001     FT_Fixed         length, thcos;
1002     FT_Vector        delta;
1003     FT_Error         error = FT_Err_Ok;
1004     FT_Bool          intersect;          /* use intersection of lines? */
1005 
1006 
1007     rotate = FT_SIDE_TO_ROTATE( side );
1008 
1009     theta = FT_Angle_Diff( stroker->angle_in, stroker->angle_out ) / 2;
1010 
1011     /* Only intersect borders if between two lineto's and both */
1012     /* lines are long enough (line_length is zero for curves). */
1013     /* Also avoid U-turns of nearly 180 degree.                */
1014     if ( !border->movable || line_length == 0  ||
1015          theta > 0x59C000 || theta < -0x59C000 )
1016       intersect = FALSE;
1017     else
1018     {
1019       /* compute minimum required length of lines */
1020       FT_Fixed  min_length = ft_pos_abs( FT_MulFix( stroker->radius,
1021                                                     FT_Tan( theta ) ) );
1022 
1023 
1024       intersect = FT_BOOL( min_length                         &&
1025                            stroker->line_length >= min_length &&
1026                            line_length          >= min_length );
1027     }
1028 
1029     if ( !intersect )
1030     {
1031       FT_Vector_From_Polar( &delta, stroker->radius,
1032                             stroker->angle_out + rotate );
1033       delta.x += stroker->center.x;
1034       delta.y += stroker->center.y;
1035 
1036       border->movable = FALSE;
1037     }
1038     else
1039     {
1040       /* compute median angle */
1041       phi = stroker->angle_in + theta;
1042 
1043       thcos = FT_Cos( theta );
1044 
1045       length = FT_DivFix( stroker->radius, thcos );
1046 
1047       FT_Vector_From_Polar( &delta, length, phi + rotate );
1048       delta.x += stroker->center.x;
1049       delta.y += stroker->center.y;
1050     }
1051 
1052     error = ft_stroke_border_lineto( border, &delta, FALSE );
1053 
1054     return error;
1055   }
1056 
1057 
1058   /* process an outside corner, i.e. compute bevel/miter/round */
1059   static FT_Error
ft_stroker_outside(FT_Stroker stroker,FT_Int side,FT_Fixed line_length)1060   ft_stroker_outside( FT_Stroker  stroker,
1061                       FT_Int      side,
1062                       FT_Fixed    line_length )
1063   {
1064     FT_StrokeBorder  border = stroker->borders + side;
1065     FT_Error         error;
1066     FT_Angle         rotate;
1067 
1068 
1069     if ( stroker->line_join == FT_STROKER_LINEJOIN_ROUND )
1070       error = ft_stroker_arcto( stroker, side );
1071     else
1072     {
1073       /* this is a mitered (pointed) or beveled (truncated) corner */
1074       FT_Fixed  sigma = 0, radius = stroker->radius;
1075       FT_Angle  theta = 0, phi = 0;
1076       FT_Fixed  thcos = 0;
1077       FT_Bool   bevel, fixed_bevel;
1078 
1079 
1080       rotate = FT_SIDE_TO_ROTATE( side );
1081 
1082       bevel =
1083         FT_BOOL( stroker->line_join == FT_STROKER_LINEJOIN_BEVEL );
1084 
1085       fixed_bevel =
1086         FT_BOOL( stroker->line_join != FT_STROKER_LINEJOIN_MITER_VARIABLE );
1087 
1088       if ( !bevel )
1089       {
1090         theta = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
1091 
1092         if ( theta == FT_ANGLE_PI )
1093         {
1094           theta = rotate;
1095           phi   = stroker->angle_in;
1096         }
1097         else
1098         {
1099           theta /= 2;
1100           phi    = stroker->angle_in + theta + rotate;
1101         }
1102 
1103         thcos = FT_Cos( theta );
1104         sigma = FT_MulFix( stroker->miter_limit, thcos );
1105 
1106         /* is miter limit exceeded? */
1107         if ( sigma < 0x10000L )
1108         {
1109           /* don't create variable bevels for very small deviations; */
1110           /* FT_Sin(x) = 0 for x <= 57                               */
1111           if ( fixed_bevel || ft_pos_abs( theta ) > 57 )
1112             bevel = TRUE;
1113         }
1114       }
1115 
1116       if ( bevel )  /* this is a bevel (broken angle) */
1117       {
1118         if ( fixed_bevel )
1119         {
1120           /* the outer corners are simply joined together */
1121           FT_Vector  delta;
1122 
1123 
1124           /* add bevel */
1125           FT_Vector_From_Polar( &delta,
1126                                 radius,
1127                                 stroker->angle_out + rotate );
1128           delta.x += stroker->center.x;
1129           delta.y += stroker->center.y;
1130 
1131           border->movable = FALSE;
1132           error = ft_stroke_border_lineto( border, &delta, FALSE );
1133         }
1134         else /* variable bevel */
1135         {
1136           /* the miter is truncated */
1137           FT_Vector  middle, delta;
1138           FT_Fixed   length;
1139 
1140 
1141           /* compute middle point */
1142           FT_Vector_From_Polar( &middle,
1143                                 FT_MulFix( radius, stroker->miter_limit ),
1144                                 phi );
1145           middle.x += stroker->center.x;
1146           middle.y += stroker->center.y;
1147 
1148           /* compute first angle point */
1149           length = FT_MulDiv( radius, 0x10000L - sigma,
1150                               ft_pos_abs( FT_Sin( theta ) ) );
1151 
1152           FT_Vector_From_Polar( &delta, length, phi + rotate );
1153           delta.x += middle.x;
1154           delta.y += middle.y;
1155 
1156           error = ft_stroke_border_lineto( border, &delta, FALSE );
1157           if ( error )
1158             goto Exit;
1159 
1160           /* compute second angle point */
1161           FT_Vector_From_Polar( &delta, length, phi - rotate );
1162           delta.x += middle.x;
1163           delta.y += middle.y;
1164 
1165           error = ft_stroke_border_lineto( border, &delta, FALSE );
1166           if ( error )
1167             goto Exit;
1168 
1169           /* finally, 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                                   radius,
1175                                   stroker->angle_out + rotate );
1176 
1177             delta.x += stroker->center.x;
1178             delta.y += stroker->center.y;
1179 
1180             error = ft_stroke_border_lineto( border, &delta, FALSE );
1181           }
1182         }
1183       }
1184       else /* this is a miter (intersection) */
1185       {
1186         FT_Fixed   length;
1187         FT_Vector  delta;
1188 
1189 
1190         length = FT_DivFix( stroker->radius, thcos );
1191 
1192         FT_Vector_From_Polar( &delta, length, phi );
1193         delta.x += stroker->center.x;
1194         delta.y += stroker->center.y;
1195 
1196         error = ft_stroke_border_lineto( border, &delta, FALSE );
1197         if ( error )
1198           goto Exit;
1199 
1200         /* now add an end point; only needed if not lineto */
1201         /* (line_length is zero for curves)                */
1202         if ( line_length == 0 )
1203         {
1204           FT_Vector_From_Polar( &delta,
1205                                 stroker->radius,
1206                                 stroker->angle_out + rotate );
1207           delta.x += stroker->center.x;
1208           delta.y += stroker->center.y;
1209 
1210           error = ft_stroke_border_lineto( border, &delta, FALSE );
1211         }
1212       }
1213     }
1214 
1215   Exit:
1216     return error;
1217   }
1218 
1219 
1220   static FT_Error
ft_stroker_process_corner(FT_Stroker stroker,FT_Fixed line_length)1221   ft_stroker_process_corner( FT_Stroker  stroker,
1222                              FT_Fixed    line_length )
1223   {
1224     FT_Error  error = FT_Err_Ok;
1225     FT_Angle  turn;
1226     FT_Int    inside_side;
1227 
1228 
1229     turn = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
1230 
1231     /* no specific corner processing is required if the turn is 0 */
1232     if ( turn == 0 )
1233       goto Exit;
1234 
1235     /* when we turn to the right, the inside side is 0 */
1236     /* otherwise, the inside side is 1 */
1237     inside_side = ( turn < 0 );
1238 
1239     /* process the inside side */
1240     error = ft_stroker_inside( stroker, inside_side, line_length );
1241     if ( error )
1242       goto Exit;
1243 
1244     /* process the outside side */
1245     error = ft_stroker_outside( stroker, !inside_side, line_length );
1246 
1247   Exit:
1248     return error;
1249   }
1250 
1251 
1252   /* add two points to the left and right borders corresponding to the */
1253   /* start of the subpath                                              */
1254   static FT_Error
ft_stroker_subpath_start(FT_Stroker stroker,FT_Angle start_angle,FT_Fixed line_length)1255   ft_stroker_subpath_start( FT_Stroker  stroker,
1256                             FT_Angle    start_angle,
1257                             FT_Fixed    line_length )
1258   {
1259     FT_Vector        delta;
1260     FT_Vector        point;
1261     FT_Error         error;
1262     FT_StrokeBorder  border;
1263 
1264 
1265     FT_Vector_From_Polar( &delta, stroker->radius,
1266                           start_angle + FT_ANGLE_PI2 );
1267 
1268     point.x = stroker->center.x + delta.x;
1269     point.y = stroker->center.y + delta.y;
1270 
1271     border = stroker->borders;
1272     error = ft_stroke_border_moveto( border, &point );
1273     if ( error )
1274       goto Exit;
1275 
1276     point.x = stroker->center.x - delta.x;
1277     point.y = stroker->center.y - delta.y;
1278 
1279     border++;
1280     error = ft_stroke_border_moveto( border, &point );
1281 
1282     /* save angle, position, and line length for last join */
1283     /* (line_length is zero for curves)                    */
1284     stroker->subpath_angle       = start_angle;
1285     stroker->first_point         = FALSE;
1286     stroker->subpath_line_length = line_length;
1287 
1288   Exit:
1289     return error;
1290   }
1291 
1292 
1293   /* documentation is in ftstroke.h */
1294 
1295   FT_EXPORT_DEF( FT_Error )
FT_Stroker_LineTo(FT_Stroker stroker,FT_Vector * to)1296   FT_Stroker_LineTo( FT_Stroker  stroker,
1297                      FT_Vector*  to )
1298   {
1299     FT_Error         error = FT_Err_Ok;
1300     FT_StrokeBorder  border;
1301     FT_Vector        delta;
1302     FT_Angle         angle;
1303     FT_Int           side;
1304     FT_Fixed         line_length;
1305 
1306 
1307     if ( !stroker || !to )
1308       return FT_THROW( Invalid_Argument );
1309 
1310     delta.x = to->x - stroker->center.x;
1311     delta.y = to->y - stroker->center.y;
1312 
1313     /* a zero-length lineto is a no-op; avoid creating a spurious corner */
1314     if ( delta.x == 0 && delta.y == 0 )
1315        goto Exit;
1316 
1317     /* compute length of line */
1318     line_length = FT_Vector_Length( &delta );
1319 
1320     angle = FT_Atan2( delta.x, delta.y );
1321     FT_Vector_From_Polar( &delta, stroker->radius, angle + FT_ANGLE_PI2 );
1322 
1323     /* process corner if necessary */
1324     if ( stroker->first_point )
1325     {
1326       /* This is the first segment of a subpath.  We need to     */
1327       /* add a point to each border at their respective starting */
1328       /* point locations.                                        */
1329       error = ft_stroker_subpath_start( stroker, angle, line_length );
1330       if ( error )
1331         goto Exit;
1332     }
1333     else
1334     {
1335       /* process the current corner */
1336       stroker->angle_out = angle;
1337       error = ft_stroker_process_corner( stroker, line_length );
1338       if ( error )
1339         goto Exit;
1340     }
1341 
1342     /* now add a line segment to both the `inside' and `outside' paths */
1343     for ( border = stroker->borders, side = 1; side >= 0; side--, border++ )
1344     {
1345       FT_Vector  point;
1346 
1347 
1348       point.x = to->x + delta.x;
1349       point.y = to->y + delta.y;
1350 
1351       /* the ends of lineto borders are movable */
1352       error = ft_stroke_border_lineto( border, &point, TRUE );
1353       if ( error )
1354         goto Exit;
1355 
1356       delta.x = -delta.x;
1357       delta.y = -delta.y;
1358     }
1359 
1360     stroker->angle_in    = angle;
1361     stroker->center      = *to;
1362     stroker->line_length = line_length;
1363 
1364   Exit:
1365     return error;
1366   }
1367 
1368 
1369   /* documentation is in ftstroke.h */
1370 
1371   FT_EXPORT_DEF( FT_Error )
FT_Stroker_ConicTo(FT_Stroker stroker,FT_Vector * control,FT_Vector * to)1372   FT_Stroker_ConicTo( FT_Stroker  stroker,
1373                       FT_Vector*  control,
1374                       FT_Vector*  to )
1375   {
1376     FT_Error    error = FT_Err_Ok;
1377     FT_Vector   bez_stack[34];
1378     FT_Vector*  arc;
1379     FT_Vector*  limit = bez_stack + 30;
1380     FT_Bool     first_arc = TRUE;
1381 
1382 
1383     if ( !stroker || !control || !to )
1384     {
1385       error = FT_THROW( Invalid_Argument );
1386       goto Exit;
1387     }
1388 
1389     /* if all control points are coincident, this is a no-op; */
1390     /* avoid creating a spurious corner                       */
1391     if ( FT_IS_SMALL( stroker->center.x - control->x ) &&
1392          FT_IS_SMALL( stroker->center.y - control->y ) &&
1393          FT_IS_SMALL( control->x        - to->x      ) &&
1394          FT_IS_SMALL( control->y        - to->y      ) )
1395     {
1396        stroker->center = *to;
1397        goto Exit;
1398     }
1399 
1400     arc    = bez_stack;
1401     arc[0] = *to;
1402     arc[1] = *control;
1403     arc[2] = stroker->center;
1404 
1405     while ( arc >= bez_stack )
1406     {
1407       FT_Angle  angle_in, angle_out;
1408 
1409 
1410       /* initialize with current direction */
1411       angle_in = angle_out = stroker->angle_in;
1412 
1413       if ( arc < limit                                             &&
1414            !ft_conic_is_small_enough( arc, &angle_in, &angle_out ) )
1415       {
1416         if ( stroker->first_point )
1417           stroker->angle_in = angle_in;
1418 
1419         ft_conic_split( arc );
1420         arc += 2;
1421         continue;
1422       }
1423 
1424       if ( first_arc )
1425       {
1426         first_arc = FALSE;
1427 
1428         /* process corner if necessary */
1429         if ( stroker->first_point )
1430           error = ft_stroker_subpath_start( stroker, angle_in, 0 );
1431         else
1432         {
1433           stroker->angle_out = angle_in;
1434           error = ft_stroker_process_corner( stroker, 0 );
1435         }
1436       }
1437       else if ( ft_pos_abs( FT_Angle_Diff( stroker->angle_in, angle_in ) ) >
1438                   FT_SMALL_CONIC_THRESHOLD / 4                             )
1439       {
1440         /* if the deviation from one arc to the next is too great, */
1441         /* add a round corner                                      */
1442         stroker->center    = arc[2];
1443         stroker->angle_out = angle_in;
1444         stroker->line_join = FT_STROKER_LINEJOIN_ROUND;
1445 
1446         error = ft_stroker_process_corner( stroker, 0 );
1447 
1448         /* reinstate line join style */
1449         stroker->line_join = stroker->line_join_saved;
1450       }
1451 
1452       if ( error )
1453         goto Exit;
1454 
1455       /* the arc's angle is small enough; we can add it directly to each */
1456       /* border                                                          */
1457       {
1458         FT_Vector        ctrl, end;
1459         FT_Angle         theta, phi, rotate, alpha0 = 0;
1460         FT_Fixed         length;
1461         FT_StrokeBorder  border;
1462         FT_Int           side;
1463 
1464 
1465         theta  = FT_Angle_Diff( angle_in, angle_out ) / 2;
1466         phi    = angle_in + theta;
1467         length = FT_DivFix( stroker->radius, FT_Cos( theta ) );
1468 
1469         /* compute direction of original arc */
1470         if ( stroker->handle_wide_strokes )
1471           alpha0 = FT_Atan2( arc[0].x - arc[2].x, arc[0].y - arc[2].y );
1472 
1473         for ( border = stroker->borders, side = 0;
1474               side <= 1;
1475               side++, border++ )
1476         {
1477           rotate = FT_SIDE_TO_ROTATE( side );
1478 
1479           /* compute control point */
1480           FT_Vector_From_Polar( &ctrl, length, phi + rotate );
1481           ctrl.x += arc[1].x;
1482           ctrl.y += arc[1].y;
1483 
1484           /* compute end point */
1485           FT_Vector_From_Polar( &end, stroker->radius, angle_out + rotate );
1486           end.x += arc[0].x;
1487           end.y += arc[0].y;
1488 
1489           if ( stroker->handle_wide_strokes )
1490           {
1491             FT_Vector  start;
1492             FT_Angle   alpha1;
1493 
1494 
1495             /* determine whether the border radius is greater than the */
1496             /* radius of curvature of the original arc                 */
1497             start = border->points[border->num_points - 1];
1498 
1499             alpha1 = FT_Atan2( end.x - start.x, end.y - start.y );
1500 
1501             /* is the direction of the border arc opposite to */
1502             /* that of the original arc? */
1503             if ( ft_pos_abs( FT_Angle_Diff( alpha0, alpha1 ) ) >
1504                    FT_ANGLE_PI / 2                             )
1505             {
1506               FT_Angle   beta, gamma;
1507               FT_Vector  bvec, delta;
1508               FT_Fixed   blen, sinA, sinB, alen;
1509 
1510 
1511               /* use the sine rule to find the intersection point */
1512               beta  = FT_Atan2( arc[2].x - start.x, arc[2].y - start.y );
1513               gamma = FT_Atan2( arc[0].x - end.x,   arc[0].y - end.y );
1514 
1515               bvec.x = end.x - start.x;
1516               bvec.y = end.y - start.y;
1517 
1518               blen = FT_Vector_Length( &bvec );
1519 
1520               sinA = ft_pos_abs( FT_Sin( alpha1 - gamma ) );
1521               sinB = ft_pos_abs( FT_Sin( beta - gamma ) );
1522 
1523               alen = FT_MulDiv( blen, sinA, sinB );
1524 
1525               FT_Vector_From_Polar( &delta, alen, beta );
1526               delta.x += start.x;
1527               delta.y += start.y;
1528 
1529               /* circumnavigate the negative sector backwards */
1530               border->movable = FALSE;
1531               error = ft_stroke_border_lineto( border, &delta, FALSE );
1532               if ( error )
1533                 goto Exit;
1534               error = ft_stroke_border_lineto( border, &end, FALSE );
1535               if ( error )
1536                 goto Exit;
1537               error = ft_stroke_border_conicto( border, &ctrl, &start );
1538               if ( error )
1539                 goto Exit;
1540               /* and then move to the endpoint */
1541               error = ft_stroke_border_lineto( border, &end, FALSE );
1542               if ( error )
1543                 goto Exit;
1544 
1545               continue;
1546             }
1547 
1548             /* else fall through */
1549           }
1550 
1551           /* simply add an arc */
1552           error = ft_stroke_border_conicto( border, &ctrl, &end );
1553           if ( error )
1554             goto Exit;
1555         }
1556       }
1557 
1558       arc -= 2;
1559 
1560       stroker->angle_in = angle_out;
1561     }
1562 
1563     stroker->center = *to;
1564 
1565   Exit:
1566     return error;
1567   }
1568 
1569 
1570   /* documentation is in ftstroke.h */
1571 
1572   FT_EXPORT_DEF( FT_Error )
FT_Stroker_CubicTo(FT_Stroker stroker,FT_Vector * control1,FT_Vector * control2,FT_Vector * to)1573   FT_Stroker_CubicTo( FT_Stroker  stroker,
1574                       FT_Vector*  control1,
1575                       FT_Vector*  control2,
1576                       FT_Vector*  to )
1577   {
1578     FT_Error    error = FT_Err_Ok;
1579     FT_Vector   bez_stack[37];
1580     FT_Vector*  arc;
1581     FT_Vector*  limit = bez_stack + 32;
1582     FT_Bool     first_arc = TRUE;
1583 
1584 
1585     if ( !stroker || !control1 || !control2 || !to )
1586     {
1587       error = FT_THROW( Invalid_Argument );
1588       goto Exit;
1589     }
1590 
1591     /* if all control points are coincident, this is a no-op; */
1592     /* avoid creating a spurious corner */
1593     if ( FT_IS_SMALL( stroker->center.x - control1->x ) &&
1594          FT_IS_SMALL( stroker->center.y - control1->y ) &&
1595          FT_IS_SMALL( control1->x       - control2->x ) &&
1596          FT_IS_SMALL( control1->y       - control2->y ) &&
1597          FT_IS_SMALL( control2->x       - to->x       ) &&
1598          FT_IS_SMALL( control2->y       - to->y       ) )
1599     {
1600        stroker->center = *to;
1601        goto Exit;
1602     }
1603 
1604     arc    = bez_stack;
1605     arc[0] = *to;
1606     arc[1] = *control2;
1607     arc[2] = *control1;
1608     arc[3] = stroker->center;
1609 
1610     while ( arc >= bez_stack )
1611     {
1612       FT_Angle  angle_in, angle_mid, angle_out;
1613 
1614 
1615       /* initialize with current direction */
1616       angle_in = angle_out = angle_mid = stroker->angle_in;
1617 
1618       if ( arc < limit                                         &&
1619            !ft_cubic_is_small_enough( arc, &angle_in,
1620                                       &angle_mid, &angle_out ) )
1621       {
1622         if ( stroker->first_point )
1623           stroker->angle_in = angle_in;
1624 
1625         ft_cubic_split( arc );
1626         arc += 3;
1627         continue;
1628       }
1629 
1630       if ( first_arc )
1631       {
1632         first_arc = FALSE;
1633 
1634         /* process corner if necessary */
1635         if ( stroker->first_point )
1636           error = ft_stroker_subpath_start( stroker, angle_in, 0 );
1637         else
1638         {
1639           stroker->angle_out = angle_in;
1640           error = ft_stroker_process_corner( stroker, 0 );
1641         }
1642       }
1643       else if ( ft_pos_abs( FT_Angle_Diff( stroker->angle_in, angle_in ) ) >
1644                   FT_SMALL_CUBIC_THRESHOLD / 4                             )
1645       {
1646         /* if the deviation from one arc to the next is too great, */
1647         /* add a round corner                                      */
1648         stroker->center    = arc[3];
1649         stroker->angle_out = angle_in;
1650         stroker->line_join = FT_STROKER_LINEJOIN_ROUND;
1651 
1652         error = ft_stroker_process_corner( stroker, 0 );
1653 
1654         /* reinstate line join style */
1655         stroker->line_join = stroker->line_join_saved;
1656       }
1657 
1658       if ( error )
1659         goto Exit;
1660 
1661       /* the arc's angle is small enough; we can add it directly to each */
1662       /* border                                                          */
1663       {
1664         FT_Vector        ctrl1, ctrl2, end;
1665         FT_Angle         theta1, phi1, theta2, phi2, rotate, alpha0 = 0;
1666         FT_Fixed         length1, length2;
1667         FT_StrokeBorder  border;
1668         FT_Int           side;
1669 
1670 
1671         theta1  = FT_Angle_Diff( angle_in,  angle_mid ) / 2;
1672         theta2  = FT_Angle_Diff( angle_mid, angle_out ) / 2;
1673         phi1    = ft_angle_mean( angle_in,  angle_mid );
1674         phi2    = ft_angle_mean( angle_mid, angle_out );
1675         length1 = FT_DivFix( stroker->radius, FT_Cos( theta1 ) );
1676         length2 = FT_DivFix( stroker->radius, FT_Cos( theta2 ) );
1677 
1678         /* compute direction of original arc */
1679         if ( stroker->handle_wide_strokes )
1680           alpha0 = FT_Atan2( arc[0].x - arc[3].x, arc[0].y - arc[3].y );
1681 
1682         for ( border = stroker->borders, side = 0;
1683               side <= 1;
1684               side++, border++ )
1685         {
1686           rotate = FT_SIDE_TO_ROTATE( side );
1687 
1688           /* compute control points */
1689           FT_Vector_From_Polar( &ctrl1, length1, phi1 + rotate );
1690           ctrl1.x += arc[2].x;
1691           ctrl1.y += arc[2].y;
1692 
1693           FT_Vector_From_Polar( &ctrl2, length2, phi2 + rotate );
1694           ctrl2.x += arc[1].x;
1695           ctrl2.y += arc[1].y;
1696 
1697           /* compute end point */
1698           FT_Vector_From_Polar( &end, stroker->radius, angle_out + rotate );
1699           end.x += arc[0].x;
1700           end.y += arc[0].y;
1701 
1702           if ( stroker->handle_wide_strokes )
1703           {
1704             FT_Vector  start;
1705             FT_Angle   alpha1;
1706 
1707 
1708             /* determine whether the border radius is greater than the */
1709             /* radius of curvature of the original arc                 */
1710             start = border->points[border->num_points - 1];
1711 
1712             alpha1 = FT_Atan2( end.x - start.x, end.y - start.y );
1713 
1714             /* is the direction of the border arc opposite to */
1715             /* that of the original arc? */
1716             if ( ft_pos_abs( FT_Angle_Diff( alpha0, alpha1 ) ) >
1717                    FT_ANGLE_PI / 2                             )
1718             {
1719               FT_Angle   beta, gamma;
1720               FT_Vector  bvec, delta;
1721               FT_Fixed   blen, sinA, sinB, alen;
1722 
1723 
1724               /* use the sine rule to find the intersection point */
1725               beta  = FT_Atan2( arc[3].x - start.x, arc[3].y - start.y );
1726               gamma = FT_Atan2( arc[0].x - end.x,   arc[0].y - end.y );
1727 
1728               bvec.x = end.x - start.x;
1729               bvec.y = end.y - start.y;
1730 
1731               blen = FT_Vector_Length( &bvec );
1732 
1733               sinA = ft_pos_abs( FT_Sin( alpha1 - gamma ) );
1734               sinB = ft_pos_abs( FT_Sin( beta - gamma ) );
1735 
1736               alen = FT_MulDiv( blen, sinA, sinB );
1737 
1738               FT_Vector_From_Polar( &delta, alen, beta );
1739               delta.x += start.x;
1740               delta.y += start.y;
1741 
1742               /* circumnavigate the negative sector backwards */
1743               border->movable = FALSE;
1744               error = ft_stroke_border_lineto( border, &delta, FALSE );
1745               if ( error )
1746                 goto Exit;
1747               error = ft_stroke_border_lineto( border, &end, FALSE );
1748               if ( error )
1749                 goto Exit;
1750               error = ft_stroke_border_cubicto( border,
1751                                                 &ctrl2,
1752                                                 &ctrl1,
1753                                                 &start );
1754               if ( error )
1755                 goto Exit;
1756               /* and then move to the endpoint */
1757               error = ft_stroke_border_lineto( border, &end, FALSE );
1758               if ( error )
1759                 goto Exit;
1760 
1761               continue;
1762             }
1763 
1764             /* else fall through */
1765           }
1766 
1767           /* simply add an arc */
1768           error = ft_stroke_border_cubicto( border, &ctrl1, &ctrl2, &end );
1769           if ( error )
1770             goto Exit;
1771         }
1772       }
1773 
1774       arc -= 3;
1775 
1776       stroker->angle_in = angle_out;
1777     }
1778 
1779     stroker->center = *to;
1780 
1781   Exit:
1782     return error;
1783   }
1784 
1785 
1786   /* documentation is in ftstroke.h */
1787 
1788   FT_EXPORT_DEF( FT_Error )
FT_Stroker_BeginSubPath(FT_Stroker stroker,FT_Vector * to,FT_Bool open)1789   FT_Stroker_BeginSubPath( FT_Stroker  stroker,
1790                            FT_Vector*  to,
1791                            FT_Bool     open )
1792   {
1793     if ( !stroker || !to )
1794       return FT_THROW( Invalid_Argument );
1795 
1796     /* We cannot process the first point, because there is not enough      */
1797     /* information regarding its corner/cap.  The latter will be processed */
1798     /* in the `FT_Stroker_EndSubPath' routine.                             */
1799     /*                                                                     */
1800     stroker->first_point  = TRUE;
1801     stroker->center       = *to;
1802     stroker->subpath_open = open;
1803 
1804     /* Determine if we need to check whether the border radius is greater */
1805     /* than the radius of curvature of a curve, to handle this case       */
1806     /* specially.  This is only required if bevel joins or butt caps may  */
1807     /* be created, because round & miter joins and round & square caps    */
1808     /* cover the negative sector created with wide strokes.               */
1809     stroker->handle_wide_strokes =
1810       FT_BOOL( stroker->line_join != FT_STROKER_LINEJOIN_ROUND  ||
1811                ( stroker->subpath_open                        &&
1812                  stroker->line_cap == FT_STROKER_LINECAP_BUTT ) );
1813 
1814     /* record the subpath start point for each border */
1815     stroker->subpath_start = *to;
1816 
1817     stroker->angle_in = 0;
1818 
1819     return FT_Err_Ok;
1820   }
1821 
1822 
1823   static FT_Error
ft_stroker_add_reverse_left(FT_Stroker stroker,FT_Bool open)1824   ft_stroker_add_reverse_left( FT_Stroker  stroker,
1825                                FT_Bool     open )
1826   {
1827     FT_StrokeBorder  right = stroker->borders + 0;
1828     FT_StrokeBorder  left  = stroker->borders + 1;
1829     FT_Int           new_points;
1830     FT_Error         error = FT_Err_Ok;
1831 
1832 
1833     FT_ASSERT( left->start >= 0 );
1834 
1835     new_points = (FT_Int)left->num_points - left->start;
1836     if ( new_points > 0 )
1837     {
1838       error = ft_stroke_border_grow( right, (FT_UInt)new_points );
1839       if ( error )
1840         goto Exit;
1841 
1842       {
1843         FT_Vector*  dst_point = right->points + right->num_points;
1844         FT_Byte*    dst_tag   = right->tags   + right->num_points;
1845         FT_Vector*  src_point = left->points  + left->num_points - 1;
1846         FT_Byte*    src_tag   = left->tags    + left->num_points - 1;
1847 
1848 
1849         while ( src_point >= left->points + left->start )
1850         {
1851           *dst_point = *src_point;
1852           *dst_tag   = *src_tag;
1853 
1854           if ( open )
1855             dst_tag[0] &= ~FT_STROKE_TAG_BEGIN_END;
1856           else
1857           {
1858             FT_Byte  ttag =
1859                        (FT_Byte)( dst_tag[0] & FT_STROKE_TAG_BEGIN_END );
1860 
1861 
1862             /* switch begin/end tags if necessary */
1863             if ( ttag == FT_STROKE_TAG_BEGIN ||
1864                  ttag == FT_STROKE_TAG_END   )
1865               dst_tag[0] ^= FT_STROKE_TAG_BEGIN_END;
1866           }
1867 
1868           src_point--;
1869           src_tag--;
1870           dst_point++;
1871           dst_tag++;
1872         }
1873       }
1874 
1875       left->num_points   = (FT_UInt)left->start;
1876       right->num_points += (FT_UInt)new_points;
1877 
1878       right->movable = FALSE;
1879       left->movable  = FALSE;
1880     }
1881 
1882   Exit:
1883     return error;
1884   }
1885 
1886 
1887   /* documentation is in ftstroke.h */
1888 
1889   /* there's a lot of magic in this function! */
1890   FT_EXPORT_DEF( FT_Error )
FT_Stroker_EndSubPath(FT_Stroker stroker)1891   FT_Stroker_EndSubPath( FT_Stroker  stroker )
1892   {
1893     FT_Error  error = FT_Err_Ok;
1894 
1895 
1896     if ( !stroker )
1897     {
1898       error = FT_THROW( Invalid_Argument );
1899       goto Exit;
1900     }
1901 
1902     if ( stroker->subpath_open )
1903     {
1904       FT_StrokeBorder  right = stroker->borders;
1905 
1906 
1907       /* All right, this is an opened path, we need to add a cap between */
1908       /* right & left, add the reverse of left, then add a final cap     */
1909       /* between left & right.                                           */
1910       error = ft_stroker_cap( stroker, stroker->angle_in, 0 );
1911       if ( error )
1912         goto Exit;
1913 
1914       /* add reversed points from `left' to `right' */
1915       error = ft_stroker_add_reverse_left( stroker, TRUE );
1916       if ( error )
1917         goto Exit;
1918 
1919       /* now add the final cap */
1920       stroker->center = stroker->subpath_start;
1921       error = ft_stroker_cap( stroker,
1922                               stroker->subpath_angle + FT_ANGLE_PI, 0 );
1923       if ( error )
1924         goto Exit;
1925 
1926       /* Now end the right subpath accordingly.  The left one is */
1927       /* rewind and doesn't need further processing.             */
1928       ft_stroke_border_close( right, FALSE );
1929     }
1930     else
1931     {
1932       FT_Angle  turn;
1933       FT_Int    inside_side;
1934 
1935 
1936       /* close the path if needed */
1937       if ( stroker->center.x != stroker->subpath_start.x ||
1938            stroker->center.y != stroker->subpath_start.y )
1939       {
1940          error = FT_Stroker_LineTo( stroker, &stroker->subpath_start );
1941          if ( error )
1942            goto Exit;
1943       }
1944 
1945       /* process the corner */
1946       stroker->angle_out = stroker->subpath_angle;
1947       turn               = FT_Angle_Diff( stroker->angle_in,
1948                                           stroker->angle_out );
1949 
1950       /* no specific corner processing is required if the turn is 0 */
1951       if ( turn != 0 )
1952       {
1953         /* when we turn to the right, the inside side is 0 */
1954         /* otherwise, the inside side is 1 */
1955         inside_side = ( turn < 0 );
1956 
1957         error = ft_stroker_inside( stroker,
1958                                    inside_side,
1959                                    stroker->subpath_line_length );
1960         if ( error )
1961           goto Exit;
1962 
1963         /* process the outside side */
1964         error = ft_stroker_outside( stroker,
1965                                     !inside_side,
1966                                     stroker->subpath_line_length );
1967         if ( error )
1968           goto Exit;
1969       }
1970 
1971       /* then end our two subpaths */
1972       ft_stroke_border_close( stroker->borders + 0, FALSE );
1973       ft_stroke_border_close( stroker->borders + 1, TRUE );
1974     }
1975 
1976   Exit:
1977     return error;
1978   }
1979 
1980 
1981   /* documentation is in ftstroke.h */
1982 
1983   FT_EXPORT_DEF( FT_Error )
FT_Stroker_GetBorderCounts(FT_Stroker stroker,FT_StrokerBorder border,FT_UInt * anum_points,FT_UInt * anum_contours)1984   FT_Stroker_GetBorderCounts( FT_Stroker        stroker,
1985                               FT_StrokerBorder  border,
1986                               FT_UInt          *anum_points,
1987                               FT_UInt          *anum_contours )
1988   {
1989     FT_UInt   num_points = 0, num_contours = 0;
1990     FT_Error  error;
1991 
1992 
1993     if ( !stroker || border > 1 )
1994     {
1995       error = FT_THROW( Invalid_Argument );
1996       goto Exit;
1997     }
1998 
1999     error = ft_stroke_border_get_counts( stroker->borders + border,
2000                                          &num_points, &num_contours );
2001   Exit:
2002     if ( anum_points )
2003       *anum_points = num_points;
2004 
2005     if ( anum_contours )
2006       *anum_contours = num_contours;
2007 
2008     return error;
2009   }
2010 
2011 
2012   /* documentation is in ftstroke.h */
2013 
2014   FT_EXPORT_DEF( FT_Error )
FT_Stroker_GetCounts(FT_Stroker stroker,FT_UInt * anum_points,FT_UInt * anum_contours)2015   FT_Stroker_GetCounts( FT_Stroker  stroker,
2016                         FT_UInt    *anum_points,
2017                         FT_UInt    *anum_contours )
2018   {
2019     FT_UInt   count1, count2, num_points   = 0;
2020     FT_UInt   count3, count4, num_contours = 0;
2021     FT_Error  error;
2022 
2023 
2024     if ( !stroker )
2025     {
2026       error = FT_THROW( Invalid_Argument );
2027       goto Exit;
2028     }
2029 
2030     error = ft_stroke_border_get_counts( stroker->borders + 0,
2031                                          &count1, &count2 );
2032     if ( error )
2033       goto Exit;
2034 
2035     error = ft_stroke_border_get_counts( stroker->borders + 1,
2036                                          &count3, &count4 );
2037     if ( error )
2038       goto Exit;
2039 
2040     num_points   = count1 + count3;
2041     num_contours = count2 + count4;
2042 
2043   Exit:
2044     if ( anum_points )
2045       *anum_points   = num_points;
2046 
2047     if ( anum_contours )
2048       *anum_contours = num_contours;
2049 
2050     return error;
2051   }
2052 
2053 
2054   /* documentation is in ftstroke.h */
2055 
2056   FT_EXPORT_DEF( void )
FT_Stroker_ExportBorder(FT_Stroker stroker,FT_StrokerBorder border,FT_Outline * outline)2057   FT_Stroker_ExportBorder( FT_Stroker        stroker,
2058                            FT_StrokerBorder  border,
2059                            FT_Outline*       outline )
2060   {
2061     if ( !stroker || !outline )
2062       return;
2063 
2064     if ( border == FT_STROKER_BORDER_LEFT  ||
2065          border == FT_STROKER_BORDER_RIGHT )
2066     {
2067       FT_StrokeBorder  sborder = & stroker->borders[border];
2068 
2069 
2070       if ( sborder->valid )
2071         ft_stroke_border_export( sborder, outline );
2072     }
2073   }
2074 
2075 
2076   /* documentation is in ftstroke.h */
2077 
2078   FT_EXPORT_DEF( void )
FT_Stroker_Export(FT_Stroker stroker,FT_Outline * outline)2079   FT_Stroker_Export( FT_Stroker   stroker,
2080                      FT_Outline*  outline )
2081   {
2082     FT_Stroker_ExportBorder( stroker, FT_STROKER_BORDER_LEFT, outline );
2083     FT_Stroker_ExportBorder( stroker, FT_STROKER_BORDER_RIGHT, outline );
2084   }
2085 
2086 
2087   /* documentation is in ftstroke.h */
2088 
2089   /*
2090    *  The following is very similar to FT_Outline_Decompose, except
2091    *  that we do support opened paths, and do not scale the outline.
2092    */
2093   FT_EXPORT_DEF( FT_Error )
FT_Stroker_ParseOutline(FT_Stroker stroker,FT_Outline * outline,FT_Bool opened)2094   FT_Stroker_ParseOutline( FT_Stroker   stroker,
2095                            FT_Outline*  outline,
2096                            FT_Bool      opened )
2097   {
2098     FT_Vector   v_last;
2099     FT_Vector   v_control;
2100     FT_Vector   v_start;
2101 
2102     FT_Vector*  point;
2103     FT_Vector*  limit;
2104     char*       tags;
2105 
2106     FT_Error    error;
2107 
2108     FT_Int      n;         /* index of contour in outline     */
2109     FT_UInt     first;     /* index of first point in contour */
2110     FT_Int      tag;       /* current point's state           */
2111 
2112 
2113     if ( !outline )
2114       return FT_THROW( Invalid_Outline );
2115 
2116     if ( !stroker )
2117       return FT_THROW( Invalid_Argument );
2118 
2119     FT_Stroker_Rewind( stroker );
2120 
2121     first = 0;
2122 
2123     for ( n = 0; n < outline->n_contours; n++ )
2124     {
2125       FT_UInt  last;  /* index of last point in contour */
2126 
2127 
2128       last  = (FT_UInt)outline->contours[n];
2129       limit = outline->points + last;
2130 
2131       /* skip empty points; we don't stroke these */
2132       if ( last <= first )
2133       {
2134         first = last + 1;
2135         continue;
2136       }
2137 
2138       v_start = outline->points[first];
2139       v_last  = outline->points[last];
2140 
2141       v_control = v_start;
2142 
2143       point = outline->points + first;
2144       tags  = outline->tags   + first;
2145       tag   = FT_CURVE_TAG( tags[0] );
2146 
2147       /* A contour cannot start with a cubic control point! */
2148       if ( tag == FT_CURVE_TAG_CUBIC )
2149         goto Invalid_Outline;
2150 
2151       /* check first point to determine origin */
2152       if ( tag == FT_CURVE_TAG_CONIC )
2153       {
2154         /* First point is conic control.  Yes, this happens. */
2155         if ( FT_CURVE_TAG( outline->tags[last] ) == FT_CURVE_TAG_ON )
2156         {
2157           /* start at last point if it is on the curve */
2158           v_start = v_last;
2159           limit--;
2160         }
2161         else
2162         {
2163           /* if both first and last points are conic, */
2164           /* start at their middle                    */
2165           v_start.x = ( v_start.x + v_last.x ) / 2;
2166           v_start.y = ( v_start.y + v_last.y ) / 2;
2167         }
2168         point--;
2169         tags--;
2170       }
2171 
2172       error = FT_Stroker_BeginSubPath( stroker, &v_start, opened );
2173       if ( error )
2174         goto Exit;
2175 
2176       while ( point < limit )
2177       {
2178         point++;
2179         tags++;
2180 
2181         tag = FT_CURVE_TAG( tags[0] );
2182         switch ( tag )
2183         {
2184         case FT_CURVE_TAG_ON:  /* emit a single line_to */
2185           {
2186             FT_Vector  vec;
2187 
2188 
2189             vec.x = point->x;
2190             vec.y = point->y;
2191 
2192             error = FT_Stroker_LineTo( stroker, &vec );
2193             if ( error )
2194               goto Exit;
2195             continue;
2196           }
2197 
2198         case FT_CURVE_TAG_CONIC:  /* consume conic arcs */
2199           v_control.x = point->x;
2200           v_control.y = point->y;
2201 
2202         Do_Conic:
2203           if ( point < limit )
2204           {
2205             FT_Vector  vec;
2206             FT_Vector  v_middle;
2207 
2208 
2209             point++;
2210             tags++;
2211             tag = FT_CURVE_TAG( tags[0] );
2212 
2213             vec = point[0];
2214 
2215             if ( tag == FT_CURVE_TAG_ON )
2216             {
2217               error = FT_Stroker_ConicTo( stroker, &v_control, &vec );
2218               if ( error )
2219                 goto Exit;
2220               continue;
2221             }
2222 
2223             if ( tag != FT_CURVE_TAG_CONIC )
2224               goto Invalid_Outline;
2225 
2226             v_middle.x = ( v_control.x + vec.x ) / 2;
2227             v_middle.y = ( v_control.y + vec.y ) / 2;
2228 
2229             error = FT_Stroker_ConicTo( stroker, &v_control, &v_middle );
2230             if ( error )
2231               goto Exit;
2232 
2233             v_control = vec;
2234             goto Do_Conic;
2235           }
2236 
2237           error = FT_Stroker_ConicTo( stroker, &v_control, &v_start );
2238           goto Close;
2239 
2240         default:  /* FT_CURVE_TAG_CUBIC */
2241           {
2242             FT_Vector  vec1, vec2;
2243 
2244 
2245             if ( point + 1 > limit                             ||
2246                  FT_CURVE_TAG( tags[1] ) != FT_CURVE_TAG_CUBIC )
2247               goto Invalid_Outline;
2248 
2249             point += 2;
2250             tags  += 2;
2251 
2252             vec1 = point[-2];
2253             vec2 = point[-1];
2254 
2255             if ( point <= limit )
2256             {
2257               FT_Vector  vec;
2258 
2259 
2260               vec = point[0];
2261 
2262               error = FT_Stroker_CubicTo( stroker, &vec1, &vec2, &vec );
2263               if ( error )
2264                 goto Exit;
2265               continue;
2266             }
2267 
2268             error = FT_Stroker_CubicTo( stroker, &vec1, &vec2, &v_start );
2269             goto Close;
2270           }
2271         }
2272       }
2273 
2274     Close:
2275       if ( error )
2276         goto Exit;
2277 
2278       /* don't try to end the path if no segments have been generated */
2279       if ( !stroker->first_point )
2280       {
2281         error = FT_Stroker_EndSubPath( stroker );
2282         if ( error )
2283           goto Exit;
2284       }
2285 
2286       first = last + 1;
2287     }
2288 
2289     return FT_Err_Ok;
2290 
2291   Exit:
2292     return error;
2293 
2294   Invalid_Outline:
2295     return FT_THROW( Invalid_Outline );
2296   }
2297 
2298 
2299   /* documentation is in ftstroke.h */
2300 
2301   FT_EXPORT_DEF( FT_Error )
FT_Glyph_Stroke(FT_Glyph * pglyph,FT_Stroker stroker,FT_Bool destroy)2302   FT_Glyph_Stroke( FT_Glyph    *pglyph,
2303                    FT_Stroker   stroker,
2304                    FT_Bool      destroy )
2305   {
2306     FT_Error  error = FT_ERR( Invalid_Argument );
2307     FT_Glyph  glyph = NULL;
2308 
2309     /* for FT_OUTLINE_GLYPH_CLASS_GET (in PIC mode) */
2310     FT_Library  library = stroker->library;
2311 
2312     FT_UNUSED( library );
2313 
2314 
2315     if ( !pglyph )
2316       goto Exit;
2317 
2318     glyph = *pglyph;
2319     if ( !glyph || glyph->clazz != FT_OUTLINE_GLYPH_CLASS_GET )
2320       goto Exit;
2321 
2322     {
2323       FT_Glyph  copy;
2324 
2325 
2326       error = FT_Glyph_Copy( glyph, &copy );
2327       if ( error )
2328         goto Exit;
2329 
2330       glyph = copy;
2331     }
2332 
2333     {
2334       FT_OutlineGlyph  oglyph  = (FT_OutlineGlyph)glyph;
2335       FT_Outline*      outline = &oglyph->outline;
2336       FT_UInt          num_points, num_contours;
2337 
2338 
2339       error = FT_Stroker_ParseOutline( stroker, outline, FALSE );
2340       if ( error )
2341         goto Fail;
2342 
2343       FT_Stroker_GetCounts( stroker, &num_points, &num_contours );
2344 
2345       FT_Outline_Done( glyph->library, outline );
2346 
2347       error = FT_Outline_New( glyph->library,
2348                               num_points,
2349                               (FT_Int)num_contours,
2350                               outline );
2351       if ( error )
2352         goto Fail;
2353 
2354       outline->n_points   = 0;
2355       outline->n_contours = 0;
2356 
2357       FT_Stroker_Export( stroker, outline );
2358     }
2359 
2360     if ( destroy )
2361       FT_Done_Glyph( *pglyph );
2362 
2363     *pglyph = glyph;
2364     goto Exit;
2365 
2366   Fail:
2367     FT_Done_Glyph( glyph );
2368     glyph = NULL;
2369 
2370     if ( !destroy )
2371       *pglyph = NULL;
2372 
2373   Exit:
2374     return error;
2375   }
2376 
2377 
2378   /* documentation is in ftstroke.h */
2379 
2380   FT_EXPORT_DEF( FT_Error )
FT_Glyph_StrokeBorder(FT_Glyph * pglyph,FT_Stroker stroker,FT_Bool inside,FT_Bool destroy)2381   FT_Glyph_StrokeBorder( FT_Glyph    *pglyph,
2382                          FT_Stroker   stroker,
2383                          FT_Bool      inside,
2384                          FT_Bool      destroy )
2385   {
2386     FT_Error  error = FT_ERR( Invalid_Argument );
2387     FT_Glyph  glyph = NULL;
2388 
2389     /* for FT_OUTLINE_GLYPH_CLASS_GET (in PIC mode) */
2390     FT_Library  library = stroker->library;
2391 
2392     FT_UNUSED( library );
2393 
2394 
2395     if ( !pglyph )
2396       goto Exit;
2397 
2398     glyph = *pglyph;
2399     if ( !glyph || glyph->clazz != FT_OUTLINE_GLYPH_CLASS_GET )
2400       goto Exit;
2401 
2402     {
2403       FT_Glyph  copy;
2404 
2405 
2406       error = FT_Glyph_Copy( glyph, &copy );
2407       if ( error )
2408         goto Exit;
2409 
2410       glyph = copy;
2411     }
2412 
2413     {
2414       FT_OutlineGlyph   oglyph  = (FT_OutlineGlyph)glyph;
2415       FT_StrokerBorder  border;
2416       FT_Outline*       outline = &oglyph->outline;
2417       FT_UInt           num_points, num_contours;
2418 
2419 
2420       border = FT_Outline_GetOutsideBorder( outline );
2421       if ( inside )
2422       {
2423         if ( border == FT_STROKER_BORDER_LEFT )
2424           border = FT_STROKER_BORDER_RIGHT;
2425         else
2426           border = FT_STROKER_BORDER_LEFT;
2427       }
2428 
2429       error = FT_Stroker_ParseOutline( stroker, outline, FALSE );
2430       if ( error )
2431         goto Fail;
2432 
2433       FT_Stroker_GetBorderCounts( stroker, border,
2434                                   &num_points, &num_contours );
2435 
2436       FT_Outline_Done( glyph->library, outline );
2437 
2438       error = FT_Outline_New( glyph->library,
2439                               num_points,
2440                               (FT_Int)num_contours,
2441                               outline );
2442       if ( error )
2443         goto Fail;
2444 
2445       outline->n_points   = 0;
2446       outline->n_contours = 0;
2447 
2448       FT_Stroker_ExportBorder( stroker, border, outline );
2449     }
2450 
2451     if ( destroy )
2452       FT_Done_Glyph( *pglyph );
2453 
2454     *pglyph = glyph;
2455     goto Exit;
2456 
2457   Fail:
2458     FT_Done_Glyph( glyph );
2459     glyph = NULL;
2460 
2461     if ( !destroy )
2462       *pglyph = NULL;
2463 
2464   Exit:
2465     return error;
2466   }
2467 
2468 
2469 /* END */
2470