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      1 /***************************************************************************/
      2 /*                                                                         */
      3 /*  cf2hints.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,    */
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     14 /*  FreeType Project License, each contributor to the Work hereby grants   */
     15 /*  to any individual or legal entity exercising permissions granted by    */
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     30 /*                                                                         */
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     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 (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   /* 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     if ( hintmap->count == 0 || ! hintmap->hinted )
    308     {
    309       /* there are no hints; use uniform scale and zero offset */
    310       return FT_MulFix( csCoord, hintmap->scale );
    311     }
    312     else
    313     {
    314       /* start linear search from last hit */
    315       CF2_UInt  i = hintmap->lastIndex;
    316 
    317       FT_ASSERT( hintmap->lastIndex < CF2_MAX_HINT_EDGES );
    318 
    319       /* search up */
    320       while ( i < hintmap->count - 1                  &&
    321               csCoord >= hintmap->edge[i + 1].csCoord )
    322         i += 1;
    323 
    324       /* search down */
    325       while ( i > 0 && csCoord < hintmap->edge[i].csCoord )
    326         i -= 1;
    327 
    328       hintmap->lastIndex = i;
    329 
    330       if ( i == 0 && csCoord < hintmap->edge[0].csCoord )
    331       {
    332         /* special case for points below first edge: use uniform scale */
    333         return FT_MulFix( csCoord - hintmap->edge[0].csCoord,
    334                           hintmap->scale ) +
    335                  hintmap->edge[0].dsCoord;
    336       }
    337       else
    338       {
    339         /*
    340          * Note: entries with duplicate csCoord are allowed.
    341          * Use edge[i], the highest entry where csCoord >= entry[i].csCoord
    342          */
    343         return FT_MulFix( csCoord - hintmap->edge[i].csCoord,
    344                           hintmap->edge[i].scale ) +
    345                  hintmap->edge[i].dsCoord;
    346       }
    347     }
    348   }
    349 
    350 
    351   /*
    352    * This hinting policy moves a hint pair in device space so that one of
    353    * its two edges is on a device pixel boundary (its fractional part is
    354    * zero).  `cf2_hintmap_insertHint' guarantees no overlap in CS
    355    * space.  Ensure here that there is no overlap in DS.
    356    *
    357    * In the first pass, edges are adjusted relative to adjacent hints.
    358    * Those that are below have already been adjusted.  Those that are
    359    * above have not yet been adjusted.  If a hint above blocks an
    360    * adjustment to an optimal position, we will try again in a second
    361    * pass.  The second pass is top-down.
    362    *
    363    */
    364 
    365   static void
    366   cf2_hintmap_adjustHints( CF2_HintMap  hintmap )
    367   {
    368     size_t  i, j;
    369 
    370 
    371     cf2_arrstack_clear( hintmap->hintMoves );      /* working storage */
    372 
    373     /*
    374      * First pass is bottom-up (font hint order) without look-ahead.
    375      * Locked edges are already adjusted.
    376      * Unlocked edges begin with dsCoord from `initialHintMap'.
    377      * Save edges that are not optimally adjusted in `hintMoves' array,
    378      * and process them in second pass.
    379      */
    380 
    381     for ( i = 0; i < hintmap->count; i++ )
    382     {
    383       FT_Bool  isPair = cf2_hint_isPair( &hintmap->edge[i] );
    384 
    385 
    386       /* index of upper edge (same value for ghost hint) */
    387       j = isPair ? i + 1 : i;
    388 
    389       FT_ASSERT( j < hintmap->count );
    390       FT_ASSERT( cf2_hint_isValid( &hintmap->edge[i] ) );
    391       FT_ASSERT( cf2_hint_isValid( &hintmap->edge[j] ) );
    392       FT_ASSERT( cf2_hint_isLocked( &hintmap->edge[i] ) ==
    393                    cf2_hint_isLocked( &hintmap->edge[j] ) );
    394 
    395       if ( !cf2_hint_isLocked( &hintmap->edge[i] ) )
    396       {
    397         /* hint edge is not locked, we can adjust it */
    398         CF2_Fixed  fracDown = cf2_fixedFraction( hintmap->edge[i].dsCoord );
    399         CF2_Fixed  fracUp   = cf2_fixedFraction( hintmap->edge[j].dsCoord );
    400 
    401         /* calculate all four possibilities; moves down are negative */
    402         CF2_Fixed  downMoveDown = 0 - fracDown;
    403         CF2_Fixed  upMoveDown   = 0 - fracUp;
    404         CF2_Fixed  downMoveUp   = fracDown == 0
    405                                     ? 0
    406                                     : cf2_intToFixed( 1 ) - fracDown;
    407         CF2_Fixed  upMoveUp     = fracUp == 0
    408                                     ? 0
    409                                     : cf2_intToFixed( 1 ) - fracUp;
    410 
    411         /* smallest move up */
    412         CF2_Fixed  moveUp   = FT_MIN( downMoveUp, upMoveUp );
    413         /* smallest move down */
    414         CF2_Fixed  moveDown = FT_MAX( downMoveDown, upMoveDown );
    415 
    416         /* final amount to move edge or edge pair */
    417         CF2_Fixed  move;
    418 
    419         CF2_Fixed  downMinCounter = CF2_MIN_COUNTER;
    420         CF2_Fixed  upMinCounter   = CF2_MIN_COUNTER;
    421         FT_Bool    saveEdge       = FALSE;
    422 
    423 
    424         /* minimum counter constraint doesn't apply when adjacent edges */
    425         /* are synthetic                                                */
    426         /* TODO: doesn't seem a big effect; for now, reduce the code    */
    427 #if 0
    428         if ( i == 0                                        ||
    429              cf2_hint_isSynthetic( &hintmap->edge[i - 1] ) )
    430           downMinCounter = 0;
    431 
    432         if ( j >= hintmap->count - 1                       ||
    433              cf2_hint_isSynthetic( &hintmap->edge[j + 1] ) )
    434           upMinCounter = 0;
    435 #endif
    436 
    437         /* is there room to move up?                                    */
    438         /* there is if we are at top of array or the next edge is at or */
    439         /* beyond proposed move up?                                     */
    440         if ( j >= hintmap->count - 1                            ||
    441              hintmap->edge[j + 1].dsCoord >=
    442                hintmap->edge[j].dsCoord + moveUp + upMinCounter )
    443         {
    444           /* there is room to move up; is there also room to move down? */
    445           if ( i == 0                                                 ||
    446                hintmap->edge[i - 1].dsCoord <=
    447                  hintmap->edge[i].dsCoord + moveDown - downMinCounter )
    448           {
    449             /* move smaller absolute amount */
    450             move = ( -moveDown < moveUp ) ? moveDown : moveUp;  /* optimum */
    451           }
    452           else
    453             move = moveUp;
    454         }
    455         else
    456         {
    457           /* is there room to move down? */
    458           if ( i == 0                                                 ||
    459                hintmap->edge[i - 1].dsCoord <=
    460                  hintmap->edge[i].dsCoord + moveDown - downMinCounter )
    461           {
    462             move     = moveDown;
    463             /* true if non-optimum move */
    464             saveEdge = (FT_Bool)( moveUp < -moveDown );
    465           }
    466           else
    467           {
    468             /* no room to move either way without overlapping or reducing */
    469             /* the counter too much                                       */
    470             move     = 0;
    471             saveEdge = TRUE;
    472           }
    473         }
    474 
    475         /* Identify non-moves and moves down that aren't optimal, and save */
    476         /* them for second pass.                                           */
    477         /* Do this only if there is an unlocked edge above (which could    */
    478         /* possibly move).                                                 */
    479         if ( saveEdge                                    &&
    480              j < hintmap->count - 1                      &&
    481              !cf2_hint_isLocked( &hintmap->edge[j + 1] ) )
    482         {
    483           CF2_HintMoveRec  savedMove;
    484 
    485 
    486           savedMove.j      = j;
    487           /* desired adjustment in second pass */
    488           savedMove.moveUp = moveUp - move;
    489 
    490           cf2_arrstack_push( hintmap->hintMoves, &savedMove );
    491         }
    492 
    493         /* move the edge(s) */
    494         hintmap->edge[i].dsCoord += move;
    495         if ( isPair )
    496           hintmap->edge[j].dsCoord += move;
    497       }
    498 
    499       /* assert there are no overlaps in device space */
    500       FT_ASSERT( i == 0                                                   ||
    501                  hintmap->edge[i - 1].dsCoord <= hintmap->edge[i].dsCoord );
    502       FT_ASSERT( i < j                                                ||
    503                  hintmap->edge[i].dsCoord <= hintmap->edge[j].dsCoord );
    504 
    505       /* adjust the scales, avoiding divide by zero */
    506       if ( i > 0 )
    507       {
    508         if ( hintmap->edge[i].csCoord != hintmap->edge[i - 1].csCoord )
    509           hintmap->edge[i - 1].scale =
    510             FT_DivFix(
    511               hintmap->edge[i].dsCoord - hintmap->edge[i - 1].dsCoord,
    512               hintmap->edge[i].csCoord - hintmap->edge[i - 1].csCoord );
    513       }
    514 
    515       if ( isPair )
    516       {
    517         if ( hintmap->edge[j].csCoord != hintmap->edge[j - 1].csCoord )
    518           hintmap->edge[j - 1].scale =
    519             FT_DivFix(
    520               hintmap->edge[j].dsCoord - hintmap->edge[j - 1].dsCoord,
    521               hintmap->edge[j].csCoord - hintmap->edge[j - 1].csCoord );
    522 
    523         i += 1;     /* skip upper edge on next loop */
    524       }
    525     }
    526 
    527     /* second pass tries to move non-optimal hints up, in case there is */
    528     /* room now                                                         */
    529     for ( i = cf2_arrstack_size( hintmap->hintMoves ); i > 0; i-- )
    530     {
    531       CF2_HintMove  hintMove = (CF2_HintMove)
    532                       cf2_arrstack_getPointer( hintmap->hintMoves, i - 1 );
    533 
    534 
    535       j = hintMove->j;
    536 
    537       /* this was tested before the push, above */
    538       FT_ASSERT( j < hintmap->count - 1 );
    539 
    540       /* is there room to move up? */
    541       if ( hintmap->edge[j + 1].dsCoord >=
    542              hintmap->edge[j].dsCoord + hintMove->moveUp + CF2_MIN_COUNTER )
    543       {
    544         /* there is more room now, move edge up */
    545         hintmap->edge[j].dsCoord += hintMove->moveUp;
    546 
    547         if ( cf2_hint_isPair( &hintmap->edge[j] ) )
    548         {
    549           FT_ASSERT( j > 0 );
    550           hintmap->edge[j - 1].dsCoord += hintMove->moveUp;
    551         }
    552       }
    553     }
    554   }
    555 
    556 
    557   /* insert hint edges into map, sorted by csCoord */
    558   static void
    559   cf2_hintmap_insertHint( CF2_HintMap  hintmap,
    560                           CF2_Hint     bottomHintEdge,
    561                           CF2_Hint     topHintEdge )
    562   {
    563     CF2_UInt  indexInsert;
    564 
    565     /* set default values, then check for edge hints */
    566     FT_Bool   isPair         = TRUE;
    567     CF2_Hint  firstHintEdge  = bottomHintEdge;
    568     CF2_Hint  secondHintEdge = topHintEdge;
    569 
    570 
    571     /* one or none of the input params may be invalid when dealing with */
    572     /* edge hints; at least one edge must be valid                      */
    573     FT_ASSERT( cf2_hint_isValid( bottomHintEdge ) ||
    574                cf2_hint_isValid( topHintEdge )    );
    575 
    576     /* determine how many and which edges to insert */
    577     if ( !cf2_hint_isValid( bottomHintEdge ) )
    578     {
    579       /* insert only the top edge */
    580       firstHintEdge = topHintEdge;
    581       isPair        = FALSE;
    582     }
    583     else if ( !cf2_hint_isValid( topHintEdge ) )
    584     {
    585       /* insert only the bottom edge */
    586       isPair = FALSE;
    587     }
    588 
    589     /* paired edges must be in proper order */
    590     FT_ASSERT( !isPair                                         ||
    591                topHintEdge->csCoord >= bottomHintEdge->csCoord );
    592 
    593     /* linear search to find index value of insertion point */
    594     indexInsert = 0;
    595     for ( ; indexInsert < hintmap->count; indexInsert++ )
    596     {
    597       if ( hintmap->edge[indexInsert].csCoord >= firstHintEdge->csCoord )
    598         break;
    599     }
    600 
    601     /*
    602      * Discard any hints that overlap in character space.  Most often, this
    603      * is while building the initial map, where captured hints from all
    604      * zones are combined.  Define overlap to include hints that `touch'
    605      * (overlap zero).  Hiragino Sans/Gothic fonts have numerous hints that
    606      * touch.  Some fonts have non-ideographic glyphs that overlap our
    607      * synthetic hints.
    608      *
    609      * Overlap also occurs when darkening stem hints that are close.
    610      *
    611      */
    612     if ( indexInsert < hintmap->count )
    613     {
    614       /* we are inserting before an existing edge:    */
    615       /* verify that an existing edge is not the same */
    616       if ( hintmap->edge[indexInsert].csCoord == firstHintEdge->csCoord )
    617         return; /* ignore overlapping stem hint */
    618 
    619       /* verify that a new pair does not straddle the next edge */
    620       if ( isPair                                                        &&
    621            hintmap->edge[indexInsert].csCoord <= secondHintEdge->csCoord )
    622         return; /* ignore overlapping stem hint */
    623 
    624       /* verify that we are not inserting between paired edges */
    625       if ( cf2_hint_isPairTop( &hintmap->edge[indexInsert] ) )
    626         return; /* ignore overlapping stem hint */
    627     }
    628 
    629     /* recompute device space locations using initial hint map */
    630     if ( cf2_hintmap_isValid( hintmap->initialHintMap ) &&
    631          !cf2_hint_isLocked( firstHintEdge )            )
    632     {
    633       if ( isPair )
    634       {
    635         /* Use hint map to position the center of stem, and nominal scale */
    636         /* to position the two edges.  This preserves the stem width.     */
    637         CF2_Fixed  midpoint  = cf2_hintmap_map(
    638                                  hintmap->initialHintMap,
    639                                  ( secondHintEdge->csCoord +
    640                                    firstHintEdge->csCoord ) / 2 );
    641         CF2_Fixed  halfWidth = FT_MulFix(
    642                                  ( secondHintEdge->csCoord -
    643                                    firstHintEdge->csCoord ) / 2,
    644                                  hintmap->scale );
    645 
    646 
    647         firstHintEdge->dsCoord  = midpoint - halfWidth;
    648         secondHintEdge->dsCoord = midpoint + halfWidth;
    649       }
    650       else
    651         firstHintEdge->dsCoord = cf2_hintmap_map( hintmap->initialHintMap,
    652                                                   firstHintEdge->csCoord );
    653     }
    654 
    655     /*
    656      * Discard any hints that overlap in device space; this can occur
    657      * because locked hints have been moved to align with blue zones.
    658      *
    659      * TODO: Although we might correct this later during adjustment, we
    660      * don't currently have a way to delete a conflicting hint once it has
    661      * been inserted.  See v2.030 MinionPro-Regular, 12 ppem darkened,
    662      * initial hint map for second path, glyph 945 (the perispomeni (tilde)
    663      * in U+1F6E, Greek omega with psili and perispomeni).  Darkening is
    664      * 25.  Pair 667,747 initially conflicts in design space with top edge
    665      * 660.  This is because 667 maps to 7.87, and the top edge was
    666      * captured by a zone at 8.0.  The pair is later successfully inserted
    667      * in a zone without the top edge.  In this zone it is adjusted to 8.0,
    668      * and no longer conflicts with the top edge in design space.  This
    669      * means it can be included in yet a later zone which does have the top
    670      * edge hint.  This produces a small mismatch between the first and
    671      * last points of this path, even though the hint masks are the same.
    672      * The density map difference is tiny (1/256).
    673      *
    674      */
    675 
    676     if ( indexInsert > 0 )
    677     {
    678       /* we are inserting after an existing edge */
    679       if ( firstHintEdge->dsCoord < hintmap->edge[indexInsert - 1].dsCoord )
    680         return;
    681     }
    682 
    683     if ( indexInsert < hintmap->count )
    684     {
    685       /* we are inserting before an existing edge */
    686       if ( isPair )
    687       {
    688         if ( secondHintEdge->dsCoord > hintmap->edge[indexInsert].dsCoord )
    689           return;
    690       }
    691       else
    692       {
    693         if ( firstHintEdge->dsCoord > hintmap->edge[indexInsert].dsCoord )
    694           return;
    695       }
    696     }
    697 
    698     /* make room to insert */
    699     {
    700       CF2_UInt  iSrc = hintmap->count - 1;
    701       CF2_UInt  iDst = isPair ? hintmap->count + 1 : hintmap->count;
    702 
    703       CF2_UInt  count = hintmap->count - indexInsert;
    704 
    705 
    706       if ( iDst >= CF2_MAX_HINT_EDGES )
    707       {
    708         FT_TRACE4(( "cf2_hintmap_insertHint: too many hintmaps\n" ));
    709         return;
    710       }
    711 
    712       while ( count-- )
    713         hintmap->edge[iDst--] = hintmap->edge[iSrc--];
    714 
    715       /* insert first edge */
    716       hintmap->edge[indexInsert] = *firstHintEdge;         /* copy struct */
    717       hintmap->count += 1;
    718 
    719       if ( isPair )
    720       {
    721         /* insert second edge */
    722         hintmap->edge[indexInsert + 1] = *secondHintEdge;  /* copy struct */
    723         hintmap->count                += 1;
    724       }
    725     }
    726 
    727     return;
    728   }
    729 
    730 
    731   /*
    732    * Build a map from hints and mask.
    733    *
    734    * This function may recur one level if `hintmap->initialHintMap' is not yet
    735    * valid.
    736    * If `initialMap' is true, simply build initial map.
    737    *
    738    * Synthetic hints are used in two ways.  A hint at zero is inserted, if
    739    * needed, in the initial hint map, to prevent translations from
    740    * propagating across the origin.  If synthetic em box hints are enabled
    741    * for ideographic dictionaries, then they are inserted in all hint
    742    * maps, including the initial one.
    743    *
    744    */
    745   FT_LOCAL_DEF( void )
    746   cf2_hintmap_build( CF2_HintMap   hintmap,
    747                      CF2_ArrStack  hStemHintArray,
    748                      CF2_ArrStack  vStemHintArray,
    749                      CF2_HintMask  hintMask,
    750                      CF2_Fixed     hintOrigin,
    751                      FT_Bool       initialMap )
    752   {
    753     FT_Byte*  maskPtr;
    754 
    755     CF2_Font         font = hintmap->font;
    756     CF2_HintMaskRec  tempHintMask;
    757 
    758     size_t   bitCount, i;
    759     FT_Byte  maskByte;
    760 
    761 
    762     /* check whether initial map is constructed */
    763     if ( !initialMap && !cf2_hintmap_isValid( hintmap->initialHintMap ) )
    764     {
    765       /* make recursive call with initialHintMap and temporary mask; */
    766       /* temporary mask will get all bits set, below */
    767       cf2_hintmask_init( &tempHintMask, hintMask->error );
    768       cf2_hintmap_build( hintmap->initialHintMap,
    769                          hStemHintArray,
    770                          vStemHintArray,
    771                          &tempHintMask,
    772                          hintOrigin,
    773                          TRUE );
    774     }
    775 
    776     if ( !cf2_hintmask_isValid( hintMask ) )
    777     {
    778       /* without a hint mask, assume all hints are active */
    779       cf2_hintmask_setAll( hintMask,
    780                            cf2_arrstack_size( hStemHintArray ) +
    781                              cf2_arrstack_size( vStemHintArray ) );
    782       if ( !cf2_hintmask_isValid( hintMask ) )
    783           return;                   /* too many stem hints */
    784     }
    785 
    786     /* begin by clearing the map */
    787     hintmap->count     = 0;
    788     hintmap->lastIndex = 0;
    789 
    790     /* make a copy of the hint mask so we can modify it */
    791     tempHintMask = *hintMask;
    792     maskPtr      = cf2_hintmask_getMaskPtr( &tempHintMask );
    793 
    794     /* use the hStem hints only, which are first in the mask */
    795     bitCount = cf2_arrstack_size( hStemHintArray );
    796 
    797     /* Defense-in-depth.  Should never return here. */
    798     if ( bitCount > hintMask->bitCount )
    799         return;
    800 
    801     /* synthetic embox hints get highest priority */
    802     if ( font->blues.doEmBoxHints )
    803     {
    804       CF2_HintRec  dummy;
    805 
    806 
    807       cf2_hint_initZero( &dummy );   /* invalid hint map element */
    808 
    809       /* ghost bottom */
    810       cf2_hintmap_insertHint( hintmap,
    811                               &font->blues.emBoxBottomEdge,
    812                               &dummy );
    813       /* ghost top */
    814       cf2_hintmap_insertHint( hintmap,
    815                               &dummy,
    816                               &font->blues.emBoxTopEdge );
    817     }
    818 
    819     /* insert hints captured by a blue zone or already locked (higher */
    820     /* priority)                                                      */
    821     for ( i = 0, maskByte = 0x80; i < bitCount; i++ )
    822     {
    823       if ( maskByte & *maskPtr )
    824       {
    825         /* expand StemHint into two `CF2_Hint' elements */
    826         CF2_HintRec  bottomHintEdge, topHintEdge;
    827 
    828 
    829         cf2_hint_init( &bottomHintEdge,
    830                        hStemHintArray,
    831                        i,
    832                        font,
    833                        hintOrigin,
    834                        hintmap->scale,
    835                        TRUE /* bottom */ );
    836         cf2_hint_init( &topHintEdge,
    837                        hStemHintArray,
    838                        i,
    839                        font,
    840                        hintOrigin,
    841                        hintmap->scale,
    842                        FALSE /* top */ );
    843 
    844         if ( cf2_hint_isLocked( &bottomHintEdge ) ||
    845              cf2_hint_isLocked( &topHintEdge )    ||
    846              cf2_blues_capture( &font->blues,
    847                                 &bottomHintEdge,
    848                                 &topHintEdge )   )
    849         {
    850           /* insert captured hint into map */
    851           cf2_hintmap_insertHint( hintmap, &bottomHintEdge, &topHintEdge );
    852 
    853           *maskPtr &= ~maskByte;      /* turn off the bit for this hint */
    854         }
    855       }
    856 
    857       if ( ( i & 7 ) == 7 )
    858       {
    859         /* move to next mask byte */
    860         maskPtr++;
    861         maskByte = 0x80;
    862       }
    863       else
    864         maskByte >>= 1;
    865     }
    866 
    867     /* initial hint map includes only captured hints plus maybe one at 0 */
    868 
    869     /*
    870      * TODO: There is a problem here because we are trying to build a
    871      *       single hint map containing all captured hints.  It is
    872      *       possible for there to be conflicts between captured hints,
    873      *       either because of darkening or because the hints are in
    874      *       separate hint zones (we are ignoring hint zones for the
    875      *       initial map).  An example of the latter is MinionPro-Regular
    876      *       v2.030 glyph 883 (Greek Capital Alpha with Psili) at 15ppem.
    877      *       A stem hint for the psili conflicts with the top edge hint
    878      *       for the base character.  The stem hint gets priority because
    879      *       of its sort order.  In glyph 884 (Greek Capital Alpha with
    880      *       Psili and Oxia), the top of the base character gets a stem
    881      *       hint, and the psili does not.  This creates different initial
    882      *       maps for the two glyphs resulting in different renderings of
    883      *       the base character.  Will probably defer this either as not
    884      *       worth the cost or as a font bug.  I don't think there is any
    885      *       good reason for an accent to be captured by an alignment
    886      *       zone.  -darnold 2/12/10
    887      */
    888 
    889     if ( initialMap )
    890     {
    891       /* Apply a heuristic that inserts a point for (0,0), unless it's     */
    892       /* already covered by a mapping.  This locks the baseline for glyphs */
    893       /* that have no baseline hints.                                      */
    894 
    895       if ( hintmap->count == 0                           ||
    896            hintmap->edge[0].csCoord > 0                  ||
    897            hintmap->edge[hintmap->count - 1].csCoord < 0 )
    898       {
    899         /* all edges are above 0 or all edges are below 0; */
    900         /* construct a locked edge hint at 0               */
    901 
    902         CF2_HintRec  edge, invalid;
    903 
    904 
    905         cf2_hint_initZero( &edge );
    906 
    907         edge.flags = CF2_GhostBottom |
    908                      CF2_Locked      |
    909                      CF2_Synthetic;
    910         edge.scale = hintmap->scale;
    911 
    912         cf2_hint_initZero( &invalid );
    913         cf2_hintmap_insertHint( hintmap, &edge, &invalid );
    914       }
    915     }
    916     else
    917     {
    918       /* insert remaining hints */
    919 
    920       maskPtr = cf2_hintmask_getMaskPtr( &tempHintMask );
    921 
    922       for ( i = 0, maskByte = 0x80; i < bitCount; i++ )
    923       {
    924         if ( maskByte & *maskPtr )
    925         {
    926           CF2_HintRec  bottomHintEdge, topHintEdge;
    927 
    928 
    929           cf2_hint_init( &bottomHintEdge,
    930                          hStemHintArray,
    931                          i,
    932                          font,
    933                          hintOrigin,
    934                          hintmap->scale,
    935                          TRUE /* bottom */ );
    936           cf2_hint_init( &topHintEdge,
    937                          hStemHintArray,
    938                          i,
    939                          font,
    940                          hintOrigin,
    941                          hintmap->scale,
    942                          FALSE /* top */ );
    943 
    944           cf2_hintmap_insertHint( hintmap, &bottomHintEdge, &topHintEdge );
    945         }
    946 
    947         if ( ( i & 7 ) == 7 )
    948         {
    949           /* move to next mask byte */
    950           maskPtr++;
    951           maskByte = 0x80;
    952         }
    953         else
    954           maskByte >>= 1;
    955       }
    956     }
    957 
    958     /*
    959      * Note: The following line is a convenient place to break when
    960      *       debugging hinting.  Examine `hintmap->edge' for the list of
    961      *       enabled hints, then step over the call to see the effect of
    962      *       adjustment.  We stop here first on the recursive call that
    963      *       creates the initial map, and then on each counter group and
    964      *       hint zone.
    965      */
    966 
    967     /* adjust positions of hint edges that are not locked to blue zones */
    968     cf2_hintmap_adjustHints( hintmap );
    969 
    970     /* save the position of all hints that were used in this hint map; */
    971     /* if we use them again, we'll locate them in the same position    */
    972     if ( !initialMap )
    973     {
    974       for ( i = 0; i < hintmap->count; i++ )
    975       {
    976         if ( !cf2_hint_isSynthetic( &hintmap->edge[i] ) )
    977         {
    978           /* Note: include both valid and invalid edges            */
    979           /* Note: top and bottom edges are copied back separately */
    980           CF2_StemHint  stemhint = (CF2_StemHint)
    981                           cf2_arrstack_getPointer( hStemHintArray,
    982                                                    hintmap->edge[i].index );
    983 
    984 
    985           if ( cf2_hint_isTop( &hintmap->edge[i] ) )
    986             stemhint->maxDS = hintmap->edge[i].dsCoord;
    987           else
    988             stemhint->minDS = hintmap->edge[i].dsCoord;
    989 
    990           stemhint->used = TRUE;
    991         }
    992       }
    993     }
    994 
    995     /* hint map is ready to use */
    996     hintmap->isValid = TRUE;
    997 
    998     /* remember this mask has been used */
    999     cf2_hintmask_setNew( hintMask, FALSE );
   1000   }
   1001 
   1002 
   1003   FT_LOCAL_DEF( void )
   1004   cf2_glyphpath_init( CF2_GlyphPath         glyphpath,
   1005                       CF2_Font              font,
   1006                       CF2_OutlineCallbacks  callbacks,
   1007                       CF2_Fixed             scaleY,
   1008                       /* CF2_Fixed  hShift, */
   1009                       CF2_ArrStack          hStemHintArray,
   1010                       CF2_ArrStack          vStemHintArray,
   1011                       CF2_HintMask          hintMask,
   1012                       CF2_Fixed             hintOriginY,
   1013                       const CF2_Blues       blues,
   1014                       const FT_Vector*      fractionalTranslation )
   1015   {
   1016     FT_ZERO( glyphpath );
   1017 
   1018     glyphpath->font      = font;
   1019     glyphpath->callbacks = callbacks;
   1020 
   1021     cf2_arrstack_init( &glyphpath->hintMoves,
   1022                        font->memory,
   1023                        &font->error,
   1024                        sizeof ( CF2_HintMoveRec ) );
   1025 
   1026     cf2_hintmap_init( &glyphpath->initialHintMap,
   1027                       font,
   1028                       &glyphpath->initialHintMap,
   1029                       &glyphpath->hintMoves,
   1030                       scaleY );
   1031     cf2_hintmap_init( &glyphpath->firstHintMap,
   1032                       font,
   1033                       &glyphpath->initialHintMap,
   1034                       &glyphpath->hintMoves,
   1035                       scaleY );
   1036     cf2_hintmap_init( &glyphpath->hintMap,
   1037                       font,
   1038                       &glyphpath->initialHintMap,
   1039                       &glyphpath->hintMoves,
   1040                       scaleY );
   1041 
   1042     glyphpath->scaleX = font->innerTransform.a;
   1043     glyphpath->scaleC = font->innerTransform.c;
   1044     glyphpath->scaleY = font->innerTransform.d;
   1045 
   1046     glyphpath->fractionalTranslation = *fractionalTranslation;
   1047 
   1048 #if 0
   1049     glyphpath->hShift = hShift;       /* for fauxing */
   1050 #endif
   1051 
   1052     glyphpath->hStemHintArray = hStemHintArray;
   1053     glyphpath->vStemHintArray = vStemHintArray;
   1054     glyphpath->hintMask       = hintMask;      /* ptr to current mask */
   1055     glyphpath->hintOriginY    = hintOriginY;
   1056     glyphpath->blues          = blues;
   1057     glyphpath->darken         = font->darkened; /* TODO: should we make copies? */
   1058     glyphpath->xOffset        = font->darkenX;
   1059     glyphpath->yOffset        = font->darkenY;
   1060     glyphpath->miterLimit     = 2 * FT_MAX(
   1061                                      cf2_fixedAbs( glyphpath->xOffset ),
   1062                                      cf2_fixedAbs( glyphpath->yOffset ) );
   1063 
   1064     /* .1 character space unit */
   1065     glyphpath->snapThreshold = cf2_floatToFixed( 0.1f );
   1066 
   1067     glyphpath->moveIsPending = TRUE;
   1068     glyphpath->pathIsOpen    = FALSE;
   1069     glyphpath->pathIsClosing = FALSE;
   1070     glyphpath->elemIsQueued  = FALSE;
   1071   }
   1072 
   1073 
   1074   FT_LOCAL_DEF( void )
   1075   cf2_glyphpath_finalize( CF2_GlyphPath  glyphpath )
   1076   {
   1077     cf2_arrstack_finalize( &glyphpath->hintMoves );
   1078   }
   1079 
   1080 
   1081   /*
   1082    * Hint point in y-direction and apply outerTransform.
   1083    * Input `current' hint map (which is actually delayed by one element).
   1084    * Input x,y point in Character Space.
   1085    * Output x,y point in Device Space, including translation.
   1086    */
   1087   static void
   1088   cf2_glyphpath_hintPoint( CF2_GlyphPath  glyphpath,
   1089                            CF2_HintMap    hintmap,
   1090                            FT_Vector*     ppt,
   1091                            CF2_Fixed      x,
   1092                            CF2_Fixed      y )
   1093   {
   1094     FT_Vector  pt;   /* hinted point in upright DS */
   1095 
   1096 
   1097     pt.x = FT_MulFix( glyphpath->scaleX, x ) +
   1098              FT_MulFix( glyphpath->scaleC, y );
   1099     pt.y = cf2_hintmap_map( hintmap, y );
   1100 
   1101     ppt->x = FT_MulFix( glyphpath->font->outerTransform.a, pt.x )   +
   1102                FT_MulFix( glyphpath->font->outerTransform.c, pt.y ) +
   1103                glyphpath->fractionalTranslation.x;
   1104     ppt->y = FT_MulFix( glyphpath->font->outerTransform.b, pt.x )   +
   1105                FT_MulFix( glyphpath->font->outerTransform.d, pt.y ) +
   1106                glyphpath->fractionalTranslation.y;
   1107   }
   1108 
   1109 
   1110   /*
   1111    * From two line segments, (u1,u2) and (v1,v2), compute a point of
   1112    * intersection on the corresponding lines.
   1113    * Return false if no intersection is found, or if the intersection is
   1114    * too far away from the ends of the line segments, u2 and v1.
   1115    *
   1116    */
   1117   static FT_Bool
   1118   cf2_glyphpath_computeIntersection( CF2_GlyphPath     glyphpath,
   1119                                      const FT_Vector*  u1,
   1120                                      const FT_Vector*  u2,
   1121                                      const FT_Vector*  v1,
   1122                                      const FT_Vector*  v2,
   1123                                      FT_Vector*        intersection )
   1124   {
   1125     /*
   1126      * Let `u' be a zero-based vector from the first segment, `v' from the
   1127      * second segment.
   1128      * Let `w 'be the zero-based vector from `u1' to `v1'.
   1129      * `perp' is the `perpendicular dot product'; see
   1130      * http://mathworld.wolfram.com/PerpDotProduct.html.
   1131      * `s' is the parameter for the parametric line for the first segment
   1132      * (`u').
   1133      *
   1134      * See notation in
   1135      * http://softsurfer.com/Archive/algorithm_0104/algorithm_0104B.htm.
   1136      * Calculations are done in 16.16, but must handle the squaring of
   1137      * line lengths in character space.  We scale all vectors by 1/32 to
   1138      * avoid overflow.  This allows values up to 4095 to be squared.  The
   1139      * scale factor cancels in the divide.
   1140      *
   1141      * TODO: the scale factor could be computed from UnitsPerEm.
   1142      *
   1143      */
   1144 
   1145 #define cf2_perp( a, b )                                    \
   1146           ( FT_MulFix( a.x, b.y ) - FT_MulFix( a.y, b.x ) )
   1147 
   1148   /* round and divide by 32 */
   1149 #define CF2_CS_SCALE( x )         \
   1150           ( ( (x) + 0x10 ) >> 5 )
   1151 
   1152     FT_Vector  u, v, w;      /* scaled vectors */
   1153     CF2_Fixed  denominator, s;
   1154 
   1155 
   1156     u.x = CF2_CS_SCALE( u2->x - u1->x );
   1157     u.y = CF2_CS_SCALE( u2->y - u1->y );
   1158     v.x = CF2_CS_SCALE( v2->x - v1->x );
   1159     v.y = CF2_CS_SCALE( v2->y - v1->y );
   1160     w.x = CF2_CS_SCALE( v1->x - u1->x );
   1161     w.y = CF2_CS_SCALE( v1->y - u1->y );
   1162 
   1163     denominator = cf2_perp( u, v );
   1164 
   1165     if ( denominator == 0 )
   1166       return FALSE;           /* parallel or coincident lines */
   1167 
   1168     s = FT_DivFix( cf2_perp( w, v ), denominator );
   1169 
   1170     intersection->x = u1->x + FT_MulFix( s, u2->x - u1->x );
   1171     intersection->y = u1->y + FT_MulFix( s, u2->y - u1->y );
   1172 
   1173     /*
   1174      * Special case snapping for horizontal and vertical lines.
   1175      * This cleans up intersections and reduces problems with winding
   1176      * order detection.
   1177      * Sample case is sbc cd KozGoPr6N-Medium.otf 20 16685.
   1178      * Note: these calculations are in character space.
   1179      *
   1180      */
   1181 
   1182     if ( u1->x == u2->x                                                     &&
   1183          cf2_fixedAbs( intersection->x - u1->x ) < glyphpath->snapThreshold )
   1184       intersection->x = u1->x;
   1185     if ( u1->y == u2->y                                                     &&
   1186          cf2_fixedAbs( intersection->y - u1->y ) < glyphpath->snapThreshold )
   1187       intersection->y = u1->y;
   1188 
   1189     if ( v1->x == v2->x                                                     &&
   1190          cf2_fixedAbs( intersection->x - v1->x ) < glyphpath->snapThreshold )
   1191       intersection->x = v1->x;
   1192     if ( v1->y == v2->y                                                     &&
   1193          cf2_fixedAbs( intersection->y - v1->y ) < glyphpath->snapThreshold )
   1194       intersection->y = v1->y;
   1195 
   1196     /* limit the intersection distance from midpoint of u2 and v1 */
   1197     if ( cf2_fixedAbs( intersection->x - ( u2->x + v1->x ) / 2 ) >
   1198            glyphpath->miterLimit                                   ||
   1199          cf2_fixedAbs( intersection->y - ( u2->y + v1->y ) / 2 ) >
   1200            glyphpath->miterLimit                                   )
   1201       return FALSE;
   1202 
   1203     return TRUE;
   1204   }
   1205 
   1206 
   1207   /*
   1208    * Push the cached element (glyphpath->prevElem*) to the outline
   1209    * consumer.  When a darkening offset is used, the end point of the
   1210    * cached element may be adjusted to an intersection point or we may
   1211    * synthesize a connecting line to the current element.  If we are
   1212    * closing a subpath, we may also generate a connecting line to the start
   1213    * point.
   1214    *
   1215    * This is where Character Space (CS) is converted to Device Space (DS)
   1216    * using a hint map.  This calculation must use a HintMap that was valid
   1217    * at the time the element was saved.  For the first point in a subpath,
   1218    * that is a saved HintMap.  For most elements, it just means the caller
   1219    * has delayed building a HintMap from the current HintMask.
   1220    *
   1221    * Transform each point with outerTransform and call the outline
   1222    * callbacks.  This is a general 3x3 transform:
   1223    *
   1224    *   x' = a*x + c*y + tx, y' = b*x + d*y + ty
   1225    *
   1226    * but it uses 4 elements from CF2_Font and the translation part
   1227    * from CF2_GlyphPath.
   1228    *
   1229    */
   1230   static void
   1231   cf2_glyphpath_pushPrevElem( CF2_GlyphPath  glyphpath,
   1232                               CF2_HintMap    hintmap,
   1233                               FT_Vector*     nextP0,
   1234                               FT_Vector      nextP1,
   1235                               FT_Bool        close )
   1236   {
   1237     CF2_CallbackParamsRec  params;
   1238 
   1239     FT_Vector*  prevP0;
   1240     FT_Vector*  prevP1;
   1241 
   1242     FT_Vector  intersection    = { 0, 0 };
   1243     FT_Bool    useIntersection = FALSE;
   1244 
   1245 
   1246     FT_ASSERT( glyphpath->prevElemOp == CF2_PathOpLineTo ||
   1247                glyphpath->prevElemOp == CF2_PathOpCubeTo );
   1248 
   1249     if ( glyphpath->prevElemOp == CF2_PathOpLineTo )
   1250     {
   1251       prevP0 = &glyphpath->prevElemP0;
   1252       prevP1 = &glyphpath->prevElemP1;
   1253     }
   1254     else
   1255     {
   1256       prevP0 = &glyphpath->prevElemP2;
   1257       prevP1 = &glyphpath->prevElemP3;
   1258     }
   1259 
   1260     /* optimization: if previous and next elements are offset by the same */
   1261     /* amount, then there will be no gap, and no need to compute an       */
   1262     /* intersection.                                                      */
   1263     if ( prevP1->x != nextP0->x || prevP1->y != nextP0->y )
   1264     {
   1265       /* previous element does not join next element:             */
   1266       /* adjust end point of previous element to the intersection */
   1267       useIntersection = cf2_glyphpath_computeIntersection( glyphpath,
   1268                                                            prevP0,
   1269                                                            prevP1,
   1270                                                            nextP0,
   1271                                                            &nextP1,
   1272                                                            &intersection );
   1273       if ( useIntersection )
   1274       {
   1275         /* modify the last point of the cached element (either line or */
   1276         /* curve)                                                      */
   1277         *prevP1 = intersection;
   1278       }
   1279     }
   1280 
   1281     params.pt0 = glyphpath->currentDS;
   1282 
   1283     switch( glyphpath->prevElemOp )
   1284     {
   1285     case CF2_PathOpLineTo:
   1286       params.op = CF2_PathOpLineTo;
   1287 
   1288       /* note: pt2 and pt3 are unused */
   1289 
   1290       if ( close )
   1291       {
   1292         /* use first hint map if closing */
   1293         cf2_glyphpath_hintPoint( glyphpath,
   1294                                  &glyphpath->firstHintMap,
   1295                                  &params.pt1,
   1296                                  glyphpath->prevElemP1.x,
   1297                                  glyphpath->prevElemP1.y );
   1298       }
   1299       else
   1300       {
   1301         cf2_glyphpath_hintPoint( glyphpath,
   1302                                  hintmap,
   1303                                  &params.pt1,
   1304                                  glyphpath->prevElemP1.x,
   1305                                  glyphpath->prevElemP1.y );
   1306       }
   1307 
   1308       /* output only non-zero length lines */
   1309       if ( params.pt0.x != params.pt1.x || params.pt0.y != params.pt1.y )
   1310       {
   1311         glyphpath->callbacks->lineTo( glyphpath->callbacks, &params );
   1312 
   1313         glyphpath->currentDS = params.pt1;
   1314       }
   1315       break;
   1316 
   1317     case CF2_PathOpCubeTo:
   1318       params.op = CF2_PathOpCubeTo;
   1319 
   1320       /* TODO: should we intersect the interior joins (p1-p2 and p2-p3)? */
   1321       cf2_glyphpath_hintPoint( glyphpath,
   1322                                hintmap,
   1323                                &params.pt1,
   1324                                glyphpath->prevElemP1.x,
   1325                                glyphpath->prevElemP1.y );
   1326       cf2_glyphpath_hintPoint( glyphpath,
   1327                                hintmap,
   1328                                &params.pt2,
   1329                                glyphpath->prevElemP2.x,
   1330                                glyphpath->prevElemP2.y );
   1331       cf2_glyphpath_hintPoint( glyphpath,
   1332                                hintmap,
   1333                                &params.pt3,
   1334                                glyphpath->prevElemP3.x,
   1335                                glyphpath->prevElemP3.y );
   1336 
   1337       glyphpath->callbacks->cubeTo( glyphpath->callbacks, &params );
   1338 
   1339       glyphpath->currentDS = params.pt3;
   1340 
   1341       break;
   1342     }
   1343 
   1344     if ( !useIntersection || close )
   1345     {
   1346       /* insert connecting line between end of previous element and start */
   1347       /* of current one                                                   */
   1348       /* note: at the end of a subpath, we might do both, so use `nextP0' */
   1349       /* before we change it, below                                       */
   1350 
   1351       if ( close )
   1352       {
   1353         /* if we are closing the subpath, then nextP0 is in the first     */
   1354         /* hint zone                                                      */
   1355         cf2_glyphpath_hintPoint( glyphpath,
   1356                                  &glyphpath->firstHintMap,
   1357                                  &params.pt1,
   1358                                  nextP0->x,
   1359                                  nextP0->y );
   1360       }
   1361       else
   1362       {
   1363         cf2_glyphpath_hintPoint( glyphpath,
   1364                                  hintmap,
   1365                                  &params.pt1,
   1366                                  nextP0->x,
   1367                                  nextP0->y );
   1368       }
   1369 
   1370       if ( params.pt1.x != glyphpath->currentDS.x ||
   1371            params.pt1.y != glyphpath->currentDS.y )
   1372       {
   1373         /* length is nonzero */
   1374         params.op  = CF2_PathOpLineTo;
   1375         params.pt0 = glyphpath->currentDS;
   1376 
   1377         /* note: pt2 and pt3 are unused */
   1378         glyphpath->callbacks->lineTo( glyphpath->callbacks, &params );
   1379 
   1380         glyphpath->currentDS = params.pt1;
   1381       }
   1382     }
   1383 
   1384     if ( useIntersection )
   1385     {
   1386       /* return intersection point to caller */
   1387       *nextP0 = intersection;
   1388     }
   1389   }
   1390 
   1391 
   1392   /* push a MoveTo element based on current point and offset of current */
   1393   /* element                                                            */
   1394   static void
   1395   cf2_glyphpath_pushMove( CF2_GlyphPath  glyphpath,
   1396                           FT_Vector      start )
   1397   {
   1398     CF2_CallbackParamsRec  params;
   1399 
   1400 
   1401     params.op  = CF2_PathOpMoveTo;
   1402     params.pt0 = glyphpath->currentDS;
   1403 
   1404     /* Test if move has really happened yet; it would have called */
   1405     /* `cf2_hintmap_build' to set `isValid'.                   */
   1406     if ( !cf2_hintmap_isValid( &glyphpath->hintMap ) )
   1407     {
   1408       /* we are here iff first subpath is missing a moveto operator: */
   1409       /* synthesize first moveTo to finish initialization of hintMap */
   1410       cf2_glyphpath_moveTo( glyphpath,
   1411                             glyphpath->start.x,
   1412                             glyphpath->start.y );
   1413     }
   1414 
   1415     cf2_glyphpath_hintPoint( glyphpath,
   1416                              &glyphpath->hintMap,
   1417                              &params.pt1,
   1418                              start.x,
   1419                              start.y );
   1420 
   1421     /* note: pt2 and pt3 are unused */
   1422     glyphpath->callbacks->moveTo( glyphpath->callbacks, &params );
   1423 
   1424     glyphpath->currentDS    = params.pt1;
   1425     glyphpath->offsetStart0 = start;
   1426   }
   1427 
   1428 
   1429   /*
   1430    * All coordinates are in character space.
   1431    * On input, (x1, y1) and (x2, y2) give line segment.
   1432    * On output, (x, y) give offset vector.
   1433    * We use a piecewise approximation to trig functions.
   1434    *
   1435    * TODO: Offset true perpendicular and proper length
   1436    *       supply the y-translation for hinting here, too,
   1437    *       that adds yOffset unconditionally to *y.
   1438    */
   1439   static void
   1440   cf2_glyphpath_computeOffset( CF2_GlyphPath  glyphpath,
   1441                                CF2_Fixed      x1,
   1442                                CF2_Fixed      y1,
   1443                                CF2_Fixed      x2,
   1444                                CF2_Fixed      y2,
   1445                                CF2_Fixed*     x,
   1446                                CF2_Fixed*     y )
   1447   {
   1448     CF2_Fixed  dx = x2 - x1;
   1449     CF2_Fixed  dy = y2 - y1;
   1450 
   1451 
   1452     /* note: negative offsets don't work here; negate deltas to change */
   1453     /* quadrants, below                                                */
   1454     if ( glyphpath->font->reverseWinding )
   1455     {
   1456       dx = -dx;
   1457       dy = -dy;
   1458     }
   1459 
   1460     *x = *y = 0;
   1461 
   1462     if ( !glyphpath->darken )
   1463         return;
   1464 
   1465     /* add momentum for this path element */
   1466     glyphpath->callbacks->windingMomentum +=
   1467       cf2_getWindingMomentum( x1, y1, x2, y2 );
   1468 
   1469     /* note: allow mixed integer and fixed multiplication here */
   1470     if ( dx >= 0 )
   1471     {
   1472       if ( dy >= 0 )
   1473       {
   1474         /* first quadrant, +x +y */
   1475 
   1476         if ( dx > 2 * dy )
   1477         {
   1478           /* +x */
   1479           *x = 0;
   1480           *y = 0;
   1481         }
   1482         else if ( dy > 2 * dx )
   1483         {
   1484           /* +y */
   1485           *x = glyphpath->xOffset;
   1486           *y = glyphpath->yOffset;
   1487         }
   1488         else
   1489         {
   1490           /* +x +y */
   1491           *x = FT_MulFix( cf2_floatToFixed( 0.7 ),
   1492                           glyphpath->xOffset );
   1493           *y = FT_MulFix( cf2_floatToFixed( 1.0 - 0.7 ),
   1494                           glyphpath->yOffset );
   1495         }
   1496       }
   1497       else
   1498       {
   1499         /* fourth quadrant, +x -y */
   1500 
   1501         if ( dx > -2 * dy )
   1502         {
   1503           /* +x */
   1504           *x = 0;
   1505           *y = 0;
   1506         }
   1507         else if ( -dy > 2 * dx )
   1508         {
   1509           /* -y */
   1510           *x = -glyphpath->xOffset;
   1511           *y = glyphpath->yOffset;
   1512         }
   1513         else
   1514         {
   1515           /* +x -y */
   1516           *x = FT_MulFix( cf2_floatToFixed( -0.7 ),
   1517                           glyphpath->xOffset );
   1518           *y = FT_MulFix( cf2_floatToFixed( 1.0 - 0.7 ),
   1519                           glyphpath->yOffset );
   1520         }
   1521       }
   1522     }
   1523     else
   1524     {
   1525       if ( dy >= 0 )
   1526       {
   1527         /* second quadrant, -x +y */
   1528 
   1529         if ( -dx > 2 * dy )
   1530         {
   1531           /* -x */
   1532           *x = 0;
   1533           *y = 2 * glyphpath->yOffset;
   1534         }
   1535         else if ( dy > -2 * dx )
   1536         {
   1537           /* +y */
   1538           *x = glyphpath->xOffset;
   1539           *y = glyphpath->yOffset;
   1540         }
   1541         else
   1542         {
   1543           /* -x +y */
   1544           *x = FT_MulFix( cf2_floatToFixed( 0.7 ),
   1545                           glyphpath->xOffset );
   1546           *y = FT_MulFix( cf2_floatToFixed( 1.0 + 0.7 ),
   1547                           glyphpath->yOffset );
   1548         }
   1549       }
   1550       else
   1551       {
   1552         /* third quadrant, -x -y */
   1553 
   1554         if ( -dx > -2 * dy )
   1555         {
   1556           /* -x */
   1557           *x = 0;
   1558           *y = 2 * glyphpath->yOffset;
   1559         }
   1560         else if ( -dy > -2 * dx )
   1561         {
   1562           /* -y */
   1563           *x = -glyphpath->xOffset;
   1564           *y = glyphpath->yOffset;
   1565         }
   1566         else
   1567         {
   1568           /* -x -y */
   1569           *x = FT_MulFix( cf2_floatToFixed( -0.7 ),
   1570                           glyphpath->xOffset );
   1571           *y = FT_MulFix( cf2_floatToFixed( 1.0 + 0.7 ),
   1572                           glyphpath->yOffset );
   1573         }
   1574       }
   1575     }
   1576   }
   1577 
   1578 
   1579   /*
   1580    * The functions cf2_glyphpath_{moveTo,lineTo,curveTo,closeOpenPath} are
   1581    * called by the interpreter with Character Space (CS) coordinates.  Each
   1582    * path element is placed into a queue of length one to await the
   1583    * calculation of the following element.  At that time, the darkening
   1584    * offset of the following element is known and joins can be computed,
   1585    * including possible modification of this element, before mapping to
   1586    * Device Space (DS) and passing it on to the outline consumer.
   1587    *
   1588    */
   1589   FT_LOCAL_DEF( void )
   1590   cf2_glyphpath_moveTo( CF2_GlyphPath  glyphpath,
   1591                         CF2_Fixed      x,
   1592                         CF2_Fixed      y )
   1593   {
   1594     cf2_glyphpath_closeOpenPath( glyphpath );
   1595 
   1596     /* save the parameters of the move for later, when we'll know how to */
   1597     /* offset it;                                                        */
   1598     /* also save last move point */
   1599     glyphpath->currentCS.x = glyphpath->start.x = x;
   1600     glyphpath->currentCS.y = glyphpath->start.y = y;
   1601 
   1602     glyphpath->moveIsPending = TRUE;
   1603 
   1604     /* ensure we have a valid map with current mask */
   1605     if ( !cf2_hintmap_isValid( &glyphpath->hintMap ) ||
   1606          cf2_hintmask_isNew( glyphpath->hintMask )   )
   1607       cf2_hintmap_build( &glyphpath->hintMap,
   1608                          glyphpath->hStemHintArray,
   1609                          glyphpath->vStemHintArray,
   1610                          glyphpath->hintMask,
   1611                          glyphpath->hintOriginY,
   1612                          FALSE );
   1613 
   1614     /* save a copy of current HintMap to use when drawing initial point */
   1615     glyphpath->firstHintMap = glyphpath->hintMap;     /* structure copy */
   1616   }
   1617 
   1618 
   1619   FT_LOCAL_DEF( void )
   1620   cf2_glyphpath_lineTo( CF2_GlyphPath  glyphpath,
   1621                         CF2_Fixed      x,
   1622                         CF2_Fixed      y )
   1623   {
   1624     CF2_Fixed  xOffset, yOffset;
   1625     FT_Vector  P0, P1;
   1626     FT_Bool    newHintMap;
   1627 
   1628     /*
   1629      * New hints will be applied after cf2_glyphpath_pushPrevElem has run.
   1630      * In case this is a synthesized closing line, any new hints should be
   1631      * delayed until this path is closed (`cf2_hintmask_isNew' will be
   1632      * called again before the next line or curve).
   1633      */
   1634 
   1635     /* true if new hint map not on close */
   1636     newHintMap = cf2_hintmask_isNew( glyphpath->hintMask ) &&
   1637                  !glyphpath->pathIsClosing;
   1638 
   1639     /*
   1640      * Zero-length lines may occur in the charstring.  Because we cannot
   1641      * compute darkening offsets or intersections from zero-length lines,
   1642      * it is best to remove them and avoid artifacts.  However, zero-length
   1643      * lines in CS at the start of a new hint map can generate non-zero
   1644      * lines in DS due to hint substitution.  We detect a change in hint
   1645      * map here and pass those zero-length lines along.
   1646      */
   1647 
   1648     /*
   1649      * Note: Find explicitly closed paths here with a conditional
   1650      *       breakpoint using
   1651      *
   1652      *         !gp->pathIsClosing && gp->start.x == x && gp->start.y == y
   1653      *
   1654      */
   1655 
   1656     if ( glyphpath->currentCS.x == x &&
   1657          glyphpath->currentCS.y == y &&
   1658          !newHintMap                 )
   1659       /*
   1660        * Ignore zero-length lines in CS where the hint map is the same
   1661        * because the line in DS will also be zero length.
   1662        *
   1663        * Ignore zero-length lines when we synthesize a closing line because
   1664        * the close will be handled in cf2_glyphPath_pushPrevElem.
   1665        */
   1666       return;
   1667 
   1668     cf2_glyphpath_computeOffset( glyphpath,
   1669                                  glyphpath->currentCS.x,
   1670                                  glyphpath->currentCS.y,
   1671                                  x,
   1672                                  y,
   1673                                  &xOffset,
   1674                                  &yOffset );
   1675 
   1676     /* construct offset points */
   1677     P0.x = glyphpath->currentCS.x + xOffset;
   1678     P0.y = glyphpath->currentCS.y + yOffset;
   1679     P1.x = x + xOffset;
   1680     P1.y = y + yOffset;
   1681 
   1682     if ( glyphpath->moveIsPending )
   1683     {
   1684       /* emit offset 1st point as MoveTo */
   1685       cf2_glyphpath_pushMove( glyphpath, P0 );
   1686 
   1687       glyphpath->moveIsPending = FALSE;  /* adjust state machine */
   1688       glyphpath->pathIsOpen    = TRUE;
   1689 
   1690       glyphpath->offsetStart1 = P1;              /* record second point */
   1691     }
   1692 
   1693     if ( glyphpath->elemIsQueued )
   1694     {
   1695       FT_ASSERT( cf2_hintmap_isValid( &glyphpath->hintMap ) ||
   1696                  glyphpath->hintMap.count == 0              );
   1697 
   1698       cf2_glyphpath_pushPrevElem( glyphpath,
   1699                                   &glyphpath->hintMap,
   1700                                   &P0,
   1701                                   P1,
   1702                                   FALSE );
   1703     }
   1704 
   1705     /* queue the current element with offset points */
   1706     glyphpath->elemIsQueued = TRUE;
   1707     glyphpath->prevElemOp   = CF2_PathOpLineTo;
   1708     glyphpath->prevElemP0   = P0;
   1709     glyphpath->prevElemP1   = P1;
   1710 
   1711     /* update current map */
   1712     if ( newHintMap )
   1713       cf2_hintmap_build( &glyphpath->hintMap,
   1714                          glyphpath->hStemHintArray,
   1715                          glyphpath->vStemHintArray,
   1716                          glyphpath->hintMask,
   1717                          glyphpath->hintOriginY,
   1718                          FALSE );
   1719 
   1720     glyphpath->currentCS.x = x;     /* pre-offset current point */
   1721     glyphpath->currentCS.y = y;
   1722   }
   1723 
   1724 
   1725   FT_LOCAL_DEF( void )
   1726   cf2_glyphpath_curveTo( CF2_GlyphPath  glyphpath,
   1727                          CF2_Fixed      x1,
   1728                          CF2_Fixed      y1,
   1729                          CF2_Fixed      x2,
   1730                          CF2_Fixed      y2,
   1731                          CF2_Fixed      x3,
   1732                          CF2_Fixed      y3 )
   1733   {
   1734     CF2_Fixed  xOffset1, yOffset1, xOffset3, yOffset3;
   1735     FT_Vector  P0, P1, P2, P3;
   1736 
   1737 
   1738     /* TODO: ignore zero length portions of curve?? */
   1739     cf2_glyphpath_computeOffset( glyphpath,
   1740                                  glyphpath->currentCS.x,
   1741                                  glyphpath->currentCS.y,
   1742                                  x1,
   1743                                  y1,
   1744                                  &xOffset1,
   1745                                  &yOffset1 );
   1746     cf2_glyphpath_computeOffset( glyphpath,
   1747                                  x2,
   1748                                  y2,
   1749                                  x3,
   1750                                  y3,
   1751                                  &xOffset3,
   1752                                  &yOffset3 );
   1753 
   1754     /* add momentum from the middle segment */
   1755     glyphpath->callbacks->windingMomentum +=
   1756       cf2_getWindingMomentum( x1, y1, x2, y2 );
   1757 
   1758     /* construct offset points */
   1759     P0.x = glyphpath->currentCS.x + xOffset1;
   1760     P0.y = glyphpath->currentCS.y + yOffset1;
   1761     P1.x = x1 + xOffset1;
   1762     P1.y = y1 + yOffset1;
   1763     /* note: preserve angle of final segment by using offset3 at both ends */
   1764     P2.x = x2 + xOffset3;
   1765     P2.y = y2 + yOffset3;
   1766     P3.x = x3 + xOffset3;
   1767     P3.y = y3 + yOffset3;
   1768 
   1769     if ( glyphpath->moveIsPending )
   1770     {
   1771       /* emit offset 1st point as MoveTo */
   1772       cf2_glyphpath_pushMove( glyphpath, P0 );
   1773 
   1774       glyphpath->moveIsPending = FALSE;
   1775       glyphpath->pathIsOpen    = TRUE;
   1776 
   1777       glyphpath->offsetStart1 = P1;              /* record second point */
   1778     }
   1779 
   1780     if ( glyphpath->elemIsQueued )
   1781     {
   1782       FT_ASSERT( cf2_hintmap_isValid( &glyphpath->hintMap ) ||
   1783                  glyphpath->hintMap.count == 0              );
   1784 
   1785       cf2_glyphpath_pushPrevElem( glyphpath,
   1786                                   &glyphpath->hintMap,
   1787                                   &P0,
   1788                                   P1,
   1789                                   FALSE );
   1790     }
   1791 
   1792     /* queue the current element with offset points */
   1793     glyphpath->elemIsQueued = TRUE;
   1794     glyphpath->prevElemOp   = CF2_PathOpCubeTo;
   1795     glyphpath->prevElemP0   = P0;
   1796     glyphpath->prevElemP1   = P1;
   1797     glyphpath->prevElemP2   = P2;
   1798     glyphpath->prevElemP3   = P3;
   1799 
   1800     /* update current map */
   1801     if ( cf2_hintmask_isNew( glyphpath->hintMask ) )
   1802       cf2_hintmap_build( &glyphpath->hintMap,
   1803                          glyphpath->hStemHintArray,
   1804                          glyphpath->vStemHintArray,
   1805                          glyphpath->hintMask,
   1806                          glyphpath->hintOriginY,
   1807                          FALSE );
   1808 
   1809     glyphpath->currentCS.x = x3;       /* pre-offset current point */
   1810     glyphpath->currentCS.y = y3;
   1811   }
   1812 
   1813 
   1814   FT_LOCAL_DEF( void )
   1815   cf2_glyphpath_closeOpenPath( CF2_GlyphPath  glyphpath )
   1816   {
   1817     if ( glyphpath->pathIsOpen )
   1818     {
   1819       /*
   1820        * A closing line in Character Space line is always generated below
   1821        * with `cf2_glyphPath_lineTo'.  It may be ignored later if it turns
   1822        * out to be zero length in Device Space.
   1823        */
   1824       glyphpath->pathIsClosing = TRUE;
   1825 
   1826       cf2_glyphpath_lineTo( glyphpath,
   1827                             glyphpath->start.x,
   1828                             glyphpath->start.y );
   1829 
   1830       /* empty the final element from the queue and close the path */
   1831       if ( glyphpath->elemIsQueued )
   1832         cf2_glyphpath_pushPrevElem( glyphpath,
   1833                                     &glyphpath->hintMap,
   1834                                     &glyphpath->offsetStart0,
   1835                                     glyphpath->offsetStart1,
   1836                                     TRUE );
   1837 
   1838       /* reset state machine */
   1839       glyphpath->moveIsPending = TRUE;
   1840       glyphpath->pathIsOpen    = FALSE;
   1841       glyphpath->pathIsClosing = FALSE;
   1842       glyphpath->elemIsQueued  = FALSE;
   1843     }
   1844   }
   1845 
   1846 
   1847 /* END */
   1848