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      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 )
     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 )
     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
     81   ft_pos_abs( FT_Pos  x )
     82   {
     83     return x >= 0 ? x : -x;
     84   }
     85 
     86 
     87   static void
     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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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 )
    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 )
    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 )
    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 )
    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
    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
    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
    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
   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
   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
   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 )
   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 )
   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 )
   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 )
   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
   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 )
   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 )
   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 )
   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 )
   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 )
   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 )
   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 )
   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 )
   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