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      1 /***************************************************************************/
      2 /*                                                                         */
      3 /*  ftstroke.c                                                             */
      4 /*                                                                         */
      5 /*    FreeType path stroker (body).                                        */
      6 /*                                                                         */
      7 /*  Copyright 2002-2006, 2008-2011, 2013 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 
     28   /* documentation is in ftstroke.h */
     29 
     30   FT_EXPORT_DEF( FT_StrokerBorder )
     31   FT_Outline_GetInsideBorder( FT_Outline*  outline )
     32   {
     33     FT_Orientation  o = FT_Outline_Get_Orientation( outline );
     34 
     35 
     36     return o == FT_ORIENTATION_TRUETYPE ? FT_STROKER_BORDER_RIGHT
     37                                         : FT_STROKER_BORDER_LEFT;
     38   }
     39 
     40 
     41   /* documentation is in ftstroke.h */
     42 
     43   FT_EXPORT_DEF( FT_StrokerBorder )
     44   FT_Outline_GetOutsideBorder( FT_Outline*  outline )
     45   {
     46     FT_Orientation  o = FT_Outline_Get_Orientation( outline );
     47 
     48 
     49     return o == FT_ORIENTATION_TRUETYPE ? FT_STROKER_BORDER_LEFT
     50                                         : FT_STROKER_BORDER_RIGHT;
     51   }
     52 
     53 
     54   /*************************************************************************/
     55   /*************************************************************************/
     56   /*****                                                               *****/
     57   /*****                      BEZIER COMPUTATIONS                      *****/
     58   /*****                                                               *****/
     59   /*************************************************************************/
     60   /*************************************************************************/
     61 
     62 #define FT_SMALL_CONIC_THRESHOLD  ( FT_ANGLE_PI / 6 )
     63 #define FT_SMALL_CUBIC_THRESHOLD  ( FT_ANGLE_PI / 8 )
     64 
     65 #define FT_EPSILON  2
     66 
     67 #define FT_IS_SMALL( x )  ( (x) > -FT_EPSILON && (x) < FT_EPSILON )
     68 
     69 
     70   static FT_Pos
     71   ft_pos_abs( FT_Pos  x )
     72   {
     73     return x >= 0 ? x : -x;
     74   }
     75 
     76 
     77   static void
     78   ft_conic_split( FT_Vector*  base )
     79   {
     80     FT_Pos  a, b;
     81 
     82 
     83     base[4].x = base[2].x;
     84     b = base[1].x;
     85     a = base[3].x = ( base[2].x + b ) / 2;
     86     b = base[1].x = ( base[0].x + b ) / 2;
     87     base[2].x = ( a + b ) / 2;
     88 
     89     base[4].y = base[2].y;
     90     b = base[1].y;
     91     a = base[3].y = ( base[2].y + b ) / 2;
     92     b = base[1].y = ( base[0].y + b ) / 2;
     93     base[2].y = ( a + b ) / 2;
     94   }
     95 
     96 
     97   static FT_Bool
     98   ft_conic_is_small_enough( FT_Vector*  base,
     99                             FT_Angle   *angle_in,
    100                             FT_Angle   *angle_out )
    101   {
    102     FT_Vector  d1, d2;
    103     FT_Angle   theta;
    104     FT_Int     close1, close2;
    105 
    106 
    107     d1.x = base[1].x - base[2].x;
    108     d1.y = base[1].y - base[2].y;
    109     d2.x = base[0].x - base[1].x;
    110     d2.y = base[0].y - base[1].y;
    111 
    112     close1 = FT_IS_SMALL( d1.x ) && FT_IS_SMALL( d1.y );
    113     close2 = FT_IS_SMALL( d2.x ) && FT_IS_SMALL( d2.y );
    114 
    115     if ( close1 )
    116     {
    117       if ( close2 )
    118       {
    119         /* basically a point;                      */
    120         /* do nothing to retain original direction */
    121       }
    122       else
    123       {
    124         *angle_in  =
    125         *angle_out = FT_Atan2( d2.x, d2.y );
    126       }
    127     }
    128     else /* !close1 */
    129     {
    130       if ( close2 )
    131       {
    132         *angle_in  =
    133         *angle_out = FT_Atan2( d1.x, d1.y );
    134       }
    135       else
    136       {
    137         *angle_in  = FT_Atan2( d1.x, d1.y );
    138         *angle_out = FT_Atan2( d2.x, d2.y );
    139       }
    140     }
    141 
    142     theta = ft_pos_abs( FT_Angle_Diff( *angle_in, *angle_out ) );
    143 
    144     return FT_BOOL( theta < FT_SMALL_CONIC_THRESHOLD );
    145   }
    146 
    147 
    148   static void
    149   ft_cubic_split( FT_Vector*  base )
    150   {
    151     FT_Pos  a, b, c, d;
    152 
    153 
    154     base[6].x = base[3].x;
    155     c = base[1].x;
    156     d = base[2].x;
    157     base[1].x = a = ( base[0].x + c ) / 2;
    158     base[5].x = b = ( base[3].x + d ) / 2;
    159     c = ( c + d ) / 2;
    160     base[2].x = a = ( a + c ) / 2;
    161     base[4].x = b = ( b + c ) / 2;
    162     base[3].x = ( a + b ) / 2;
    163 
    164     base[6].y = base[3].y;
    165     c = base[1].y;
    166     d = base[2].y;
    167     base[1].y = a = ( base[0].y + c ) / 2;
    168     base[5].y = b = ( base[3].y + d ) / 2;
    169     c = ( c + d ) / 2;
    170     base[2].y = a = ( a + c ) / 2;
    171     base[4].y = b = ( b + c ) / 2;
    172     base[3].y = ( a + b ) / 2;
    173   }
    174 
    175 
    176   /* Return the average of `angle1' and `angle2'.            */
    177   /* This gives correct result even if `angle1' and `angle2' */
    178   /* have opposite signs.                                    */
    179   static FT_Angle
    180   ft_angle_mean( FT_Angle  angle1,
    181                  FT_Angle  angle2 )
    182   {
    183     return angle1 + FT_Angle_Diff( angle1, angle2 ) / 2;
    184   }
    185 
    186 
    187   static FT_Bool
    188   ft_cubic_is_small_enough( FT_Vector*  base,
    189                             FT_Angle   *angle_in,
    190                             FT_Angle   *angle_mid,
    191                             FT_Angle   *angle_out )
    192   {
    193     FT_Vector  d1, d2, d3;
    194     FT_Angle   theta1, theta2;
    195     FT_Int     close1, close2, close3;
    196 
    197 
    198     d1.x = base[2].x - base[3].x;
    199     d1.y = base[2].y - base[3].y;
    200     d2.x = base[1].x - base[2].x;
    201     d2.y = base[1].y - base[2].y;
    202     d3.x = base[0].x - base[1].x;
    203     d3.y = base[0].y - base[1].y;
    204 
    205     close1 = FT_IS_SMALL( d1.x ) && FT_IS_SMALL( d1.y );
    206     close2 = FT_IS_SMALL( d2.x ) && FT_IS_SMALL( d2.y );
    207     close3 = FT_IS_SMALL( d3.x ) && FT_IS_SMALL( d3.y );
    208 
    209     if ( close1 )
    210     {
    211       if ( close2 )
    212       {
    213         if ( close3 )
    214         {
    215           /* basically a point;                      */
    216           /* do nothing to retain original direction */
    217         }
    218         else /* !close3 */
    219         {
    220           *angle_in  =
    221           *angle_mid =
    222           *angle_out = FT_Atan2( d3.x, d3.y );
    223         }
    224       }
    225       else /* !close2 */
    226       {
    227         if ( close3 )
    228         {
    229           *angle_in  =
    230           *angle_mid =
    231           *angle_out = FT_Atan2( d2.x, d2.y );
    232         }
    233         else /* !close3 */
    234         {
    235           *angle_in  =
    236           *angle_mid = FT_Atan2( d2.x, d2.y );
    237           *angle_out = FT_Atan2( d3.x, d3.y );
    238         }
    239       }
    240     }
    241     else /* !close1 */
    242     {
    243       if ( close2 )
    244       {
    245         if ( close3 )
    246         {
    247           *angle_in  =
    248           *angle_mid =
    249           *angle_out = FT_Atan2( d1.x, d1.y );
    250         }
    251         else /* !close3 */
    252         {
    253           *angle_in  = FT_Atan2( d1.x, d1.y );
    254           *angle_out = FT_Atan2( d3.x, d3.y );
    255           *angle_mid = ft_angle_mean( *angle_in, *angle_out );
    256         }
    257       }
    258       else /* !close2 */
    259       {
    260         if ( close3 )
    261         {
    262           *angle_in  = FT_Atan2( d1.x, d1.y );
    263           *angle_mid =
    264           *angle_out = FT_Atan2( d2.x, d2.y );
    265         }
    266         else /* !close3 */
    267         {
    268           *angle_in  = FT_Atan2( d1.x, d1.y );
    269           *angle_mid = FT_Atan2( d2.x, d2.y );
    270           *angle_out = FT_Atan2( d3.x, d3.y );
    271         }
    272       }
    273     }
    274 
    275     theta1 = ft_pos_abs( FT_Angle_Diff( *angle_in,  *angle_mid ) );
    276     theta2 = ft_pos_abs( FT_Angle_Diff( *angle_mid, *angle_out ) );
    277 
    278     return FT_BOOL( theta1 < FT_SMALL_CUBIC_THRESHOLD &&
    279                     theta2 < FT_SMALL_CUBIC_THRESHOLD );
    280   }
    281 
    282 
    283   /*************************************************************************/
    284   /*************************************************************************/
    285   /*****                                                               *****/
    286   /*****                       STROKE BORDERS                          *****/
    287   /*****                                                               *****/
    288   /*************************************************************************/
    289   /*************************************************************************/
    290 
    291   typedef enum  FT_StrokeTags_
    292   {
    293     FT_STROKE_TAG_ON    = 1,   /* on-curve point  */
    294     FT_STROKE_TAG_CUBIC = 2,   /* cubic off-point */
    295     FT_STROKE_TAG_BEGIN = 4,   /* sub-path start  */
    296     FT_STROKE_TAG_END   = 8    /* sub-path end    */
    297 
    298   } FT_StrokeTags;
    299 
    300 #define  FT_STROKE_TAG_BEGIN_END  ( FT_STROKE_TAG_BEGIN | FT_STROKE_TAG_END )
    301 
    302   typedef struct  FT_StrokeBorderRec_
    303   {
    304     FT_UInt     num_points;
    305     FT_UInt     max_points;
    306     FT_Vector*  points;
    307     FT_Byte*    tags;
    308     FT_Bool     movable;  /* TRUE for ends of lineto borders */
    309     FT_Int      start;    /* index of current sub-path start point */
    310     FT_Memory   memory;
    311     FT_Bool     valid;
    312 
    313   } FT_StrokeBorderRec, *FT_StrokeBorder;
    314 
    315 
    316   static FT_Error
    317   ft_stroke_border_grow( FT_StrokeBorder  border,
    318                          FT_UInt          new_points )
    319   {
    320     FT_UInt   old_max = border->max_points;
    321     FT_UInt   new_max = border->num_points + new_points;
    322     FT_Error  error   = FT_Err_Ok;
    323 
    324 
    325     if ( new_max > old_max )
    326     {
    327       FT_UInt    cur_max = old_max;
    328       FT_Memory  memory  = border->memory;
    329 
    330 
    331       while ( cur_max < new_max )
    332         cur_max += ( cur_max >> 1 ) + 16;
    333 
    334       if ( FT_RENEW_ARRAY( border->points, old_max, cur_max ) ||
    335            FT_RENEW_ARRAY( border->tags,   old_max, cur_max ) )
    336         goto Exit;
    337 
    338       border->max_points = cur_max;
    339     }
    340 
    341   Exit:
    342     return error;
    343   }
    344 
    345 
    346   static void
    347   ft_stroke_border_close( FT_StrokeBorder  border,
    348                           FT_Bool          reverse )
    349   {
    350     FT_UInt  start = border->start;
    351     FT_UInt  count = border->num_points;
    352 
    353 
    354     FT_ASSERT( border->start >= 0 );
    355 
    356     /* don't record empty paths! */
    357     if ( count <= start + 1U )
    358       border->num_points = start;
    359     else
    360     {
    361       /* copy the last point to the start of this sub-path, since */
    362       /* it contains the `adjusted' starting coordinates          */
    363       border->num_points    = --count;
    364       border->points[start] = border->points[count];
    365 
    366       if ( reverse )
    367       {
    368         /* reverse the points */
    369         {
    370           FT_Vector*  vec1 = border->points + start + 1;
    371           FT_Vector*  vec2 = border->points + count - 1;
    372 
    373 
    374           for ( ; vec1 < vec2; vec1++, vec2-- )
    375           {
    376             FT_Vector  tmp;
    377 
    378 
    379             tmp   = *vec1;
    380             *vec1 = *vec2;
    381             *vec2 = tmp;
    382           }
    383         }
    384 
    385         /* then the tags */
    386         {
    387           FT_Byte*  tag1 = border->tags + start + 1;
    388           FT_Byte*  tag2 = border->tags + count - 1;
    389 
    390 
    391           for ( ; tag1 < tag2; tag1++, tag2-- )
    392           {
    393             FT_Byte  tmp;
    394 
    395 
    396             tmp   = *tag1;
    397             *tag1 = *tag2;
    398             *tag2 = tmp;
    399           }
    400         }
    401       }
    402 
    403       border->tags[start    ] |= FT_STROKE_TAG_BEGIN;
    404       border->tags[count - 1] |= FT_STROKE_TAG_END;
    405     }
    406 
    407     border->start   = -1;
    408     border->movable = FALSE;
    409   }
    410 
    411 
    412   static FT_Error
    413   ft_stroke_border_lineto( FT_StrokeBorder  border,
    414                            FT_Vector*       to,
    415                            FT_Bool          movable )
    416   {
    417     FT_Error  error = FT_Err_Ok;
    418 
    419 
    420     FT_ASSERT( border->start >= 0 );
    421 
    422     if ( border->movable )
    423     {
    424       /* move last point */
    425       border->points[border->num_points - 1] = *to;
    426     }
    427     else
    428     {
    429       /* don't add zero-length lineto */
    430       if ( border->num_points > 0                                          &&
    431            FT_IS_SMALL( border->points[border->num_points - 1].x - to->x ) &&
    432            FT_IS_SMALL( border->points[border->num_points - 1].y - to->y ) )
    433         return error;
    434 
    435       /* add one point */
    436       error = ft_stroke_border_grow( border, 1 );
    437       if ( !error )
    438       {
    439         FT_Vector*  vec = border->points + border->num_points;
    440         FT_Byte*    tag = border->tags   + border->num_points;
    441 
    442 
    443         vec[0] = *to;
    444         tag[0] = FT_STROKE_TAG_ON;
    445 
    446         border->num_points += 1;
    447       }
    448     }
    449     border->movable = movable;
    450     return error;
    451   }
    452 
    453 
    454   static FT_Error
    455   ft_stroke_border_conicto( FT_StrokeBorder  border,
    456                             FT_Vector*       control,
    457                             FT_Vector*       to )
    458   {
    459     FT_Error  error;
    460 
    461 
    462     FT_ASSERT( border->start >= 0 );
    463 
    464     error = ft_stroke_border_grow( border, 2 );
    465     if ( !error )
    466     {
    467       FT_Vector*  vec = border->points + border->num_points;
    468       FT_Byte*    tag = border->tags   + border->num_points;
    469 
    470 
    471       vec[0] = *control;
    472       vec[1] = *to;
    473 
    474       tag[0] = 0;
    475       tag[1] = FT_STROKE_TAG_ON;
    476 
    477       border->num_points += 2;
    478     }
    479 
    480     border->movable = FALSE;
    481 
    482     return error;
    483   }
    484 
    485 
    486   static FT_Error
    487   ft_stroke_border_cubicto( FT_StrokeBorder  border,
    488                             FT_Vector*       control1,
    489                             FT_Vector*       control2,
    490                             FT_Vector*       to )
    491   {
    492     FT_Error  error;
    493 
    494 
    495     FT_ASSERT( border->start >= 0 );
    496 
    497     error = ft_stroke_border_grow( border, 3 );
    498     if ( !error )
    499     {
    500       FT_Vector*  vec = border->points + border->num_points;
    501       FT_Byte*    tag = border->tags   + border->num_points;
    502 
    503 
    504       vec[0] = *control1;
    505       vec[1] = *control2;
    506       vec[2] = *to;
    507 
    508       tag[0] = FT_STROKE_TAG_CUBIC;
    509       tag[1] = FT_STROKE_TAG_CUBIC;
    510       tag[2] = FT_STROKE_TAG_ON;
    511 
    512       border->num_points += 3;
    513     }
    514 
    515     border->movable = FALSE;
    516 
    517     return error;
    518   }
    519 
    520 
    521 #define FT_ARC_CUBIC_ANGLE  ( FT_ANGLE_PI / 2 )
    522 
    523 
    524   static FT_Error
    525   ft_stroke_border_arcto( FT_StrokeBorder  border,
    526                           FT_Vector*       center,
    527                           FT_Fixed         radius,
    528                           FT_Angle         angle_start,
    529                           FT_Angle         angle_diff )
    530   {
    531     FT_Angle   total, angle, step, rotate, next, theta;
    532     FT_Vector  a, b, a2, b2;
    533     FT_Fixed   length;
    534     FT_Error   error = FT_Err_Ok;
    535 
    536 
    537     /* compute start point */
    538     FT_Vector_From_Polar( &a, radius, angle_start );
    539     a.x += center->x;
    540     a.y += center->y;
    541 
    542     total  = angle_diff;
    543     angle  = angle_start;
    544     rotate = ( angle_diff >= 0 ) ? FT_ANGLE_PI2 : -FT_ANGLE_PI2;
    545 
    546     while ( total != 0 )
    547     {
    548       step = total;
    549       if ( step > FT_ARC_CUBIC_ANGLE )
    550         step = FT_ARC_CUBIC_ANGLE;
    551 
    552       else if ( step < -FT_ARC_CUBIC_ANGLE )
    553         step = -FT_ARC_CUBIC_ANGLE;
    554 
    555       next  = angle + step;
    556       theta = step;
    557       if ( theta < 0 )
    558         theta = -theta;
    559 
    560       theta >>= 1;
    561 
    562       /* compute end point */
    563       FT_Vector_From_Polar( &b, radius, next );
    564       b.x += center->x;
    565       b.y += center->y;
    566 
    567       /* compute first and second control points */
    568       length = FT_MulDiv( radius, FT_Sin( theta ) * 4,
    569                           ( 0x10000L + FT_Cos( theta ) ) * 3 );
    570 
    571       FT_Vector_From_Polar( &a2, length, angle + rotate );
    572       a2.x += a.x;
    573       a2.y += a.y;
    574 
    575       FT_Vector_From_Polar( &b2, length, next - rotate );
    576       b2.x += b.x;
    577       b2.y += b.y;
    578 
    579       /* add cubic arc */
    580       error = ft_stroke_border_cubicto( border, &a2, &b2, &b );
    581       if ( error )
    582         break;
    583 
    584       /* process the rest of the arc ?? */
    585       a      = b;
    586       total -= step;
    587       angle  = next;
    588     }
    589 
    590     return error;
    591   }
    592 
    593 
    594   static FT_Error
    595   ft_stroke_border_moveto( FT_StrokeBorder  border,
    596                            FT_Vector*       to )
    597   {
    598     /* close current open path if any ? */
    599     if ( border->start >= 0 )
    600       ft_stroke_border_close( border, FALSE );
    601 
    602     border->start = border->num_points;
    603     border->movable = FALSE;
    604 
    605     return ft_stroke_border_lineto( border, to, FALSE );
    606   }
    607 
    608 
    609   static void
    610   ft_stroke_border_init( FT_StrokeBorder  border,
    611                          FT_Memory        memory )
    612   {
    613     border->memory = memory;
    614     border->points = NULL;
    615     border->tags   = NULL;
    616 
    617     border->num_points = 0;
    618     border->max_points = 0;
    619     border->start      = -1;
    620     border->valid      = FALSE;
    621   }
    622 
    623 
    624   static void
    625   ft_stroke_border_reset( FT_StrokeBorder  border )
    626   {
    627     border->num_points = 0;
    628     border->start      = -1;
    629     border->valid      = FALSE;
    630   }
    631 
    632 
    633   static void
    634   ft_stroke_border_done( FT_StrokeBorder  border )
    635   {
    636     FT_Memory  memory = border->memory;
    637 
    638 
    639     FT_FREE( border->points );
    640     FT_FREE( border->tags );
    641 
    642     border->num_points = 0;
    643     border->max_points = 0;
    644     border->start      = -1;
    645     border->valid      = FALSE;
    646   }
    647 
    648 
    649   static FT_Error
    650   ft_stroke_border_get_counts( FT_StrokeBorder  border,
    651                                FT_UInt         *anum_points,
    652                                FT_UInt         *anum_contours )
    653   {
    654     FT_Error  error        = FT_Err_Ok;
    655     FT_UInt   num_points   = 0;
    656     FT_UInt   num_contours = 0;
    657 
    658     FT_UInt     count      = border->num_points;
    659     FT_Vector*  point      = border->points;
    660     FT_Byte*    tags       = border->tags;
    661     FT_Int      in_contour = 0;
    662 
    663 
    664     for ( ; count > 0; count--, num_points++, point++, tags++ )
    665     {
    666       if ( tags[0] & FT_STROKE_TAG_BEGIN )
    667       {
    668         if ( in_contour != 0 )
    669           goto Fail;
    670 
    671         in_contour = 1;
    672       }
    673       else if ( in_contour == 0 )
    674         goto Fail;
    675 
    676       if ( tags[0] & FT_STROKE_TAG_END )
    677       {
    678         in_contour = 0;
    679         num_contours++;
    680       }
    681     }
    682 
    683     if ( in_contour != 0 )
    684       goto Fail;
    685 
    686     border->valid = TRUE;
    687 
    688   Exit:
    689     *anum_points   = num_points;
    690     *anum_contours = num_contours;
    691     return error;
    692 
    693   Fail:
    694     num_points   = 0;
    695     num_contours = 0;
    696     goto Exit;
    697   }
    698 
    699 
    700   static void
    701   ft_stroke_border_export( FT_StrokeBorder  border,
    702                            FT_Outline*      outline )
    703   {
    704     /* copy point locations */
    705     FT_ARRAY_COPY( outline->points + outline->n_points,
    706                    border->points,
    707                    border->num_points );
    708 
    709     /* copy tags */
    710     {
    711       FT_UInt   count = border->num_points;
    712       FT_Byte*  read  = border->tags;
    713       FT_Byte*  write = (FT_Byte*)outline->tags + outline->n_points;
    714 
    715 
    716       for ( ; count > 0; count--, read++, write++ )
    717       {
    718         if ( *read & FT_STROKE_TAG_ON )
    719           *write = FT_CURVE_TAG_ON;
    720         else if ( *read & FT_STROKE_TAG_CUBIC )
    721           *write = FT_CURVE_TAG_CUBIC;
    722         else
    723           *write = FT_CURVE_TAG_CONIC;
    724       }
    725     }
    726 
    727     /* copy contours */
    728     {
    729       FT_UInt    count = border->num_points;
    730       FT_Byte*   tags  = border->tags;
    731       FT_Short*  write = outline->contours + outline->n_contours;
    732       FT_Short   idx   = (FT_Short)outline->n_points;
    733 
    734 
    735       for ( ; count > 0; count--, tags++, idx++ )
    736       {
    737         if ( *tags & FT_STROKE_TAG_END )
    738         {
    739           *write++ = idx;
    740           outline->n_contours++;
    741         }
    742       }
    743     }
    744 
    745     outline->n_points = (short)( outline->n_points + border->num_points );
    746 
    747     FT_ASSERT( FT_Outline_Check( outline ) == 0 );
    748   }
    749 
    750 
    751   /*************************************************************************/
    752   /*************************************************************************/
    753   /*****                                                               *****/
    754   /*****                           STROKER                             *****/
    755   /*****                                                               *****/
    756   /*************************************************************************/
    757   /*************************************************************************/
    758 
    759 #define FT_SIDE_TO_ROTATE( s )   ( FT_ANGLE_PI2 - (s) * FT_ANGLE_PI )
    760 
    761   typedef struct  FT_StrokerRec_
    762   {
    763     FT_Angle             angle_in;             /* direction into curr join */
    764     FT_Angle             angle_out;            /* direction out of join  */
    765     FT_Vector            center;               /* current position */
    766     FT_Fixed             line_length;          /* length of last lineto */
    767     FT_Bool              first_point;          /* is this the start? */
    768     FT_Bool              subpath_open;         /* is the subpath open? */
    769     FT_Angle             subpath_angle;        /* subpath start direction */
    770     FT_Vector            subpath_start;        /* subpath start position */
    771     FT_Fixed             subpath_line_length;  /* subpath start lineto len */
    772     FT_Bool              handle_wide_strokes;  /* use wide strokes logic? */
    773 
    774     FT_Stroker_LineCap   line_cap;
    775     FT_Stroker_LineJoin  line_join;
    776     FT_Stroker_LineJoin  line_join_saved;
    777     FT_Fixed             miter_limit;
    778     FT_Fixed             radius;
    779 
    780     FT_StrokeBorderRec   borders[2];
    781     FT_Library           library;
    782 
    783   } FT_StrokerRec;
    784 
    785 
    786   /* documentation is in ftstroke.h */
    787 
    788   FT_EXPORT_DEF( FT_Error )
    789   FT_Stroker_New( FT_Library   library,
    790                   FT_Stroker  *astroker )
    791   {
    792     FT_Error    error;           /* assigned in FT_NEW */
    793     FT_Memory   memory;
    794     FT_Stroker  stroker = NULL;
    795 
    796 
    797     if ( !library )
    798       return FT_THROW( Invalid_Argument );
    799 
    800     memory = library->memory;
    801 
    802     if ( !FT_NEW( stroker ) )
    803     {
    804       stroker->library = library;
    805 
    806       ft_stroke_border_init( &stroker->borders[0], memory );
    807       ft_stroke_border_init( &stroker->borders[1], memory );
    808     }
    809 
    810     *astroker = stroker;
    811 
    812     return error;
    813   }
    814 
    815 
    816   /* documentation is in ftstroke.h */
    817 
    818   FT_EXPORT_DEF( void )
    819   FT_Stroker_Set( FT_Stroker           stroker,
    820                   FT_Fixed             radius,
    821                   FT_Stroker_LineCap   line_cap,
    822                   FT_Stroker_LineJoin  line_join,
    823                   FT_Fixed             miter_limit )
    824   {
    825     stroker->radius      = radius;
    826     stroker->line_cap    = line_cap;
    827     stroker->line_join   = line_join;
    828     stroker->miter_limit = miter_limit;
    829 
    830     /* ensure miter limit has sensible value */
    831     if ( stroker->miter_limit < 0x10000 )
    832       stroker->miter_limit = 0x10000;
    833 
    834     /* save line join style:                                           */
    835     /* line join style can be temporarily changed when stroking curves */
    836     stroker->line_join_saved = line_join;
    837 
    838     FT_Stroker_Rewind( stroker );
    839   }
    840 
    841 
    842   /* documentation is in ftstroke.h */
    843 
    844   FT_EXPORT_DEF( void )
    845   FT_Stroker_Rewind( FT_Stroker  stroker )
    846   {
    847     if ( stroker )
    848     {
    849       ft_stroke_border_reset( &stroker->borders[0] );
    850       ft_stroke_border_reset( &stroker->borders[1] );
    851     }
    852   }
    853 
    854 
    855   /* documentation is in ftstroke.h */
    856 
    857   FT_EXPORT_DEF( void )
    858   FT_Stroker_Done( FT_Stroker  stroker )
    859   {
    860     if ( stroker )
    861     {
    862       FT_Memory  memory = stroker->library->memory;
    863 
    864 
    865       ft_stroke_border_done( &stroker->borders[0] );
    866       ft_stroke_border_done( &stroker->borders[1] );
    867 
    868       stroker->library = NULL;
    869       FT_FREE( stroker );
    870     }
    871   }
    872 
    873 
    874   /* create a circular arc at a corner or cap */
    875   static FT_Error
    876   ft_stroker_arcto( FT_Stroker  stroker,
    877                     FT_Int      side )
    878   {
    879     FT_Angle         total, rotate;
    880     FT_Fixed         radius = stroker->radius;
    881     FT_Error         error  = FT_Err_Ok;
    882     FT_StrokeBorder  border = stroker->borders + side;
    883 
    884 
    885     rotate = FT_SIDE_TO_ROTATE( side );
    886 
    887     total = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
    888     if ( total == FT_ANGLE_PI )
    889       total = -rotate * 2;
    890 
    891     error = ft_stroke_border_arcto( border,
    892                                     &stroker->center,
    893                                     radius,
    894                                     stroker->angle_in + rotate,
    895                                     total );
    896     border->movable = FALSE;
    897     return error;
    898   }
    899 
    900 
    901   /* add a cap at the end of an opened path */
    902   static FT_Error
    903   ft_stroker_cap( FT_Stroker  stroker,
    904                   FT_Angle    angle,
    905                   FT_Int      side )
    906   {
    907     FT_Error  error = FT_Err_Ok;
    908 
    909 
    910     if ( stroker->line_cap == FT_STROKER_LINECAP_ROUND )
    911     {
    912       /* add a round cap */
    913       stroker->angle_in  = angle;
    914       stroker->angle_out = angle + FT_ANGLE_PI;
    915 
    916       error = ft_stroker_arcto( stroker, side );
    917     }
    918     else if ( stroker->line_cap == FT_STROKER_LINECAP_SQUARE )
    919     {
    920       /* add a square cap */
    921       FT_Vector        delta, delta2;
    922       FT_Angle         rotate = FT_SIDE_TO_ROTATE( side );
    923       FT_Fixed         radius = stroker->radius;
    924       FT_StrokeBorder  border = stroker->borders + side;
    925 
    926 
    927       FT_Vector_From_Polar( &delta2, radius, angle + rotate );
    928       FT_Vector_From_Polar( &delta,  radius, angle );
    929 
    930       delta.x += stroker->center.x + delta2.x;
    931       delta.y += stroker->center.y + delta2.y;
    932 
    933       error = ft_stroke_border_lineto( border, &delta, FALSE );
    934       if ( error )
    935         goto Exit;
    936 
    937       FT_Vector_From_Polar( &delta2, radius, angle - rotate );
    938       FT_Vector_From_Polar( &delta,  radius, angle );
    939 
    940       delta.x += delta2.x + stroker->center.x;
    941       delta.y += delta2.y + stroker->center.y;
    942 
    943       error = ft_stroke_border_lineto( border, &delta, FALSE );
    944     }
    945     else if ( stroker->line_cap == FT_STROKER_LINECAP_BUTT )
    946     {
    947       /* add a butt ending */
    948       FT_Vector        delta;
    949       FT_Angle         rotate = FT_SIDE_TO_ROTATE( side );
    950       FT_Fixed         radius = stroker->radius;
    951       FT_StrokeBorder  border = stroker->borders + side;
    952 
    953 
    954       FT_Vector_From_Polar( &delta, radius, angle + rotate );
    955 
    956       delta.x += stroker->center.x;
    957       delta.y += stroker->center.y;
    958 
    959       error = ft_stroke_border_lineto( border, &delta, FALSE );
    960       if ( error )
    961         goto Exit;
    962 
    963       FT_Vector_From_Polar( &delta, radius, angle - rotate );
    964 
    965       delta.x += stroker->center.x;
    966       delta.y += stroker->center.y;
    967 
    968       error = ft_stroke_border_lineto( border, &delta, FALSE );
    969     }
    970 
    971   Exit:
    972     return error;
    973   }
    974 
    975 
    976   /* process an inside corner, i.e. compute intersection */
    977   static FT_Error
    978   ft_stroker_inside( FT_Stroker  stroker,
    979                      FT_Int      side,
    980                      FT_Fixed    line_length )
    981   {
    982     FT_StrokeBorder  border = stroker->borders + side;
    983     FT_Angle         phi, theta, rotate;
    984     FT_Fixed         length, thcos;
    985     FT_Vector        delta;
    986     FT_Error         error = FT_Err_Ok;
    987     FT_Bool          intersect;          /* use intersection of lines? */
    988 
    989 
    990     rotate = FT_SIDE_TO_ROTATE( side );
    991 
    992     theta = FT_Angle_Diff( stroker->angle_in, stroker->angle_out ) / 2;
    993 
    994     /* Only intersect borders if between two lineto's and both */
    995     /* lines are long enough (line_length is zero for curves). */
    996     if ( !border->movable || line_length == 0 )
    997       intersect = FALSE;
    998     else
    999     {
   1000       /* compute minimum required length of lines */
   1001       FT_Fixed  min_length = ft_pos_abs( FT_MulFix( stroker->radius,
   1002                                                     FT_Tan( theta ) ) );
   1003 
   1004 
   1005       intersect = FT_BOOL( stroker->line_length >= min_length &&
   1006                            line_length          >= min_length );
   1007     }
   1008 
   1009     if ( !intersect )
   1010     {
   1011       FT_Vector_From_Polar( &delta, stroker->radius,
   1012                             stroker->angle_out + rotate );
   1013       delta.x += stroker->center.x;
   1014       delta.y += stroker->center.y;
   1015 
   1016       border->movable = FALSE;
   1017     }
   1018     else
   1019     {
   1020       /* compute median angle */
   1021       phi = stroker->angle_in + theta;
   1022 
   1023       thcos = FT_Cos( theta );
   1024 
   1025       length = FT_DivFix( stroker->radius, thcos );
   1026 
   1027       FT_Vector_From_Polar( &delta, length, phi + rotate );
   1028       delta.x += stroker->center.x;
   1029       delta.y += stroker->center.y;
   1030     }
   1031 
   1032     error = ft_stroke_border_lineto( border, &delta, FALSE );
   1033 
   1034     return error;
   1035   }
   1036 
   1037 
   1038   /* process an outside corner, i.e. compute bevel/miter/round */
   1039   static FT_Error
   1040   ft_stroker_outside( FT_Stroker  stroker,
   1041                       FT_Int      side,
   1042                       FT_Fixed    line_length )
   1043   {
   1044     FT_StrokeBorder  border = stroker->borders + side;
   1045     FT_Error         error;
   1046     FT_Angle         rotate;
   1047 
   1048 
   1049     if ( stroker->line_join == FT_STROKER_LINEJOIN_ROUND )
   1050       error = ft_stroker_arcto( stroker, side );
   1051     else
   1052     {
   1053       /* this is a mitered (pointed) or beveled (truncated) corner */
   1054       FT_Fixed  sigma = 0, radius = stroker->radius;
   1055       FT_Angle  theta = 0, phi = 0;
   1056       FT_Fixed  thcos = 0;
   1057       FT_Bool   bevel, fixed_bevel;
   1058 
   1059 
   1060       rotate = FT_SIDE_TO_ROTATE( side );
   1061 
   1062       bevel =
   1063         FT_BOOL( stroker->line_join == FT_STROKER_LINEJOIN_BEVEL );
   1064 
   1065       fixed_bevel =
   1066         FT_BOOL( stroker->line_join != FT_STROKER_LINEJOIN_MITER_VARIABLE );
   1067 
   1068       if ( !bevel )
   1069       {
   1070         theta = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
   1071 
   1072         if ( theta == FT_ANGLE_PI )
   1073         {
   1074           theta = rotate;
   1075           phi   = stroker->angle_in;
   1076         }
   1077         else
   1078         {
   1079           theta /= 2;
   1080           phi    = stroker->angle_in + theta + rotate;
   1081         }
   1082 
   1083         thcos = FT_Cos( theta );
   1084         sigma = FT_MulFix( stroker->miter_limit, thcos );
   1085 
   1086         /* is miter limit exceeded? */
   1087         if ( sigma < 0x10000L )
   1088         {
   1089           /* don't create variable bevels for very small deviations; */
   1090           /* FT_Sin(x) = 0 for x <= 57                               */
   1091           if ( fixed_bevel || ft_pos_abs( theta ) > 57 )
   1092             bevel = TRUE;
   1093         }
   1094       }
   1095 
   1096       if ( bevel )  /* this is a bevel (broken angle) */
   1097       {
   1098         if ( fixed_bevel )
   1099         {
   1100           /* the outer corners are simply joined together */
   1101           FT_Vector  delta;
   1102 
   1103 
   1104           /* add bevel */
   1105           FT_Vector_From_Polar( &delta,
   1106                                 radius,
   1107                                 stroker->angle_out + rotate );
   1108           delta.x += stroker->center.x;
   1109           delta.y += stroker->center.y;
   1110 
   1111           border->movable = FALSE;
   1112           error = ft_stroke_border_lineto( border, &delta, FALSE );
   1113         }
   1114         else /* variable bevel */
   1115         {
   1116           /* the miter is truncated */
   1117           FT_Vector  middle, delta;
   1118           FT_Fixed   length;
   1119 
   1120 
   1121           /* compute middle point */
   1122           FT_Vector_From_Polar( &middle,
   1123                                 FT_MulFix( radius, stroker->miter_limit ),
   1124                                 phi );
   1125           middle.x += stroker->center.x;
   1126           middle.y += stroker->center.y;
   1127 
   1128           /* compute first angle point */
   1129           length = FT_MulDiv( radius, 0x10000L - sigma,
   1130                               ft_pos_abs( FT_Sin( theta ) ) );
   1131 
   1132           FT_Vector_From_Polar( &delta, length, phi + rotate );
   1133           delta.x += middle.x;
   1134           delta.y += middle.y;
   1135 
   1136           error = ft_stroke_border_lineto( border, &delta, FALSE );
   1137           if ( error )
   1138             goto Exit;
   1139 
   1140           /* compute second angle point */
   1141           FT_Vector_From_Polar( &delta, length, phi - rotate );
   1142           delta.x += middle.x;
   1143           delta.y += middle.y;
   1144 
   1145           error = ft_stroke_border_lineto( border, &delta, FALSE );
   1146           if ( error )
   1147             goto Exit;
   1148 
   1149           /* finally, add an end point; only needed if not lineto */
   1150           /* (line_length is zero for curves)                     */
   1151           if ( line_length == 0 )
   1152           {
   1153             FT_Vector_From_Polar( &delta,
   1154                                   radius,
   1155                                   stroker->angle_out + rotate );
   1156 
   1157             delta.x += stroker->center.x;
   1158             delta.y += stroker->center.y;
   1159 
   1160             error = ft_stroke_border_lineto( border, &delta, FALSE );
   1161           }
   1162         }
   1163       }
   1164       else /* this is a miter (intersection) */
   1165       {
   1166         FT_Fixed   length;
   1167         FT_Vector  delta;
   1168 
   1169 
   1170         length = FT_DivFix( stroker->radius, thcos );
   1171 
   1172         FT_Vector_From_Polar( &delta, length, phi );
   1173         delta.x += stroker->center.x;
   1174         delta.y += stroker->center.y;
   1175 
   1176         error = ft_stroke_border_lineto( border, &delta, FALSE );
   1177         if ( error )
   1178           goto Exit;
   1179 
   1180         /* now add an end point; only needed if not lineto */
   1181         /* (line_length is zero for curves)                */
   1182         if ( line_length == 0 )
   1183         {
   1184           FT_Vector_From_Polar( &delta,
   1185                                 stroker->radius,
   1186                                 stroker->angle_out + rotate );
   1187           delta.x += stroker->center.x;
   1188           delta.y += stroker->center.y;
   1189 
   1190           error = ft_stroke_border_lineto( border, &delta, FALSE );
   1191         }
   1192       }
   1193     }
   1194 
   1195   Exit:
   1196     return error;
   1197   }
   1198 
   1199 
   1200   static FT_Error
   1201   ft_stroker_process_corner( FT_Stroker  stroker,
   1202                              FT_Fixed    line_length )
   1203   {
   1204     FT_Error  error = FT_Err_Ok;
   1205     FT_Angle  turn;
   1206     FT_Int    inside_side;
   1207 
   1208 
   1209     turn = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
   1210 
   1211     /* no specific corner processing is required if the turn is 0 */
   1212     if ( turn == 0 )
   1213       goto Exit;
   1214 
   1215     /* when we turn to the right, the inside side is 0 */
   1216     inside_side = 0;
   1217 
   1218     /* otherwise, the inside side is 1 */
   1219     if ( turn < 0 )
   1220       inside_side = 1;
   1221 
   1222     /* process the inside side */
   1223     error = ft_stroker_inside( stroker, inside_side, line_length );
   1224     if ( error )
   1225       goto Exit;
   1226 
   1227     /* process the outside side */
   1228     error = ft_stroker_outside( stroker, 1 - inside_side, line_length );
   1229 
   1230   Exit:
   1231     return error;
   1232   }
   1233 
   1234 
   1235   /* add two points to the left and right borders corresponding to the */
   1236   /* start of the subpath                                              */
   1237   static FT_Error
   1238   ft_stroker_subpath_start( FT_Stroker  stroker,
   1239                             FT_Angle    start_angle,
   1240                             FT_Fixed    line_length )
   1241   {
   1242     FT_Vector        delta;
   1243     FT_Vector        point;
   1244     FT_Error         error;
   1245     FT_StrokeBorder  border;
   1246 
   1247 
   1248     FT_Vector_From_Polar( &delta, stroker->radius,
   1249                           start_angle + FT_ANGLE_PI2 );
   1250 
   1251     point.x = stroker->center.x + delta.x;
   1252     point.y = stroker->center.y + delta.y;
   1253 
   1254     border = stroker->borders;
   1255     error = ft_stroke_border_moveto( border, &point );
   1256     if ( error )
   1257       goto Exit;
   1258 
   1259     point.x = stroker->center.x - delta.x;
   1260     point.y = stroker->center.y - delta.y;
   1261 
   1262     border++;
   1263     error = ft_stroke_border_moveto( border, &point );
   1264 
   1265     /* save angle, position, and line length for last join */
   1266     /* (line_length is zero for curves)                    */
   1267     stroker->subpath_angle       = start_angle;
   1268     stroker->first_point         = FALSE;
   1269     stroker->subpath_line_length = line_length;
   1270 
   1271   Exit:
   1272     return error;
   1273   }
   1274 
   1275 
   1276   /* documentation is in ftstroke.h */
   1277 
   1278   FT_EXPORT_DEF( FT_Error )
   1279   FT_Stroker_LineTo( FT_Stroker  stroker,
   1280                      FT_Vector*  to )
   1281   {
   1282     FT_Error         error = FT_Err_Ok;
   1283     FT_StrokeBorder  border;
   1284     FT_Vector        delta;
   1285     FT_Angle         angle;
   1286     FT_Int           side;
   1287     FT_Fixed         line_length;
   1288 
   1289 
   1290     delta.x = to->x - stroker->center.x;
   1291     delta.y = to->y - stroker->center.y;
   1292 
   1293     /* a zero-length lineto is a no-op; avoid creating a spurious corner */
   1294     if ( delta.x == 0 && delta.y == 0 )
   1295        goto Exit;
   1296 
   1297     /* compute length of line */
   1298     line_length = FT_Vector_Length( &delta );
   1299 
   1300     angle = FT_Atan2( delta.x, delta.y );
   1301     FT_Vector_From_Polar( &delta, stroker->radius, angle + FT_ANGLE_PI2 );
   1302 
   1303     /* process corner if necessary */
   1304     if ( stroker->first_point )
   1305     {
   1306       /* This is the first segment of a subpath.  We need to     */
   1307       /* add a point to each border at their respective starting */
   1308       /* point locations.                                        */
   1309       error = ft_stroker_subpath_start( stroker, angle, line_length );
   1310       if ( error )
   1311         goto Exit;
   1312     }
   1313     else
   1314     {
   1315       /* process the current corner */
   1316       stroker->angle_out = angle;
   1317       error = ft_stroker_process_corner( stroker, line_length );
   1318       if ( error )
   1319         goto Exit;
   1320     }
   1321 
   1322     /* now add a line segment to both the `inside' and `outside' paths */
   1323     for ( border = stroker->borders, side = 1; side >= 0; side--, border++ )
   1324     {
   1325       FT_Vector  point;
   1326 
   1327 
   1328       point.x = to->x + delta.x;
   1329       point.y = to->y + delta.y;
   1330 
   1331       /* the ends of lineto borders are movable */
   1332       error = ft_stroke_border_lineto( border, &point, TRUE );
   1333       if ( error )
   1334         goto Exit;
   1335 
   1336       delta.x = -delta.x;
   1337       delta.y = -delta.y;
   1338     }
   1339 
   1340     stroker->angle_in    = angle;
   1341     stroker->center      = *to;
   1342     stroker->line_length = line_length;
   1343 
   1344   Exit:
   1345     return error;
   1346   }
   1347 
   1348 
   1349   /* documentation is in ftstroke.h */
   1350 
   1351   FT_EXPORT_DEF( FT_Error )
   1352   FT_Stroker_ConicTo( FT_Stroker  stroker,
   1353                       FT_Vector*  control,
   1354                       FT_Vector*  to )
   1355   {
   1356     FT_Error    error = FT_Err_Ok;
   1357     FT_Vector   bez_stack[34];
   1358     FT_Vector*  arc;
   1359     FT_Vector*  limit = bez_stack + 30;
   1360     FT_Bool     first_arc = TRUE;
   1361 
   1362 
   1363     /* if all control points are coincident, this is a no-op; */
   1364     /* avoid creating a spurious corner                       */
   1365     if ( FT_IS_SMALL( stroker->center.x - control->x ) &&
   1366          FT_IS_SMALL( stroker->center.y - control->y ) &&
   1367          FT_IS_SMALL( control->x        - to->x      ) &&
   1368          FT_IS_SMALL( control->y        - to->y      ) )
   1369     {
   1370        stroker->center = *to;
   1371        goto Exit;
   1372     }
   1373 
   1374     arc    = bez_stack;
   1375     arc[0] = *to;
   1376     arc[1] = *control;
   1377     arc[2] = stroker->center;
   1378 
   1379     while ( arc >= bez_stack )
   1380     {
   1381       FT_Angle  angle_in, angle_out;
   1382 
   1383 
   1384       /* initialize with current direction */
   1385       angle_in = angle_out = stroker->angle_in;
   1386 
   1387       if ( arc < limit                                             &&
   1388            !ft_conic_is_small_enough( arc, &angle_in, &angle_out ) )
   1389       {
   1390         if ( stroker->first_point )
   1391           stroker->angle_in = angle_in;
   1392 
   1393         ft_conic_split( arc );
   1394         arc += 2;
   1395         continue;
   1396       }
   1397 
   1398       if ( first_arc )
   1399       {
   1400         first_arc = FALSE;
   1401 
   1402         /* process corner if necessary */
   1403         if ( stroker->first_point )
   1404           error = ft_stroker_subpath_start( stroker, angle_in, 0 );
   1405         else
   1406         {
   1407           stroker->angle_out = angle_in;
   1408           error = ft_stroker_process_corner( stroker, 0 );
   1409         }
   1410       }
   1411       else if ( ft_pos_abs( FT_Angle_Diff( stroker->angle_in, angle_in ) ) >
   1412                   FT_SMALL_CONIC_THRESHOLD / 4                             )
   1413       {
   1414         /* if the deviation from one arc to the next is too great, */
   1415         /* add a round corner                                      */
   1416         stroker->center    = arc[2];
   1417         stroker->angle_out = angle_in;
   1418         stroker->line_join = FT_STROKER_LINEJOIN_ROUND;
   1419 
   1420         error = ft_stroker_process_corner( stroker, 0 );
   1421 
   1422         /* reinstate line join style */
   1423         stroker->line_join = stroker->line_join_saved;
   1424       }
   1425 
   1426       if ( error )
   1427         goto Exit;
   1428 
   1429       /* the arc's angle is small enough; we can add it directly to each */
   1430       /* border                                                          */
   1431       {
   1432         FT_Vector        ctrl, end;
   1433         FT_Angle         theta, phi, rotate, alpha0 = 0;
   1434         FT_Fixed         length;
   1435         FT_StrokeBorder  border;
   1436         FT_Int           side;
   1437 
   1438 
   1439         theta  = FT_Angle_Diff( angle_in, angle_out ) / 2;
   1440         phi    = angle_in + theta;
   1441         length = FT_DivFix( stroker->radius, FT_Cos( theta ) );
   1442 
   1443         /* compute direction of original arc */
   1444         if ( stroker->handle_wide_strokes )
   1445           alpha0 = FT_Atan2( arc[0].x - arc[2].x, arc[0].y - arc[2].y );
   1446 
   1447         for ( border = stroker->borders, side = 0;
   1448               side <= 1;
   1449               side++, border++ )
   1450         {
   1451           rotate = FT_SIDE_TO_ROTATE( side );
   1452 
   1453           /* compute control point */
   1454           FT_Vector_From_Polar( &ctrl, length, phi + rotate );
   1455           ctrl.x += arc[1].x;
   1456           ctrl.y += arc[1].y;
   1457 
   1458           /* compute end point */
   1459           FT_Vector_From_Polar( &end, stroker->radius, angle_out + rotate );
   1460           end.x += arc[0].x;
   1461           end.y += arc[0].y;
   1462 
   1463           if ( stroker->handle_wide_strokes )
   1464           {
   1465             FT_Vector  start;
   1466             FT_Angle   alpha1;
   1467 
   1468 
   1469             /* determine whether the border radius is greater than the */
   1470             /* radius of curvature of the original arc                 */
   1471             start = border->points[border->num_points - 1];
   1472 
   1473             alpha1 = FT_Atan2( end.x - start.x, end.y - start.y );
   1474 
   1475             /* is the direction of the border arc opposite to */
   1476             /* that of the original arc? */
   1477             if ( ft_pos_abs( FT_Angle_Diff( alpha0, alpha1 ) ) >
   1478                    FT_ANGLE_PI / 2                             )
   1479             {
   1480               FT_Angle   beta, gamma;
   1481               FT_Vector  bvec, delta;
   1482               FT_Fixed   blen, sinA, sinB, alen;
   1483 
   1484 
   1485               /* use the sine rule to find the intersection point */
   1486               beta  = FT_Atan2( arc[2].x - start.x, arc[2].y - start.y );
   1487               gamma = FT_Atan2( arc[0].x - end.x,   arc[0].y - end.y );
   1488 
   1489               bvec.x = end.x - start.x;
   1490               bvec.y = end.y - start.y;
   1491 
   1492               blen = FT_Vector_Length( &bvec );
   1493 
   1494               sinA = ft_pos_abs( FT_Sin( alpha1 - gamma ) );
   1495               sinB = ft_pos_abs( FT_Sin( beta - gamma ) );
   1496 
   1497               alen = FT_MulDiv( blen, sinA, sinB );
   1498 
   1499               FT_Vector_From_Polar( &delta, alen, beta );
   1500               delta.x += start.x;
   1501               delta.y += start.y;
   1502 
   1503               /* circumnavigate the negative sector backwards */
   1504               border->movable = FALSE;
   1505               error = ft_stroke_border_lineto( border, &delta, FALSE );
   1506               if ( error )
   1507                 goto Exit;
   1508               error = ft_stroke_border_lineto( border, &end, FALSE );
   1509               if ( error )
   1510                 goto Exit;
   1511               error = ft_stroke_border_conicto( border, &ctrl, &start );
   1512               if ( error )
   1513                 goto Exit;
   1514               /* and then move to the endpoint */
   1515               error = ft_stroke_border_lineto( border, &end, FALSE );
   1516               if ( error )
   1517                 goto Exit;
   1518 
   1519               continue;
   1520             }
   1521 
   1522             /* else fall through */
   1523           }
   1524 
   1525           /* simply add an arc */
   1526           error = ft_stroke_border_conicto( border, &ctrl, &end );
   1527           if ( error )
   1528             goto Exit;
   1529         }
   1530       }
   1531 
   1532       arc -= 2;
   1533 
   1534       stroker->angle_in = angle_out;
   1535     }
   1536 
   1537     stroker->center = *to;
   1538 
   1539   Exit:
   1540     return error;
   1541   }
   1542 
   1543 
   1544   /* documentation is in ftstroke.h */
   1545 
   1546   FT_EXPORT_DEF( FT_Error )
   1547   FT_Stroker_CubicTo( FT_Stroker  stroker,
   1548                       FT_Vector*  control1,
   1549                       FT_Vector*  control2,
   1550                       FT_Vector*  to )
   1551   {
   1552     FT_Error    error = FT_Err_Ok;
   1553     FT_Vector   bez_stack[37];
   1554     FT_Vector*  arc;
   1555     FT_Vector*  limit = bez_stack + 32;
   1556     FT_Bool     first_arc = TRUE;
   1557 
   1558 
   1559     /* if all control points are coincident, this is a no-op; */
   1560     /* avoid creating a spurious corner */
   1561     if ( FT_IS_SMALL( stroker->center.x - control1->x ) &&
   1562          FT_IS_SMALL( stroker->center.y - control1->y ) &&
   1563          FT_IS_SMALL( control1->x       - control2->x ) &&
   1564          FT_IS_SMALL( control1->y       - control2->y ) &&
   1565          FT_IS_SMALL( control2->x       - to->x       ) &&
   1566          FT_IS_SMALL( control2->y       - to->y       ) )
   1567     {
   1568        stroker->center = *to;
   1569        goto Exit;
   1570     }
   1571 
   1572     arc    = bez_stack;
   1573     arc[0] = *to;
   1574     arc[1] = *control2;
   1575     arc[2] = *control1;
   1576     arc[3] = stroker->center;
   1577 
   1578     while ( arc >= bez_stack )
   1579     {
   1580       FT_Angle  angle_in, angle_mid, angle_out;
   1581 
   1582 
   1583       /* initialize with current direction */
   1584       angle_in = angle_out = angle_mid = stroker->angle_in;
   1585 
   1586       if ( arc < limit                                         &&
   1587            !ft_cubic_is_small_enough( arc, &angle_in,
   1588                                       &angle_mid, &angle_out ) )
   1589       {
   1590         if ( stroker->first_point )
   1591           stroker->angle_in = angle_in;
   1592 
   1593         ft_cubic_split( arc );
   1594         arc += 3;
   1595         continue;
   1596       }
   1597 
   1598       if ( first_arc )
   1599       {
   1600         first_arc = FALSE;
   1601 
   1602         /* process corner if necessary */
   1603         if ( stroker->first_point )
   1604           error = ft_stroker_subpath_start( stroker, angle_in, 0 );
   1605         else
   1606         {
   1607           stroker->angle_out = angle_in;
   1608           error = ft_stroker_process_corner( stroker, 0 );
   1609         }
   1610       }
   1611       else if ( ft_pos_abs( FT_Angle_Diff( stroker->angle_in, angle_in ) ) >
   1612                   FT_SMALL_CUBIC_THRESHOLD / 4                             )
   1613       {
   1614         /* if the deviation from one arc to the next is too great, */
   1615         /* add a round corner                                      */
   1616         stroker->center    = arc[3];
   1617         stroker->angle_out = angle_in;
   1618         stroker->line_join = FT_STROKER_LINEJOIN_ROUND;
   1619 
   1620         error = ft_stroker_process_corner( stroker, 0 );
   1621 
   1622         /* reinstate line join style */
   1623         stroker->line_join = stroker->line_join_saved;
   1624       }
   1625 
   1626       if ( error )
   1627         goto Exit;
   1628 
   1629       /* the arc's angle is small enough; we can add it directly to each */
   1630       /* border                                                          */
   1631       {
   1632         FT_Vector        ctrl1, ctrl2, end;
   1633         FT_Angle         theta1, phi1, theta2, phi2, rotate, alpha0 = 0;
   1634         FT_Fixed         length1, length2;
   1635         FT_StrokeBorder  border;
   1636         FT_Int           side;
   1637 
   1638 
   1639         theta1  = FT_Angle_Diff( angle_in,  angle_mid ) / 2;
   1640         theta2  = FT_Angle_Diff( angle_mid, angle_out ) / 2;
   1641         phi1    = ft_angle_mean( angle_in,  angle_mid );
   1642         phi2    = ft_angle_mean( angle_mid, angle_out );
   1643         length1 = FT_DivFix( stroker->radius, FT_Cos( theta1 ) );
   1644         length2 = FT_DivFix( stroker->radius, FT_Cos( theta2 ) );
   1645 
   1646         /* compute direction of original arc */
   1647         if ( stroker->handle_wide_strokes )
   1648           alpha0 = FT_Atan2( arc[0].x - arc[3].x, arc[0].y - arc[3].y );
   1649 
   1650         for ( border = stroker->borders, side = 0;
   1651               side <= 1;
   1652               side++, border++ )
   1653         {
   1654           rotate = FT_SIDE_TO_ROTATE( side );
   1655 
   1656           /* compute control points */
   1657           FT_Vector_From_Polar( &ctrl1, length1, phi1 + rotate );
   1658           ctrl1.x += arc[2].x;
   1659           ctrl1.y += arc[2].y;
   1660 
   1661           FT_Vector_From_Polar( &ctrl2, length2, phi2 + rotate );
   1662           ctrl2.x += arc[1].x;
   1663           ctrl2.y += arc[1].y;
   1664 
   1665           /* compute end point */
   1666           FT_Vector_From_Polar( &end, stroker->radius, angle_out + rotate );
   1667           end.x += arc[0].x;
   1668           end.y += arc[0].y;
   1669 
   1670           if ( stroker->handle_wide_strokes )
   1671           {
   1672             FT_Vector  start;
   1673             FT_Angle   alpha1;
   1674 
   1675 
   1676             /* determine whether the border radius is greater than the */
   1677             /* radius of curvature of the original arc                 */
   1678             start = border->points[border->num_points - 1];
   1679 
   1680             alpha1 = FT_Atan2( end.x - start.x, end.y - start.y );
   1681 
   1682             /* is the direction of the border arc opposite to */
   1683             /* that of the original arc? */
   1684             if ( ft_pos_abs( FT_Angle_Diff( alpha0, alpha1 ) ) >
   1685                    FT_ANGLE_PI / 2                             )
   1686             {
   1687               FT_Angle   beta, gamma;
   1688               FT_Vector  bvec, delta;
   1689               FT_Fixed   blen, sinA, sinB, alen;
   1690 
   1691 
   1692               /* use the sine rule to find the intersection point */
   1693               beta  = FT_Atan2( arc[3].x - start.x, arc[3].y - start.y );
   1694               gamma = FT_Atan2( arc[0].x - end.x,   arc[0].y - end.y );
   1695 
   1696               bvec.x = end.x - start.x;
   1697               bvec.y = end.y - start.y;
   1698 
   1699               blen = FT_Vector_Length( &bvec );
   1700 
   1701               sinA = ft_pos_abs( FT_Sin( alpha1 - gamma ) );
   1702               sinB = ft_pos_abs( FT_Sin( beta - gamma ) );
   1703 
   1704               alen = FT_MulDiv( blen, sinA, sinB );
   1705 
   1706               FT_Vector_From_Polar( &delta, alen, beta );
   1707               delta.x += start.x;
   1708               delta.y += start.y;
   1709 
   1710               /* circumnavigate the negative sector backwards */
   1711               border->movable = FALSE;
   1712               error = ft_stroke_border_lineto( border, &delta, FALSE );
   1713               if ( error )
   1714                 goto Exit;
   1715               error = ft_stroke_border_lineto( border, &end, FALSE );
   1716               if ( error )
   1717                 goto Exit;
   1718               error = ft_stroke_border_cubicto( border,
   1719                                                 &ctrl2,
   1720                                                 &ctrl1,
   1721                                                 &start );
   1722               if ( error )
   1723                 goto Exit;
   1724               /* and then move to the endpoint */
   1725               error = ft_stroke_border_lineto( border, &end, FALSE );
   1726               if ( error )
   1727                 goto Exit;
   1728 
   1729               continue;
   1730             }
   1731 
   1732             /* else fall through */
   1733           }
   1734 
   1735           /* simply add an arc */
   1736           error = ft_stroke_border_cubicto( border, &ctrl1, &ctrl2, &end );
   1737           if ( error )
   1738             goto Exit;
   1739         }
   1740       }
   1741 
   1742       arc -= 3;
   1743 
   1744       stroker->angle_in = angle_out;
   1745     }
   1746 
   1747     stroker->center = *to;
   1748 
   1749   Exit:
   1750     return error;
   1751   }
   1752 
   1753 
   1754   /* documentation is in ftstroke.h */
   1755 
   1756   FT_EXPORT_DEF( FT_Error )
   1757   FT_Stroker_BeginSubPath( FT_Stroker  stroker,
   1758                            FT_Vector*  to,
   1759                            FT_Bool     open )
   1760   {
   1761     /* We cannot process the first point, because there is not enough      */
   1762     /* information regarding its corner/cap.  The latter will be processed */
   1763     /* in the `FT_Stroker_EndSubPath' routine.                             */
   1764     /*                                                                     */
   1765     stroker->first_point  = TRUE;
   1766     stroker->center       = *to;
   1767     stroker->subpath_open = open;
   1768 
   1769     /* Determine if we need to check whether the border radius is greater */
   1770     /* than the radius of curvature of a curve, to handle this case       */
   1771     /* specially.  This is only required if bevel joins or butt caps may  */
   1772     /* be created, because round & miter joins and round & square caps    */
   1773     /* cover the negative sector created with wide strokes.               */
   1774     stroker->handle_wide_strokes =
   1775       FT_BOOL( stroker->line_join != FT_STROKER_LINEJOIN_ROUND  ||
   1776                ( stroker->subpath_open                        &&
   1777                  stroker->line_cap == FT_STROKER_LINECAP_BUTT ) );
   1778 
   1779     /* record the subpath start point for each border */
   1780     stroker->subpath_start = *to;
   1781 
   1782     stroker->angle_in = 0;
   1783 
   1784     return FT_Err_Ok;
   1785   }
   1786 
   1787 
   1788   static FT_Error
   1789   ft_stroker_add_reverse_left( FT_Stroker  stroker,
   1790                                FT_Bool     open )
   1791   {
   1792     FT_StrokeBorder  right = stroker->borders + 0;
   1793     FT_StrokeBorder  left  = stroker->borders + 1;
   1794     FT_Int           new_points;
   1795     FT_Error         error = FT_Err_Ok;
   1796 
   1797 
   1798     FT_ASSERT( left->start >= 0 );
   1799 
   1800     new_points = left->num_points - left->start;
   1801     if ( new_points > 0 )
   1802     {
   1803       error = ft_stroke_border_grow( right, (FT_UInt)new_points );
   1804       if ( error )
   1805         goto Exit;
   1806 
   1807       {
   1808         FT_Vector*  dst_point = right->points + right->num_points;
   1809         FT_Byte*    dst_tag   = right->tags   + right->num_points;
   1810         FT_Vector*  src_point = left->points  + left->num_points - 1;
   1811         FT_Byte*    src_tag   = left->tags    + left->num_points - 1;
   1812 
   1813 
   1814         while ( src_point >= left->points + left->start )
   1815         {
   1816           *dst_point = *src_point;
   1817           *dst_tag   = *src_tag;
   1818 
   1819           if ( open )
   1820             dst_tag[0] &= ~FT_STROKE_TAG_BEGIN_END;
   1821           else
   1822           {
   1823             FT_Byte  ttag =
   1824                        (FT_Byte)( dst_tag[0] & FT_STROKE_TAG_BEGIN_END );
   1825 
   1826 
   1827             /* switch begin/end tags if necessary */
   1828             if ( ttag == FT_STROKE_TAG_BEGIN ||
   1829                  ttag == FT_STROKE_TAG_END   )
   1830               dst_tag[0] ^= FT_STROKE_TAG_BEGIN_END;
   1831           }
   1832 
   1833           src_point--;
   1834           src_tag--;
   1835           dst_point++;
   1836           dst_tag++;
   1837         }
   1838       }
   1839 
   1840       left->num_points   = left->start;
   1841       right->num_points += new_points;
   1842 
   1843       right->movable = FALSE;
   1844       left->movable  = FALSE;
   1845     }
   1846 
   1847   Exit:
   1848     return error;
   1849   }
   1850 
   1851 
   1852   /* documentation is in ftstroke.h */
   1853 
   1854   /* there's a lot of magic in this function! */
   1855   FT_EXPORT_DEF( FT_Error )
   1856   FT_Stroker_EndSubPath( FT_Stroker  stroker )
   1857   {
   1858     FT_Error  error = FT_Err_Ok;
   1859 
   1860 
   1861     if ( stroker->subpath_open )
   1862     {
   1863       FT_StrokeBorder  right = stroker->borders;
   1864 
   1865 
   1866       /* All right, this is an opened path, we need to add a cap between */
   1867       /* right & left, add the reverse of left, then add a final cap     */
   1868       /* between left & right.                                           */
   1869       error = ft_stroker_cap( stroker, stroker->angle_in, 0 );
   1870       if ( error )
   1871         goto Exit;
   1872 
   1873       /* add reversed points from `left' to `right' */
   1874       error = ft_stroker_add_reverse_left( stroker, TRUE );
   1875       if ( error )
   1876         goto Exit;
   1877 
   1878       /* now add the final cap */
   1879       stroker->center = stroker->subpath_start;
   1880       error = ft_stroker_cap( stroker,
   1881                               stroker->subpath_angle + FT_ANGLE_PI, 0 );
   1882       if ( error )
   1883         goto Exit;
   1884 
   1885       /* Now end the right subpath accordingly.  The left one is */
   1886       /* rewind and doesn't need further processing.             */
   1887       ft_stroke_border_close( right, FALSE );
   1888     }
   1889     else
   1890     {
   1891       FT_Angle  turn;
   1892       FT_Int    inside_side;
   1893 
   1894 
   1895       /* close the path if needed */
   1896       if ( stroker->center.x != stroker->subpath_start.x ||
   1897            stroker->center.y != stroker->subpath_start.y )
   1898       {
   1899          error = FT_Stroker_LineTo( stroker, &stroker->subpath_start );
   1900          if ( error )
   1901            goto Exit;
   1902       }
   1903 
   1904       /* process the corner */
   1905       stroker->angle_out = stroker->subpath_angle;
   1906       turn               = FT_Angle_Diff( stroker->angle_in,
   1907                                           stroker->angle_out );
   1908 
   1909       /* no specific corner processing is required if the turn is 0 */
   1910       if ( turn != 0 )
   1911       {
   1912         /* when we turn to the right, the inside side is 0 */
   1913         inside_side = 0;
   1914 
   1915         /* otherwise, the inside side is 1 */
   1916         if ( turn < 0 )
   1917           inside_side = 1;
   1918 
   1919         error = ft_stroker_inside( stroker,
   1920                                    inside_side,
   1921                                    stroker->subpath_line_length );
   1922         if ( error )
   1923           goto Exit;
   1924 
   1925         /* process the outside side */
   1926         error = ft_stroker_outside( stroker,
   1927                                     1 - inside_side,
   1928                                     stroker->subpath_line_length );
   1929         if ( error )
   1930           goto Exit;
   1931       }
   1932 
   1933       /* then end our two subpaths */
   1934       ft_stroke_border_close( stroker->borders + 0, FALSE );
   1935       ft_stroke_border_close( stroker->borders + 1, TRUE );
   1936     }
   1937 
   1938   Exit:
   1939     return error;
   1940   }
   1941 
   1942 
   1943   /* documentation is in ftstroke.h */
   1944 
   1945   FT_EXPORT_DEF( FT_Error )
   1946   FT_Stroker_GetBorderCounts( FT_Stroker        stroker,
   1947                               FT_StrokerBorder  border,
   1948                               FT_UInt          *anum_points,
   1949                               FT_UInt          *anum_contours )
   1950   {
   1951     FT_UInt   num_points = 0, num_contours = 0;
   1952     FT_Error  error;
   1953 
   1954 
   1955     if ( !stroker || border > 1 )
   1956     {
   1957       error = FT_THROW( Invalid_Argument );
   1958       goto Exit;
   1959     }
   1960 
   1961     error = ft_stroke_border_get_counts( stroker->borders + border,
   1962                                          &num_points, &num_contours );
   1963   Exit:
   1964     if ( anum_points )
   1965       *anum_points = num_points;
   1966 
   1967     if ( anum_contours )
   1968       *anum_contours = num_contours;
   1969 
   1970     return error;
   1971   }
   1972 
   1973 
   1974   /* documentation is in ftstroke.h */
   1975 
   1976   FT_EXPORT_DEF( FT_Error )
   1977   FT_Stroker_GetCounts( FT_Stroker  stroker,
   1978                         FT_UInt    *anum_points,
   1979                         FT_UInt    *anum_contours )
   1980   {
   1981     FT_UInt   count1, count2, num_points   = 0;
   1982     FT_UInt   count3, count4, num_contours = 0;
   1983     FT_Error  error;
   1984 
   1985 
   1986     error = ft_stroke_border_get_counts( stroker->borders + 0,
   1987                                          &count1, &count2 );
   1988     if ( error )
   1989       goto Exit;
   1990 
   1991     error = ft_stroke_border_get_counts( stroker->borders + 1,
   1992                                          &count3, &count4 );
   1993     if ( error )
   1994       goto Exit;
   1995 
   1996     num_points   = count1 + count3;
   1997     num_contours = count2 + count4;
   1998 
   1999   Exit:
   2000     *anum_points   = num_points;
   2001     *anum_contours = num_contours;
   2002     return error;
   2003   }
   2004 
   2005 
   2006   /* documentation is in ftstroke.h */
   2007 
   2008   FT_EXPORT_DEF( void )
   2009   FT_Stroker_ExportBorder( FT_Stroker        stroker,
   2010                            FT_StrokerBorder  border,
   2011                            FT_Outline*       outline )
   2012   {
   2013     if ( border == FT_STROKER_BORDER_LEFT  ||
   2014          border == FT_STROKER_BORDER_RIGHT )
   2015     {
   2016       FT_StrokeBorder  sborder = & stroker->borders[border];
   2017 
   2018 
   2019       if ( sborder->valid )
   2020         ft_stroke_border_export( sborder, outline );
   2021     }
   2022   }
   2023 
   2024 
   2025   /* documentation is in ftstroke.h */
   2026 
   2027   FT_EXPORT_DEF( void )
   2028   FT_Stroker_Export( FT_Stroker   stroker,
   2029                      FT_Outline*  outline )
   2030   {
   2031     FT_Stroker_ExportBorder( stroker, FT_STROKER_BORDER_LEFT, outline );
   2032     FT_Stroker_ExportBorder( stroker, FT_STROKER_BORDER_RIGHT, outline );
   2033   }
   2034 
   2035 
   2036   /* documentation is in ftstroke.h */
   2037 
   2038   /*
   2039    *  The following is very similar to FT_Outline_Decompose, except
   2040    *  that we do support opened paths, and do not scale the outline.
   2041    */
   2042   FT_EXPORT_DEF( FT_Error )
   2043   FT_Stroker_ParseOutline( FT_Stroker   stroker,
   2044                            FT_Outline*  outline,
   2045                            FT_Bool      opened )
   2046   {
   2047     FT_Vector   v_last;
   2048     FT_Vector   v_control;
   2049     FT_Vector   v_start;
   2050 
   2051     FT_Vector*  point;
   2052     FT_Vector*  limit;
   2053     char*       tags;
   2054 
   2055     FT_Error    error;
   2056 
   2057     FT_Int      n;         /* index of contour in outline     */
   2058     FT_UInt     first;     /* index of first point in contour */
   2059     FT_Int      tag;       /* current point's state           */
   2060 
   2061 
   2062     if ( !outline || !stroker )
   2063       return FT_THROW( Invalid_Argument );
   2064 
   2065     FT_Stroker_Rewind( stroker );
   2066 
   2067     first = 0;
   2068 
   2069     for ( n = 0; n < outline->n_contours; n++ )
   2070     {
   2071       FT_UInt  last;  /* index of last point in contour */
   2072 
   2073 
   2074       last  = outline->contours[n];
   2075       limit = outline->points + last;
   2076 
   2077       /* skip empty points; we don't stroke these */
   2078       if ( last <= first )
   2079       {
   2080         first = last + 1;
   2081         continue;
   2082       }
   2083 
   2084       v_start = outline->points[first];
   2085       v_last  = outline->points[last];
   2086 
   2087       v_control = v_start;
   2088 
   2089       point = outline->points + first;
   2090       tags  = outline->tags   + first;
   2091       tag   = FT_CURVE_TAG( tags[0] );
   2092 
   2093       /* A contour cannot start with a cubic control point! */
   2094       if ( tag == FT_CURVE_TAG_CUBIC )
   2095         goto Invalid_Outline;
   2096 
   2097       /* check first point to determine origin */
   2098       if ( tag == FT_CURVE_TAG_CONIC )
   2099       {
   2100         /* First point is conic control.  Yes, this happens. */
   2101         if ( FT_CURVE_TAG( outline->tags[last] ) == FT_CURVE_TAG_ON )
   2102         {
   2103           /* start at last point if it is on the curve */
   2104           v_start = v_last;
   2105           limit--;
   2106         }
   2107         else
   2108         {
   2109           /* if both first and last points are conic, */
   2110           /* start at their middle                    */
   2111           v_start.x = ( v_start.x + v_last.x ) / 2;
   2112           v_start.y = ( v_start.y + v_last.y ) / 2;
   2113         }
   2114         point--;
   2115         tags--;
   2116       }
   2117 
   2118       error = FT_Stroker_BeginSubPath( stroker, &v_start, opened );
   2119       if ( error )
   2120         goto Exit;
   2121 
   2122       while ( point < limit )
   2123       {
   2124         point++;
   2125         tags++;
   2126 
   2127         tag = FT_CURVE_TAG( tags[0] );
   2128         switch ( tag )
   2129         {
   2130         case FT_CURVE_TAG_ON:  /* emit a single line_to */
   2131           {
   2132             FT_Vector  vec;
   2133 
   2134 
   2135             vec.x = point->x;
   2136             vec.y = point->y;
   2137 
   2138             error = FT_Stroker_LineTo( stroker, &vec );
   2139             if ( error )
   2140               goto Exit;
   2141             continue;
   2142           }
   2143 
   2144         case FT_CURVE_TAG_CONIC:  /* consume conic arcs */
   2145           v_control.x = point->x;
   2146           v_control.y = point->y;
   2147 
   2148         Do_Conic:
   2149           if ( point < limit )
   2150           {
   2151             FT_Vector  vec;
   2152             FT_Vector  v_middle;
   2153 
   2154 
   2155             point++;
   2156             tags++;
   2157             tag = FT_CURVE_TAG( tags[0] );
   2158 
   2159             vec = point[0];
   2160 
   2161             if ( tag == FT_CURVE_TAG_ON )
   2162             {
   2163               error = FT_Stroker_ConicTo( stroker, &v_control, &vec );
   2164               if ( error )
   2165                 goto Exit;
   2166               continue;
   2167             }
   2168 
   2169             if ( tag != FT_CURVE_TAG_CONIC )
   2170               goto Invalid_Outline;
   2171 
   2172             v_middle.x = ( v_control.x + vec.x ) / 2;
   2173             v_middle.y = ( v_control.y + vec.y ) / 2;
   2174 
   2175             error = FT_Stroker_ConicTo( stroker, &v_control, &v_middle );
   2176             if ( error )
   2177               goto Exit;
   2178 
   2179             v_control = vec;
   2180             goto Do_Conic;
   2181           }
   2182 
   2183           error = FT_Stroker_ConicTo( stroker, &v_control, &v_start );
   2184           goto Close;
   2185 
   2186         default:  /* FT_CURVE_TAG_CUBIC */
   2187           {
   2188             FT_Vector  vec1, vec2;
   2189 
   2190 
   2191             if ( point + 1 > limit                             ||
   2192                  FT_CURVE_TAG( tags[1] ) != FT_CURVE_TAG_CUBIC )
   2193               goto Invalid_Outline;
   2194 
   2195             point += 2;
   2196             tags  += 2;
   2197 
   2198             vec1 = point[-2];
   2199             vec2 = point[-1];
   2200 
   2201             if ( point <= limit )
   2202             {
   2203               FT_Vector  vec;
   2204 
   2205 
   2206               vec = point[0];
   2207 
   2208               error = FT_Stroker_CubicTo( stroker, &vec1, &vec2, &vec );
   2209               if ( error )
   2210                 goto Exit;
   2211               continue;
   2212             }
   2213 
   2214             error = FT_Stroker_CubicTo( stroker, &vec1, &vec2, &v_start );
   2215             goto Close;
   2216           }
   2217         }
   2218       }
   2219 
   2220     Close:
   2221       if ( error )
   2222         goto Exit;
   2223 
   2224       /* don't try to end the path if no segments have been generated */
   2225       if ( !stroker->first_point )
   2226       {
   2227         error = FT_Stroker_EndSubPath( stroker );
   2228         if ( error )
   2229           goto Exit;
   2230       }
   2231 
   2232       first = last + 1;
   2233     }
   2234 
   2235     return FT_Err_Ok;
   2236 
   2237   Exit:
   2238     return error;
   2239 
   2240   Invalid_Outline:
   2241     return FT_THROW( Invalid_Outline );
   2242   }
   2243 
   2244 
   2245   /* declare an extern to access `ft_outline_glyph_class' globally     */
   2246   /* allocated  in `ftglyph.c', and use the FT_OUTLINE_GLYPH_CLASS_GET */
   2247   /* macro to access it when FT_CONFIG_OPTION_PIC is defined           */
   2248 #ifndef FT_CONFIG_OPTION_PIC
   2249   extern const FT_Glyph_Class  ft_outline_glyph_class;
   2250 #endif
   2251 #include "basepic.h"
   2252 
   2253 
   2254   /* documentation is in ftstroke.h */
   2255 
   2256   FT_EXPORT_DEF( FT_Error )
   2257   FT_Glyph_Stroke( FT_Glyph    *pglyph,
   2258                    FT_Stroker   stroker,
   2259                    FT_Bool      destroy )
   2260   {
   2261     FT_Error    error   = FT_ERR( Invalid_Argument );
   2262     FT_Glyph    glyph   = NULL;
   2263     FT_Library  library = stroker->library;
   2264 
   2265     FT_UNUSED( library );
   2266 
   2267 
   2268     if ( pglyph == NULL )
   2269       goto Exit;
   2270 
   2271     glyph = *pglyph;
   2272     if ( glyph == NULL || glyph->clazz != FT_OUTLINE_GLYPH_CLASS_GET )
   2273       goto Exit;
   2274 
   2275     {
   2276       FT_Glyph  copy;
   2277 
   2278 
   2279       error = FT_Glyph_Copy( glyph, &copy );
   2280       if ( error )
   2281         goto Exit;
   2282 
   2283       glyph = copy;
   2284     }
   2285 
   2286     {
   2287       FT_OutlineGlyph  oglyph  = (FT_OutlineGlyph)glyph;
   2288       FT_Outline*      outline = &oglyph->outline;
   2289       FT_UInt          num_points, num_contours;
   2290 
   2291 
   2292       error = FT_Stroker_ParseOutline( stroker, outline, FALSE );
   2293       if ( error )
   2294         goto Fail;
   2295 
   2296       (void)FT_Stroker_GetCounts( stroker, &num_points, &num_contours );
   2297 
   2298       FT_Outline_Done( glyph->library, outline );
   2299 
   2300       error = FT_Outline_New( glyph->library,
   2301                               num_points, num_contours, outline );
   2302       if ( error )
   2303         goto Fail;
   2304 
   2305       outline->n_points   = 0;
   2306       outline->n_contours = 0;
   2307 
   2308       FT_Stroker_Export( stroker, outline );
   2309     }
   2310 
   2311     if ( destroy )
   2312       FT_Done_Glyph( *pglyph );
   2313 
   2314     *pglyph = glyph;
   2315     goto Exit;
   2316 
   2317   Fail:
   2318     FT_Done_Glyph( glyph );
   2319     glyph = NULL;
   2320 
   2321     if ( !destroy )
   2322       *pglyph = NULL;
   2323 
   2324   Exit:
   2325     return error;
   2326   }
   2327 
   2328 
   2329   /* documentation is in ftstroke.h */
   2330 
   2331   FT_EXPORT_DEF( FT_Error )
   2332   FT_Glyph_StrokeBorder( FT_Glyph    *pglyph,
   2333                          FT_Stroker   stroker,
   2334                          FT_Bool      inside,
   2335                          FT_Bool      destroy )
   2336   {
   2337     FT_Error    error   = FT_ERR( Invalid_Argument );
   2338     FT_Glyph    glyph   = NULL;
   2339     FT_Library  library = stroker->library;
   2340 
   2341     FT_UNUSED( library );
   2342 
   2343 
   2344     if ( pglyph == NULL )
   2345       goto Exit;
   2346 
   2347     glyph = *pglyph;
   2348     if ( glyph == NULL || glyph->clazz != FT_OUTLINE_GLYPH_CLASS_GET )
   2349       goto Exit;
   2350 
   2351     {
   2352       FT_Glyph  copy;
   2353 
   2354 
   2355       error = FT_Glyph_Copy( glyph, &copy );
   2356       if ( error )
   2357         goto Exit;
   2358 
   2359       glyph = copy;
   2360     }
   2361 
   2362     {
   2363       FT_OutlineGlyph   oglyph  = (FT_OutlineGlyph)glyph;
   2364       FT_StrokerBorder  border;
   2365       FT_Outline*       outline = &oglyph->outline;
   2366       FT_UInt           num_points, num_contours;
   2367 
   2368 
   2369       border = FT_Outline_GetOutsideBorder( outline );
   2370       if ( inside )
   2371       {
   2372         if ( border == FT_STROKER_BORDER_LEFT )
   2373           border = FT_STROKER_BORDER_RIGHT;
   2374         else
   2375           border = FT_STROKER_BORDER_LEFT;
   2376       }
   2377 
   2378       error = FT_Stroker_ParseOutline( stroker, outline, FALSE );
   2379       if ( error )
   2380         goto Fail;
   2381 
   2382       (void)FT_Stroker_GetBorderCounts( stroker, border,
   2383                                         &num_points, &num_contours );
   2384 
   2385       FT_Outline_Done( glyph->library, outline );
   2386 
   2387       error = FT_Outline_New( glyph->library,
   2388                               num_points,
   2389                               num_contours,
   2390                               outline );
   2391       if ( error )
   2392         goto Fail;
   2393 
   2394       outline->n_points   = 0;
   2395       outline->n_contours = 0;
   2396 
   2397       FT_Stroker_ExportBorder( stroker, border, outline );
   2398     }
   2399 
   2400     if ( destroy )
   2401       FT_Done_Glyph( *pglyph );
   2402 
   2403     *pglyph = glyph;
   2404     goto Exit;
   2405 
   2406   Fail:
   2407     FT_Done_Glyph( glyph );
   2408     glyph = NULL;
   2409 
   2410     if ( !destroy )
   2411       *pglyph = NULL;
   2412 
   2413   Exit:
   2414     return error;
   2415   }
   2416 
   2417 
   2418 /* END */
   2419