Home | History | Annotate | Download | only in psaux
      1 /***************************************************************************/
      2 /*                                                                         */
      3 /*  pshints.c                                                              */
      4 /*                                                                         */
      5 /*    Adobe's code for handling CFF hints (body).                          */
      6 /*                                                                         */
      7 /*  Copyright 2007-2014 Adobe Systems Incorporated.                        */
      8 /*                                                                         */
      9 /*  This software, and all works of authorship, whether in source or       */
     10 /*  object code form as indicated by the copyright notice(s) included      */
     11 /*  herein (collectively, the "Work") is made available, and may only be   */
     12 /*  used, modified, and distributed under the FreeType Project License,    */
     13 /*  LICENSE.TXT.  Additionally, subject to the terms and conditions of the */
     14 /*  FreeType Project License, each contributor to the Work hereby grants   */
     15 /*  to any individual or legal entity exercising permissions granted by    */
     16 /*  the FreeType Project License and this section (hereafter, "You" or     */
     17 /*  "Your") a perpetual, worldwide, non-exclusive, no-charge,              */
     18 /*  royalty-free, irrevocable (except as stated in this section) patent    */
     19 /*  license to make, have made, use, offer to sell, sell, import, and      */
     20 /*  otherwise transfer the Work, where such license applies only to those  */
     21 /*  patent claims licensable by such contributor that are necessarily      */
     22 /*  infringed by their contribution(s) alone or by combination of their    */
     23 /*  contribution(s) with the Work to which such contribution(s) was        */
     24 /*  submitted.  If You institute patent litigation against any entity      */
     25 /*  (including a cross-claim or counterclaim in a lawsuit) alleging that   */
     26 /*  the Work or a contribution incorporated within the Work constitutes    */
     27 /*  direct or contributory patent infringement, then any patent licenses   */
     28 /*  granted to You under this License for that Work shall terminate as of  */
     29 /*  the date such litigation is filed.                                     */
     30 /*                                                                         */
     31 /*  By using, modifying, or distributing the Work you indicate that you    */
     32 /*  have read and understood the terms and conditions of the               */
     33 /*  FreeType Project License as well as those provided in this section,    */
     34 /*  and you accept them fully.                                             */
     35 /*                                                                         */
     36 /***************************************************************************/
     37 
     38 
     39 #include "psft.h"
     40 #include FT_INTERNAL_DEBUG_H
     41 
     42 #include "psglue.h"
     43 #include "psfont.h"
     44 #include "pshints.h"
     45 #include "psintrp.h"
     46 
     47 
     48   /*************************************************************************/
     49   /*                                                                       */
     50   /* The macro FT_COMPONENT is used in trace mode.  It is an implicit      */
     51   /* parameter of the FT_TRACE() and FT_ERROR() macros, used to print/log  */
     52   /* messages during execution.                                            */
     53   /*                                                                       */
     54 #undef  FT_COMPONENT
     55 #define FT_COMPONENT  trace_cf2hints
     56 
     57 
     58   typedef struct  CF2_HintMoveRec_
     59   {
     60     size_t     j;          /* index of upper hint map edge   */
     61     CF2_Fixed  moveUp;     /* adjustment to optimum position */
     62 
     63   } CF2_HintMoveRec, *CF2_HintMove;
     64 
     65 
     66   /* Compute angular momentum for winding order detection.  It is called */
     67   /* for all lines and curves, but not necessarily in element order.     */
     68   static CF2_Int
     69   cf2_getWindingMomentum( CF2_Fixed  x1,
     70                           CF2_Fixed  y1,
     71                           CF2_Fixed  x2,
     72                           CF2_Fixed  y2 )
     73   {
     74     /* cross product of pt1 position from origin with pt2 position from  */
     75     /* pt1; we reduce the precision so that the result fits into 32 bits */
     76 
     77     return ( x1 >> 16 ) * ( SUB_INT32( y2, y1 ) >> 16 ) -
     78            ( y1 >> 16 ) * ( SUB_INT32( x2, x1 ) >> 16 );
     79   }
     80 
     81 
     82   /*
     83    * Construct from a StemHint; this is used as a parameter to
     84    * `cf2_blues_capture'.
     85    * `hintOrigin' is the character space displacement of a seac accent.
     86    * Adjust stem hint for darkening here.
     87    *
     88    */
     89   static void
     90   cf2_hint_init( CF2_Hint            hint,
     91                  const CF2_ArrStack  stemHintArray,
     92                  size_t              indexStemHint,
     93                  const CF2_Font      font,
     94                  CF2_Fixed           hintOrigin,
     95                  CF2_Fixed           scale,
     96                  FT_Bool             bottom )
     97   {
     98     CF2_Fixed               width;
     99     const CF2_StemHintRec*  stemHint;
    100 
    101 
    102     FT_ZERO( hint );
    103 
    104     stemHint = (const CF2_StemHintRec*)cf2_arrstack_getPointer(
    105                                          stemHintArray,
    106                                          indexStemHint );
    107 
    108     width = SUB_INT32( stemHint->max, stemHint->min );
    109 
    110     if ( width == cf2_intToFixed( -21 ) )
    111     {
    112       /* ghost bottom */
    113 
    114       if ( bottom )
    115       {
    116         hint->csCoord = stemHint->max;
    117         hint->flags   = CF2_GhostBottom;
    118       }
    119       else
    120         hint->flags = 0;
    121     }
    122 
    123     else if ( width == cf2_intToFixed( -20 ) )
    124     {
    125       /* ghost top */
    126 
    127       if ( bottom )
    128         hint->flags = 0;
    129       else
    130       {
    131         hint->csCoord = stemHint->min;
    132         hint->flags   = CF2_GhostTop;
    133       }
    134     }
    135 
    136     else if ( width < 0 )
    137     {
    138       /* inverted pair */
    139 
    140       /*
    141        * Hints with negative widths were produced by an early version of a
    142        * non-Adobe font tool.  The Type 2 spec allows edge (ghost) hints
    143        * with negative widths, but says
    144        *
    145        *   All other negative widths have undefined meaning.
    146        *
    147        * CoolType has a silent workaround that negates the hint width; for
    148        * permissive mode, we do the same here.
    149        *
    150        * Note: Such fonts cannot use ghost hints, but should otherwise work.
    151        * Note: Some poor hints in our faux fonts can produce negative
    152        *       widths at some blends.  For example, see a light weight of
    153        *       `u' in ASerifMM.
    154        *
    155        */
    156       if ( bottom )
    157       {
    158         hint->csCoord = stemHint->max;
    159         hint->flags   = CF2_PairBottom;
    160       }
    161       else
    162       {
    163         hint->csCoord = stemHint->min;
    164         hint->flags   = CF2_PairTop;
    165       }
    166     }
    167 
    168     else
    169     {
    170       /* normal pair */
    171 
    172       if ( bottom )
    173       {
    174         hint->csCoord = stemHint->min;
    175         hint->flags   = CF2_PairBottom;
    176       }
    177       else
    178       {
    179         hint->csCoord = stemHint->max;
    180         hint->flags   = CF2_PairTop;
    181       }
    182     }
    183 
    184     /* Now that ghost hints have been detected, adjust this edge for      */
    185     /* darkening.  Bottoms are not changed; tops are incremented by twice */
    186     /* `darkenY'.                                                         */
    187     if ( cf2_hint_isTop( hint ) )
    188       hint->csCoord = ADD_INT32( hint->csCoord, 2 * font->darkenY );
    189 
    190     hint->csCoord = ADD_INT32( hint->csCoord, hintOrigin );
    191     hint->scale   = scale;
    192     hint->index   = indexStemHint;   /* index in original stem hint array */
    193 
    194     /* if original stem hint has been used, use the same position */
    195     if ( hint->flags != 0 && stemHint->used )
    196     {
    197       if ( cf2_hint_isTop( hint ) )
    198         hint->dsCoord = stemHint->maxDS;
    199       else
    200         hint->dsCoord = stemHint->minDS;
    201 
    202       cf2_hint_lock( hint );
    203     }
    204     else
    205       hint->dsCoord = FT_MulFix( hint->csCoord, scale );
    206   }
    207 
    208 
    209   /* initialize an invalid hint map element */
    210   static void
    211   cf2_hint_initZero( CF2_Hint  hint )
    212   {
    213     FT_ZERO( hint );
    214   }
    215 
    216 
    217   FT_LOCAL_DEF( FT_Bool )
    218   cf2_hint_isValid( const CF2_Hint  hint )
    219   {
    220     return (FT_Bool)( hint->flags != 0 );
    221   }
    222 
    223 
    224   static FT_Bool
    225   cf2_hint_isPair( const CF2_Hint  hint )
    226   {
    227     return (FT_Bool)( ( hint->flags                      &
    228                         ( CF2_PairBottom | CF2_PairTop ) ) != 0 );
    229   }
    230 
    231 
    232   static FT_Bool
    233   cf2_hint_isPairTop( const CF2_Hint  hint )
    234   {
    235     return (FT_Bool)( ( hint->flags & CF2_PairTop ) != 0 );
    236   }
    237 
    238 
    239   FT_LOCAL_DEF( FT_Bool )
    240   cf2_hint_isTop( const CF2_Hint  hint )
    241   {
    242     return (FT_Bool)( ( hint->flags                    &
    243                         ( CF2_PairTop | CF2_GhostTop ) ) != 0 );
    244   }
    245 
    246 
    247   FT_LOCAL_DEF( FT_Bool )
    248   cf2_hint_isBottom( const CF2_Hint  hint )
    249   {
    250     return (FT_Bool)( ( hint->flags                          &
    251                         ( CF2_PairBottom | CF2_GhostBottom ) ) != 0 );
    252   }
    253 
    254 
    255   static FT_Bool
    256   cf2_hint_isLocked( const CF2_Hint  hint )
    257   {
    258     return (FT_Bool)( ( hint->flags & CF2_Locked ) != 0 );
    259   }
    260 
    261 
    262   static FT_Bool
    263   cf2_hint_isSynthetic( const CF2_Hint  hint )
    264   {
    265     return (FT_Bool)( ( hint->flags & CF2_Synthetic ) != 0 );
    266   }
    267 
    268 
    269   FT_LOCAL_DEF( void )
    270   cf2_hint_lock( CF2_Hint  hint )
    271   {
    272     hint->flags |= CF2_Locked;
    273   }
    274 
    275 
    276   FT_LOCAL_DEF( void )
    277   cf2_hintmap_init( CF2_HintMap   hintmap,
    278                     CF2_Font      font,
    279                     CF2_HintMap   initialMap,
    280                     CF2_ArrStack  hintMoves,
    281                     CF2_Fixed     scale )
    282   {
    283     FT_ZERO( hintmap );
    284 
    285     /* copy parameters from font instance */
    286     hintmap->hinted         = font->hinted;
    287     hintmap->scale          = scale;
    288     hintmap->font           = font;
    289     hintmap->initialHintMap = initialMap;
    290     /* will clear in `cf2_hintmap_adjustHints' */
    291     hintmap->hintMoves      = hintMoves;
    292   }
    293 
    294 
    295   static FT_Bool
    296   cf2_hintmap_isValid( const CF2_HintMap  hintmap )
    297   {
    298     return hintmap->isValid;
    299   }
    300 
    301 
    302   static void
    303   cf2_hintmap_dump( CF2_HintMap  hintmap )
    304   {
    305 #ifdef FT_DEBUG_LEVEL_TRACE
    306     CF2_UInt  i;
    307 
    308 
    309     FT_TRACE6(( "  index  csCoord  dsCoord  scale  flags\n" ));
    310 
    311     for ( i = 0; i < hintmap->count; i++ )
    312     {
    313       CF2_Hint  hint = &hintmap->edge[i];
    314 
    315 
    316       FT_TRACE6(( "  %3d    %7.2f  %7.2f  %5d  %s%s%s%s\n",
    317                   hint->index,
    318                   hint->csCoord / 65536.0,
    319                   hint->dsCoord / ( hint->scale * 1.0 ),
    320                   hint->scale,
    321                   ( cf2_hint_isPair( hint ) ? "p" : "g" ),
    322                   ( cf2_hint_isTop( hint ) ? "t" : "b" ),
    323                   ( cf2_hint_isLocked( hint ) ? "L" : ""),
    324                   ( cf2_hint_isSynthetic( hint ) ? "S" : "" ) ));
    325     }
    326 #else
    327     FT_UNUSED( hintmap );
    328 #endif
    329   }
    330 
    331 
    332   /* transform character space coordinate to device space using hint map */
    333   static CF2_Fixed
    334   cf2_hintmap_map( CF2_HintMap  hintmap,
    335                    CF2_Fixed    csCoord )
    336   {
    337     if ( hintmap->count == 0 || ! hintmap->hinted )
    338     {
    339       /* there are no hints; use uniform scale and zero offset */
    340       return FT_MulFix( csCoord, hintmap->scale );
    341     }
    342     else
    343     {
    344       /* start linear search from last hit */
    345       CF2_UInt  i = hintmap->lastIndex;
    346 
    347 
    348       FT_ASSERT( hintmap->lastIndex < CF2_MAX_HINT_EDGES );
    349 
    350       /* search up */
    351       while ( i < hintmap->count - 1                  &&
    352               csCoord >= hintmap->edge[i + 1].csCoord )
    353         i += 1;
    354 
    355       /* search down */
    356       while ( i > 0 && csCoord < hintmap->edge[i].csCoord )
    357         i -= 1;
    358 
    359       hintmap->lastIndex = i;
    360 
    361       if ( i == 0 && csCoord < hintmap->edge[0].csCoord )
    362       {
    363         /* special case for points below first edge: use uniform scale */
    364         return ADD_INT32( FT_MulFix( SUB_INT32( csCoord,
    365                                                 hintmap->edge[0].csCoord ),
    366                                      hintmap->scale ),
    367                           hintmap->edge[0].dsCoord );
    368       }
    369       else
    370       {
    371         /*
    372          * Note: entries with duplicate csCoord are allowed.
    373          * Use edge[i], the highest entry where csCoord >= entry[i].csCoord
    374          */
    375         return ADD_INT32( FT_MulFix( SUB_INT32( csCoord,
    376                                                 hintmap->edge[i].csCoord ),
    377                                      hintmap->edge[i].scale ),
    378                           hintmap->edge[i].dsCoord );
    379       }
    380     }
    381   }
    382 
    383 
    384   /*
    385    * This hinting policy moves a hint pair in device space so that one of
    386    * its two edges is on a device pixel boundary (its fractional part is
    387    * zero).  `cf2_hintmap_insertHint' guarantees no overlap in CS
    388    * space.  Ensure here that there is no overlap in DS.
    389    *
    390    * In the first pass, edges are adjusted relative to adjacent hints.
    391    * Those that are below have already been adjusted.  Those that are
    392    * above have not yet been adjusted.  If a hint above blocks an
    393    * adjustment to an optimal position, we will try again in a second
    394    * pass.  The second pass is top-down.
    395    *
    396    */
    397 
    398   static void
    399   cf2_hintmap_adjustHints( CF2_HintMap  hintmap )
    400   {
    401     size_t  i, j;
    402 
    403 
    404     cf2_arrstack_clear( hintmap->hintMoves );      /* working storage */
    405 
    406     /*
    407      * First pass is bottom-up (font hint order) without look-ahead.
    408      * Locked edges are already adjusted.
    409      * Unlocked edges begin with dsCoord from `initialHintMap'.
    410      * Save edges that are not optimally adjusted in `hintMoves' array,
    411      * and process them in second pass.
    412      */
    413 
    414     for ( i = 0; i < hintmap->count; i++ )
    415     {
    416       FT_Bool  isPair = cf2_hint_isPair( &hintmap->edge[i] );
    417 
    418 
    419       /* index of upper edge (same value for ghost hint) */
    420       j = isPair ? i + 1 : i;
    421 
    422       FT_ASSERT( j < hintmap->count );
    423       FT_ASSERT( cf2_hint_isValid( &hintmap->edge[i] ) );
    424       FT_ASSERT( cf2_hint_isValid( &hintmap->edge[j] ) );
    425       FT_ASSERT( cf2_hint_isLocked( &hintmap->edge[i] ) ==
    426                    cf2_hint_isLocked( &hintmap->edge[j] ) );
    427 
    428       if ( !cf2_hint_isLocked( &hintmap->edge[i] ) )
    429       {
    430         /* hint edge is not locked, we can adjust it */
    431         CF2_Fixed  fracDown = cf2_fixedFraction( hintmap->edge[i].dsCoord );
    432         CF2_Fixed  fracUp   = cf2_fixedFraction( hintmap->edge[j].dsCoord );
    433 
    434         /* calculate all four possibilities; moves down are negative */
    435         CF2_Fixed  downMoveDown = 0 - fracDown;
    436         CF2_Fixed  upMoveDown   = 0 - fracUp;
    437         CF2_Fixed  downMoveUp   = ( fracDown == 0 )
    438                                     ? 0
    439                                     : cf2_intToFixed( 1 ) - fracDown;
    440         CF2_Fixed  upMoveUp     = ( fracUp == 0 )
    441                                     ? 0
    442                                     : cf2_intToFixed( 1 ) - fracUp;
    443 
    444         /* smallest move up */
    445         CF2_Fixed  moveUp   = FT_MIN( downMoveUp, upMoveUp );
    446         /* smallest move down */
    447         CF2_Fixed  moveDown = FT_MAX( downMoveDown, upMoveDown );
    448 
    449         /* final amount to move edge or edge pair */
    450         CF2_Fixed  move;
    451 
    452         CF2_Fixed  downMinCounter = CF2_MIN_COUNTER;
    453         CF2_Fixed  upMinCounter   = CF2_MIN_COUNTER;
    454         FT_Bool    saveEdge       = FALSE;
    455 
    456 
    457         /* minimum counter constraint doesn't apply when adjacent edges */
    458         /* are synthetic                                                */
    459         /* TODO: doesn't seem a big effect; for now, reduce the code    */
    460 #if 0
    461         if ( i == 0                                        ||
    462              cf2_hint_isSynthetic( &hintmap->edge[i - 1] ) )
    463           downMinCounter = 0;
    464 
    465         if ( j >= hintmap->count - 1                       ||
    466              cf2_hint_isSynthetic( &hintmap->edge[j + 1] ) )
    467           upMinCounter = 0;
    468 #endif
    469 
    470         /* is there room to move up?                                    */
    471         /* there is if we are at top of array or the next edge is at or */
    472         /* beyond proposed move up?                                     */
    473         if ( j >= hintmap->count - 1                ||
    474              hintmap->edge[j + 1].dsCoord >=
    475                ADD_INT32( hintmap->edge[j].dsCoord,
    476                           moveUp + upMinCounter )   )
    477         {
    478           /* there is room to move up; is there also room to move down? */
    479           if ( i == 0                                   ||
    480                hintmap->edge[i - 1].dsCoord <=
    481                  ADD_INT32( hintmap->edge[i].dsCoord,
    482                             moveDown - downMinCounter ) )
    483           {
    484             /* move smaller absolute amount */
    485             move = ( -moveDown < moveUp ) ? moveDown : moveUp;  /* optimum */
    486           }
    487           else
    488             move = moveUp;
    489         }
    490         else
    491         {
    492           /* is there room to move down? */
    493           if ( i == 0                                   ||
    494                hintmap->edge[i - 1].dsCoord <=
    495                  ADD_INT32( hintmap->edge[i].dsCoord,
    496                             moveDown - downMinCounter ) )
    497           {
    498             move     = moveDown;
    499             /* true if non-optimum move */
    500             saveEdge = (FT_Bool)( moveUp < -moveDown );
    501           }
    502           else
    503           {
    504             /* no room to move either way without overlapping or reducing */
    505             /* the counter too much                                       */
    506             move     = 0;
    507             saveEdge = TRUE;
    508           }
    509         }
    510 
    511         /* Identify non-moves and moves down that aren't optimal, and save */
    512         /* them for second pass.                                           */
    513         /* Do this only if there is an unlocked edge above (which could    */
    514         /* possibly move).                                                 */
    515         if ( saveEdge                                    &&
    516              j < hintmap->count - 1                      &&
    517              !cf2_hint_isLocked( &hintmap->edge[j + 1] ) )
    518         {
    519           CF2_HintMoveRec  savedMove;
    520 
    521 
    522           savedMove.j      = j;
    523           /* desired adjustment in second pass */
    524           savedMove.moveUp = moveUp - move;
    525 
    526           cf2_arrstack_push( hintmap->hintMoves, &savedMove );
    527         }
    528 
    529         /* move the edge(s) */
    530         hintmap->edge[i].dsCoord = ADD_INT32( hintmap->edge[i].dsCoord,
    531                                               move );
    532         if ( isPair )
    533           hintmap->edge[j].dsCoord = ADD_INT32( hintmap->edge[j].dsCoord,
    534                                                 move );
    535       }
    536 
    537       /* assert there are no overlaps in device space */
    538       FT_ASSERT( i == 0                                                   ||
    539                  hintmap->edge[i - 1].dsCoord <= hintmap->edge[i].dsCoord );
    540       FT_ASSERT( i < j                                                ||
    541                  hintmap->edge[i].dsCoord <= hintmap->edge[j].dsCoord );
    542 
    543       /* adjust the scales, avoiding divide by zero */
    544       if ( i > 0 )
    545       {
    546         if ( hintmap->edge[i].csCoord != hintmap->edge[i - 1].csCoord )
    547           hintmap->edge[i - 1].scale =
    548             FT_DivFix( SUB_INT32( hintmap->edge[i].dsCoord,
    549                                   hintmap->edge[i - 1].dsCoord ),
    550                        SUB_INT32( hintmap->edge[i].csCoord,
    551                                   hintmap->edge[i - 1].csCoord ) );
    552       }
    553 
    554       if ( isPair )
    555       {
    556         if ( hintmap->edge[j].csCoord != hintmap->edge[j - 1].csCoord )
    557           hintmap->edge[j - 1].scale =
    558             FT_DivFix( SUB_INT32( hintmap->edge[j].dsCoord,
    559                                   hintmap->edge[j - 1].dsCoord ),
    560                        SUB_INT32( hintmap->edge[j].csCoord,
    561                                   hintmap->edge[j - 1].csCoord ) );
    562 
    563         i += 1;     /* skip upper edge on next loop */
    564       }
    565     }
    566 
    567     /* second pass tries to move non-optimal hints up, in case there is */
    568     /* room now                                                         */
    569     for ( i = cf2_arrstack_size( hintmap->hintMoves ); i > 0; i-- )
    570     {
    571       CF2_HintMove  hintMove = (CF2_HintMove)
    572                       cf2_arrstack_getPointer( hintmap->hintMoves, i - 1 );
    573 
    574 
    575       j = hintMove->j;
    576 
    577       /* this was tested before the push, above */
    578       FT_ASSERT( j < hintmap->count - 1 );
    579 
    580       /* is there room to move up? */
    581       if ( hintmap->edge[j + 1].dsCoord >=
    582              ADD_INT32( hintmap->edge[j].dsCoord,
    583                         hintMove->moveUp + CF2_MIN_COUNTER ) )
    584       {
    585         /* there is more room now, move edge up */
    586         hintmap->edge[j].dsCoord = ADD_INT32( hintmap->edge[j].dsCoord,
    587                                               hintMove->moveUp );
    588 
    589         if ( cf2_hint_isPair( &hintmap->edge[j] ) )
    590         {
    591           FT_ASSERT( j > 0 );
    592           hintmap->edge[j - 1].dsCoord =
    593             ADD_INT32( hintmap->edge[j - 1].dsCoord, hintMove->moveUp );
    594         }
    595       }
    596     }
    597   }
    598 
    599 
    600   /* insert hint edges into map, sorted by csCoord */
    601   static void
    602   cf2_hintmap_insertHint( CF2_HintMap  hintmap,
    603                           CF2_Hint     bottomHintEdge,
    604                           CF2_Hint     topHintEdge )
    605   {
    606     CF2_UInt  indexInsert;
    607 
    608     /* set default values, then check for edge hints */
    609     FT_Bool   isPair         = TRUE;
    610     CF2_Hint  firstHintEdge  = bottomHintEdge;
    611     CF2_Hint  secondHintEdge = topHintEdge;
    612 
    613 
    614     /* one or none of the input params may be invalid when dealing with */
    615     /* edge hints; at least one edge must be valid                      */
    616     FT_ASSERT( cf2_hint_isValid( bottomHintEdge ) ||
    617                cf2_hint_isValid( topHintEdge )    );
    618 
    619     /* determine how many and which edges to insert */
    620     if ( !cf2_hint_isValid( bottomHintEdge ) )
    621     {
    622       /* insert only the top edge */
    623       firstHintEdge = topHintEdge;
    624       isPair        = FALSE;
    625     }
    626     else if ( !cf2_hint_isValid( topHintEdge ) )
    627     {
    628       /* insert only the bottom edge */
    629       isPair = FALSE;
    630     }
    631 
    632     /* paired edges must be in proper order */
    633     if ( isPair                                         &&
    634          topHintEdge->csCoord < bottomHintEdge->csCoord )
    635       return;
    636 
    637     /* linear search to find index value of insertion point */
    638     indexInsert = 0;
    639     for ( ; indexInsert < hintmap->count; indexInsert++ )
    640     {
    641       if ( hintmap->edge[indexInsert].csCoord >= firstHintEdge->csCoord )
    642         break;
    643     }
    644 
    645     FT_TRACE7(( "  Got hint at %.2f (%.2f)\n",
    646                 firstHintEdge->csCoord / 65536.0,
    647                 firstHintEdge->dsCoord / 65536.0 ));
    648     if ( isPair )
    649       FT_TRACE7(( "  Got hint at %.2f (%.2f)\n",
    650                   secondHintEdge->csCoord / 65536.0,
    651                   secondHintEdge->dsCoord / 65536.0 ));
    652 
    653     /*
    654      * Discard any hints that overlap in character space.  Most often, this
    655      * is while building the initial map, where captured hints from all
    656      * zones are combined.  Define overlap to include hints that `touch'
    657      * (overlap zero).  Hiragino Sans/Gothic fonts have numerous hints that
    658      * touch.  Some fonts have non-ideographic glyphs that overlap our
    659      * synthetic hints.
    660      *
    661      * Overlap also occurs when darkening stem hints that are close.
    662      *
    663      */
    664     if ( indexInsert < hintmap->count )
    665     {
    666       /* we are inserting before an existing edge:    */
    667       /* verify that an existing edge is not the same */
    668       if ( hintmap->edge[indexInsert].csCoord == firstHintEdge->csCoord )
    669         return; /* ignore overlapping stem hint */
    670 
    671       /* verify that a new pair does not straddle the next edge */
    672       if ( isPair                                                        &&
    673            hintmap->edge[indexInsert].csCoord <= secondHintEdge->csCoord )
    674         return; /* ignore overlapping stem hint */
    675 
    676       /* verify that we are not inserting between paired edges */
    677       if ( cf2_hint_isPairTop( &hintmap->edge[indexInsert] ) )
    678         return; /* ignore overlapping stem hint */
    679     }
    680 
    681     /* recompute device space locations using initial hint map */
    682     if ( cf2_hintmap_isValid( hintmap->initialHintMap ) &&
    683          !cf2_hint_isLocked( firstHintEdge )            )
    684     {
    685       if ( isPair )
    686       {
    687         /* Use hint map to position the center of stem, and nominal scale */
    688         /* to position the two edges.  This preserves the stem width.     */
    689         CF2_Fixed  midpoint =
    690                      cf2_hintmap_map(
    691                        hintmap->initialHintMap,
    692                        ADD_INT32( secondHintEdge->csCoord,
    693                                   firstHintEdge->csCoord ) / 2 );
    694         CF2_Fixed  halfWidth =
    695                      FT_MulFix( SUB_INT32( secondHintEdge->csCoord,
    696                                            firstHintEdge->csCoord ) / 2,
    697                                 hintmap->scale );
    698 
    699 
    700         firstHintEdge->dsCoord  = SUB_INT32( midpoint, halfWidth );
    701         secondHintEdge->dsCoord = ADD_INT32( midpoint, halfWidth );
    702       }
    703       else
    704         firstHintEdge->dsCoord = cf2_hintmap_map( hintmap->initialHintMap,
    705                                                   firstHintEdge->csCoord );
    706     }
    707 
    708     /*
    709      * Discard any hints that overlap in device space; this can occur
    710      * because locked hints have been moved to align with blue zones.
    711      *
    712      * TODO: Although we might correct this later during adjustment, we
    713      * don't currently have a way to delete a conflicting hint once it has
    714      * been inserted.  See v2.030 MinionPro-Regular, 12 ppem darkened,
    715      * initial hint map for second path, glyph 945 (the perispomeni (tilde)
    716      * in U+1F6E, Greek omega with psili and perispomeni).  Darkening is
    717      * 25.  Pair 667,747 initially conflicts in design space with top edge
    718      * 660.  This is because 667 maps to 7.87, and the top edge was
    719      * captured by a zone at 8.0.  The pair is later successfully inserted
    720      * in a zone without the top edge.  In this zone it is adjusted to 8.0,
    721      * and no longer conflicts with the top edge in design space.  This
    722      * means it can be included in yet a later zone which does have the top
    723      * edge hint.  This produces a small mismatch between the first and
    724      * last points of this path, even though the hint masks are the same.
    725      * The density map difference is tiny (1/256).
    726      *
    727      */
    728 
    729     if ( indexInsert > 0 )
    730     {
    731       /* we are inserting after an existing edge */
    732       if ( firstHintEdge->dsCoord < hintmap->edge[indexInsert - 1].dsCoord )
    733         return;
    734     }
    735 
    736     if ( indexInsert < hintmap->count )
    737     {
    738       /* we are inserting before an existing edge */
    739       if ( isPair )
    740       {
    741         if ( secondHintEdge->dsCoord > hintmap->edge[indexInsert].dsCoord )
    742           return;
    743       }
    744       else
    745       {
    746         if ( firstHintEdge->dsCoord > hintmap->edge[indexInsert].dsCoord )
    747           return;
    748       }
    749     }
    750 
    751     /* make room to insert */
    752     {
    753       CF2_UInt  iSrc = hintmap->count - 1;
    754       CF2_UInt  iDst = isPair ? hintmap->count + 1 : hintmap->count;
    755 
    756       CF2_UInt  count = hintmap->count - indexInsert;
    757 
    758 
    759       if ( iDst >= CF2_MAX_HINT_EDGES )
    760       {
    761         FT_TRACE4(( "cf2_hintmap_insertHint: too many hintmaps\n" ));
    762         return;
    763       }
    764 
    765       while ( count-- )
    766         hintmap->edge[iDst--] = hintmap->edge[iSrc--];
    767 
    768       /* insert first edge */
    769       hintmap->edge[indexInsert] = *firstHintEdge;         /* copy struct */
    770       hintmap->count            += 1;
    771 
    772       FT_TRACE7(( "  Inserting hint %.2f (%.2f)\n",
    773                   firstHintEdge->csCoord / 65536.0,
    774                   firstHintEdge->dsCoord / 65536.0 ));
    775 
    776       if ( isPair )
    777       {
    778         /* insert second edge */
    779         hintmap->edge[indexInsert + 1] = *secondHintEdge;  /* copy struct */
    780         hintmap->count                += 1;
    781 
    782         FT_TRACE7(( "  Inserting hint %.2f (%.2f)\n",
    783                     secondHintEdge->csCoord / 65536.0,
    784                     secondHintEdge->dsCoord / 65536.0 ));
    785 
    786       }
    787     }
    788 
    789     return;
    790   }
    791 
    792 
    793   /*
    794    * Build a map from hints and mask.
    795    *
    796    * This function may recur one level if `hintmap->initialHintMap' is not yet
    797    * valid.
    798    * If `initialMap' is true, simply build initial map.
    799    *
    800    * Synthetic hints are used in two ways.  A hint at zero is inserted, if
    801    * needed, in the initial hint map, to prevent translations from
    802    * propagating across the origin.  If synthetic em box hints are enabled
    803    * for ideographic dictionaries, then they are inserted in all hint
    804    * maps, including the initial one.
    805    *
    806    */
    807   FT_LOCAL_DEF( void )
    808   cf2_hintmap_build( CF2_HintMap   hintmap,
    809                      CF2_ArrStack  hStemHintArray,
    810                      CF2_ArrStack  vStemHintArray,
    811                      CF2_HintMask  hintMask,
    812                      CF2_Fixed     hintOrigin,
    813                      FT_Bool       initialMap )
    814   {
    815     FT_Byte*  maskPtr;
    816 
    817     CF2_Font         font = hintmap->font;
    818     CF2_HintMaskRec  tempHintMask;
    819 
    820     size_t   bitCount, i;
    821     FT_Byte  maskByte;
    822 
    823 
    824     /* check whether initial map is constructed */
    825     if ( !initialMap && !cf2_hintmap_isValid( hintmap->initialHintMap ) )
    826     {
    827       /* make recursive call with initialHintMap and temporary mask; */
    828       /* temporary mask will get all bits set, below */
    829       cf2_hintmask_init( &tempHintMask, hintMask->error );
    830       cf2_hintmap_build( hintmap->initialHintMap,
    831                          hStemHintArray,
    832                          vStemHintArray,
    833                          &tempHintMask,
    834                          hintOrigin,
    835                          TRUE );
    836     }
    837 
    838     if ( !cf2_hintmask_isValid( hintMask ) )
    839     {
    840       /* without a hint mask, assume all hints are active */
    841       cf2_hintmask_setAll( hintMask,
    842                            cf2_arrstack_size( hStemHintArray ) +
    843                              cf2_arrstack_size( vStemHintArray ) );
    844       if ( !cf2_hintmask_isValid( hintMask ) )
    845       {
    846         if ( font->isT1 )
    847         {
    848           /* no error, just continue unhinted */
    849           *hintMask->error = FT_Err_Ok;
    850           hintmap->hinted  = FALSE;
    851         }
    852         return;                   /* too many stem hints */
    853       }
    854     }
    855 
    856     /* begin by clearing the map */
    857     hintmap->count     = 0;
    858     hintmap->lastIndex = 0;
    859 
    860     /* make a copy of the hint mask so we can modify it */
    861     tempHintMask = *hintMask;
    862     maskPtr      = cf2_hintmask_getMaskPtr( &tempHintMask );
    863 
    864     /* use the hStem hints only, which are first in the mask */
    865     bitCount = cf2_arrstack_size( hStemHintArray );
    866 
    867     /* Defense-in-depth.  Should never return here. */
    868     if ( bitCount > hintMask->bitCount )
    869       return;
    870 
    871     /* synthetic embox hints get highest priority */
    872     if ( font->blues.doEmBoxHints )
    873     {
    874       CF2_HintRec  dummy;
    875 
    876 
    877       cf2_hint_initZero( &dummy );   /* invalid hint map element */
    878 
    879       /* ghost bottom */
    880       cf2_hintmap_insertHint( hintmap,
    881                               &font->blues.emBoxBottomEdge,
    882                               &dummy );
    883       /* ghost top */
    884       cf2_hintmap_insertHint( hintmap,
    885                               &dummy,
    886                               &font->blues.emBoxTopEdge );
    887     }
    888 
    889     /* insert hints captured by a blue zone or already locked (higher */
    890     /* priority)                                                      */
    891     for ( i = 0, maskByte = 0x80; i < bitCount; i++ )
    892     {
    893       if ( maskByte & *maskPtr )
    894       {
    895         /* expand StemHint into two `CF2_Hint' elements */
    896         CF2_HintRec  bottomHintEdge, topHintEdge;
    897 
    898 
    899         cf2_hint_init( &bottomHintEdge,
    900                        hStemHintArray,
    901                        i,
    902                        font,
    903                        hintOrigin,
    904                        hintmap->scale,
    905                        TRUE /* bottom */ );
    906         cf2_hint_init( &topHintEdge,
    907                        hStemHintArray,
    908                        i,
    909                        font,
    910                        hintOrigin,
    911                        hintmap->scale,
    912                        FALSE /* top */ );
    913 
    914         if ( cf2_hint_isLocked( &bottomHintEdge ) ||
    915              cf2_hint_isLocked( &topHintEdge )    ||
    916              cf2_blues_capture( &font->blues,
    917                                 &bottomHintEdge,
    918                                 &topHintEdge )   )
    919         {
    920           /* insert captured hint into map */
    921           cf2_hintmap_insertHint( hintmap, &bottomHintEdge, &topHintEdge );
    922 
    923           *maskPtr &= ~maskByte;      /* turn off the bit for this hint */
    924         }
    925       }
    926 
    927       if ( ( i & 7 ) == 7 )
    928       {
    929         /* move to next mask byte */
    930         maskPtr++;
    931         maskByte = 0x80;
    932       }
    933       else
    934         maskByte >>= 1;
    935     }
    936 
    937     /* initial hint map includes only captured hints plus maybe one at 0 */
    938 
    939     /*
    940      * TODO: There is a problem here because we are trying to build a
    941      *       single hint map containing all captured hints.  It is
    942      *       possible for there to be conflicts between captured hints,
    943      *       either because of darkening or because the hints are in
    944      *       separate hint zones (we are ignoring hint zones for the
    945      *       initial map).  An example of the latter is MinionPro-Regular
    946      *       v2.030 glyph 883 (Greek Capital Alpha with Psili) at 15ppem.
    947      *       A stem hint for the psili conflicts with the top edge hint
    948      *       for the base character.  The stem hint gets priority because
    949      *       of its sort order.  In glyph 884 (Greek Capital Alpha with
    950      *       Psili and Oxia), the top of the base character gets a stem
    951      *       hint, and the psili does not.  This creates different initial
    952      *       maps for the two glyphs resulting in different renderings of
    953      *       the base character.  Will probably defer this either as not
    954      *       worth the cost or as a font bug.  I don't think there is any
    955      *       good reason for an accent to be captured by an alignment
    956      *       zone.  -darnold 2/12/10
    957      */
    958 
    959     if ( initialMap )
    960     {
    961       /* Apply a heuristic that inserts a point for (0,0), unless it's     */
    962       /* already covered by a mapping.  This locks the baseline for glyphs */
    963       /* that have no baseline hints.                                      */
    964 
    965       if ( hintmap->count == 0                           ||
    966            hintmap->edge[0].csCoord > 0                  ||
    967            hintmap->edge[hintmap->count - 1].csCoord < 0 )
    968       {
    969         /* all edges are above 0 or all edges are below 0; */
    970         /* construct a locked edge hint at 0               */
    971 
    972         CF2_HintRec  edge, invalid;
    973 
    974 
    975         cf2_hint_initZero( &edge );
    976 
    977         edge.flags = CF2_GhostBottom |
    978                      CF2_Locked      |
    979                      CF2_Synthetic;
    980         edge.scale = hintmap->scale;
    981 
    982         cf2_hint_initZero( &invalid );
    983         cf2_hintmap_insertHint( hintmap, &edge, &invalid );
    984       }
    985     }
    986     else
    987     {
    988       /* insert remaining hints */
    989 
    990       maskPtr = cf2_hintmask_getMaskPtr( &tempHintMask );
    991 
    992       for ( i = 0, maskByte = 0x80; i < bitCount; i++ )
    993       {
    994         if ( maskByte & *maskPtr )
    995         {
    996           CF2_HintRec  bottomHintEdge, topHintEdge;
    997 
    998 
    999           cf2_hint_init( &bottomHintEdge,
   1000                          hStemHintArray,
   1001                          i,
   1002                          font,
   1003                          hintOrigin,
   1004                          hintmap->scale,
   1005                          TRUE /* bottom */ );
   1006           cf2_hint_init( &topHintEdge,
   1007                          hStemHintArray,
   1008                          i,
   1009                          font,
   1010                          hintOrigin,
   1011                          hintmap->scale,
   1012                          FALSE /* top */ );
   1013 
   1014           cf2_hintmap_insertHint( hintmap, &bottomHintEdge, &topHintEdge );
   1015         }
   1016 
   1017         if ( ( i & 7 ) == 7 )
   1018         {
   1019           /* move to next mask byte */
   1020           maskPtr++;
   1021           maskByte = 0x80;
   1022         }
   1023         else
   1024           maskByte >>= 1;
   1025       }
   1026     }
   1027 
   1028     FT_TRACE6(( initialMap ? "flags: [p]air [g]host [t]op "
   1029                              "[b]ottom [L]ocked [S]ynthetic\n"
   1030                              "Initial hintmap\n"
   1031                            : "Hints:\n" ));
   1032     cf2_hintmap_dump( hintmap );
   1033 
   1034     /*
   1035      * Note: The following line is a convenient place to break when
   1036      *       debugging hinting.  Examine `hintmap->edge' for the list of
   1037      *       enabled hints, then step over the call to see the effect of
   1038      *       adjustment.  We stop here first on the recursive call that
   1039      *       creates the initial map, and then on each counter group and
   1040      *       hint zone.
   1041      */
   1042 
   1043     /* adjust positions of hint edges that are not locked to blue zones */
   1044     cf2_hintmap_adjustHints( hintmap );
   1045 
   1046     FT_TRACE6(( "(adjusted)\n" ));
   1047     cf2_hintmap_dump( hintmap );
   1048 
   1049     /* save the position of all hints that were used in this hint map; */
   1050     /* if we use them again, we'll locate them in the same position    */
   1051     if ( !initialMap )
   1052     {
   1053       for ( i = 0; i < hintmap->count; i++ )
   1054       {
   1055         if ( !cf2_hint_isSynthetic( &hintmap->edge[i] ) )
   1056         {
   1057           /* Note: include both valid and invalid edges            */
   1058           /* Note: top and bottom edges are copied back separately */
   1059           CF2_StemHint  stemhint = (CF2_StemHint)
   1060                           cf2_arrstack_getPointer( hStemHintArray,
   1061                                                    hintmap->edge[i].index );
   1062 
   1063 
   1064           if ( cf2_hint_isTop( &hintmap->edge[i] ) )
   1065             stemhint->maxDS = hintmap->edge[i].dsCoord;
   1066           else
   1067             stemhint->minDS = hintmap->edge[i].dsCoord;
   1068 
   1069           stemhint->used = TRUE;
   1070         }
   1071       }
   1072     }
   1073 
   1074     /* hint map is ready to use */
   1075     hintmap->isValid = TRUE;
   1076 
   1077     /* remember this mask has been used */
   1078     cf2_hintmask_setNew( hintMask, FALSE );
   1079   }
   1080 
   1081 
   1082   FT_LOCAL_DEF( void )
   1083   cf2_glyphpath_init( CF2_GlyphPath         glyphpath,
   1084                       CF2_Font              font,
   1085                       CF2_OutlineCallbacks  callbacks,
   1086                       CF2_Fixed             scaleY,
   1087                       /* CF2_Fixed  hShift, */
   1088                       CF2_ArrStack          hStemHintArray,
   1089                       CF2_ArrStack          vStemHintArray,
   1090                       CF2_HintMask          hintMask,
   1091                       CF2_Fixed             hintOriginY,
   1092                       const CF2_Blues       blues,
   1093                       const FT_Vector*      fractionalTranslation )
   1094   {
   1095     FT_ZERO( glyphpath );
   1096 
   1097     glyphpath->font      = font;
   1098     glyphpath->callbacks = callbacks;
   1099 
   1100     cf2_arrstack_init( &glyphpath->hintMoves,
   1101                        font->memory,
   1102                        &font->error,
   1103                        sizeof ( CF2_HintMoveRec ) );
   1104 
   1105     cf2_hintmap_init( &glyphpath->initialHintMap,
   1106                       font,
   1107                       &glyphpath->initialHintMap,
   1108                       &glyphpath->hintMoves,
   1109                       scaleY );
   1110     cf2_hintmap_init( &glyphpath->firstHintMap,
   1111                       font,
   1112                       &glyphpath->initialHintMap,
   1113                       &glyphpath->hintMoves,
   1114                       scaleY );
   1115     cf2_hintmap_init( &glyphpath->hintMap,
   1116                       font,
   1117                       &glyphpath->initialHintMap,
   1118                       &glyphpath->hintMoves,
   1119                       scaleY );
   1120 
   1121     glyphpath->scaleX = font->innerTransform.a;
   1122     glyphpath->scaleC = font->innerTransform.c;
   1123     glyphpath->scaleY = font->innerTransform.d;
   1124 
   1125     glyphpath->fractionalTranslation = *fractionalTranslation;
   1126 
   1127 #if 0
   1128     glyphpath->hShift = hShift;       /* for fauxing */
   1129 #endif
   1130 
   1131     glyphpath->hStemHintArray = hStemHintArray;
   1132     glyphpath->vStemHintArray = vStemHintArray;
   1133     glyphpath->hintMask       = hintMask;      /* ptr to current mask */
   1134     glyphpath->hintOriginY    = hintOriginY;
   1135     glyphpath->blues          = blues;
   1136     glyphpath->darken         = font->darkened; /* TODO: should we make copies? */
   1137     glyphpath->xOffset        = font->darkenX;
   1138     glyphpath->yOffset        = font->darkenY;
   1139     glyphpath->miterLimit     = 2 * FT_MAX(
   1140                                      cf2_fixedAbs( glyphpath->xOffset ),
   1141                                      cf2_fixedAbs( glyphpath->yOffset ) );
   1142 
   1143     /* .1 character space unit */
   1144     glyphpath->snapThreshold = cf2_doubleToFixed( 0.1 );
   1145 
   1146     glyphpath->moveIsPending = TRUE;
   1147     glyphpath->pathIsOpen    = FALSE;
   1148     glyphpath->pathIsClosing = FALSE;
   1149     glyphpath->elemIsQueued  = FALSE;
   1150   }
   1151 
   1152 
   1153   FT_LOCAL_DEF( void )
   1154   cf2_glyphpath_finalize( CF2_GlyphPath  glyphpath )
   1155   {
   1156     cf2_arrstack_finalize( &glyphpath->hintMoves );
   1157   }
   1158 
   1159 
   1160   /*
   1161    * Hint point in y-direction and apply outerTransform.
   1162    * Input `current' hint map (which is actually delayed by one element).
   1163    * Input x,y point in Character Space.
   1164    * Output x,y point in Device Space, including translation.
   1165    */
   1166   static void
   1167   cf2_glyphpath_hintPoint( CF2_GlyphPath  glyphpath,
   1168                            CF2_HintMap    hintmap,
   1169                            FT_Vector*     ppt,
   1170                            CF2_Fixed      x,
   1171                            CF2_Fixed      y )
   1172   {
   1173     FT_Vector  pt;   /* hinted point in upright DS */
   1174 
   1175 
   1176     pt.x = ADD_INT32( FT_MulFix( glyphpath->scaleX, x ),
   1177                       FT_MulFix( glyphpath->scaleC, y ) );
   1178     pt.y = cf2_hintmap_map( hintmap, y );
   1179 
   1180     ppt->x = ADD_INT32(
   1181                FT_MulFix( glyphpath->font->outerTransform.a, pt.x ),
   1182                ADD_INT32(
   1183                  FT_MulFix( glyphpath->font->outerTransform.c, pt.y ),
   1184                  glyphpath->fractionalTranslation.x ) );
   1185     ppt->y = ADD_INT32(
   1186                FT_MulFix( glyphpath->font->outerTransform.b, pt.x ),
   1187                ADD_INT32(
   1188                  FT_MulFix( glyphpath->font->outerTransform.d, pt.y ),
   1189                  glyphpath->fractionalTranslation.y ) );
   1190   }
   1191 
   1192 
   1193   /*
   1194    * From two line segments, (u1,u2) and (v1,v2), compute a point of
   1195    * intersection on the corresponding lines.
   1196    * Return false if no intersection is found, or if the intersection is
   1197    * too far away from the ends of the line segments, u2 and v1.
   1198    *
   1199    */
   1200   static FT_Bool
   1201   cf2_glyphpath_computeIntersection( CF2_GlyphPath     glyphpath,
   1202                                      const FT_Vector*  u1,
   1203                                      const FT_Vector*  u2,
   1204                                      const FT_Vector*  v1,
   1205                                      const FT_Vector*  v2,
   1206                                      FT_Vector*        intersection )
   1207   {
   1208     /*
   1209      * Let `u' be a zero-based vector from the first segment, `v' from the
   1210      * second segment.
   1211      * Let `w 'be the zero-based vector from `u1' to `v1'.
   1212      * `perp' is the `perpendicular dot product'; see
   1213      * https://mathworld.wolfram.com/PerpDotProduct.html.
   1214      * `s' is the parameter for the parametric line for the first segment
   1215      * (`u').
   1216      *
   1217      * See notation in
   1218      * http://softsurfer.com/Archive/algorithm_0104/algorithm_0104B.htm.
   1219      * Calculations are done in 16.16, but must handle the squaring of
   1220      * line lengths in character space.  We scale all vectors by 1/32 to
   1221      * avoid overflow.  This allows values up to 4095 to be squared.  The
   1222      * scale factor cancels in the divide.
   1223      *
   1224      * TODO: the scale factor could be computed from UnitsPerEm.
   1225      *
   1226      */
   1227 
   1228 #define cf2_perp( a, b )                                    \
   1229           ( FT_MulFix( a.x, b.y ) - FT_MulFix( a.y, b.x ) )
   1230 
   1231   /* round and divide by 32 */
   1232 #define CF2_CS_SCALE( x )         \
   1233           ( ( (x) + 0x10 ) >> 5 )
   1234 
   1235     FT_Vector  u, v, w;      /* scaled vectors */
   1236     CF2_Fixed  denominator, s;
   1237 
   1238 
   1239     u.x = CF2_CS_SCALE( SUB_INT32( u2->x, u1->x ) );
   1240     u.y = CF2_CS_SCALE( SUB_INT32( u2->y, u1->y ) );
   1241     v.x = CF2_CS_SCALE( SUB_INT32( v2->x, v1->x ) );
   1242     v.y = CF2_CS_SCALE( SUB_INT32( v2->y, v1->y ) );
   1243     w.x = CF2_CS_SCALE( SUB_INT32( v1->x, u1->x ) );
   1244     w.y = CF2_CS_SCALE( SUB_INT32( v1->y, u1->y ) );
   1245 
   1246     denominator = cf2_perp( u, v );
   1247 
   1248     if ( denominator == 0 )
   1249       return FALSE;           /* parallel or coincident lines */
   1250 
   1251     s = FT_DivFix( cf2_perp( w, v ), denominator );
   1252 
   1253     intersection->x = ADD_INT32( u1->x,
   1254                                  FT_MulFix( s, SUB_INT32( u2->x, u1->x ) ) );
   1255     intersection->y = ADD_INT32( u1->y,
   1256                                  FT_MulFix( s, SUB_INT32( u2->y, u1->y ) ) );
   1257 
   1258 
   1259     /*
   1260      * Special case snapping for horizontal and vertical lines.
   1261      * This cleans up intersections and reduces problems with winding
   1262      * order detection.
   1263      * Sample case is sbc cd KozGoPr6N-Medium.otf 20 16685.
   1264      * Note: these calculations are in character space.
   1265      *
   1266      */
   1267 
   1268     if ( u1->x == u2->x                                                &&
   1269          cf2_fixedAbs( SUB_INT32( intersection->x,
   1270                                   u1->x ) ) < glyphpath->snapThreshold )
   1271       intersection->x = u1->x;
   1272     if ( u1->y == u2->y                                                &&
   1273          cf2_fixedAbs( SUB_INT32( intersection->y,
   1274                                   u1->y ) ) < glyphpath->snapThreshold )
   1275       intersection->y = u1->y;
   1276 
   1277     if ( v1->x == v2->x                                                &&
   1278          cf2_fixedAbs( SUB_INT32( intersection->x,
   1279                                   v1->x ) ) < glyphpath->snapThreshold )
   1280       intersection->x = v1->x;
   1281     if ( v1->y == v2->y                                                &&
   1282          cf2_fixedAbs( SUB_INT32( intersection->y,
   1283                                   v1->y ) ) < glyphpath->snapThreshold )
   1284       intersection->y = v1->y;
   1285 
   1286     /* limit the intersection distance from midpoint of u2 and v1 */
   1287     if ( cf2_fixedAbs( intersection->x - ADD_INT32( u2->x, v1->x ) / 2 ) >
   1288            glyphpath->miterLimit                                           ||
   1289          cf2_fixedAbs( intersection->y - ADD_INT32( u2->y, v1->y ) / 2 ) >
   1290            glyphpath->miterLimit                                           )
   1291       return FALSE;
   1292 
   1293     return TRUE;
   1294   }
   1295 
   1296 
   1297   /*
   1298    * Push the cached element (glyphpath->prevElem*) to the outline
   1299    * consumer.  When a darkening offset is used, the end point of the
   1300    * cached element may be adjusted to an intersection point or we may
   1301    * synthesize a connecting line to the current element.  If we are
   1302    * closing a subpath, we may also generate a connecting line to the start
   1303    * point.
   1304    *
   1305    * This is where Character Space (CS) is converted to Device Space (DS)
   1306    * using a hint map.  This calculation must use a HintMap that was valid
   1307    * at the time the element was saved.  For the first point in a subpath,
   1308    * that is a saved HintMap.  For most elements, it just means the caller
   1309    * has delayed building a HintMap from the current HintMask.
   1310    *
   1311    * Transform each point with outerTransform and call the outline
   1312    * callbacks.  This is a general 3x3 transform:
   1313    *
   1314    *   x' = a*x + c*y + tx, y' = b*x + d*y + ty
   1315    *
   1316    * but it uses 4 elements from CF2_Font and the translation part
   1317    * from CF2_GlyphPath.
   1318    *
   1319    */
   1320   static void
   1321   cf2_glyphpath_pushPrevElem( CF2_GlyphPath  glyphpath,
   1322                               CF2_HintMap    hintmap,
   1323                               FT_Vector*     nextP0,
   1324                               FT_Vector      nextP1,
   1325                               FT_Bool        close )
   1326   {
   1327     CF2_CallbackParamsRec  params;
   1328 
   1329     FT_Vector*  prevP0;
   1330     FT_Vector*  prevP1;
   1331 
   1332     FT_Vector  intersection    = { 0, 0 };
   1333     FT_Bool    useIntersection = FALSE;
   1334 
   1335 
   1336     FT_ASSERT( glyphpath->prevElemOp == CF2_PathOpLineTo ||
   1337                glyphpath->prevElemOp == CF2_PathOpCubeTo );
   1338 
   1339     if ( glyphpath->prevElemOp == CF2_PathOpLineTo )
   1340     {
   1341       prevP0 = &glyphpath->prevElemP0;
   1342       prevP1 = &glyphpath->prevElemP1;
   1343     }
   1344     else
   1345     {
   1346       prevP0 = &glyphpath->prevElemP2;
   1347       prevP1 = &glyphpath->prevElemP3;
   1348     }
   1349 
   1350     /* optimization: if previous and next elements are offset by the same */
   1351     /* amount, then there will be no gap, and no need to compute an       */
   1352     /* intersection.                                                      */
   1353     if ( prevP1->x != nextP0->x || prevP1->y != nextP0->y )
   1354     {
   1355       /* previous element does not join next element:             */
   1356       /* adjust end point of previous element to the intersection */
   1357       useIntersection = cf2_glyphpath_computeIntersection( glyphpath,
   1358                                                            prevP0,
   1359                                                            prevP1,
   1360                                                            nextP0,
   1361                                                            &nextP1,
   1362                                                            &intersection );
   1363       if ( useIntersection )
   1364       {
   1365         /* modify the last point of the cached element (either line or */
   1366         /* curve)                                                      */
   1367         *prevP1 = intersection;
   1368       }
   1369     }
   1370 
   1371     params.pt0 = glyphpath->currentDS;
   1372 
   1373     switch( glyphpath->prevElemOp )
   1374     {
   1375     case CF2_PathOpLineTo:
   1376       params.op = CF2_PathOpLineTo;
   1377 
   1378       /* note: pt2 and pt3 are unused */
   1379 
   1380       if ( close )
   1381       {
   1382         /* use first hint map if closing */
   1383         cf2_glyphpath_hintPoint( glyphpath,
   1384                                  &glyphpath->firstHintMap,
   1385                                  &params.pt1,
   1386                                  glyphpath->prevElemP1.x,
   1387                                  glyphpath->prevElemP1.y );
   1388       }
   1389       else
   1390       {
   1391         cf2_glyphpath_hintPoint( glyphpath,
   1392                                  hintmap,
   1393                                  &params.pt1,
   1394                                  glyphpath->prevElemP1.x,
   1395                                  glyphpath->prevElemP1.y );
   1396       }
   1397 
   1398       /* output only non-zero length lines */
   1399       if ( params.pt0.x != params.pt1.x || params.pt0.y != params.pt1.y )
   1400       {
   1401         glyphpath->callbacks->lineTo( glyphpath->callbacks, &params );
   1402 
   1403         glyphpath->currentDS = params.pt1;
   1404       }
   1405       break;
   1406 
   1407     case CF2_PathOpCubeTo:
   1408       params.op = CF2_PathOpCubeTo;
   1409 
   1410       /* TODO: should we intersect the interior joins (p1-p2 and p2-p3)? */
   1411       cf2_glyphpath_hintPoint( glyphpath,
   1412                                hintmap,
   1413                                &params.pt1,
   1414                                glyphpath->prevElemP1.x,
   1415                                glyphpath->prevElemP1.y );
   1416       cf2_glyphpath_hintPoint( glyphpath,
   1417                                hintmap,
   1418                                &params.pt2,
   1419                                glyphpath->prevElemP2.x,
   1420                                glyphpath->prevElemP2.y );
   1421       cf2_glyphpath_hintPoint( glyphpath,
   1422                                hintmap,
   1423                                &params.pt3,
   1424                                glyphpath->prevElemP3.x,
   1425                                glyphpath->prevElemP3.y );
   1426 
   1427       glyphpath->callbacks->cubeTo( glyphpath->callbacks, &params );
   1428 
   1429       glyphpath->currentDS = params.pt3;
   1430 
   1431       break;
   1432     }
   1433 
   1434     if ( !useIntersection || close )
   1435     {
   1436       /* insert connecting line between end of previous element and start */
   1437       /* of current one                                                   */
   1438       /* note: at the end of a subpath, we might do both, so use `nextP0' */
   1439       /* before we change it, below                                       */
   1440 
   1441       if ( close )
   1442       {
   1443         /* if we are closing the subpath, then nextP0 is in the first     */
   1444         /* hint zone                                                      */
   1445         cf2_glyphpath_hintPoint( glyphpath,
   1446                                  &glyphpath->firstHintMap,
   1447                                  &params.pt1,
   1448                                  nextP0->x,
   1449                                  nextP0->y );
   1450       }
   1451       else
   1452       {
   1453         cf2_glyphpath_hintPoint( glyphpath,
   1454                                  hintmap,
   1455                                  &params.pt1,
   1456                                  nextP0->x,
   1457                                  nextP0->y );
   1458       }
   1459 
   1460       if ( params.pt1.x != glyphpath->currentDS.x ||
   1461            params.pt1.y != glyphpath->currentDS.y )
   1462       {
   1463         /* length is nonzero */
   1464         params.op  = CF2_PathOpLineTo;
   1465         params.pt0 = glyphpath->currentDS;
   1466 
   1467         /* note: pt2 and pt3 are unused */
   1468         glyphpath->callbacks->lineTo( glyphpath->callbacks, &params );
   1469 
   1470         glyphpath->currentDS = params.pt1;
   1471       }
   1472     }
   1473 
   1474     if ( useIntersection )
   1475     {
   1476       /* return intersection point to caller */
   1477       *nextP0 = intersection;
   1478     }
   1479   }
   1480 
   1481 
   1482   /* push a MoveTo element based on current point and offset of current */
   1483   /* element                                                            */
   1484   static void
   1485   cf2_glyphpath_pushMove( CF2_GlyphPath  glyphpath,
   1486                           FT_Vector      start )
   1487   {
   1488     CF2_CallbackParamsRec  params;
   1489 
   1490 
   1491     params.op  = CF2_PathOpMoveTo;
   1492     params.pt0 = glyphpath->currentDS;
   1493 
   1494     /* Test if move has really happened yet; it would have called */
   1495     /* `cf2_hintmap_build' to set `isValid'.                   */
   1496     if ( !cf2_hintmap_isValid( &glyphpath->hintMap ) )
   1497     {
   1498       /* we are here iff first subpath is missing a moveto operator: */
   1499       /* synthesize first moveTo to finish initialization of hintMap */
   1500       cf2_glyphpath_moveTo( glyphpath,
   1501                             glyphpath->start.x,
   1502                             glyphpath->start.y );
   1503     }
   1504 
   1505     cf2_glyphpath_hintPoint( glyphpath,
   1506                              &glyphpath->hintMap,
   1507                              &params.pt1,
   1508                              start.x,
   1509                              start.y );
   1510 
   1511     /* note: pt2 and pt3 are unused */
   1512     glyphpath->callbacks->moveTo( glyphpath->callbacks, &params );
   1513 
   1514     glyphpath->currentDS    = params.pt1;
   1515     glyphpath->offsetStart0 = start;
   1516   }
   1517 
   1518 
   1519   /*
   1520    * All coordinates are in character space.
   1521    * On input, (x1, y1) and (x2, y2) give line segment.
   1522    * On output, (x, y) give offset vector.
   1523    * We use a piecewise approximation to trig functions.
   1524    *
   1525    * TODO: Offset true perpendicular and proper length
   1526    *       supply the y-translation for hinting here, too,
   1527    *       that adds yOffset unconditionally to *y.
   1528    */
   1529   static void
   1530   cf2_glyphpath_computeOffset( CF2_GlyphPath  glyphpath,
   1531                                CF2_Fixed      x1,
   1532                                CF2_Fixed      y1,
   1533                                CF2_Fixed      x2,
   1534                                CF2_Fixed      y2,
   1535                                CF2_Fixed*     x,
   1536                                CF2_Fixed*     y )
   1537   {
   1538     CF2_Fixed  dx = SUB_INT32( x2, x1 );
   1539     CF2_Fixed  dy = SUB_INT32( y2, y1 );
   1540 
   1541 
   1542     /* note: negative offsets don't work here; negate deltas to change */
   1543     /* quadrants, below                                                */
   1544     if ( glyphpath->font->reverseWinding )
   1545     {
   1546       dx = NEG_INT32( dx );
   1547       dy = NEG_INT32( dy );
   1548     }
   1549 
   1550     *x = *y = 0;
   1551 
   1552     if ( !glyphpath->darken )
   1553         return;
   1554 
   1555     /* add momentum for this path element */
   1556     glyphpath->callbacks->windingMomentum =
   1557       ADD_INT32( glyphpath->callbacks->windingMomentum,
   1558                  cf2_getWindingMomentum( x1, y1, x2, y2 ) );
   1559 
   1560     /* note: allow mixed integer and fixed multiplication here */
   1561     if ( dx >= 0 )
   1562     {
   1563       if ( dy >= 0 )
   1564       {
   1565         /* first quadrant, +x +y */
   1566 
   1567         if ( dx > MUL_INT32( 2, dy ) )
   1568         {
   1569           /* +x */
   1570           *x = 0;
   1571           *y = 0;
   1572         }
   1573         else if ( dy > MUL_INT32( 2, dx ) )
   1574         {
   1575           /* +y */
   1576           *x = glyphpath->xOffset;
   1577           *y = glyphpath->yOffset;
   1578         }
   1579         else
   1580         {
   1581           /* +x +y */
   1582           *x = FT_MulFix( cf2_doubleToFixed( 0.7 ),
   1583                           glyphpath->xOffset );
   1584           *y = FT_MulFix( cf2_doubleToFixed( 1.0 - 0.7 ),
   1585                           glyphpath->yOffset );
   1586         }
   1587       }
   1588       else
   1589       {
   1590         /* fourth quadrant, +x -y */
   1591 
   1592         if ( dx > MUL_INT32( -2, dy ) )
   1593         {
   1594           /* +x */
   1595           *x = 0;
   1596           *y = 0;
   1597         }
   1598         else if ( NEG_INT32( dy ) > MUL_INT32( 2, dx ) )
   1599         {
   1600           /* -y */
   1601           *x = NEG_INT32( glyphpath->xOffset );
   1602           *y = glyphpath->yOffset;
   1603         }
   1604         else
   1605         {
   1606           /* +x -y */
   1607           *x = FT_MulFix( cf2_doubleToFixed( -0.7 ),
   1608                           glyphpath->xOffset );
   1609           *y = FT_MulFix( cf2_doubleToFixed( 1.0 - 0.7 ),
   1610                           glyphpath->yOffset );
   1611         }
   1612       }
   1613     }
   1614     else
   1615     {
   1616       if ( dy >= 0 )
   1617       {
   1618         /* second quadrant, -x +y */
   1619 
   1620         if ( NEG_INT32( dx ) > MUL_INT32( 2, dy ) )
   1621         {
   1622           /* -x */
   1623           *x = 0;
   1624           *y = MUL_INT32( 2, glyphpath->yOffset );
   1625         }
   1626         else if ( dy > MUL_INT32( -2, dx ) )
   1627         {
   1628           /* +y */
   1629           *x = glyphpath->xOffset;
   1630           *y = glyphpath->yOffset;
   1631         }
   1632         else
   1633         {
   1634           /* -x +y */
   1635           *x = FT_MulFix( cf2_doubleToFixed( 0.7 ),
   1636                           glyphpath->xOffset );
   1637           *y = FT_MulFix( cf2_doubleToFixed( 1.0 + 0.7 ),
   1638                           glyphpath->yOffset );
   1639         }
   1640       }
   1641       else
   1642       {
   1643         /* third quadrant, -x -y */
   1644 
   1645         if ( NEG_INT32( dx ) > MUL_INT32( -2, dy ) )
   1646         {
   1647           /* -x */
   1648           *x = 0;
   1649           *y = MUL_INT32( 2, glyphpath->yOffset );
   1650         }
   1651         else if ( NEG_INT32( dy ) > MUL_INT32( -2, dx ) )
   1652         {
   1653           /* -y */
   1654           *x = NEG_INT32( glyphpath->xOffset );
   1655           *y = glyphpath->yOffset;
   1656         }
   1657         else
   1658         {
   1659           /* -x -y */
   1660           *x = FT_MulFix( cf2_doubleToFixed( -0.7 ),
   1661                           glyphpath->xOffset );
   1662           *y = FT_MulFix( cf2_doubleToFixed( 1.0 + 0.7 ),
   1663                           glyphpath->yOffset );
   1664         }
   1665       }
   1666     }
   1667   }
   1668 
   1669 
   1670   /*
   1671    * The functions cf2_glyphpath_{moveTo,lineTo,curveTo,closeOpenPath} are
   1672    * called by the interpreter with Character Space (CS) coordinates.  Each
   1673    * path element is placed into a queue of length one to await the
   1674    * calculation of the following element.  At that time, the darkening
   1675    * offset of the following element is known and joins can be computed,
   1676    * including possible modification of this element, before mapping to
   1677    * Device Space (DS) and passing it on to the outline consumer.
   1678    *
   1679    */
   1680   FT_LOCAL_DEF( void )
   1681   cf2_glyphpath_moveTo( CF2_GlyphPath  glyphpath,
   1682                         CF2_Fixed      x,
   1683                         CF2_Fixed      y )
   1684   {
   1685     cf2_glyphpath_closeOpenPath( glyphpath );
   1686 
   1687     /* save the parameters of the move for later, when we'll know how to */
   1688     /* offset it;                                                        */
   1689     /* also save last move point */
   1690     glyphpath->currentCS.x = glyphpath->start.x = x;
   1691     glyphpath->currentCS.y = glyphpath->start.y = y;
   1692 
   1693     glyphpath->moveIsPending = TRUE;
   1694 
   1695     /* ensure we have a valid map with current mask */
   1696     if ( !cf2_hintmap_isValid( &glyphpath->hintMap ) ||
   1697          cf2_hintmask_isNew( glyphpath->hintMask )   )
   1698       cf2_hintmap_build( &glyphpath->hintMap,
   1699                          glyphpath->hStemHintArray,
   1700                          glyphpath->vStemHintArray,
   1701                          glyphpath->hintMask,
   1702                          glyphpath->hintOriginY,
   1703                          FALSE );
   1704 
   1705     /* save a copy of current HintMap to use when drawing initial point */
   1706     glyphpath->firstHintMap = glyphpath->hintMap;     /* structure copy */
   1707   }
   1708 
   1709 
   1710   FT_LOCAL_DEF( void )
   1711   cf2_glyphpath_lineTo( CF2_GlyphPath  glyphpath,
   1712                         CF2_Fixed      x,
   1713                         CF2_Fixed      y )
   1714   {
   1715     CF2_Fixed  xOffset, yOffset;
   1716     FT_Vector  P0, P1;
   1717     FT_Bool    newHintMap;
   1718 
   1719     /*
   1720      * New hints will be applied after cf2_glyphpath_pushPrevElem has run.
   1721      * In case this is a synthesized closing line, any new hints should be
   1722      * delayed until this path is closed (`cf2_hintmask_isNew' will be
   1723      * called again before the next line or curve).
   1724      */
   1725 
   1726     /* true if new hint map not on close */
   1727     newHintMap = cf2_hintmask_isNew( glyphpath->hintMask ) &&
   1728                  !glyphpath->pathIsClosing;
   1729 
   1730     /*
   1731      * Zero-length lines may occur in the charstring.  Because we cannot
   1732      * compute darkening offsets or intersections from zero-length lines,
   1733      * it is best to remove them and avoid artifacts.  However, zero-length
   1734      * lines in CS at the start of a new hint map can generate non-zero
   1735      * lines in DS due to hint substitution.  We detect a change in hint
   1736      * map here and pass those zero-length lines along.
   1737      */
   1738 
   1739     /*
   1740      * Note: Find explicitly closed paths here with a conditional
   1741      *       breakpoint using
   1742      *
   1743      *         !gp->pathIsClosing && gp->start.x == x && gp->start.y == y
   1744      *
   1745      */
   1746 
   1747     if ( glyphpath->currentCS.x == x &&
   1748          glyphpath->currentCS.y == y &&
   1749          !newHintMap                 )
   1750       /*
   1751        * Ignore zero-length lines in CS where the hint map is the same
   1752        * because the line in DS will also be zero length.
   1753        *
   1754        * Ignore zero-length lines when we synthesize a closing line because
   1755        * the close will be handled in cf2_glyphPath_pushPrevElem.
   1756        */
   1757       return;
   1758 
   1759     cf2_glyphpath_computeOffset( glyphpath,
   1760                                  glyphpath->currentCS.x,
   1761                                  glyphpath->currentCS.y,
   1762                                  x,
   1763                                  y,
   1764                                  &xOffset,
   1765                                  &yOffset );
   1766 
   1767     /* construct offset points */
   1768     P0.x = ADD_INT32( glyphpath->currentCS.x, xOffset );
   1769     P0.y = ADD_INT32( glyphpath->currentCS.y, yOffset );
   1770     P1.x = ADD_INT32( x, xOffset );
   1771     P1.y = ADD_INT32( y, yOffset );
   1772 
   1773     if ( glyphpath->moveIsPending )
   1774     {
   1775       /* emit offset 1st point as MoveTo */
   1776       cf2_glyphpath_pushMove( glyphpath, P0 );
   1777 
   1778       glyphpath->moveIsPending = FALSE;  /* adjust state machine */
   1779       glyphpath->pathIsOpen    = TRUE;
   1780 
   1781       glyphpath->offsetStart1 = P1;              /* record second point */
   1782     }
   1783 
   1784     if ( glyphpath->elemIsQueued )
   1785     {
   1786       FT_ASSERT( cf2_hintmap_isValid( &glyphpath->hintMap ) ||
   1787                  glyphpath->hintMap.count == 0              );
   1788 
   1789       cf2_glyphpath_pushPrevElem( glyphpath,
   1790                                   &glyphpath->hintMap,
   1791                                   &P0,
   1792                                   P1,
   1793                                   FALSE );
   1794     }
   1795 
   1796     /* queue the current element with offset points */
   1797     glyphpath->elemIsQueued = TRUE;
   1798     glyphpath->prevElemOp   = CF2_PathOpLineTo;
   1799     glyphpath->prevElemP0   = P0;
   1800     glyphpath->prevElemP1   = P1;
   1801 
   1802     /* update current map */
   1803     if ( newHintMap )
   1804       cf2_hintmap_build( &glyphpath->hintMap,
   1805                          glyphpath->hStemHintArray,
   1806                          glyphpath->vStemHintArray,
   1807                          glyphpath->hintMask,
   1808                          glyphpath->hintOriginY,
   1809                          FALSE );
   1810 
   1811     glyphpath->currentCS.x = x;     /* pre-offset current point */
   1812     glyphpath->currentCS.y = y;
   1813   }
   1814 
   1815 
   1816   FT_LOCAL_DEF( void )
   1817   cf2_glyphpath_curveTo( CF2_GlyphPath  glyphpath,
   1818                          CF2_Fixed      x1,
   1819                          CF2_Fixed      y1,
   1820                          CF2_Fixed      x2,
   1821                          CF2_Fixed      y2,
   1822                          CF2_Fixed      x3,
   1823                          CF2_Fixed      y3 )
   1824   {
   1825     CF2_Fixed  xOffset1, yOffset1, xOffset3, yOffset3;
   1826     FT_Vector  P0, P1, P2, P3;
   1827 
   1828 
   1829     /* TODO: ignore zero length portions of curve?? */
   1830     cf2_glyphpath_computeOffset( glyphpath,
   1831                                  glyphpath->currentCS.x,
   1832                                  glyphpath->currentCS.y,
   1833                                  x1,
   1834                                  y1,
   1835                                  &xOffset1,
   1836                                  &yOffset1 );
   1837     cf2_glyphpath_computeOffset( glyphpath,
   1838                                  x2,
   1839                                  y2,
   1840                                  x3,
   1841                                  y3,
   1842                                  &xOffset3,
   1843                                  &yOffset3 );
   1844 
   1845     /* add momentum from the middle segment */
   1846     glyphpath->callbacks->windingMomentum =
   1847       ADD_INT32( glyphpath->callbacks->windingMomentum,
   1848                  cf2_getWindingMomentum( x1, y1, x2, y2 ) );
   1849 
   1850     /* construct offset points */
   1851     P0.x = ADD_INT32( glyphpath->currentCS.x, xOffset1 );
   1852     P0.y = ADD_INT32( glyphpath->currentCS.y, yOffset1 );
   1853     P1.x = ADD_INT32( x1, xOffset1 );
   1854     P1.y = ADD_INT32( y1, yOffset1 );
   1855     /* note: preserve angle of final segment by using offset3 at both ends */
   1856     P2.x = ADD_INT32( x2, xOffset3 );
   1857     P2.y = ADD_INT32( y2, yOffset3 );
   1858     P3.x = ADD_INT32( x3, xOffset3 );
   1859     P3.y = ADD_INT32( y3, yOffset3 );
   1860 
   1861     if ( glyphpath->moveIsPending )
   1862     {
   1863       /* emit offset 1st point as MoveTo */
   1864       cf2_glyphpath_pushMove( glyphpath, P0 );
   1865 
   1866       glyphpath->moveIsPending = FALSE;
   1867       glyphpath->pathIsOpen    = TRUE;
   1868 
   1869       glyphpath->offsetStart1 = P1;              /* record second point */
   1870     }
   1871 
   1872     if ( glyphpath->elemIsQueued )
   1873     {
   1874       FT_ASSERT( cf2_hintmap_isValid( &glyphpath->hintMap ) ||
   1875                  glyphpath->hintMap.count == 0              );
   1876 
   1877       cf2_glyphpath_pushPrevElem( glyphpath,
   1878                                   &glyphpath->hintMap,
   1879                                   &P0,
   1880                                   P1,
   1881                                   FALSE );
   1882     }
   1883 
   1884     /* queue the current element with offset points */
   1885     glyphpath->elemIsQueued = TRUE;
   1886     glyphpath->prevElemOp   = CF2_PathOpCubeTo;
   1887     glyphpath->prevElemP0   = P0;
   1888     glyphpath->prevElemP1   = P1;
   1889     glyphpath->prevElemP2   = P2;
   1890     glyphpath->prevElemP3   = P3;
   1891 
   1892     /* update current map */
   1893     if ( cf2_hintmask_isNew( glyphpath->hintMask ) )
   1894       cf2_hintmap_build( &glyphpath->hintMap,
   1895                          glyphpath->hStemHintArray,
   1896                          glyphpath->vStemHintArray,
   1897                          glyphpath->hintMask,
   1898                          glyphpath->hintOriginY,
   1899                          FALSE );
   1900 
   1901     glyphpath->currentCS.x = x3;       /* pre-offset current point */
   1902     glyphpath->currentCS.y = y3;
   1903   }
   1904 
   1905 
   1906   FT_LOCAL_DEF( void )
   1907   cf2_glyphpath_closeOpenPath( CF2_GlyphPath  glyphpath )
   1908   {
   1909     if ( glyphpath->pathIsOpen )
   1910     {
   1911       /*
   1912        * A closing line in Character Space line is always generated below
   1913        * with `cf2_glyphPath_lineTo'.  It may be ignored later if it turns
   1914        * out to be zero length in Device Space.
   1915        */
   1916       glyphpath->pathIsClosing = TRUE;
   1917 
   1918       cf2_glyphpath_lineTo( glyphpath,
   1919                             glyphpath->start.x,
   1920                             glyphpath->start.y );
   1921 
   1922       /* empty the final element from the queue and close the path */
   1923       if ( glyphpath->elemIsQueued )
   1924         cf2_glyphpath_pushPrevElem( glyphpath,
   1925                                     &glyphpath->hintMap,
   1926                                     &glyphpath->offsetStart0,
   1927                                     glyphpath->offsetStart1,
   1928                                     TRUE );
   1929 
   1930       /* reset state machine */
   1931       glyphpath->moveIsPending = TRUE;
   1932       glyphpath->pathIsOpen    = FALSE;
   1933       glyphpath->pathIsClosing = FALSE;
   1934       glyphpath->elemIsQueued  = FALSE;
   1935     }
   1936   }
   1937 
   1938 
   1939 /* END */
   1940