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      1 /***************************************************************************/
      2 /*                                                                         */
      3 /*  ftstroke.c                                                             */
      4 /*                                                                         */
      5 /*    FreeType path stroker (body).                                        */
      6 /*                                                                         */
      7 /*  Copyright 2002-2006, 2008-2011 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;
    793     FT_Memory   memory;
    794     FT_Stroker  stroker = NULL;
    795 
    796 
    797     if ( !library )
    798       return FT_Err_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_MulFix( radius,
   1130                               FT_DivFix( 0x10000L - sigma,
   1131                                          ft_pos_abs( FT_Sin( theta ) ) ) );
   1132 
   1133           FT_Vector_From_Polar( &delta, length, phi + rotate );
   1134           delta.x += middle.x;
   1135           delta.y += middle.y;
   1136 
   1137           error = ft_stroke_border_lineto( border, &delta, FALSE );
   1138           if ( error )
   1139             goto Exit;
   1140 
   1141           /* compute second angle point */
   1142           FT_Vector_From_Polar( &delta, length, phi - rotate );
   1143           delta.x += middle.x;
   1144           delta.y += middle.y;
   1145 
   1146           error = ft_stroke_border_lineto( border, &delta, FALSE );
   1147           if ( error )
   1148             goto Exit;
   1149 
   1150           /* finally, add an end point; only needed if not lineto */
   1151           /* (line_length is zero for curves)                     */
   1152           if ( line_length == 0 )
   1153           {
   1154             FT_Vector_From_Polar( &delta,
   1155                                   radius,
   1156                                   stroker->angle_out + rotate );
   1157 
   1158             delta.x += stroker->center.x;
   1159             delta.y += stroker->center.y;
   1160 
   1161             error = ft_stroke_border_lineto( border, &delta, FALSE );
   1162           }
   1163         }
   1164       }
   1165       else /* this is a miter (intersection) */
   1166       {
   1167         FT_Fixed   length;
   1168         FT_Vector  delta;
   1169 
   1170 
   1171         length = FT_DivFix( stroker->radius, thcos );
   1172 
   1173         FT_Vector_From_Polar( &delta, length, phi );
   1174         delta.x += stroker->center.x;
   1175         delta.y += stroker->center.y;
   1176 
   1177         error = ft_stroke_border_lineto( border, &delta, FALSE );
   1178         if ( error )
   1179           goto Exit;
   1180 
   1181         /* now add an end point; only needed if not lineto */
   1182         /* (line_length is zero for curves)                */
   1183         if ( line_length == 0 )
   1184         {
   1185           FT_Vector_From_Polar( &delta,
   1186                                 stroker->radius,
   1187                                 stroker->angle_out + rotate );
   1188           delta.x += stroker->center.x;
   1189           delta.y += stroker->center.y;
   1190 
   1191           error = ft_stroke_border_lineto( border, &delta, FALSE );
   1192         }
   1193       }
   1194     }
   1195 
   1196   Exit:
   1197     return error;
   1198   }
   1199 
   1200 
   1201   static FT_Error
   1202   ft_stroker_process_corner( FT_Stroker  stroker,
   1203                              FT_Fixed    line_length )
   1204   {
   1205     FT_Error  error = FT_Err_Ok;
   1206     FT_Angle  turn;
   1207     FT_Int    inside_side;
   1208 
   1209 
   1210     turn = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
   1211 
   1212     /* no specific corner processing is required if the turn is 0 */
   1213     if ( turn == 0 )
   1214       goto Exit;
   1215 
   1216     /* when we turn to the right, the inside side is 0 */
   1217     inside_side = 0;
   1218 
   1219     /* otherwise, the inside side is 1 */
   1220     if ( turn < 0 )
   1221       inside_side = 1;
   1222 
   1223     /* process the inside side */
   1224     error = ft_stroker_inside( stroker, inside_side, line_length );
   1225     if ( error )
   1226       goto Exit;
   1227 
   1228     /* process the outside side */
   1229     error = ft_stroker_outside( stroker, 1 - inside_side, line_length );
   1230 
   1231   Exit:
   1232     return error;
   1233   }
   1234 
   1235 
   1236   /* add two points to the left and right borders corresponding to the */
   1237   /* start of the subpath                                              */
   1238   static FT_Error
   1239   ft_stroker_subpath_start( FT_Stroker  stroker,
   1240                             FT_Angle    start_angle,
   1241                             FT_Fixed    line_length )
   1242   {
   1243     FT_Vector        delta;
   1244     FT_Vector        point;
   1245     FT_Error         error;
   1246     FT_StrokeBorder  border;
   1247 
   1248 
   1249     FT_Vector_From_Polar( &delta, stroker->radius,
   1250                           start_angle + FT_ANGLE_PI2 );
   1251 
   1252     point.x = stroker->center.x + delta.x;
   1253     point.y = stroker->center.y + delta.y;
   1254 
   1255     border = stroker->borders;
   1256     error = ft_stroke_border_moveto( border, &point );
   1257     if ( error )
   1258       goto Exit;
   1259 
   1260     point.x = stroker->center.x - delta.x;
   1261     point.y = stroker->center.y - delta.y;
   1262 
   1263     border++;
   1264     error = ft_stroke_border_moveto( border, &point );
   1265 
   1266     /* save angle, position, and line length for last join */
   1267     /* (line_length is zero for curves)                    */
   1268     stroker->subpath_angle       = start_angle;
   1269     stroker->first_point         = FALSE;
   1270     stroker->subpath_line_length = line_length;
   1271 
   1272   Exit:
   1273     return error;
   1274   }
   1275 
   1276 
   1277   /* documentation is in ftstroke.h */
   1278 
   1279   FT_EXPORT_DEF( FT_Error )
   1280   FT_Stroker_LineTo( FT_Stroker  stroker,
   1281                      FT_Vector*  to )
   1282   {
   1283     FT_Error         error = FT_Err_Ok;
   1284     FT_StrokeBorder  border;
   1285     FT_Vector        delta;
   1286     FT_Angle         angle;
   1287     FT_Int           side;
   1288     FT_Fixed         line_length;
   1289 
   1290 
   1291     delta.x = to->x - stroker->center.x;
   1292     delta.y = to->y - stroker->center.y;
   1293 
   1294     /* a zero-length lineto is a no-op; avoid creating a spurious corner */
   1295     if ( delta.x == 0 && delta.y == 0 )
   1296        goto Exit;
   1297 
   1298     /* compute length of line */
   1299     line_length = FT_Vector_Length( &delta );
   1300 
   1301     angle = FT_Atan2( delta.x, delta.y );
   1302     FT_Vector_From_Polar( &delta, stroker->radius, angle + FT_ANGLE_PI2 );
   1303 
   1304     /* process corner if necessary */
   1305     if ( stroker->first_point )
   1306     {
   1307       /* This is the first segment of a subpath.  We need to     */
   1308       /* add a point to each border at their respective starting */
   1309       /* point locations.                                        */
   1310       error = ft_stroker_subpath_start( stroker, angle, line_length );
   1311       if ( error )
   1312         goto Exit;
   1313     }
   1314     else
   1315     {
   1316       /* process the current corner */
   1317       stroker->angle_out = angle;
   1318       error = ft_stroker_process_corner( stroker, line_length );
   1319       if ( error )
   1320         goto Exit;
   1321     }
   1322 
   1323     /* now add a line segment to both the `inside' and `outside' paths */
   1324     for ( border = stroker->borders, side = 1; side >= 0; side--, border++ )
   1325     {
   1326       FT_Vector  point;
   1327 
   1328 
   1329       point.x = to->x + delta.x;
   1330       point.y = to->y + delta.y;
   1331 
   1332       /* the ends of lineto borders are movable */
   1333       error = ft_stroke_border_lineto( border, &point, TRUE );
   1334       if ( error )
   1335         goto Exit;
   1336 
   1337       delta.x = -delta.x;
   1338       delta.y = -delta.y;
   1339     }
   1340 
   1341     stroker->angle_in    = angle;
   1342     stroker->center      = *to;
   1343     stroker->line_length = line_length;
   1344 
   1345   Exit:
   1346     return error;
   1347   }
   1348 
   1349 
   1350   /* documentation is in ftstroke.h */
   1351 
   1352   FT_EXPORT_DEF( FT_Error )
   1353   FT_Stroker_ConicTo( FT_Stroker  stroker,
   1354                       FT_Vector*  control,
   1355                       FT_Vector*  to )
   1356   {
   1357     FT_Error    error = FT_Err_Ok;
   1358     FT_Vector   bez_stack[34];
   1359     FT_Vector*  arc;
   1360     FT_Vector*  limit = bez_stack + 30;
   1361     FT_Bool     first_arc = TRUE;
   1362 
   1363 
   1364     /* if all control points are coincident, this is a no-op; */
   1365     /* avoid creating a spurious corner                       */
   1366     if ( FT_IS_SMALL( stroker->center.x - control->x ) &&
   1367          FT_IS_SMALL( stroker->center.y - control->y ) &&
   1368          FT_IS_SMALL( control->x        - to->x      ) &&
   1369          FT_IS_SMALL( control->y        - to->y      ) )
   1370     {
   1371        stroker->center = *to;
   1372        goto Exit;
   1373     }
   1374 
   1375     arc    = bez_stack;
   1376     arc[0] = *to;
   1377     arc[1] = *control;
   1378     arc[2] = stroker->center;
   1379 
   1380     while ( arc >= bez_stack )
   1381     {
   1382       FT_Angle  angle_in, angle_out;
   1383 
   1384 
   1385       /* initialize with current direction */
   1386       angle_in = angle_out = stroker->angle_in;
   1387 
   1388       if ( arc < limit                                             &&
   1389            !ft_conic_is_small_enough( arc, &angle_in, &angle_out ) )
   1390       {
   1391         if ( stroker->first_point )
   1392           stroker->angle_in = angle_in;
   1393 
   1394         ft_conic_split( arc );
   1395         arc += 2;
   1396         continue;
   1397       }
   1398 
   1399       if ( first_arc )
   1400       {
   1401         first_arc = FALSE;
   1402 
   1403         /* process corner if necessary */
   1404         if ( stroker->first_point )
   1405           error = ft_stroker_subpath_start( stroker, angle_in, 0 );
   1406         else
   1407         {
   1408           stroker->angle_out = angle_in;
   1409           error = ft_stroker_process_corner( stroker, 0 );
   1410         }
   1411       }
   1412       else if ( ft_pos_abs( FT_Angle_Diff( stroker->angle_in, angle_in ) ) >
   1413                   FT_SMALL_CONIC_THRESHOLD / 4                             )
   1414       {
   1415         /* if the deviation from one arc to the next is too great, */
   1416         /* add a round corner                                      */
   1417         stroker->center    = arc[2];
   1418         stroker->angle_out = angle_in;
   1419         stroker->line_join = FT_STROKER_LINEJOIN_ROUND;
   1420 
   1421         error = ft_stroker_process_corner( stroker, 0 );
   1422 
   1423         /* reinstate line join style */
   1424         stroker->line_join = stroker->line_join_saved;
   1425       }
   1426 
   1427       if ( error )
   1428         goto Exit;
   1429 
   1430       /* the arc's angle is small enough; we can add it directly to each */
   1431       /* border                                                          */
   1432       {
   1433         FT_Vector        ctrl, end;
   1434         FT_Angle         theta, phi, rotate, alpha0 = 0;
   1435         FT_Fixed         length;
   1436         FT_StrokeBorder  border;
   1437         FT_Int           side;
   1438 
   1439 
   1440         theta  = FT_Angle_Diff( angle_in, angle_out ) / 2;
   1441         phi    = angle_in + theta;
   1442         length = FT_DivFix( stroker->radius, FT_Cos( theta ) );
   1443 
   1444         /* compute direction of original arc */
   1445         if ( stroker->handle_wide_strokes )
   1446           alpha0 = FT_Atan2( arc[0].x - arc[2].x, arc[0].y - arc[2].y );
   1447 
   1448         for ( border = stroker->borders, side = 0;
   1449               side <= 1;
   1450               side++, border++ )
   1451         {
   1452           rotate = FT_SIDE_TO_ROTATE( side );
   1453 
   1454           /* compute control point */
   1455           FT_Vector_From_Polar( &ctrl, length, phi + rotate );
   1456           ctrl.x += arc[1].x;
   1457           ctrl.y += arc[1].y;
   1458 
   1459           /* compute end point */
   1460           FT_Vector_From_Polar( &end, stroker->radius, angle_out + rotate );
   1461           end.x += arc[0].x;
   1462           end.y += arc[0].y;
   1463 
   1464           if ( stroker->handle_wide_strokes )
   1465           {
   1466             FT_Vector  start;
   1467             FT_Angle   alpha1;
   1468 
   1469 
   1470             /* determine whether the border radius is greater than the */
   1471             /* radius of curvature of the original arc                 */
   1472             start = border->points[border->num_points - 1];
   1473 
   1474             alpha1 = FT_Atan2( end.x - start.x, end.y - start.y );
   1475 
   1476             /* is the direction of the border arc opposite to */
   1477             /* that of the original arc? */
   1478             if ( ft_pos_abs( FT_Angle_Diff( alpha0, alpha1 ) ) >
   1479                    FT_ANGLE_PI / 2                             )
   1480             {
   1481               FT_Angle   beta, gamma;
   1482               FT_Vector  bvec, delta;
   1483               FT_Fixed   blen, sinA, sinB, alen;
   1484 
   1485 
   1486               /* use the sine rule to find the intersection point */
   1487               beta  = FT_Atan2( arc[2].x - start.x, arc[2].y - start.y );
   1488               gamma = FT_Atan2( arc[0].x - end.x,   arc[0].y - end.y );
   1489 
   1490               bvec.x = end.x - start.x;
   1491               bvec.y = end.y - start.y;
   1492 
   1493               blen = FT_Vector_Length( &bvec );
   1494 
   1495               sinA = ft_pos_abs( FT_Sin( alpha1 - gamma ) );
   1496               sinB = ft_pos_abs( FT_Sin( beta - gamma ) );
   1497 
   1498               alen = FT_DivFix( FT_MulFix( blen, sinA ), sinB );
   1499 
   1500               FT_Vector_From_Polar( &delta, alen, beta );
   1501               delta.x += start.x;
   1502               delta.y += start.y;
   1503 
   1504               /* circumnavigate the negative sector backwards */
   1505               border->movable = FALSE;
   1506               error = ft_stroke_border_lineto( border, &delta, FALSE );
   1507               if ( error )
   1508                 goto Exit;
   1509               error = ft_stroke_border_lineto( border, &end, FALSE );
   1510               if ( error )
   1511                 goto Exit;
   1512               error = ft_stroke_border_conicto( border, &ctrl, &start );
   1513               if ( error )
   1514                 goto Exit;
   1515               /* and then move to the endpoint */
   1516               error = ft_stroke_border_lineto( border, &end, FALSE );
   1517               if ( error )
   1518                 goto Exit;
   1519 
   1520               continue;
   1521             }
   1522 
   1523             /* else fall through */
   1524           }
   1525 
   1526           /* simply add an arc */
   1527           error = ft_stroke_border_conicto( border, &ctrl, &end );
   1528           if ( error )
   1529             goto Exit;
   1530         }
   1531       }
   1532 
   1533       arc -= 2;
   1534 
   1535       stroker->angle_in = angle_out;
   1536     }
   1537 
   1538     stroker->center = *to;
   1539 
   1540   Exit:
   1541     return error;
   1542   }
   1543 
   1544 
   1545   /* documentation is in ftstroke.h */
   1546 
   1547   FT_EXPORT_DEF( FT_Error )
   1548   FT_Stroker_CubicTo( FT_Stroker  stroker,
   1549                       FT_Vector*  control1,
   1550                       FT_Vector*  control2,
   1551                       FT_Vector*  to )
   1552   {
   1553     FT_Error    error = FT_Err_Ok;
   1554     FT_Vector   bez_stack[37];
   1555     FT_Vector*  arc;
   1556     FT_Vector*  limit = bez_stack + 32;
   1557     FT_Bool     first_arc = TRUE;
   1558 
   1559 
   1560     /* if all control points are coincident, this is a no-op; */
   1561     /* avoid creating a spurious corner */
   1562     if ( FT_IS_SMALL( stroker->center.x - control1->x ) &&
   1563          FT_IS_SMALL( stroker->center.y - control1->y ) &&
   1564          FT_IS_SMALL( control1->x       - control2->x ) &&
   1565          FT_IS_SMALL( control1->y       - control2->y ) &&
   1566          FT_IS_SMALL( control2->x       - to->x       ) &&
   1567          FT_IS_SMALL( control2->y       - to->y       ) )
   1568     {
   1569        stroker->center = *to;
   1570        goto Exit;
   1571     }
   1572 
   1573     arc    = bez_stack;
   1574     arc[0] = *to;
   1575     arc[1] = *control2;
   1576     arc[2] = *control1;
   1577     arc[3] = stroker->center;
   1578 
   1579     while ( arc >= bez_stack )
   1580     {
   1581       FT_Angle  angle_in, angle_mid, angle_out;
   1582 
   1583 
   1584       /* initialize with current direction */
   1585       angle_in = angle_out = angle_mid = stroker->angle_in;
   1586 
   1587       if ( arc < limit                                         &&
   1588            !ft_cubic_is_small_enough( arc, &angle_in,
   1589                                       &angle_mid, &angle_out ) )
   1590       {
   1591         if ( stroker->first_point )
   1592           stroker->angle_in = angle_in;
   1593 
   1594         ft_cubic_split( arc );
   1595         arc += 3;
   1596         continue;
   1597       }
   1598 
   1599       if ( first_arc )
   1600       {
   1601         first_arc = FALSE;
   1602 
   1603         /* process corner if necessary */
   1604         if ( stroker->first_point )
   1605           error = ft_stroker_subpath_start( stroker, angle_in, 0 );
   1606         else
   1607         {
   1608           stroker->angle_out = angle_in;
   1609           error = ft_stroker_process_corner( stroker, 0 );
   1610         }
   1611       }
   1612       else if ( ft_pos_abs( FT_Angle_Diff( stroker->angle_in, angle_in ) ) >
   1613                   FT_SMALL_CUBIC_THRESHOLD / 4                             )
   1614       {
   1615         /* if the deviation from one arc to the next is too great, */
   1616         /* add a round corner                                      */
   1617         stroker->center    = arc[3];
   1618         stroker->angle_out = angle_in;
   1619         stroker->line_join = FT_STROKER_LINEJOIN_ROUND;
   1620 
   1621         error = ft_stroker_process_corner( stroker, 0 );
   1622 
   1623         /* reinstate line join style */
   1624         stroker->line_join = stroker->line_join_saved;
   1625       }
   1626 
   1627       if ( error )
   1628         goto Exit;
   1629 
   1630       /* the arc's angle is small enough; we can add it directly to each */
   1631       /* border                                                          */
   1632       {
   1633         FT_Vector        ctrl1, ctrl2, end;
   1634         FT_Angle         theta1, phi1, theta2, phi2, rotate, alpha0 = 0;
   1635         FT_Fixed         length1, length2;
   1636         FT_StrokeBorder  border;
   1637         FT_Int           side;
   1638 
   1639 
   1640         theta1  = FT_Angle_Diff( angle_in,  angle_mid ) / 2;
   1641         theta2  = FT_Angle_Diff( angle_mid, angle_out ) / 2;
   1642         phi1    = ft_angle_mean( angle_in,  angle_mid );
   1643         phi2    = ft_angle_mean( angle_mid, angle_out );
   1644         length1 = FT_DivFix( stroker->radius, FT_Cos( theta1 ) );
   1645         length2 = FT_DivFix( stroker->radius, FT_Cos( theta2 ) );
   1646 
   1647         /* compute direction of original arc */
   1648         if ( stroker->handle_wide_strokes )
   1649           alpha0 = FT_Atan2( arc[0].x - arc[3].x, arc[0].y - arc[3].y );
   1650 
   1651         for ( border = stroker->borders, side = 0;
   1652               side <= 1;
   1653               side++, border++ )
   1654         {
   1655           rotate = FT_SIDE_TO_ROTATE( side );
   1656 
   1657           /* compute control points */
   1658           FT_Vector_From_Polar( &ctrl1, length1, phi1 + rotate );
   1659           ctrl1.x += arc[2].x;
   1660           ctrl1.y += arc[2].y;
   1661 
   1662           FT_Vector_From_Polar( &ctrl2, length2, phi2 + rotate );
   1663           ctrl2.x += arc[1].x;
   1664           ctrl2.y += arc[1].y;
   1665 
   1666           /* compute end point */
   1667           FT_Vector_From_Polar( &end, stroker->radius, angle_out + rotate );
   1668           end.x += arc[0].x;
   1669           end.y += arc[0].y;
   1670 
   1671           if ( stroker->handle_wide_strokes )
   1672           {
   1673             FT_Vector  start;
   1674             FT_Angle   alpha1;
   1675 
   1676 
   1677             /* determine whether the border radius is greater than the */
   1678             /* radius of curvature of the original arc                 */
   1679             start = border->points[border->num_points - 1];
   1680 
   1681             alpha1 = FT_Atan2( end.x - start.x, end.y - start.y );
   1682 
   1683             /* is the direction of the border arc opposite to */
   1684             /* that of the original arc? */
   1685             if ( ft_pos_abs( FT_Angle_Diff( alpha0, alpha1 ) ) >
   1686                    FT_ANGLE_PI / 2                             )
   1687             {
   1688               FT_Angle   beta, gamma;
   1689               FT_Vector  bvec, delta;
   1690               FT_Fixed   blen, sinA, sinB, alen;
   1691 
   1692 
   1693               /* use the sine rule to find the intersection point */
   1694               beta  = FT_Atan2( arc[3].x - start.x, arc[3].y - start.y );
   1695               gamma = FT_Atan2( arc[0].x - end.x,   arc[0].y - end.y );
   1696 
   1697               bvec.x = end.x - start.x;
   1698               bvec.y = end.y - start.y;
   1699 
   1700               blen = FT_Vector_Length( &bvec );
   1701 
   1702               sinA = ft_pos_abs( FT_Sin( alpha1 - gamma ) );
   1703               sinB = ft_pos_abs( FT_Sin( beta - gamma ) );
   1704 
   1705               alen = FT_DivFix( FT_MulFix( blen, sinA ), sinB );
   1706 
   1707               FT_Vector_From_Polar( &delta, alen, beta );
   1708               delta.x += start.x;
   1709               delta.y += start.y;
   1710 
   1711               /* circumnavigate the negative sector backwards */
   1712               border->movable = FALSE;
   1713               error = ft_stroke_border_lineto( border, &delta, FALSE );
   1714               if ( error )
   1715                 goto Exit;
   1716               error = ft_stroke_border_lineto( border, &end, FALSE );
   1717               if ( error )
   1718                 goto Exit;
   1719               error = ft_stroke_border_cubicto( border,
   1720                                                 &ctrl2,
   1721                                                 &ctrl1,
   1722                                                 &start );
   1723               if ( error )
   1724                 goto Exit;
   1725               /* and then move to the endpoint */
   1726               error = ft_stroke_border_lineto( border, &end, FALSE );
   1727               if ( error )
   1728                 goto Exit;
   1729 
   1730               continue;
   1731             }
   1732 
   1733             /* else fall through */
   1734           }
   1735 
   1736           /* simply add an arc */
   1737           error = ft_stroke_border_cubicto( border, &ctrl1, &ctrl2, &end );
   1738           if ( error )
   1739             goto Exit;
   1740         }
   1741       }
   1742 
   1743       arc -= 3;
   1744 
   1745       stroker->angle_in = angle_out;
   1746     }
   1747 
   1748     stroker->center = *to;
   1749 
   1750   Exit:
   1751     return error;
   1752   }
   1753 
   1754 
   1755   /* documentation is in ftstroke.h */
   1756 
   1757   FT_EXPORT_DEF( FT_Error )
   1758   FT_Stroker_BeginSubPath( FT_Stroker  stroker,
   1759                            FT_Vector*  to,
   1760                            FT_Bool     open )
   1761   {
   1762     /* We cannot process the first point, because there is not enough      */
   1763     /* information regarding its corner/cap.  The latter will be processed */
   1764     /* in the `FT_Stroker_EndSubPath' routine.                             */
   1765     /*                                                                     */
   1766     stroker->first_point  = TRUE;
   1767     stroker->center       = *to;
   1768     stroker->subpath_open = open;
   1769 
   1770     /* Determine if we need to check whether the border radius is greater */
   1771     /* than the radius of curvature of a curve, to handle this case       */
   1772     /* specially.  This is only required if bevel joins or butt caps may  */
   1773     /* be created, because round & miter joins and round & square caps    */
   1774     /* cover the negative sector created with wide strokes.               */
   1775     stroker->handle_wide_strokes =
   1776       FT_BOOL( stroker->line_join != FT_STROKER_LINEJOIN_ROUND  ||
   1777                ( stroker->subpath_open                        &&
   1778                  stroker->line_cap == FT_STROKER_LINECAP_BUTT ) );
   1779 
   1780     /* record the subpath start point for each border */
   1781     stroker->subpath_start = *to;
   1782 
   1783     stroker->angle_in = 0;
   1784 
   1785     return FT_Err_Ok;
   1786   }
   1787 
   1788 
   1789   static FT_Error
   1790   ft_stroker_add_reverse_left( FT_Stroker  stroker,
   1791                                FT_Bool     open )
   1792   {
   1793     FT_StrokeBorder  right = stroker->borders + 0;
   1794     FT_StrokeBorder  left  = stroker->borders + 1;
   1795     FT_Int           new_points;
   1796     FT_Error         error = FT_Err_Ok;
   1797 
   1798 
   1799     FT_ASSERT( left->start >= 0 );
   1800 
   1801     new_points = left->num_points - left->start;
   1802     if ( new_points > 0 )
   1803     {
   1804       error = ft_stroke_border_grow( right, (FT_UInt)new_points );
   1805       if ( error )
   1806         goto Exit;
   1807 
   1808       {
   1809         FT_Vector*  dst_point = right->points + right->num_points;
   1810         FT_Byte*    dst_tag   = right->tags   + right->num_points;
   1811         FT_Vector*  src_point = left->points  + left->num_points - 1;
   1812         FT_Byte*    src_tag   = left->tags    + left->num_points - 1;
   1813 
   1814 
   1815         while ( src_point >= left->points + left->start )
   1816         {
   1817           *dst_point = *src_point;
   1818           *dst_tag   = *src_tag;
   1819 
   1820           if ( open )
   1821             dst_tag[0] &= ~FT_STROKE_TAG_BEGIN_END;
   1822           else
   1823           {
   1824             FT_Byte  ttag =
   1825                        (FT_Byte)( dst_tag[0] & FT_STROKE_TAG_BEGIN_END );
   1826 
   1827 
   1828             /* switch begin/end tags if necessary */
   1829             if ( ttag == FT_STROKE_TAG_BEGIN ||
   1830                  ttag == FT_STROKE_TAG_END   )
   1831               dst_tag[0] ^= FT_STROKE_TAG_BEGIN_END;
   1832           }
   1833 
   1834           src_point--;
   1835           src_tag--;
   1836           dst_point++;
   1837           dst_tag++;
   1838         }
   1839       }
   1840 
   1841       left->num_points   = left->start;
   1842       right->num_points += new_points;
   1843 
   1844       right->movable = FALSE;
   1845       left->movable  = FALSE;
   1846     }
   1847 
   1848   Exit:
   1849     return error;
   1850   }
   1851 
   1852 
   1853   /* documentation is in ftstroke.h */
   1854 
   1855   /* there's a lot of magic in this function! */
   1856   FT_EXPORT_DEF( FT_Error )
   1857   FT_Stroker_EndSubPath( FT_Stroker  stroker )
   1858   {
   1859     FT_Error  error = FT_Err_Ok;
   1860 
   1861 
   1862     if ( stroker->subpath_open )
   1863     {
   1864       FT_StrokeBorder  right = stroker->borders;
   1865 
   1866 
   1867       /* All right, this is an opened path, we need to add a cap between */
   1868       /* right & left, add the reverse of left, then add a final cap     */
   1869       /* between left & right.                                           */
   1870       error = ft_stroker_cap( stroker, stroker->angle_in, 0 );
   1871       if ( error )
   1872         goto Exit;
   1873 
   1874       /* add reversed points from `left' to `right' */
   1875       error = ft_stroker_add_reverse_left( stroker, TRUE );
   1876       if ( error )
   1877         goto Exit;
   1878 
   1879       /* now add the final cap */
   1880       stroker->center = stroker->subpath_start;
   1881       error = ft_stroker_cap( stroker,
   1882                               stroker->subpath_angle + FT_ANGLE_PI, 0 );
   1883       if ( error )
   1884         goto Exit;
   1885 
   1886       /* Now end the right subpath accordingly.  The left one is */
   1887       /* rewind and doesn't need further processing.             */
   1888       ft_stroke_border_close( right, FALSE );
   1889     }
   1890     else
   1891     {
   1892       FT_Angle  turn;
   1893       FT_Int    inside_side;
   1894 
   1895 
   1896       /* close the path if needed */
   1897       if ( stroker->center.x != stroker->subpath_start.x ||
   1898            stroker->center.y != stroker->subpath_start.y )
   1899       {
   1900          error = FT_Stroker_LineTo( stroker, &stroker->subpath_start );
   1901          if ( error )
   1902            goto Exit;
   1903       }
   1904 
   1905       /* process the corner */
   1906       stroker->angle_out = stroker->subpath_angle;
   1907       turn               = FT_Angle_Diff( stroker->angle_in,
   1908                                           stroker->angle_out );
   1909 
   1910       /* no specific corner processing is required if the turn is 0 */
   1911       if ( turn != 0 )
   1912       {
   1913         /* when we turn to the right, the inside side is 0 */
   1914         inside_side = 0;
   1915 
   1916         /* otherwise, the inside side is 1 */
   1917         if ( turn < 0 )
   1918           inside_side = 1;
   1919 
   1920         error = ft_stroker_inside( stroker,
   1921                                    inside_side,
   1922                                    stroker->subpath_line_length );
   1923         if ( error )
   1924           goto Exit;
   1925 
   1926         /* process the outside side */
   1927         error = ft_stroker_outside( stroker,
   1928                                     1 - inside_side,
   1929                                     stroker->subpath_line_length );
   1930         if ( error )
   1931           goto Exit;
   1932       }
   1933 
   1934       /* then end our two subpaths */
   1935       ft_stroke_border_close( stroker->borders + 0, FALSE );
   1936       ft_stroke_border_close( stroker->borders + 1, TRUE );
   1937     }
   1938 
   1939   Exit:
   1940     return error;
   1941   }
   1942 
   1943 
   1944   /* documentation is in ftstroke.h */
   1945 
   1946   FT_EXPORT_DEF( FT_Error )
   1947   FT_Stroker_GetBorderCounts( FT_Stroker        stroker,
   1948                               FT_StrokerBorder  border,
   1949                               FT_UInt          *anum_points,
   1950                               FT_UInt          *anum_contours )
   1951   {
   1952     FT_UInt   num_points = 0, num_contours = 0;
   1953     FT_Error  error;
   1954 
   1955 
   1956     if ( !stroker || border > 1 )
   1957     {
   1958       error = FT_Err_Invalid_Argument;
   1959       goto Exit;
   1960     }
   1961 
   1962     error = ft_stroke_border_get_counts( stroker->borders + border,
   1963                                          &num_points, &num_contours );
   1964   Exit:
   1965     if ( anum_points )
   1966       *anum_points = num_points;
   1967 
   1968     if ( anum_contours )
   1969       *anum_contours = num_contours;
   1970 
   1971     return error;
   1972   }
   1973 
   1974 
   1975   /* documentation is in ftstroke.h */
   1976 
   1977   FT_EXPORT_DEF( FT_Error )
   1978   FT_Stroker_GetCounts( FT_Stroker  stroker,
   1979                         FT_UInt    *anum_points,
   1980                         FT_UInt    *anum_contours )
   1981   {
   1982     FT_UInt   count1, count2, num_points   = 0;
   1983     FT_UInt   count3, count4, num_contours = 0;
   1984     FT_Error  error;
   1985 
   1986 
   1987     error = ft_stroke_border_get_counts( stroker->borders + 0,
   1988                                          &count1, &count2 );
   1989     if ( error )
   1990       goto Exit;
   1991 
   1992     error = ft_stroke_border_get_counts( stroker->borders + 1,
   1993                                          &count3, &count4 );
   1994     if ( error )
   1995       goto Exit;
   1996 
   1997     num_points   = count1 + count3;
   1998     num_contours = count2 + count4;
   1999 
   2000   Exit:
   2001     *anum_points   = num_points;
   2002     *anum_contours = num_contours;
   2003     return error;
   2004   }
   2005 
   2006 
   2007   /* documentation is in ftstroke.h */
   2008 
   2009   FT_EXPORT_DEF( void )
   2010   FT_Stroker_ExportBorder( FT_Stroker        stroker,
   2011                            FT_StrokerBorder  border,
   2012                            FT_Outline*       outline )
   2013   {
   2014     if ( border == FT_STROKER_BORDER_LEFT  ||
   2015          border == FT_STROKER_BORDER_RIGHT )
   2016     {
   2017       FT_StrokeBorder  sborder = & stroker->borders[border];
   2018 
   2019 
   2020       if ( sborder->valid )
   2021         ft_stroke_border_export( sborder, outline );
   2022     }
   2023   }
   2024 
   2025 
   2026   /* documentation is in ftstroke.h */
   2027 
   2028   FT_EXPORT_DEF( void )
   2029   FT_Stroker_Export( FT_Stroker   stroker,
   2030                      FT_Outline*  outline )
   2031   {
   2032     FT_Stroker_ExportBorder( stroker, FT_STROKER_BORDER_LEFT, outline );
   2033     FT_Stroker_ExportBorder( stroker, FT_STROKER_BORDER_RIGHT, outline );
   2034   }
   2035 
   2036 
   2037   /* documentation is in ftstroke.h */
   2038 
   2039   /*
   2040    *  The following is very similar to FT_Outline_Decompose, except
   2041    *  that we do support opened paths, and do not scale the outline.
   2042    */
   2043   FT_EXPORT_DEF( FT_Error )
   2044   FT_Stroker_ParseOutline( FT_Stroker   stroker,
   2045                            FT_Outline*  outline,
   2046                            FT_Bool      opened )
   2047   {
   2048     FT_Vector   v_last;
   2049     FT_Vector   v_control;
   2050     FT_Vector   v_start;
   2051 
   2052     FT_Vector*  point;
   2053     FT_Vector*  limit;
   2054     char*       tags;
   2055 
   2056     FT_Error    error;
   2057 
   2058     FT_Int      n;         /* index of contour in outline     */
   2059     FT_UInt     first;     /* index of first point in contour */
   2060     FT_Int      tag;       /* current point's state           */
   2061 
   2062 
   2063     if ( !outline || !stroker )
   2064       return FT_Err_Invalid_Argument;
   2065 
   2066     FT_Stroker_Rewind( stroker );
   2067 
   2068     first = 0;
   2069 
   2070     for ( n = 0; n < outline->n_contours; n++ )
   2071     {
   2072       FT_UInt  last;  /* index of last point in contour */
   2073 
   2074 
   2075       last  = outline->contours[n];
   2076       limit = outline->points + last;
   2077 
   2078       /* skip empty points; we don't stroke these */
   2079       if ( last <= first )
   2080       {
   2081         first = last + 1;
   2082         continue;
   2083       }
   2084 
   2085       v_start = outline->points[first];
   2086       v_last  = outline->points[last];
   2087 
   2088       v_control = v_start;
   2089 
   2090       point = outline->points + first;
   2091       tags  = outline->tags   + first;
   2092       tag   = FT_CURVE_TAG( tags[0] );
   2093 
   2094       /* A contour cannot start with a cubic control point! */
   2095       if ( tag == FT_CURVE_TAG_CUBIC )
   2096         goto Invalid_Outline;
   2097 
   2098       /* check first point to determine origin */
   2099       if ( tag == FT_CURVE_TAG_CONIC )
   2100       {
   2101         /* First point is conic control.  Yes, this happens. */
   2102         if ( FT_CURVE_TAG( outline->tags[last] ) == FT_CURVE_TAG_ON )
   2103         {
   2104           /* start at last point if it is on the curve */
   2105           v_start = v_last;
   2106           limit--;
   2107         }
   2108         else
   2109         {
   2110           /* if both first and last points are conic, */
   2111           /* start at their middle                    */
   2112           v_start.x = ( v_start.x + v_last.x ) / 2;
   2113           v_start.y = ( v_start.y + v_last.y ) / 2;
   2114         }
   2115         point--;
   2116         tags--;
   2117       }
   2118 
   2119       error = FT_Stroker_BeginSubPath( stroker, &v_start, opened );
   2120       if ( error )
   2121         goto Exit;
   2122 
   2123       while ( point < limit )
   2124       {
   2125         point++;
   2126         tags++;
   2127 
   2128         tag = FT_CURVE_TAG( tags[0] );
   2129         switch ( tag )
   2130         {
   2131         case FT_CURVE_TAG_ON:  /* emit a single line_to */
   2132           {
   2133             FT_Vector  vec;
   2134 
   2135 
   2136             vec.x = point->x;
   2137             vec.y = point->y;
   2138 
   2139             error = FT_Stroker_LineTo( stroker, &vec );
   2140             if ( error )
   2141               goto Exit;
   2142             continue;
   2143           }
   2144 
   2145         case FT_CURVE_TAG_CONIC:  /* consume conic arcs */
   2146           v_control.x = point->x;
   2147           v_control.y = point->y;
   2148 
   2149         Do_Conic:
   2150           if ( point < limit )
   2151           {
   2152             FT_Vector  vec;
   2153             FT_Vector  v_middle;
   2154 
   2155 
   2156             point++;
   2157             tags++;
   2158             tag = FT_CURVE_TAG( tags[0] );
   2159 
   2160             vec = point[0];
   2161 
   2162             if ( tag == FT_CURVE_TAG_ON )
   2163             {
   2164               error = FT_Stroker_ConicTo( stroker, &v_control, &vec );
   2165               if ( error )
   2166                 goto Exit;
   2167               continue;
   2168             }
   2169 
   2170             if ( tag != FT_CURVE_TAG_CONIC )
   2171               goto Invalid_Outline;
   2172 
   2173             v_middle.x = ( v_control.x + vec.x ) / 2;
   2174             v_middle.y = ( v_control.y + vec.y ) / 2;
   2175 
   2176             error = FT_Stroker_ConicTo( stroker, &v_control, &v_middle );
   2177             if ( error )
   2178               goto Exit;
   2179 
   2180             v_control = vec;
   2181             goto Do_Conic;
   2182           }
   2183 
   2184           error = FT_Stroker_ConicTo( stroker, &v_control, &v_start );
   2185           goto Close;
   2186 
   2187         default:  /* FT_CURVE_TAG_CUBIC */
   2188           {
   2189             FT_Vector  vec1, vec2;
   2190 
   2191 
   2192             if ( point + 1 > limit                             ||
   2193                  FT_CURVE_TAG( tags[1] ) != FT_CURVE_TAG_CUBIC )
   2194               goto Invalid_Outline;
   2195 
   2196             point += 2;
   2197             tags  += 2;
   2198 
   2199             vec1 = point[-2];
   2200             vec2 = point[-1];
   2201 
   2202             if ( point <= limit )
   2203             {
   2204               FT_Vector  vec;
   2205 
   2206 
   2207               vec = point[0];
   2208 
   2209               error = FT_Stroker_CubicTo( stroker, &vec1, &vec2, &vec );
   2210               if ( error )
   2211                 goto Exit;
   2212               continue;
   2213             }
   2214 
   2215             error = FT_Stroker_CubicTo( stroker, &vec1, &vec2, &v_start );
   2216             goto Close;
   2217           }
   2218         }
   2219       }
   2220 
   2221     Close:
   2222       if ( error )
   2223         goto Exit;
   2224 
   2225       /* don't try to end the path if no segments have been generated */
   2226       if ( !stroker->first_point )
   2227       {
   2228         error = FT_Stroker_EndSubPath( stroker );
   2229         if ( error )
   2230           goto Exit;
   2231       }
   2232 
   2233       first = last + 1;
   2234     }
   2235 
   2236     return FT_Err_Ok;
   2237 
   2238   Exit:
   2239     return error;
   2240 
   2241   Invalid_Outline:
   2242     return FT_Err_Invalid_Outline;
   2243   }
   2244 
   2245 
   2246   /* declare an extern to access `ft_outline_glyph_class' globally     */
   2247   /* allocated  in `ftglyph.c', and use the FT_OUTLINE_GLYPH_CLASS_GET */
   2248   /* macro to access it when FT_CONFIG_OPTION_PIC is defined           */
   2249 #ifndef FT_CONFIG_OPTION_PIC
   2250   extern const FT_Glyph_Class  ft_outline_glyph_class;
   2251 #endif
   2252 #include "basepic.h"
   2253 
   2254 
   2255   /* documentation is in ftstroke.h */
   2256 
   2257   FT_EXPORT_DEF( FT_Error )
   2258   FT_Glyph_Stroke( FT_Glyph    *pglyph,
   2259                    FT_Stroker   stroker,
   2260                    FT_Bool      destroy )
   2261   {
   2262     FT_Error    error   = FT_Err_Invalid_Argument;
   2263     FT_Glyph    glyph   = NULL;
   2264     FT_Library  library = stroker->library;
   2265 
   2266     FT_UNUSED( library );
   2267 
   2268 
   2269     if ( pglyph == NULL )
   2270       goto Exit;
   2271 
   2272     glyph = *pglyph;
   2273     if ( glyph == NULL || glyph->clazz != FT_OUTLINE_GLYPH_CLASS_GET )
   2274       goto Exit;
   2275 
   2276     {
   2277       FT_Glyph  copy;
   2278 
   2279 
   2280       error = FT_Glyph_Copy( glyph, &copy );
   2281       if ( error )
   2282         goto Exit;
   2283 
   2284       glyph = copy;
   2285     }
   2286 
   2287     {
   2288       FT_OutlineGlyph  oglyph  = (FT_OutlineGlyph)glyph;
   2289       FT_Outline*      outline = &oglyph->outline;
   2290       FT_UInt          num_points, num_contours;
   2291 
   2292 
   2293       error = FT_Stroker_ParseOutline( stroker, outline, FALSE );
   2294       if ( error )
   2295         goto Fail;
   2296 
   2297       (void)FT_Stroker_GetCounts( stroker, &num_points, &num_contours );
   2298 
   2299       FT_Outline_Done( glyph->library, outline );
   2300 
   2301       error = FT_Outline_New( glyph->library,
   2302                               num_points, num_contours, outline );
   2303       if ( error )
   2304         goto Fail;
   2305 
   2306       outline->n_points   = 0;
   2307       outline->n_contours = 0;
   2308 
   2309       FT_Stroker_Export( stroker, outline );
   2310     }
   2311 
   2312     if ( destroy )
   2313       FT_Done_Glyph( *pglyph );
   2314 
   2315     *pglyph = glyph;
   2316     goto Exit;
   2317 
   2318   Fail:
   2319     FT_Done_Glyph( glyph );
   2320     glyph = NULL;
   2321 
   2322     if ( !destroy )
   2323       *pglyph = NULL;
   2324 
   2325   Exit:
   2326     return error;
   2327   }
   2328 
   2329 
   2330   /* documentation is in ftstroke.h */
   2331 
   2332   FT_EXPORT_DEF( FT_Error )
   2333   FT_Glyph_StrokeBorder( FT_Glyph    *pglyph,
   2334                          FT_Stroker   stroker,
   2335                          FT_Bool      inside,
   2336                          FT_Bool      destroy )
   2337   {
   2338     FT_Error    error   = FT_Err_Invalid_Argument;
   2339     FT_Glyph    glyph   = NULL;
   2340     FT_Library  library = stroker->library;
   2341 
   2342     FT_UNUSED( library );
   2343 
   2344 
   2345     if ( pglyph == NULL )
   2346       goto Exit;
   2347 
   2348     glyph = *pglyph;
   2349     if ( glyph == NULL || glyph->clazz != FT_OUTLINE_GLYPH_CLASS_GET )
   2350       goto Exit;
   2351 
   2352     {
   2353       FT_Glyph  copy;
   2354 
   2355 
   2356       error = FT_Glyph_Copy( glyph, &copy );
   2357       if ( error )
   2358         goto Exit;
   2359 
   2360       glyph = copy;
   2361     }
   2362 
   2363     {
   2364       FT_OutlineGlyph   oglyph  = (FT_OutlineGlyph)glyph;
   2365       FT_StrokerBorder  border;
   2366       FT_Outline*       outline = &oglyph->outline;
   2367       FT_UInt           num_points, num_contours;
   2368 
   2369 
   2370       border = FT_Outline_GetOutsideBorder( outline );
   2371       if ( inside )
   2372       {
   2373         if ( border == FT_STROKER_BORDER_LEFT )
   2374           border = FT_STROKER_BORDER_RIGHT;
   2375         else
   2376           border = FT_STROKER_BORDER_LEFT;
   2377       }
   2378 
   2379       error = FT_Stroker_ParseOutline( stroker, outline, FALSE );
   2380       if ( error )
   2381         goto Fail;
   2382 
   2383       (void)FT_Stroker_GetBorderCounts( stroker, border,
   2384                                         &num_points, &num_contours );
   2385 
   2386       FT_Outline_Done( glyph->library, outline );
   2387 
   2388       error = FT_Outline_New( glyph->library,
   2389                               num_points,
   2390                               num_contours,
   2391                               outline );
   2392       if ( error )
   2393         goto Fail;
   2394 
   2395       outline->n_points   = 0;
   2396       outline->n_contours = 0;
   2397 
   2398       FT_Stroker_ExportBorder( stroker, border, outline );
   2399     }
   2400 
   2401     if ( destroy )
   2402       FT_Done_Glyph( *pglyph );
   2403 
   2404     *pglyph = glyph;
   2405     goto Exit;
   2406 
   2407   Fail:
   2408     FT_Done_Glyph( glyph );
   2409     glyph = NULL;
   2410 
   2411     if ( !destroy )
   2412       *pglyph = NULL;
   2413 
   2414   Exit:
   2415     return error;
   2416   }
   2417 
   2418 
   2419 /* END */
   2420