Home | History | Annotate | Download | only in cff
      1 /***************************************************************************/
      2 /*                                                                         */
      3 /*  cf2hints.c                                                             */
      4 /*                                                                         */
      5 /*    Adobe's code for handling CFF hints (body).                          */
      6 /*                                                                         */
      7 /*  Copyright 2007-2013 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 "cf2ft.h"
     40 #include FT_INTERNAL_DEBUG_H
     41 
     42 #include "cf2glue.h"
     43 #include "cf2font.h"
     44 #include "cf2hints.h"
     45 #include "cf2intrp.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 ) * ( ( y2 - y1 ) >> 16 ) -
     78            ( y1 >> 16 ) * ( ( 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 = 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 += 2 * font->darkenY;
    189 
    190     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 hint->flags != 0;
    221   }
    222 
    223 
    224   static FT_Bool
    225   cf2_hint_isPair( const CF2_Hint  hint )
    226   {
    227     return ( 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 ( 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 ( 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 ( 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 ( hint->flags & CF2_Locked ) != 0;
    259   }
    260 
    261 
    262   static FT_Bool
    263   cf2_hint_isSynthetic( const CF2_Hint  hint )
    264   {
    265     return ( 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   /* transform character space coordinate to device space using hint map */
    303   static CF2_Fixed
    304   cf2_hintmap_map( CF2_HintMap  hintmap,
    305                    CF2_Fixed    csCoord )
    306   {
    307     FT_ASSERT( hintmap->isValid );  /* must call Build before Map */
    308     FT_ASSERT( hintmap->lastIndex < CF2_MAX_HINT_EDGES );
    309 
    310     if ( hintmap->count == 0 || ! hintmap->hinted )
    311     {
    312       /* there are no hints; use uniform scale and zero offset */
    313       return FT_MulFix( csCoord, hintmap->scale );
    314     }
    315     else
    316     {
    317       /* start linear search from last hit */
    318       CF2_UInt  i = hintmap->lastIndex;
    319 
    320 
    321       /* search up */
    322       while ( i < hintmap->count - 1                  &&
    323               csCoord >= hintmap->edge[i + 1].csCoord )
    324         i += 1;
    325 
    326       /* search down */
    327       while ( i > 0 && csCoord < hintmap->edge[i].csCoord )
    328         i -= 1;
    329 
    330       hintmap->lastIndex = i;
    331 
    332       if ( i == 0 && csCoord < hintmap->edge[0].csCoord )
    333       {
    334         /* special case for points below first edge: use uniform scale */
    335         return FT_MulFix( csCoord - hintmap->edge[0].csCoord,
    336                           hintmap->scale ) +
    337                  hintmap->edge[0].dsCoord;
    338       }
    339       else
    340       {
    341         /*
    342          * Note: entries with duplicate csCoord are allowed.
    343          * Use edge[i], the highest entry where csCoord >= entry[i].csCoord
    344          */
    345         return FT_MulFix( csCoord - hintmap->edge[i].csCoord,
    346                           hintmap->edge[i].scale ) +
    347                  hintmap->edge[i].dsCoord;
    348       }
    349     }
    350   }
    351 
    352 
    353   /*
    354    * This hinting policy moves a hint pair in device space so that one of
    355    * its two edges is on a device pixel boundary (its fractional part is
    356    * zero).  `cf2_hintmap_insertHint' guarantees no overlap in CS
    357    * space.  Ensure here that there is no overlap in DS.
    358    *
    359    * In the first pass, edges are adjusted relative to adjacent hints.
    360    * Those that are below have already been adjusted.  Those that are
    361    * above have not yet been adjusted.  If a hint above blocks an
    362    * adjustment to an optimal position, we will try again in a second
    363    * pass.  The second pass is top-down.
    364    *
    365    */
    366 
    367   static void
    368   cf2_hintmap_adjustHints( CF2_HintMap  hintmap )
    369   {
    370     size_t  i, j;
    371 
    372 
    373     cf2_arrstack_clear( hintmap->hintMoves );      /* working storage */
    374 
    375     /*
    376      * First pass is bottom-up (font hint order) without look-ahead.
    377      * Locked edges are already adjusted.
    378      * Unlocked edges begin with dsCoord from `initialHintMap'.
    379      * Save edges that are not optimally adjusted in `hintMoves' array,
    380      * and process them in second pass.
    381      */
    382 
    383     for ( i = 0; i < hintmap->count; i++ )
    384     {
    385       FT_Bool  isPair = cf2_hint_isPair( &hintmap->edge[i] );
    386 
    387 
    388       /* index of upper edge (same value for ghost hint) */
    389       j = isPair ? i + 1 : i;
    390 
    391       FT_ASSERT( j < hintmap->count );
    392       FT_ASSERT( cf2_hint_isValid( &hintmap->edge[i] ) );
    393       FT_ASSERT( cf2_hint_isValid( &hintmap->edge[j] ) );
    394       FT_ASSERT( cf2_hint_isLocked( &hintmap->edge[i] ) ==
    395                    cf2_hint_isLocked( &hintmap->edge[j] ) );
    396 
    397       if ( !cf2_hint_isLocked( &hintmap->edge[i] ) )
    398       {
    399         /* hint edge is not locked, we can adjust it */
    400         CF2_Fixed  fracDown = cf2_fixedFraction( hintmap->edge[i].dsCoord );
    401         CF2_Fixed  fracUp   = cf2_fixedFraction( hintmap->edge[j].dsCoord );
    402 
    403         /* calculate all four possibilities; moves down are negative */
    404         CF2_Fixed  downMoveDown = 0 - fracDown;
    405         CF2_Fixed  upMoveDown   = 0 - fracUp;
    406         CF2_Fixed  downMoveUp   = fracDown == 0
    407                                     ? 0
    408                                     : cf2_intToFixed( 1 ) - fracDown;
    409         CF2_Fixed  upMoveUp     = fracUp == 0
    410                                     ? 0
    411                                     : cf2_intToFixed( 1 ) - fracUp;
    412 
    413         /* smallest move up */
    414         CF2_Fixed  moveUp   = FT_MIN( downMoveUp, upMoveUp );
    415         /* smallest move down */
    416         CF2_Fixed  moveDown = FT_MAX( downMoveDown, upMoveDown );
    417 
    418         /* final amount to move edge or edge pair */
    419         CF2_Fixed  move;
    420 
    421         CF2_Fixed  downMinCounter = CF2_MIN_COUNTER;
    422         CF2_Fixed  upMinCounter   = CF2_MIN_COUNTER;
    423         FT_Bool    saveEdge       = FALSE;
    424 
    425 
    426         /* minimum counter constraint doesn't apply when adjacent edges */
    427         /* are synthetic                                                */
    428         /* TODO: doesn't seem a big effect; for now, reduce the code    */
    429 #if 0
    430         if ( i == 0                                        ||
    431              cf2_hint_isSynthetic( &hintmap->edge[i - 1] ) )
    432           downMinCounter = 0;
    433 
    434         if ( j >= hintmap->count - 1                       ||
    435              cf2_hint_isSynthetic( &hintmap->edge[j + 1] ) )
    436           upMinCounter = 0;
    437 #endif
    438 
    439         /* is there room to move up?                                    */
    440         /* there is if we are at top of array or the next edge is at or */
    441         /* beyond proposed move up?                                     */
    442         if ( j >= hintmap->count - 1                            ||
    443              hintmap->edge[j + 1].dsCoord >=
    444                hintmap->edge[j].dsCoord + moveUp + upMinCounter )
    445         {
    446           /* there is room to move up; is there also room to move down? */
    447           if ( i == 0                                                 ||
    448                hintmap->edge[i - 1].dsCoord <=
    449                  hintmap->edge[i].dsCoord + moveDown - downMinCounter )
    450           {
    451             /* move smaller absolute amount */
    452             move = ( -moveDown < moveUp ) ? moveDown : moveUp;  /* optimum */
    453           }
    454           else
    455             move = moveUp;
    456         }
    457         else
    458         {
    459           /* is there room to move down? */
    460           if ( i == 0                                                 ||
    461                hintmap->edge[i - 1].dsCoord <=
    462                  hintmap->edge[i].dsCoord + moveDown - downMinCounter )
    463           {
    464             move     = moveDown;
    465             saveEdge = moveUp < -moveDown;  /* true if non-optimum move */
    466           }
    467           else
    468           {
    469             /* no room to move either way without overlapping or reducing */
    470             /* the counter too much                                       */
    471             move     = 0;
    472             saveEdge = TRUE;
    473           }
    474         }
    475 
    476         /* Identify non-moves and moves down that aren't optimal, and save */
    477         /* them for second pass.                                           */
    478         /* Do this only if there is an unlocked edge above (which could    */
    479         /* possibly move).                                                 */
    480         if ( saveEdge                                    &&
    481              j < hintmap->count - 1                      &&
    482              !cf2_hint_isLocked( &hintmap->edge[j + 1] ) )
    483         {
    484           CF2_HintMoveRec  savedMove;
    485 
    486 
    487           savedMove.j      = j;
    488           /* desired adjustment in second pass */
    489           savedMove.moveUp = moveUp - move;
    490 
    491           cf2_arrstack_push( hintmap->hintMoves, &savedMove );
    492         }
    493 
    494         /* move the edge(s) */
    495         hintmap->edge[i].dsCoord += move;
    496         if ( isPair )
    497           hintmap->edge[j].dsCoord += move;
    498       }
    499 
    500       /* assert there are no overlaps in device space */
    501       FT_ASSERT( i == 0                                                   ||
    502                  hintmap->edge[i - 1].dsCoord <= hintmap->edge[i].dsCoord );
    503       FT_ASSERT( i < j                                                ||
    504                  hintmap->edge[i].dsCoord <= hintmap->edge[j].dsCoord );
    505 
    506       /* adjust the scales, avoiding divide by zero */
    507       if ( i > 0 )
    508       {
    509         if ( hintmap->edge[i].csCoord != hintmap->edge[i - 1].csCoord )
    510           hintmap->edge[i - 1].scale =
    511             FT_DivFix(
    512               hintmap->edge[i].dsCoord - hintmap->edge[i - 1].dsCoord,
    513               hintmap->edge[i].csCoord - hintmap->edge[i - 1].csCoord );
    514       }
    515 
    516       if ( isPair )
    517       {
    518         if ( hintmap->edge[j].csCoord != hintmap->edge[j - 1].csCoord )
    519           hintmap->edge[j - 1].scale =
    520             FT_DivFix(
    521               hintmap->edge[j].dsCoord - hintmap->edge[j - 1].dsCoord,
    522               hintmap->edge[j].csCoord - hintmap->edge[j - 1].csCoord );
    523 
    524         i += 1;     /* skip upper edge on next loop */
    525       }
    526     }
    527 
    528     /* second pass tries to move non-optimal hints up, in case there is */
    529     /* room now                                                         */
    530     for ( i = cf2_arrstack_size( hintmap->hintMoves ); i > 0; i-- )
    531     {
    532       CF2_HintMove  hintMove = (CF2_HintMove)
    533                       cf2_arrstack_getPointer( hintmap->hintMoves, i - 1 );
    534 
    535 
    536       j = hintMove->j;
    537 
    538       /* this was tested before the push, above */
    539       FT_ASSERT( j < hintmap->count - 1 );
    540 
    541       /* is there room to move up? */
    542       if ( hintmap->edge[j + 1].dsCoord >=
    543              hintmap->edge[j].dsCoord + hintMove->moveUp + CF2_MIN_COUNTER )
    544       {
    545         /* there is more room now, move edge up */
    546         hintmap->edge[j].dsCoord += hintMove->moveUp;
    547 
    548         if ( cf2_hint_isPair( &hintmap->edge[j] ) )
    549         {
    550           FT_ASSERT( j > 0 );
    551           hintmap->edge[j - 1].dsCoord += hintMove->moveUp;
    552         }
    553       }
    554     }
    555   }
    556 
    557 
    558   /* insert hint edges into map, sorted by csCoord */
    559   static void
    560   cf2_hintmap_insertHint( CF2_HintMap  hintmap,
    561                           CF2_Hint     bottomHintEdge,
    562                           CF2_Hint     topHintEdge )
    563   {
    564     CF2_UInt  indexInsert;
    565 
    566     /* set default values, then check for edge hints */
    567     FT_Bool   isPair         = TRUE;
    568     CF2_Hint  firstHintEdge  = bottomHintEdge;
    569     CF2_Hint  secondHintEdge = topHintEdge;
    570 
    571 
    572     /* one or none of the input params may be invalid when dealing with */
    573     /* edge hints; at least one edge must be valid                      */
    574     FT_ASSERT( cf2_hint_isValid( bottomHintEdge ) ||
    575                cf2_hint_isValid( topHintEdge )    );
    576 
    577     /* determine how many and which edges to insert */
    578     if ( !cf2_hint_isValid( bottomHintEdge ) )
    579     {
    580       /* insert only the top edge */
    581       firstHintEdge = topHintEdge;
    582       isPair        = FALSE;
    583     }
    584     else if ( !cf2_hint_isValid( topHintEdge ) )
    585     {
    586       /* insert only the bottom edge */
    587       isPair = FALSE;
    588     }
    589 
    590     /* paired edges must be in proper order */
    591     FT_ASSERT( !isPair                                         ||
    592                topHintEdge->csCoord >= bottomHintEdge->csCoord );
    593 
    594     /* linear search to find index value of insertion point */
    595     indexInsert = 0;
    596     for ( ; indexInsert < hintmap->count; indexInsert++ )
    597     {
    598       if ( hintmap->edge[indexInsert].csCoord > firstHintEdge->csCoord )
    599         break;
    600     }
    601 
    602     /*
    603      * Discard any hints that overlap in character space.  Most often,
    604      * this is while building the initial map, but in theory, it can also
    605      * occur because of darkening.
    606      *
    607      */
    608     if ( indexInsert < hintmap->count )
    609     {
    610       /* we are inserting before an existing edge:              */
    611       /* verify that a new pair does not straddle the next edge */
    612       if ( isPair                                                       &&
    613            hintmap->edge[indexInsert].csCoord < secondHintEdge->csCoord )
    614         return; /* ignore overlapping stem hint */
    615 
    616       /* verify that we are not inserting between paired edges */
    617       if ( cf2_hint_isPairTop( &hintmap->edge[indexInsert] ) )
    618         return; /* ignore overlapping stem hint */
    619     }
    620 
    621     /* recompute device space locations using initial hint map */
    622     if ( cf2_hintmap_isValid( hintmap->initialHintMap ) &&
    623          !cf2_hint_isLocked( firstHintEdge )            )
    624     {
    625       if ( isPair )
    626       {
    627         /* Use hint map to position the center of stem, and nominal scale */
    628         /* to position the two edges.  This preserves the stem width.     */
    629         CF2_Fixed  midpoint  = cf2_hintmap_map(
    630                                  hintmap->initialHintMap,
    631                                  ( secondHintEdge->csCoord +
    632                                    firstHintEdge->csCoord ) / 2 );
    633         CF2_Fixed  halfWidth = FT_MulFix(
    634                                  ( secondHintEdge->csCoord -
    635                                    firstHintEdge->csCoord ) / 2,
    636                                  hintmap->scale );
    637 
    638 
    639         firstHintEdge->dsCoord  = midpoint - halfWidth;
    640         secondHintEdge->dsCoord = midpoint + halfWidth;
    641       }
    642       else
    643         firstHintEdge->dsCoord = cf2_hintmap_map( hintmap->initialHintMap,
    644                                                   firstHintEdge->csCoord );
    645     }
    646 
    647     /* discard any hints that overlap in device space; this can occur */
    648     /* because locked hints have been moved to align with blue zones  */
    649     if ( indexInsert > 0 )
    650     {
    651       /* we are inserting after an existing edge */
    652       if ( firstHintEdge->dsCoord < hintmap->edge[indexInsert - 1].dsCoord )
    653         return;
    654     }
    655 
    656     if ( indexInsert < hintmap->count )
    657     {
    658       /* we are inserting before an existing edge */
    659       if ( isPair )
    660       {
    661         if ( secondHintEdge->dsCoord > hintmap->edge[indexInsert].dsCoord )
    662           return;
    663       }
    664       else
    665       {
    666         if ( firstHintEdge->dsCoord > hintmap->edge[indexInsert].dsCoord )
    667           return;
    668       }
    669     }
    670 
    671     /* make room to insert */
    672     {
    673       CF2_Int  iSrc = hintmap->count - 1;
    674       CF2_Int  iDst = isPair ? hintmap->count + 1 : hintmap->count;
    675 
    676       CF2_Int  count = hintmap->count - indexInsert;
    677 
    678 
    679       if ( iDst >= CF2_MAX_HINT_EDGES )
    680       {
    681         FT_TRACE4(( "cf2_hintmap_insertHint: too many hintmaps\n" ));
    682         return;
    683       }
    684 
    685       while ( count-- )
    686         hintmap->edge[iDst--] = hintmap->edge[iSrc--];
    687 
    688       /* insert first edge */
    689       hintmap->edge[indexInsert] = *firstHintEdge;         /* copy struct */
    690       hintmap->count += 1;
    691 
    692       if ( isPair )
    693       {
    694         /* insert second edge */
    695         hintmap->edge[indexInsert + 1] = *secondHintEdge;  /* copy struct */
    696         hintmap->count                += 1;
    697       }
    698     }
    699 
    700     return;
    701   }
    702 
    703 
    704   /*
    705    * Build a map from hints and mask.
    706    *
    707    * This function may recur one level if `hintmap->initialHintMap' is not yet
    708    * valid.
    709    * If `initialMap' is true, simply build initial map.
    710    *
    711    * Synthetic hints are used in two ways.  A hint at zero is inserted, if
    712    * needed, in the initial hint map, to prevent translations from
    713    * propagating across the origin.  If synthetic em box hints are enabled
    714    * for ideographic dictionaries, then they are inserted in all hint
    715    * maps, including the initial one.
    716    *
    717    */
    718   FT_LOCAL_DEF( void )
    719   cf2_hintmap_build( CF2_HintMap   hintmap,
    720                      CF2_ArrStack  hStemHintArray,
    721                      CF2_ArrStack  vStemHintArray,
    722                      CF2_HintMask  hintMask,
    723                      CF2_Fixed     hintOrigin,
    724                      FT_Bool       initialMap )
    725   {
    726     FT_Byte*  maskPtr;
    727 
    728     CF2_Font         font = hintmap->font;
    729     CF2_HintMaskRec  tempHintMask;
    730 
    731     size_t   bitCount, i;
    732     FT_Byte  maskByte;
    733 
    734 
    735     /* check whether initial map is constructed */
    736     if ( !initialMap && !cf2_hintmap_isValid( hintmap->initialHintMap ) )
    737     {
    738       /* make recursive call with initialHintMap and temporary mask; */
    739       /* temporary mask will get all bits set, below */
    740       cf2_hintmask_init( &tempHintMask, hintMask->error );
    741       cf2_hintmap_build( hintmap->initialHintMap,
    742                          hStemHintArray,
    743                          vStemHintArray,
    744                          &tempHintMask,
    745                          hintOrigin,
    746                          TRUE );
    747     }
    748 
    749     if ( !cf2_hintmask_isValid( hintMask ) )
    750     {
    751       /* without a hint mask, assume all hints are active */
    752       cf2_hintmask_setAll( hintMask,
    753                            cf2_arrstack_size( hStemHintArray ) +
    754                              cf2_arrstack_size( vStemHintArray ) );
    755     }
    756 
    757     /* begin by clearing the map */
    758     hintmap->count     = 0;
    759     hintmap->lastIndex = 0;
    760 
    761     /* make a copy of the hint mask so we can modify it */
    762     tempHintMask = *hintMask;
    763     maskPtr      = cf2_hintmask_getMaskPtr( &tempHintMask );
    764 
    765     /* use the hStem hints only, which are first in the mask */
    766     /* TODO: compare this to cffhintmaskGetBitCount */
    767     bitCount = cf2_arrstack_size( hStemHintArray );
    768 
    769     /* synthetic embox hints get highest priority */
    770     if ( font->blues.doEmBoxHints )
    771     {
    772       CF2_HintRec  dummy;
    773 
    774 
    775       cf2_hint_initZero( &dummy );   /* invalid hint map element */
    776 
    777       /* ghost bottom */
    778       cf2_hintmap_insertHint( hintmap,
    779                               &font->blues.emBoxBottomEdge,
    780                               &dummy );
    781       /* ghost top */
    782       cf2_hintmap_insertHint( hintmap,
    783                               &dummy,
    784                               &font->blues.emBoxTopEdge );
    785     }
    786 
    787     /* insert hints captured by a blue zone or already locked (higher */
    788     /* priority)                                                      */
    789     for ( i = 0, maskByte = 0x80; i < bitCount; i++ )
    790     {
    791       if ( maskByte & *maskPtr )
    792       {
    793         /* expand StemHint into two `CF2_Hint' elements */
    794         CF2_HintRec  bottomHintEdge, topHintEdge;
    795 
    796 
    797         cf2_hint_init( &bottomHintEdge,
    798                        hStemHintArray,
    799                        i,
    800                        font,
    801                        hintOrigin,
    802                        hintmap->scale,
    803                        TRUE /* bottom */ );
    804         cf2_hint_init( &topHintEdge,
    805                        hStemHintArray,
    806                        i,
    807                        font,
    808                        hintOrigin,
    809                        hintmap->scale,
    810                        FALSE /* top */ );
    811 
    812         if ( cf2_hint_isLocked( &bottomHintEdge ) ||
    813              cf2_hint_isLocked( &topHintEdge )    ||
    814              cf2_blues_capture( &font->blues,
    815                                 &bottomHintEdge,
    816                                 &topHintEdge )   )
    817         {
    818           /* insert captured hint into map */
    819           cf2_hintmap_insertHint( hintmap, &bottomHintEdge, &topHintEdge );
    820 
    821           *maskPtr &= ~maskByte;      /* turn off the bit for this hint */
    822         }
    823       }
    824 
    825       if ( ( i & 7 ) == 7 )
    826       {
    827         /* move to next mask byte */
    828         maskPtr++;
    829         maskByte = 0x80;
    830       }
    831       else
    832         maskByte >>= 1;
    833     }
    834 
    835     /* initial hint map includes only captured hints plus maybe one at 0 */
    836 
    837     /*
    838      * TODO: There is a problem here because we are trying to build a
    839      *       single hint map containing all captured hints.  It is
    840      *       possible for there to be conflicts between captured hints,
    841      *       either because of darkening or because the hints are in
    842      *       separate hint zones (we are ignoring hint zones for the
    843      *       initial map).  An example of the latter is MinionPro-Regular
    844      *       v2.030 glyph 883 (Greek Capital Alpha with Psili) at 15ppem.
    845      *       A stem hint for the psili conflicts with the top edge hint
    846      *       for the base character.  The stem hint gets priority because
    847      *       of its sort order.  In glyph 884 (Greek Capital Alpha with
    848      *       Psili and Oxia), the top of the base character gets a stem
    849      *       hint, and the psili does not.  This creates different initial
    850      *       maps for the two glyphs resulting in different renderings of
    851      *       the base character.  Will probably defer this either as not
    852      *       worth the cost or as a font bug.  I don't think there is any
    853      *       good reason for an accent to be captured by an alignment
    854      *       zone.  -darnold 2/12/10
    855      */
    856 
    857     if ( initialMap )
    858     {
    859       /* Apply a heuristic that inserts a point for (0,0), unless it's     */
    860       /* already covered by a mapping.  This locks the baseline for glyphs */
    861       /* that have no baseline hints.                                      */
    862 
    863       if ( hintmap->count == 0                           ||
    864            hintmap->edge[0].csCoord > 0                  ||
    865            hintmap->edge[hintmap->count - 1].csCoord < 0 )
    866       {
    867         /* all edges are above 0 or all edges are below 0; */
    868         /* construct a locked edge hint at 0               */
    869 
    870         CF2_HintRec  edge, invalid;
    871 
    872 
    873         cf2_hint_initZero( &edge );
    874 
    875         edge.flags = CF2_GhostBottom |
    876                      CF2_Locked      |
    877                      CF2_Synthetic;
    878         edge.scale = hintmap->scale;
    879 
    880         cf2_hint_initZero( &invalid );
    881         cf2_hintmap_insertHint( hintmap, &edge, &invalid );
    882       }
    883     }
    884     else
    885     {
    886       /* insert remaining hints */
    887 
    888       maskPtr = cf2_hintmask_getMaskPtr( &tempHintMask );
    889 
    890       for ( i = 0, maskByte = 0x80; i < bitCount; i++ )
    891       {
    892         if ( maskByte & *maskPtr )
    893         {
    894           CF2_HintRec  bottomHintEdge, topHintEdge;
    895 
    896 
    897           cf2_hint_init( &bottomHintEdge,
    898                          hStemHintArray,
    899                          i,
    900                          font,
    901                          hintOrigin,
    902                          hintmap->scale,
    903                          TRUE /* bottom */ );
    904           cf2_hint_init( &topHintEdge,
    905                          hStemHintArray,
    906                          i,
    907                          font,
    908                          hintOrigin,
    909                          hintmap->scale,
    910                          FALSE /* top */ );
    911 
    912           cf2_hintmap_insertHint( hintmap, &bottomHintEdge, &topHintEdge );
    913         }
    914 
    915         if ( ( i & 7 ) == 7 )
    916         {
    917           /* move to next mask byte */
    918           maskPtr++;
    919           maskByte = 0x80;
    920         }
    921         else
    922           maskByte >>= 1;
    923       }
    924     }
    925 
    926     /*
    927      * Note: The following line is a convenient place to break when
    928      *       debugging hinting.  Examine `hintmap->edge' for the list of
    929      *       enabled hints, then step over the call to see the effect of
    930      *       adjustment.  We stop here first on the recursive call that
    931      *       creates the initial map, and then on each counter group and
    932      *       hint zone.
    933      */
    934 
    935     /* adjust positions of hint edges that are not locked to blue zones */
    936     cf2_hintmap_adjustHints( hintmap );
    937 
    938     /* save the position of all hints that were used in this hint map; */
    939     /* if we use them again, we'll locate them in the same position    */
    940     if ( !initialMap )
    941     {
    942       for ( i = 0; i < hintmap->count; i++ )
    943       {
    944         if ( !cf2_hint_isSynthetic( &hintmap->edge[i] ) )
    945         {
    946           /* Note: include both valid and invalid edges            */
    947           /* Note: top and bottom edges are copied back separately */
    948           CF2_StemHint  stemhint = (CF2_StemHint)
    949                           cf2_arrstack_getPointer( hStemHintArray,
    950                                                    hintmap->edge[i].index );
    951 
    952 
    953           if ( cf2_hint_isTop( &hintmap->edge[i] ) )
    954             stemhint->maxDS = hintmap->edge[i].dsCoord;
    955           else
    956             stemhint->minDS = hintmap->edge[i].dsCoord;
    957 
    958           stemhint->used = TRUE;
    959         }
    960       }
    961     }
    962 
    963     /* hint map is ready to use */
    964     hintmap->isValid = TRUE;
    965 
    966     /* remember this mask has been used */
    967     cf2_hintmask_setNew( hintMask, FALSE );
    968   }
    969 
    970 
    971   FT_LOCAL_DEF( void )
    972   cf2_glyphpath_init( CF2_GlyphPath         glyphpath,
    973                       CF2_Font              font,
    974                       CF2_OutlineCallbacks  callbacks,
    975                       CF2_Fixed             scaleY,
    976                       /* CF2_Fixed  hShift, */
    977                       CF2_ArrStack          hStemHintArray,
    978                       CF2_ArrStack          vStemHintArray,
    979                       CF2_HintMask          hintMask,
    980                       CF2_Fixed             hintOriginY,
    981                       const CF2_Blues       blues,
    982                       const FT_Vector*      fractionalTranslation )
    983   {
    984     FT_ZERO( glyphpath );
    985 
    986     glyphpath->font      = font;
    987     glyphpath->callbacks = callbacks;
    988 
    989     cf2_arrstack_init( &glyphpath->hintMoves,
    990                        font->memory,
    991                        &font->error,
    992                        sizeof ( CF2_HintMoveRec ) );
    993 
    994     cf2_hintmap_init( &glyphpath->initialHintMap,
    995                       font,
    996                       &glyphpath->initialHintMap,
    997                       &glyphpath->hintMoves,
    998                       scaleY );
    999     cf2_hintmap_init( &glyphpath->firstHintMap,
   1000                       font,
   1001                       &glyphpath->initialHintMap,
   1002                       &glyphpath->hintMoves,
   1003                       scaleY );
   1004     cf2_hintmap_init( &glyphpath->hintMap,
   1005                       font,
   1006                       &glyphpath->initialHintMap,
   1007                       &glyphpath->hintMoves,
   1008                       scaleY );
   1009 
   1010     glyphpath->scaleX = font->innerTransform.a;
   1011     glyphpath->scaleC = font->innerTransform.c;
   1012     glyphpath->scaleY = font->innerTransform.d;
   1013 
   1014     glyphpath->fractionalTranslation = *fractionalTranslation;
   1015 
   1016 #if 0
   1017     glyphpath->hShift = hShift;       /* for fauxing */
   1018 #endif
   1019 
   1020     glyphpath->hStemHintArray = hStemHintArray;
   1021     glyphpath->vStemHintArray = vStemHintArray;
   1022     glyphpath->hintMask       = hintMask;      /* ptr to current mask */
   1023     glyphpath->hintOriginY    = hintOriginY;
   1024     glyphpath->blues          = blues;
   1025     glyphpath->darken         = font->darkened; /* TODO: should we make copies? */
   1026     glyphpath->xOffset        = font->darkenX;
   1027     glyphpath->yOffset        = font->darkenY;
   1028     glyphpath->miterLimit     = 2 * FT_MAX(
   1029                                      cf2_fixedAbs( glyphpath->xOffset ),
   1030                                      cf2_fixedAbs( glyphpath->yOffset ) );
   1031 
   1032     /* .1 character space unit */
   1033     glyphpath->snapThreshold = cf2_floatToFixed( 0.1f );
   1034 
   1035     glyphpath->moveIsPending = TRUE;
   1036     glyphpath->pathIsOpen    = FALSE;
   1037     glyphpath->elemIsQueued  = FALSE;
   1038   }
   1039 
   1040 
   1041   FT_LOCAL_DEF( void )
   1042   cf2_glyphpath_finalize( CF2_GlyphPath  glyphpath )
   1043   {
   1044     cf2_arrstack_finalize( &glyphpath->hintMoves );
   1045   }
   1046 
   1047 
   1048   /*
   1049    * Hint point in y-direction and apply outerTransform.
   1050    * Input `current' hint map (which is actually delayed by one element).
   1051    * Input x,y point in Character Space.
   1052    * Output x,y point in Device Space, including translation.
   1053    */
   1054   static void
   1055   cf2_glyphpath_hintPoint( CF2_GlyphPath  glyphpath,
   1056                            CF2_HintMap    hintmap,
   1057                            FT_Vector*     ppt,
   1058                            CF2_Fixed      x,
   1059                            CF2_Fixed      y )
   1060   {
   1061     FT_Vector  pt;   /* hinted point in upright DS */
   1062 
   1063 
   1064     pt.x = FT_MulFix( glyphpath->scaleX, x ) +
   1065              FT_MulFix( glyphpath->scaleC, y );
   1066     pt.y = cf2_hintmap_map( hintmap, y );
   1067 
   1068     ppt->x = FT_MulFix( glyphpath->font->outerTransform.a, pt.x )   +
   1069                FT_MulFix( glyphpath->font->outerTransform.c, pt.y ) +
   1070                glyphpath->fractionalTranslation.x;
   1071     ppt->y = FT_MulFix( glyphpath->font->outerTransform.b, pt.x )   +
   1072                FT_MulFix( glyphpath->font->outerTransform.d, pt.y ) +
   1073                glyphpath->fractionalTranslation.y;
   1074   }
   1075 
   1076 
   1077   /*
   1078    * From two line segments, (u1,u2) and (v1,v2), compute a point of
   1079    * intersection on the corresponding lines.
   1080    * Return false if no intersection is found, or if the intersection is
   1081    * too far away from the ends of the line segments, u2 and v1.
   1082    *
   1083    */
   1084   static FT_Bool
   1085   cf2_glyphpath_computeIntersection( CF2_GlyphPath     glyphpath,
   1086                                      const FT_Vector*  u1,
   1087                                      const FT_Vector*  u2,
   1088                                      const FT_Vector*  v1,
   1089                                      const FT_Vector*  v2,
   1090                                      FT_Vector*        intersection )
   1091   {
   1092     /*
   1093      * Let `u' be a zero-based vector from the first segment, `v' from the
   1094      * second segment.
   1095      * Let `w 'be the zero-based vector from `u1' to `v1'.
   1096      * `perp' is the `perpendicular dot product'; see
   1097      * http://mathworld.wolfram.com/PerpDotProduct.html.
   1098      * `s' is the parameter for the parametric line for the first segment
   1099      * (`u').
   1100      *
   1101      * See notation in
   1102      * http://softsurfer.com/Archive/algorithm_0104/algorithm_0104B.htm.
   1103      * Calculations are done in 16.16, but must handle the squaring of
   1104      * line lengths in character space.  We scale all vectors by 1/32 to
   1105      * avoid overflow.  This allows values up to 4095 to be squared.  The
   1106      * scale factor cancels in the divide.
   1107      *
   1108      * TODO: the scale factor could be computed from UnitsPerEm.
   1109      *
   1110      */
   1111 
   1112 #define cf2_perp( a, b )                                    \
   1113           ( FT_MulFix( a.x, b.y ) - FT_MulFix( a.y, b.x ) )
   1114 
   1115   /* round and divide by 32 */
   1116 #define CF2_CS_SCALE( x )         \
   1117           ( ( (x) + 0x10 ) >> 5 )
   1118 
   1119     FT_Vector  u, v, w;      /* scaled vectors */
   1120     CF2_Fixed  denominator, s;
   1121 
   1122 
   1123     u.x = CF2_CS_SCALE( u2->x - u1->x );
   1124     u.y = CF2_CS_SCALE( u2->y - u1->y );
   1125     v.x = CF2_CS_SCALE( v2->x - v1->x );
   1126     v.y = CF2_CS_SCALE( v2->y - v1->y );
   1127     w.x = CF2_CS_SCALE( v1->x - u1->x );
   1128     w.y = CF2_CS_SCALE( v1->y - u1->y );
   1129 
   1130     denominator = cf2_perp( u, v );
   1131 
   1132     if ( denominator == 0 )
   1133       return FALSE;           /* parallel or coincident lines */
   1134 
   1135     s = FT_DivFix( cf2_perp( w, v ), denominator );
   1136 
   1137     intersection->x = u1->x + FT_MulFix( s, u2->x - u1->x );
   1138     intersection->y = u1->y + FT_MulFix( s, u2->y - u1->y );
   1139 
   1140     /*
   1141      * Special case snapping for horizontal and vertical lines.
   1142      * This cleans up intersections and reduces problems with winding
   1143      * order detection.
   1144      * Sample case is sbc cd KozGoPr6N-Medium.otf 20 16685.
   1145      * Note: these calculations are in character space.
   1146      *
   1147      */
   1148 
   1149     if ( u1->x == u2->x                                                     &&
   1150          cf2_fixedAbs( intersection->x - u1->x ) < glyphpath->snapThreshold )
   1151       intersection->x = u1->x;
   1152     if ( u1->y == u2->y                                                     &&
   1153          cf2_fixedAbs( intersection->y - u1->y ) < glyphpath->snapThreshold )
   1154       intersection->y = u1->y;
   1155 
   1156     if ( v1->x == v2->x                                                     &&
   1157          cf2_fixedAbs( intersection->x - v1->x ) < glyphpath->snapThreshold )
   1158       intersection->x = v1->x;
   1159     if ( v1->y == v2->y                                                     &&
   1160          cf2_fixedAbs( intersection->y - v1->y ) < glyphpath->snapThreshold )
   1161       intersection->y = v1->y;
   1162 
   1163     /* limit the intersection distance from midpoint of u2 and v1 */
   1164     if ( cf2_fixedAbs( intersection->x - ( u2->x + v1->x ) / 2 ) >
   1165            glyphpath->miterLimit                                   ||
   1166          cf2_fixedAbs( intersection->y - ( u2->y + v1->y ) / 2 ) >
   1167            glyphpath->miterLimit                                   )
   1168       return FALSE;
   1169 
   1170     return TRUE;
   1171   }
   1172 
   1173 
   1174   /*
   1175    * Push the cached element (glyphpath->prevElem*) to the outline
   1176    * consumer.  When a darkening offset is used, the end point of the
   1177    * cached element may be adjusted to an intersection point or it may be
   1178    * connected by a line to the current element.  This calculation must
   1179    * use a HintMap that was valid at the time the element was saved.  For
   1180    * the first point in a subpath, that is a saved HintMap.  For most
   1181    * elements, it just means the caller has delayed building a HintMap
   1182    * from the current HintMask.
   1183    *
   1184    * Transform each point with outerTransform and call the outline
   1185    * callbacks.  This is a general 3x3 transform:
   1186    *
   1187    *   x' = a*x + c*y + tx, y' = b*x + d*y + ty
   1188    *
   1189    * but it uses 4 elements from CF2_Font and the translation part
   1190    * from CF2_GlyphPath.
   1191    *
   1192    */
   1193   static void
   1194   cf2_glyphpath_pushPrevElem( CF2_GlyphPath  glyphpath,
   1195                               CF2_HintMap    hintmap,
   1196                               FT_Vector*     nextP0,
   1197                               FT_Vector      nextP1,
   1198                               FT_Bool        close )
   1199   {
   1200     CF2_CallbackParamsRec  params;
   1201 
   1202     FT_Vector*  prevP0;
   1203     FT_Vector*  prevP1;
   1204 
   1205     FT_Vector  intersection    = { 0, 0 };
   1206     FT_Bool    useIntersection = FALSE;
   1207 
   1208 
   1209     FT_ASSERT( glyphpath->prevElemOp == CF2_PathOpLineTo ||
   1210                glyphpath->prevElemOp == CF2_PathOpCubeTo );
   1211 
   1212     if ( glyphpath->prevElemOp == CF2_PathOpLineTo )
   1213     {
   1214       prevP0 = &glyphpath->prevElemP0;
   1215       prevP1 = &glyphpath->prevElemP1;
   1216     }
   1217     else
   1218     {
   1219       prevP0 = &glyphpath->prevElemP2;
   1220       prevP1 = &glyphpath->prevElemP3;
   1221     }
   1222 
   1223     /* optimization: if previous and next elements are offset by the same */
   1224     /* amount, then there will be no gap, and no need to compute an       */
   1225     /* intersection.                                                      */
   1226     if ( prevP1->x != nextP0->x || prevP1->y != nextP0->y )
   1227     {
   1228       /* previous element does not join next element:             */
   1229       /* adjust end point of previous element to the intersection */
   1230       useIntersection = cf2_glyphpath_computeIntersection( glyphpath,
   1231                                                            prevP0,
   1232                                                            prevP1,
   1233                                                            nextP0,
   1234                                                            &nextP1,
   1235                                                            &intersection );
   1236       if ( useIntersection )
   1237       {
   1238         /* modify the last point of the cached element (either line or */
   1239         /* curve)                                                      */
   1240         *prevP1 = intersection;
   1241       }
   1242     }
   1243 
   1244     params.pt0 = glyphpath->currentDS;
   1245 
   1246     switch( glyphpath->prevElemOp )
   1247     {
   1248     case CF2_PathOpLineTo:
   1249       params.op = CF2_PathOpLineTo;
   1250 
   1251       /* note: pt2 and pt3 are unused */
   1252       cf2_glyphpath_hintPoint( glyphpath,
   1253                                hintmap,
   1254                                &params.pt1,
   1255                                glyphpath->prevElemP1.x,
   1256                                glyphpath->prevElemP1.y );
   1257 
   1258       glyphpath->callbacks->lineTo( glyphpath->callbacks, &params );
   1259 
   1260       glyphpath->currentDS = params.pt1;
   1261 
   1262       break;
   1263 
   1264     case CF2_PathOpCubeTo:
   1265       params.op = CF2_PathOpCubeTo;
   1266 
   1267       /* TODO: should we intersect the interior joins (p1-p2 and p2-p3)? */
   1268       cf2_glyphpath_hintPoint( glyphpath,
   1269                                hintmap,
   1270                                &params.pt1,
   1271                                glyphpath->prevElemP1.x,
   1272                                glyphpath->prevElemP1.y );
   1273       cf2_glyphpath_hintPoint( glyphpath,
   1274                                hintmap,
   1275                                &params.pt2,
   1276                                glyphpath->prevElemP2.x,
   1277                                glyphpath->prevElemP2.y );
   1278       cf2_glyphpath_hintPoint( glyphpath,
   1279                                hintmap,
   1280                                &params.pt3,
   1281                                glyphpath->prevElemP3.x,
   1282                                glyphpath->prevElemP3.y );
   1283 
   1284       glyphpath->callbacks->cubeTo( glyphpath->callbacks, &params );
   1285 
   1286       glyphpath->currentDS = params.pt3;
   1287 
   1288       break;
   1289     }
   1290 
   1291     if ( !useIntersection || close )
   1292     {
   1293       /* insert connecting line between end of previous element and start */
   1294       /* of current one                                                   */
   1295       /* note: at the end of a subpath, we might do both, so use `nextP0' */
   1296       /* before we change it, below                                       */
   1297 
   1298       cf2_glyphpath_hintPoint( glyphpath,
   1299                                hintmap,
   1300                                &params.pt1,
   1301                                nextP0->x,
   1302                                nextP0->y );
   1303 
   1304       if ( params.pt1.x != glyphpath->currentDS.x ||
   1305            params.pt1.y != glyphpath->currentDS.y )
   1306       {
   1307         /* length is nonzero */
   1308         params.op  = CF2_PathOpLineTo;
   1309         params.pt0 = glyphpath->currentDS;
   1310 
   1311         /* note: pt2 and pt3 are unused */
   1312         glyphpath->callbacks->lineTo( glyphpath->callbacks, &params );
   1313 
   1314         glyphpath->currentDS = params.pt1;
   1315       }
   1316     }
   1317 
   1318     if ( useIntersection )
   1319     {
   1320       /* return intersection point to caller */
   1321       *nextP0 = intersection;
   1322     }
   1323   }
   1324 
   1325 
   1326   /* push a MoveTo element based on current point and offset of current */
   1327   /* element                                                            */
   1328   static void
   1329   cf2_glyphpath_pushMove( CF2_GlyphPath  glyphpath,
   1330                           FT_Vector      start )
   1331   {
   1332     CF2_CallbackParamsRec  params;
   1333 
   1334 
   1335     params.op  = CF2_PathOpMoveTo;
   1336     params.pt0 = glyphpath->currentDS;
   1337 
   1338     /* Test if move has really happened yet; it would have called */
   1339     /* `cf2_hintmap_build' to set `isValid'.                   */
   1340     if ( !cf2_hintmap_isValid( &glyphpath->hintMap ) )
   1341     {
   1342       /* we are here iff first subpath is missing a moveto operator: */
   1343       /* synthesize first moveTo to finish initialization of hintMap */
   1344       cf2_glyphpath_moveTo( glyphpath,
   1345                             glyphpath->start.x,
   1346                             glyphpath->start.y );
   1347     }
   1348 
   1349     cf2_glyphpath_hintPoint( glyphpath,
   1350                              &glyphpath->hintMap,
   1351                              &params.pt1,
   1352                              start.x,
   1353                              start.y );
   1354 
   1355     /* note: pt2 and pt3 are unused */
   1356     glyphpath->callbacks->moveTo( glyphpath->callbacks, &params );
   1357 
   1358     glyphpath->currentDS    = params.pt1;
   1359     glyphpath->offsetStart0 = start;
   1360   }
   1361 
   1362 
   1363   /*
   1364    * All coordinates are in character space.
   1365    * On input, (x1, y1) and (x2, y2) give line segment.
   1366    * On output, (x, y) give offset vector.
   1367    * We use a piecewise approximation to trig functions.
   1368    *
   1369    * TODO: Offset true perpendicular and proper length
   1370    *       supply the y-translation for hinting here, too,
   1371    *       that adds yOffset unconditionally to *y.
   1372    */
   1373   static void
   1374   cf2_glyphpath_computeOffset( CF2_GlyphPath  glyphpath,
   1375                                CF2_Fixed      x1,
   1376                                CF2_Fixed      y1,
   1377                                CF2_Fixed      x2,
   1378                                CF2_Fixed      y2,
   1379                                CF2_Fixed*     x,
   1380                                CF2_Fixed*     y )
   1381   {
   1382     CF2_Fixed  dx = x2 - x1;
   1383     CF2_Fixed  dy = y2 - y1;
   1384 
   1385 
   1386     /* note: negative offsets don't work here; negate deltas to change */
   1387     /* quadrants, below                                                */
   1388     if ( glyphpath->font->reverseWinding )
   1389     {
   1390       dx = -dx;
   1391       dy = -dy;
   1392     }
   1393 
   1394     *x = *y = 0;
   1395 
   1396     if ( !glyphpath->darken )
   1397         return;
   1398 
   1399     /* add momentum for this path element */
   1400     glyphpath->callbacks->windingMomentum +=
   1401       cf2_getWindingMomentum( x1, y1, x2, y2 );
   1402 
   1403     /* note: allow mixed integer and fixed multiplication here */
   1404     if ( dx >= 0 )
   1405     {
   1406       if ( dy >= 0 )
   1407       {
   1408         /* first quadrant, +x +y */
   1409 
   1410         if ( dx > 2 * dy )
   1411         {
   1412           /* +x */
   1413           *x = 0;
   1414           *y = 0;
   1415         }
   1416         else if ( dy > 2 * dx )
   1417         {
   1418           /* +y */
   1419           *x = glyphpath->xOffset;
   1420           *y = glyphpath->yOffset;
   1421         }
   1422         else
   1423         {
   1424           /* +x +y */
   1425           *x = FT_MulFix( cf2_floatToFixed( 0.7 ),
   1426                           glyphpath->xOffset );
   1427           *y = FT_MulFix( cf2_floatToFixed( 1.0 - 0.7 ),
   1428                           glyphpath->yOffset );
   1429         }
   1430       }
   1431       else
   1432       {
   1433         /* fourth quadrant, +x -y */
   1434 
   1435         if ( dx > -2 * dy )
   1436         {
   1437           /* +x */
   1438           *x = 0;
   1439           *y = 0;
   1440         }
   1441         else if ( -dy > 2 * dx )
   1442         {
   1443           /* -y */
   1444           *x = -glyphpath->xOffset;
   1445           *y = glyphpath->yOffset;
   1446         }
   1447         else
   1448         {
   1449           /* +x -y */
   1450           *x = FT_MulFix( cf2_floatToFixed( -0.7 ),
   1451                           glyphpath->xOffset );
   1452           *y = FT_MulFix( cf2_floatToFixed( 1.0 - 0.7 ),
   1453                           glyphpath->yOffset );
   1454         }
   1455       }
   1456     }
   1457     else
   1458     {
   1459       if ( dy >= 0 )
   1460       {
   1461         /* second quadrant, -x +y */
   1462 
   1463         if ( -dx > 2 * dy )
   1464         {
   1465           /* -x */
   1466           *x = 0;
   1467           *y = 2 * glyphpath->yOffset;
   1468         }
   1469         else if ( dy > -2 * dx )
   1470         {
   1471           /* +y */
   1472           *x = glyphpath->xOffset;
   1473           *y = glyphpath->yOffset;
   1474         }
   1475         else
   1476         {
   1477           /* -x +y */
   1478           *x = FT_MulFix( cf2_floatToFixed( 0.7 ),
   1479                           glyphpath->xOffset );
   1480           *y = FT_MulFix( cf2_floatToFixed( 1.0 + 0.7 ),
   1481                           glyphpath->yOffset );
   1482         }
   1483       }
   1484       else
   1485       {
   1486         /* third quadrant, -x -y */
   1487 
   1488         if ( -dx > -2 * dy )
   1489         {
   1490           /* -x */
   1491           *x = 0;
   1492           *y = 2 * glyphpath->yOffset;
   1493         }
   1494         else if ( -dy > -2 * dx )
   1495         {
   1496           /* -y */
   1497           *x = -glyphpath->xOffset;
   1498           *y = glyphpath->xOffset;
   1499         }
   1500         else
   1501         {
   1502           /* -x -y */
   1503           *x = FT_MulFix( cf2_floatToFixed( -0.7 ),
   1504                           glyphpath->xOffset );
   1505           *y = FT_MulFix( cf2_floatToFixed( 1.0 + 0.7 ),
   1506                           glyphpath->yOffset );
   1507         }
   1508       }
   1509     }
   1510   }
   1511 
   1512 
   1513   FT_LOCAL_DEF( void )
   1514   cf2_glyphpath_moveTo( CF2_GlyphPath  glyphpath,
   1515                         CF2_Fixed      x,
   1516                         CF2_Fixed      y )
   1517   {
   1518     cf2_glyphpath_closeOpenPath( glyphpath );
   1519 
   1520     /* save the parameters of the move for later, when we'll know how to */
   1521     /* offset it;                                                        */
   1522     /* also save last move point */
   1523     glyphpath->currentCS.x = glyphpath->start.x = x;
   1524     glyphpath->currentCS.y = glyphpath->start.y = y;
   1525 
   1526     glyphpath->moveIsPending = TRUE;
   1527 
   1528     /* ensure we have a valid map with current mask */
   1529     if ( !cf2_hintmap_isValid( &glyphpath->hintMap ) ||
   1530          cf2_hintmask_isNew( glyphpath->hintMask )   )
   1531       cf2_hintmap_build( &glyphpath->hintMap,
   1532                          glyphpath->hStemHintArray,
   1533                          glyphpath->vStemHintArray,
   1534                          glyphpath->hintMask,
   1535                          glyphpath->hintOriginY,
   1536                          FALSE );
   1537 
   1538     /* save a copy of current HintMap to use when drawing initial point */
   1539     glyphpath->firstHintMap = glyphpath->hintMap;     /* structure copy */
   1540   }
   1541 
   1542 
   1543   FT_LOCAL_DEF( void )
   1544   cf2_glyphpath_lineTo( CF2_GlyphPath  glyphpath,
   1545                         CF2_Fixed      x,
   1546                         CF2_Fixed      y )
   1547   {
   1548     CF2_Fixed  xOffset, yOffset;
   1549     FT_Vector  P0, P1;
   1550 
   1551 
   1552     /* can't compute offset of zero length line, so ignore them */
   1553     if ( glyphpath->currentCS.x == x && glyphpath->currentCS.y == y )
   1554       return;
   1555 
   1556     cf2_glyphpath_computeOffset( glyphpath,
   1557                                  glyphpath->currentCS.x,
   1558                                  glyphpath->currentCS.y,
   1559                                  x,
   1560                                  y,
   1561                                  &xOffset,
   1562                                  &yOffset );
   1563 
   1564     /* construct offset points */
   1565     P0.x = glyphpath->currentCS.x + xOffset;
   1566     P0.y = glyphpath->currentCS.y + yOffset;
   1567     P1.x = x + xOffset;
   1568     P1.y = y + yOffset;
   1569 
   1570     if ( glyphpath->moveIsPending )
   1571     {
   1572       /* emit offset 1st point as MoveTo */
   1573       cf2_glyphpath_pushMove( glyphpath, P0 );
   1574 
   1575       glyphpath->moveIsPending = FALSE;  /* adjust state machine */
   1576       glyphpath->pathIsOpen    = TRUE;
   1577 
   1578       glyphpath->offsetStart1 = P1;              /* record second point */
   1579     }
   1580 
   1581     if ( glyphpath->elemIsQueued )
   1582     {
   1583       FT_ASSERT( cf2_hintmap_isValid( &glyphpath->hintMap ) );
   1584 
   1585       cf2_glyphpath_pushPrevElem( glyphpath,
   1586                                   &glyphpath->hintMap,
   1587                                   &P0,
   1588                                   P1,
   1589                                   FALSE );
   1590     }
   1591 
   1592     /* queue the current element with offset points */
   1593     glyphpath->elemIsQueued = TRUE;
   1594     glyphpath->prevElemOp   = CF2_PathOpLineTo;
   1595     glyphpath->prevElemP0   = P0;
   1596     glyphpath->prevElemP1   = P1;
   1597 
   1598     /* update current map */
   1599     if ( cf2_hintmask_isNew( glyphpath->hintMask ) )
   1600       cf2_hintmap_build( &glyphpath->hintMap,
   1601                          glyphpath->hStemHintArray,
   1602                          glyphpath->vStemHintArray,
   1603                          glyphpath->hintMask,
   1604                          glyphpath->hintOriginY,
   1605                          FALSE );
   1606 
   1607     glyphpath->currentCS.x = x;     /* pre-offset current point */
   1608     glyphpath->currentCS.y = y;
   1609   }
   1610 
   1611 
   1612   FT_LOCAL_DEF( void )
   1613   cf2_glyphpath_curveTo( CF2_GlyphPath  glyphpath,
   1614                          CF2_Fixed      x1,
   1615                          CF2_Fixed      y1,
   1616                          CF2_Fixed      x2,
   1617                          CF2_Fixed      y2,
   1618                          CF2_Fixed      x3,
   1619                          CF2_Fixed      y3 )
   1620   {
   1621     CF2_Fixed  xOffset1, yOffset1, xOffset3, yOffset3;
   1622     FT_Vector  P0, P1, P2, P3;
   1623 
   1624 
   1625     /* TODO: ignore zero length portions of curve?? */
   1626     cf2_glyphpath_computeOffset( glyphpath,
   1627                                  glyphpath->currentCS.x,
   1628                                  glyphpath->currentCS.y,
   1629                                  x1,
   1630                                  y1,
   1631                                  &xOffset1,
   1632                                  &yOffset1 );
   1633     cf2_glyphpath_computeOffset( glyphpath,
   1634                                  x2,
   1635                                  y2,
   1636                                  x3,
   1637                                  y3,
   1638                                  &xOffset3,
   1639                                  &yOffset3 );
   1640 
   1641     /* add momentum from the middle segment */
   1642     glyphpath->callbacks->windingMomentum +=
   1643       cf2_getWindingMomentum( x1, y1, x2, y2 );
   1644 
   1645     /* construct offset points */
   1646     P0.x = glyphpath->currentCS.x + xOffset1;
   1647     P0.y = glyphpath->currentCS.y + yOffset1;
   1648     P1.x = x1 + xOffset1;
   1649     P1.y = y1 + yOffset1;
   1650     /* note: preserve angle of final segment by using offset3 at both ends */
   1651     P2.x = x2 + xOffset3;
   1652     P2.y = y2 + yOffset3;
   1653     P3.x = x3 + xOffset3;
   1654     P3.y = y3 + yOffset3;
   1655 
   1656     if ( glyphpath->moveIsPending )
   1657     {
   1658       /* emit offset 1st point as MoveTo */
   1659       cf2_glyphpath_pushMove( glyphpath, P0 );
   1660 
   1661       glyphpath->moveIsPending = FALSE;
   1662       glyphpath->pathIsOpen    = TRUE;
   1663 
   1664       glyphpath->offsetStart1 = P1;              /* record second point */
   1665     }
   1666 
   1667     if ( glyphpath->elemIsQueued )
   1668     {
   1669       FT_ASSERT( cf2_hintmap_isValid( &glyphpath->hintMap ) );
   1670 
   1671       cf2_glyphpath_pushPrevElem( glyphpath,
   1672                                   &glyphpath->hintMap,
   1673                                   &P0,
   1674                                   P1,
   1675                                   FALSE );
   1676     }
   1677 
   1678     /* queue the current element with offset points */
   1679     glyphpath->elemIsQueued = TRUE;
   1680     glyphpath->prevElemOp   = CF2_PathOpCubeTo;
   1681     glyphpath->prevElemP0   = P0;
   1682     glyphpath->prevElemP1   = P1;
   1683     glyphpath->prevElemP2   = P2;
   1684     glyphpath->prevElemP3   = P3;
   1685 
   1686     /* update current map */
   1687     if ( cf2_hintmask_isNew( glyphpath->hintMask ) )
   1688       cf2_hintmap_build( &glyphpath->hintMap,
   1689                          glyphpath->hStemHintArray,
   1690                          glyphpath->vStemHintArray,
   1691                          glyphpath->hintMask,
   1692                          glyphpath->hintOriginY,
   1693                          FALSE );
   1694 
   1695     glyphpath->currentCS.x = x3;       /* pre-offset current point */
   1696     glyphpath->currentCS.y = y3;
   1697   }
   1698 
   1699 
   1700   FT_LOCAL_DEF( void )
   1701   cf2_glyphpath_closeOpenPath( CF2_GlyphPath  glyphpath )
   1702   {
   1703     if ( glyphpath->pathIsOpen )
   1704     {
   1705       FT_ASSERT( cf2_hintmap_isValid( &glyphpath->firstHintMap ) );
   1706 
   1707       /* since we need to apply an offset to the implicit lineto, we make */
   1708       /* it explicit here                                                 */
   1709       cf2_glyphpath_lineTo( glyphpath,
   1710                             glyphpath->start.x,
   1711                             glyphpath->start.y );
   1712 
   1713       /* Draw previous element (the explicit LineTo we just created,      */
   1714       /* above) and connect it to the start point, but with the offset we */
   1715       /* saved from the first element.                                    */
   1716       /* Use the saved HintMap, too. */
   1717       FT_ASSERT( glyphpath->elemIsQueued );
   1718 
   1719       cf2_glyphpath_pushPrevElem( glyphpath,
   1720                                   &glyphpath->firstHintMap,
   1721                                   &glyphpath->offsetStart0,
   1722                                   glyphpath->offsetStart1,
   1723                                   TRUE );
   1724 
   1725       /* reset state machine */
   1726       glyphpath->moveIsPending = TRUE;
   1727       glyphpath->pathIsOpen    = FALSE;
   1728       glyphpath->elemIsQueued  = FALSE;
   1729     }
   1730   }
   1731 
   1732 
   1733 /* END */
   1734