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kc3-lang/freetype/src/cff/cf2hints.c

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  • Author : Dave Arnold
    Date : 2015-10-21 13:58:43
    Hash : 748e3681
    Message : [cff] Remove an assert (#46107). * src/cff/cf2hints.c (cf2_hintmap_insertHint): Ignore paired edges in wrong order.

  • src/cff/cf2hints.c
  • /***************************************************************************/
    /*                                                                         */
    /*  cf2hints.c                                                             */
    /*                                                                         */
    /*    Adobe's code for handling CFF hints (body).                          */
    /*                                                                         */
    /*  Copyright 2007-2014 Adobe Systems Incorporated.                        */
    /*                                                                         */
    /*  This software, and all works of authorship, whether in source or       */
    /*  object code form as indicated by the copyright notice(s) included      */
    /*  herein (collectively, the "Work") is made available, and may only be   */
    /*  used, modified, and distributed under the FreeType Project License,    */
    /*  LICENSE.TXT.  Additionally, subject to the terms and conditions of the */
    /*  FreeType Project License, each contributor to the Work hereby grants   */
    /*  to any individual or legal entity exercising permissions granted by    */
    /*  the FreeType Project License and this section (hereafter, "You" or     */
    /*  "Your") a perpetual, worldwide, non-exclusive, no-charge,              */
    /*  royalty-free, irrevocable (except as stated in this section) patent    */
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    /*  otherwise transfer the Work, where such license applies only to those  */
    /*  patent claims licensable by such contributor that are necessarily      */
    /*  infringed by their contribution(s) alone or by combination of their    */
    /*  contribution(s) with the Work to which such contribution(s) was        */
    /*  submitted.  If You institute patent litigation against any entity      */
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    /*  the Work or a contribution incorporated within the Work constitutes    */
    /*  direct or contributory patent infringement, then any patent licenses   */
    /*  granted to You under this License for that Work shall terminate as of  */
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    /*  By using, modifying, or distributing the Work you indicate that you    */
    /*  have read and understood the terms and conditions of the               */
    /*  FreeType Project License as well as those provided in this section,    */
    /*  and you accept them fully.                                             */
    /*                                                                         */
    /***************************************************************************/
    
    
    #include "cf2ft.h"
    #include FT_INTERNAL_DEBUG_H
    
    #include "cf2glue.h"
    #include "cf2font.h"
    #include "cf2hints.h"
    #include "cf2intrp.h"
    
    
      /*************************************************************************/
      /*                                                                       */
      /* The macro FT_COMPONENT is used in trace mode.  It is an implicit      */
      /* parameter of the FT_TRACE() and FT_ERROR() macros, used to print/log  */
      /* messages during execution.                                            */
      /*                                                                       */
    #undef  FT_COMPONENT
    #define FT_COMPONENT  trace_cf2hints
    
    
      typedef struct  CF2_HintMoveRec_
      {
        size_t     j;          /* index of upper hint map edge   */
        CF2_Fixed  moveUp;     /* adjustment to optimum position */
    
      } CF2_HintMoveRec, *CF2_HintMove;
    
    
      /* Compute angular momentum for winding order detection.  It is called */
      /* for all lines and curves, but not necessarily in element order.     */
      static CF2_Int
      cf2_getWindingMomentum( CF2_Fixed  x1,
                              CF2_Fixed  y1,
                              CF2_Fixed  x2,
                              CF2_Fixed  y2 )
      {
        /* cross product of pt1 position from origin with pt2 position from  */
        /* pt1; we reduce the precision so that the result fits into 32 bits */
    
        return ( x1 >> 16 ) * ( ( y2 - y1 ) >> 16 ) -
               ( y1 >> 16 ) * ( ( x2 - x1 ) >> 16 );
      }
    
    
      /*
       * Construct from a StemHint; this is used as a parameter to
       * `cf2_blues_capture'.
       * `hintOrigin' is the character space displacement of a seac accent.
       * Adjust stem hint for darkening here.
       *
       */
      static void
      cf2_hint_init( CF2_Hint            hint,
                     const CF2_ArrStack  stemHintArray,
                     size_t              indexStemHint,
                     const CF2_Font      font,
                     CF2_Fixed           hintOrigin,
                     CF2_Fixed           scale,
                     FT_Bool             bottom )
      {
        CF2_Fixed               width;
        const CF2_StemHintRec*  stemHint;
    
    
        FT_ZERO( hint );
    
        stemHint = (const CF2_StemHintRec*)cf2_arrstack_getPointer(
                                             stemHintArray,
                                             indexStemHint );
    
        width = stemHint->max - stemHint->min;
    
        if ( width == cf2_intToFixed( -21 ) )
        {
          /* ghost bottom */
    
          if ( bottom )
          {
            hint->csCoord = stemHint->max;
            hint->flags   = CF2_GhostBottom;
          }
          else
            hint->flags = 0;
        }
    
        else if ( width == cf2_intToFixed( -20 ) )
        {
          /* ghost top */
    
          if ( bottom )
            hint->flags = 0;
          else
          {
            hint->csCoord = stemHint->min;
            hint->flags   = CF2_GhostTop;
          }
        }
    
        else if ( width < 0 )
        {
          /* inverted pair */
    
          /*
           * Hints with negative widths were produced by an early version of a
           * non-Adobe font tool.  The Type 2 spec allows edge (ghost) hints
           * with negative widths, but says
           *
           *   All other negative widths have undefined meaning.
           *
           * CoolType has a silent workaround that negates the hint width; for
           * permissive mode, we do the same here.
           *
           * Note: Such fonts cannot use ghost hints, but should otherwise work.
           * Note: Some poor hints in our faux fonts can produce negative
           *       widths at some blends.  For example, see a light weight of
           *       `u' in ASerifMM.
           *
           */
          if ( bottom )
          {
            hint->csCoord = stemHint->max;
            hint->flags   = CF2_PairBottom;
          }
          else
          {
            hint->csCoord = stemHint->min;
            hint->flags   = CF2_PairTop;
          }
        }
    
        else
        {
          /* normal pair */
    
          if ( bottom )
          {
            hint->csCoord = stemHint->min;
            hint->flags   = CF2_PairBottom;
          }
          else
          {
            hint->csCoord = stemHint->max;
            hint->flags   = CF2_PairTop;
          }
        }
    
        /* Now that ghost hints have been detected, adjust this edge for      */
        /* darkening.  Bottoms are not changed; tops are incremented by twice */
        /* `darkenY'.                                                         */
        if ( cf2_hint_isTop( hint ) )
          hint->csCoord += 2 * font->darkenY;
    
        hint->csCoord += hintOrigin;
        hint->scale    = scale;
        hint->index    = indexStemHint;   /* index in original stem hint array */
    
        /* if original stem hint has been used, use the same position */
        if ( hint->flags != 0 && stemHint->used )
        {
          if ( cf2_hint_isTop( hint ) )
            hint->dsCoord = stemHint->maxDS;
          else
            hint->dsCoord = stemHint->minDS;
    
          cf2_hint_lock( hint );
        }
        else
          hint->dsCoord = FT_MulFix( hint->csCoord, scale );
      }
    
    
      /* initialize an invalid hint map element */
      static void
      cf2_hint_initZero( CF2_Hint  hint )
      {
        FT_ZERO( hint );
      }
    
    
      FT_LOCAL_DEF( FT_Bool )
      cf2_hint_isValid( const CF2_Hint  hint )
      {
        return (FT_Bool)( hint->flags != 0 );
      }
    
    
      static FT_Bool
      cf2_hint_isPair( const CF2_Hint  hint )
      {
        return (FT_Bool)( ( hint->flags                      &
                            ( CF2_PairBottom | CF2_PairTop ) ) != 0 );
      }
    
    
      static FT_Bool
      cf2_hint_isPairTop( const CF2_Hint  hint )
      {
        return (FT_Bool)( ( hint->flags & CF2_PairTop ) != 0 );
      }
    
    
      FT_LOCAL_DEF( FT_Bool )
      cf2_hint_isTop( const CF2_Hint  hint )
      {
        return (FT_Bool)( ( hint->flags                    &
                            ( CF2_PairTop | CF2_GhostTop ) ) != 0 );
      }
    
    
      FT_LOCAL_DEF( FT_Bool )
      cf2_hint_isBottom( const CF2_Hint  hint )
      {
        return (FT_Bool)( ( hint->flags                          &
                            ( CF2_PairBottom | CF2_GhostBottom ) ) != 0 );
      }
    
    
      static FT_Bool
      cf2_hint_isLocked( const CF2_Hint  hint )
      {
        return (FT_Bool)( ( hint->flags & CF2_Locked ) != 0 );
      }
    
    
      static FT_Bool
      cf2_hint_isSynthetic( const CF2_Hint  hint )
      {
        return (FT_Bool)( ( hint->flags & CF2_Synthetic ) != 0 );
      }
    
    
      FT_LOCAL_DEF( void )
      cf2_hint_lock( CF2_Hint  hint )
      {
        hint->flags |= CF2_Locked;
      }
    
    
      FT_LOCAL_DEF( void )
      cf2_hintmap_init( CF2_HintMap   hintmap,
                        CF2_Font      font,
                        CF2_HintMap   initialMap,
                        CF2_ArrStack  hintMoves,
                        CF2_Fixed     scale )
      {
        FT_ZERO( hintmap );
    
        /* copy parameters from font instance */
        hintmap->hinted         = font->hinted;
        hintmap->scale          = scale;
        hintmap->font           = font;
        hintmap->initialHintMap = initialMap;
        /* will clear in `cf2_hintmap_adjustHints' */
        hintmap->hintMoves      = hintMoves;
      }
    
    
      static FT_Bool
      cf2_hintmap_isValid( const CF2_HintMap  hintmap )
      {
        return hintmap->isValid;
      }
    
    
      /* transform character space coordinate to device space using hint map */
      static CF2_Fixed
      cf2_hintmap_map( CF2_HintMap  hintmap,
                       CF2_Fixed    csCoord )
      {
        if ( hintmap->count == 0 || ! hintmap->hinted )
        {
          /* there are no hints; use uniform scale and zero offset */
          return FT_MulFix( csCoord, hintmap->scale );
        }
        else
        {
          /* start linear search from last hit */
          CF2_UInt  i = hintmap->lastIndex;
    
          FT_ASSERT( hintmap->lastIndex < CF2_MAX_HINT_EDGES );
    
          /* search up */
          while ( i < hintmap->count - 1                  &&
                  csCoord >= hintmap->edge[i + 1].csCoord )
            i += 1;
    
          /* search down */
          while ( i > 0 && csCoord < hintmap->edge[i].csCoord )
            i -= 1;
    
          hintmap->lastIndex = i;
    
          if ( i == 0 && csCoord < hintmap->edge[0].csCoord )
          {
            /* special case for points below first edge: use uniform scale */
            return FT_MulFix( csCoord - hintmap->edge[0].csCoord,
                              hintmap->scale ) +
                     hintmap->edge[0].dsCoord;
          }
          else
          {
            /*
             * Note: entries with duplicate csCoord are allowed.
             * Use edge[i], the highest entry where csCoord >= entry[i].csCoord
             */
            return FT_MulFix( csCoord - hintmap->edge[i].csCoord,
                              hintmap->edge[i].scale ) +
                     hintmap->edge[i].dsCoord;
          }
        }
      }
    
    
      /*
       * This hinting policy moves a hint pair in device space so that one of
       * its two edges is on a device pixel boundary (its fractional part is
       * zero).  `cf2_hintmap_insertHint' guarantees no overlap in CS
       * space.  Ensure here that there is no overlap in DS.
       *
       * In the first pass, edges are adjusted relative to adjacent hints.
       * Those that are below have already been adjusted.  Those that are
       * above have not yet been adjusted.  If a hint above blocks an
       * adjustment to an optimal position, we will try again in a second
       * pass.  The second pass is top-down.
       *
       */
    
      static void
      cf2_hintmap_adjustHints( CF2_HintMap  hintmap )
      {
        size_t  i, j;
    
    
        cf2_arrstack_clear( hintmap->hintMoves );      /* working storage */
    
        /*
         * First pass is bottom-up (font hint order) without look-ahead.
         * Locked edges are already adjusted.
         * Unlocked edges begin with dsCoord from `initialHintMap'.
         * Save edges that are not optimally adjusted in `hintMoves' array,
         * and process them in second pass.
         */
    
        for ( i = 0; i < hintmap->count; i++ )
        {
          FT_Bool  isPair = cf2_hint_isPair( &hintmap->edge[i] );
    
    
          /* index of upper edge (same value for ghost hint) */
          j = isPair ? i + 1 : i;
    
          FT_ASSERT( j < hintmap->count );
          FT_ASSERT( cf2_hint_isValid( &hintmap->edge[i] ) );
          FT_ASSERT( cf2_hint_isValid( &hintmap->edge[j] ) );
          FT_ASSERT( cf2_hint_isLocked( &hintmap->edge[i] ) ==
                       cf2_hint_isLocked( &hintmap->edge[j] ) );
    
          if ( !cf2_hint_isLocked( &hintmap->edge[i] ) )
          {
            /* hint edge is not locked, we can adjust it */
            CF2_Fixed  fracDown = cf2_fixedFraction( hintmap->edge[i].dsCoord );
            CF2_Fixed  fracUp   = cf2_fixedFraction( hintmap->edge[j].dsCoord );
    
            /* calculate all four possibilities; moves down are negative */
            CF2_Fixed  downMoveDown = 0 - fracDown;
            CF2_Fixed  upMoveDown   = 0 - fracUp;
            CF2_Fixed  downMoveUp   = fracDown == 0
                                        ? 0
                                        : cf2_intToFixed( 1 ) - fracDown;
            CF2_Fixed  upMoveUp     = fracUp == 0
                                        ? 0
                                        : cf2_intToFixed( 1 ) - fracUp;
    
            /* smallest move up */
            CF2_Fixed  moveUp   = FT_MIN( downMoveUp, upMoveUp );
            /* smallest move down */
            CF2_Fixed  moveDown = FT_MAX( downMoveDown, upMoveDown );
    
            /* final amount to move edge or edge pair */
            CF2_Fixed  move;
    
            CF2_Fixed  downMinCounter = CF2_MIN_COUNTER;
            CF2_Fixed  upMinCounter   = CF2_MIN_COUNTER;
            FT_Bool    saveEdge       = FALSE;
    
    
            /* minimum counter constraint doesn't apply when adjacent edges */
            /* are synthetic                                                */
            /* TODO: doesn't seem a big effect; for now, reduce the code    */
    #if 0
            if ( i == 0                                        ||
                 cf2_hint_isSynthetic( &hintmap->edge[i - 1] ) )
              downMinCounter = 0;
    
            if ( j >= hintmap->count - 1                       ||
                 cf2_hint_isSynthetic( &hintmap->edge[j + 1] ) )
              upMinCounter = 0;
    #endif
    
            /* is there room to move up?                                    */
            /* there is if we are at top of array or the next edge is at or */
            /* beyond proposed move up?                                     */
            if ( j >= hintmap->count - 1                            ||
                 hintmap->edge[j + 1].dsCoord >=
                   hintmap->edge[j].dsCoord + moveUp + upMinCounter )
            {
              /* there is room to move up; is there also room to move down? */
              if ( i == 0                                                 ||
                   hintmap->edge[i - 1].dsCoord <=
                     hintmap->edge[i].dsCoord + moveDown - downMinCounter )
              {
                /* move smaller absolute amount */
                move = ( -moveDown < moveUp ) ? moveDown : moveUp;  /* optimum */
              }
              else
                move = moveUp;
            }
            else
            {
              /* is there room to move down? */
              if ( i == 0                                                 ||
                   hintmap->edge[i - 1].dsCoord <=
                     hintmap->edge[i].dsCoord + moveDown - downMinCounter )
              {
                move     = moveDown;
                /* true if non-optimum move */
                saveEdge = (FT_Bool)( moveUp < -moveDown );
              }
              else
              {
                /* no room to move either way without overlapping or reducing */
                /* the counter too much                                       */
                move     = 0;
                saveEdge = TRUE;
              }
            }
    
            /* Identify non-moves and moves down that aren't optimal, and save */
            /* them for second pass.                                           */
            /* Do this only if there is an unlocked edge above (which could    */
            /* possibly move).                                                 */
            if ( saveEdge                                    &&
                 j < hintmap->count - 1                      &&
                 !cf2_hint_isLocked( &hintmap->edge[j + 1] ) )
            {
              CF2_HintMoveRec  savedMove;
    
    
              savedMove.j      = j;
              /* desired adjustment in second pass */
              savedMove.moveUp = moveUp - move;
    
              cf2_arrstack_push( hintmap->hintMoves, &savedMove );
            }
    
            /* move the edge(s) */
            hintmap->edge[i].dsCoord += move;
            if ( isPair )
              hintmap->edge[j].dsCoord += move;
          }
    
          /* assert there are no overlaps in device space */
          FT_ASSERT( i == 0                                                   ||
                     hintmap->edge[i - 1].dsCoord <= hintmap->edge[i].dsCoord );
          FT_ASSERT( i < j                                                ||
                     hintmap->edge[i].dsCoord <= hintmap->edge[j].dsCoord );
    
          /* adjust the scales, avoiding divide by zero */
          if ( i > 0 )
          {
            if ( hintmap->edge[i].csCoord != hintmap->edge[i - 1].csCoord )
              hintmap->edge[i - 1].scale =
                FT_DivFix(
                  hintmap->edge[i].dsCoord - hintmap->edge[i - 1].dsCoord,
                  hintmap->edge[i].csCoord - hintmap->edge[i - 1].csCoord );
          }
    
          if ( isPair )
          {
            if ( hintmap->edge[j].csCoord != hintmap->edge[j - 1].csCoord )
              hintmap->edge[j - 1].scale =
                FT_DivFix(
                  hintmap->edge[j].dsCoord - hintmap->edge[j - 1].dsCoord,
                  hintmap->edge[j].csCoord - hintmap->edge[j - 1].csCoord );
    
            i += 1;     /* skip upper edge on next loop */
          }
        }
    
        /* second pass tries to move non-optimal hints up, in case there is */
        /* room now                                                         */
        for ( i = cf2_arrstack_size( hintmap->hintMoves ); i > 0; i-- )
        {
          CF2_HintMove  hintMove = (CF2_HintMove)
                          cf2_arrstack_getPointer( hintmap->hintMoves, i - 1 );
    
    
          j = hintMove->j;
    
          /* this was tested before the push, above */
          FT_ASSERT( j < hintmap->count - 1 );
    
          /* is there room to move up? */
          if ( hintmap->edge[j + 1].dsCoord >=
                 hintmap->edge[j].dsCoord + hintMove->moveUp + CF2_MIN_COUNTER )
          {
            /* there is more room now, move edge up */
            hintmap->edge[j].dsCoord += hintMove->moveUp;
    
            if ( cf2_hint_isPair( &hintmap->edge[j] ) )
            {
              FT_ASSERT( j > 0 );
              hintmap->edge[j - 1].dsCoord += hintMove->moveUp;
            }
          }
        }
      }
    
    
      /* insert hint edges into map, sorted by csCoord */
      static void
      cf2_hintmap_insertHint( CF2_HintMap  hintmap,
                              CF2_Hint     bottomHintEdge,
                              CF2_Hint     topHintEdge )
      {
        CF2_UInt  indexInsert;
    
        /* set default values, then check for edge hints */
        FT_Bool   isPair         = TRUE;
        CF2_Hint  firstHintEdge  = bottomHintEdge;
        CF2_Hint  secondHintEdge = topHintEdge;
    
    
        /* one or none of the input params may be invalid when dealing with */
        /* edge hints; at least one edge must be valid                      */
        FT_ASSERT( cf2_hint_isValid( bottomHintEdge ) ||
                   cf2_hint_isValid( topHintEdge )    );
    
        /* determine how many and which edges to insert */
        if ( !cf2_hint_isValid( bottomHintEdge ) )
        {
          /* insert only the top edge */
          firstHintEdge = topHintEdge;
          isPair        = FALSE;
        }
        else if ( !cf2_hint_isValid( topHintEdge ) )
        {
          /* insert only the bottom edge */
          isPair = FALSE;
        }
    
        /* paired edges must be in proper order */
        if ( isPair                                         &&
             topHintEdge->csCoord < bottomHintEdge->csCoord )
          return;
    
        /* linear search to find index value of insertion point */
        indexInsert = 0;
        for ( ; indexInsert < hintmap->count; indexInsert++ )
        {
          if ( hintmap->edge[indexInsert].csCoord >= firstHintEdge->csCoord )
            break;
        }
    
        /*
         * Discard any hints that overlap in character space.  Most often, this
         * is while building the initial map, where captured hints from all
         * zones are combined.  Define overlap to include hints that `touch'
         * (overlap zero).  Hiragino Sans/Gothic fonts have numerous hints that
         * touch.  Some fonts have non-ideographic glyphs that overlap our
         * synthetic hints.
         *
         * Overlap also occurs when darkening stem hints that are close.
         *
         */
        if ( indexInsert < hintmap->count )
        {
          /* we are inserting before an existing edge:    */
          /* verify that an existing edge is not the same */
          if ( hintmap->edge[indexInsert].csCoord == firstHintEdge->csCoord )
            return; /* ignore overlapping stem hint */
    
          /* verify that a new pair does not straddle the next edge */
          if ( isPair                                                        &&
               hintmap->edge[indexInsert].csCoord <= secondHintEdge->csCoord )
            return; /* ignore overlapping stem hint */
    
          /* verify that we are not inserting between paired edges */
          if ( cf2_hint_isPairTop( &hintmap->edge[indexInsert] ) )
            return; /* ignore overlapping stem hint */
        }
    
        /* recompute device space locations using initial hint map */
        if ( cf2_hintmap_isValid( hintmap->initialHintMap ) &&
             !cf2_hint_isLocked( firstHintEdge )            )
        {
          if ( isPair )
          {
            /* Use hint map to position the center of stem, and nominal scale */
            /* to position the two edges.  This preserves the stem width.     */
            CF2_Fixed  midpoint  = cf2_hintmap_map(
                                     hintmap->initialHintMap,
                                     ( secondHintEdge->csCoord +
                                       firstHintEdge->csCoord ) / 2 );
            CF2_Fixed  halfWidth = FT_MulFix(
                                     ( secondHintEdge->csCoord -
                                       firstHintEdge->csCoord ) / 2,
                                     hintmap->scale );
    
    
            firstHintEdge->dsCoord  = midpoint - halfWidth;
            secondHintEdge->dsCoord = midpoint + halfWidth;
          }
          else
            firstHintEdge->dsCoord = cf2_hintmap_map( hintmap->initialHintMap,
                                                      firstHintEdge->csCoord );
        }
    
        /*
         * Discard any hints that overlap in device space; this can occur
         * because locked hints have been moved to align with blue zones.
         *
         * TODO: Although we might correct this later during adjustment, we
         * don't currently have a way to delete a conflicting hint once it has
         * been inserted.  See v2.030 MinionPro-Regular, 12 ppem darkened,
         * initial hint map for second path, glyph 945 (the perispomeni (tilde)
         * in U+1F6E, Greek omega with psili and perispomeni).  Darkening is
         * 25.  Pair 667,747 initially conflicts in design space with top edge
         * 660.  This is because 667 maps to 7.87, and the top edge was
         * captured by a zone at 8.0.  The pair is later successfully inserted
         * in a zone without the top edge.  In this zone it is adjusted to 8.0,
         * and no longer conflicts with the top edge in design space.  This
         * means it can be included in yet a later zone which does have the top
         * edge hint.  This produces a small mismatch between the first and
         * last points of this path, even though the hint masks are the same.
         * The density map difference is tiny (1/256).
         *
         */
    
        if ( indexInsert > 0 )
        {
          /* we are inserting after an existing edge */
          if ( firstHintEdge->dsCoord < hintmap->edge[indexInsert - 1].dsCoord )
            return;
        }
    
        if ( indexInsert < hintmap->count )
        {
          /* we are inserting before an existing edge */
          if ( isPair )
          {
            if ( secondHintEdge->dsCoord > hintmap->edge[indexInsert].dsCoord )
              return;
          }
          else
          {
            if ( firstHintEdge->dsCoord > hintmap->edge[indexInsert].dsCoord )
              return;
          }
        }
    
        /* make room to insert */
        {
          CF2_UInt  iSrc = hintmap->count - 1;
          CF2_UInt  iDst = isPair ? hintmap->count + 1 : hintmap->count;
    
          CF2_UInt  count = hintmap->count - indexInsert;
    
    
          if ( iDst >= CF2_MAX_HINT_EDGES )
          {
            FT_TRACE4(( "cf2_hintmap_insertHint: too many hintmaps\n" ));
            return;
          }
    
          while ( count-- )
            hintmap->edge[iDst--] = hintmap->edge[iSrc--];
    
          /* insert first edge */
          hintmap->edge[indexInsert] = *firstHintEdge;         /* copy struct */
          hintmap->count += 1;
    
          if ( isPair )
          {
            /* insert second edge */
            hintmap->edge[indexInsert + 1] = *secondHintEdge;  /* copy struct */
            hintmap->count                += 1;
          }
        }
    
        return;
      }
    
    
      /*
       * Build a map from hints and mask.
       *
       * This function may recur one level if `hintmap->initialHintMap' is not yet
       * valid.
       * If `initialMap' is true, simply build initial map.
       *
       * Synthetic hints are used in two ways.  A hint at zero is inserted, if
       * needed, in the initial hint map, to prevent translations from
       * propagating across the origin.  If synthetic em box hints are enabled
       * for ideographic dictionaries, then they are inserted in all hint
       * maps, including the initial one.
       *
       */
      FT_LOCAL_DEF( void )
      cf2_hintmap_build( CF2_HintMap   hintmap,
                         CF2_ArrStack  hStemHintArray,
                         CF2_ArrStack  vStemHintArray,
                         CF2_HintMask  hintMask,
                         CF2_Fixed     hintOrigin,
                         FT_Bool       initialMap )
      {
        FT_Byte*  maskPtr;
    
        CF2_Font         font = hintmap->font;
        CF2_HintMaskRec  tempHintMask;
    
        size_t   bitCount, i;
        FT_Byte  maskByte;
    
    
        /* check whether initial map is constructed */
        if ( !initialMap && !cf2_hintmap_isValid( hintmap->initialHintMap ) )
        {
          /* make recursive call with initialHintMap and temporary mask; */
          /* temporary mask will get all bits set, below */
          cf2_hintmask_init( &tempHintMask, hintMask->error );
          cf2_hintmap_build( hintmap->initialHintMap,
                             hStemHintArray,
                             vStemHintArray,
                             &tempHintMask,
                             hintOrigin,
                             TRUE );
        }
    
        if ( !cf2_hintmask_isValid( hintMask ) )
        {
          /* without a hint mask, assume all hints are active */
          cf2_hintmask_setAll( hintMask,
                               cf2_arrstack_size( hStemHintArray ) +
                                 cf2_arrstack_size( vStemHintArray ) );
          if ( !cf2_hintmask_isValid( hintMask ) )
              return;                   /* too many stem hints */
        }
    
        /* begin by clearing the map */
        hintmap->count     = 0;
        hintmap->lastIndex = 0;
    
        /* make a copy of the hint mask so we can modify it */
        tempHintMask = *hintMask;
        maskPtr      = cf2_hintmask_getMaskPtr( &tempHintMask );
    
        /* use the hStem hints only, which are first in the mask */
        bitCount = cf2_arrstack_size( hStemHintArray );
    
        /* Defense-in-depth.  Should never return here. */
        if ( bitCount > hintMask->bitCount )
            return;
    
        /* synthetic embox hints get highest priority */
        if ( font->blues.doEmBoxHints )
        {
          CF2_HintRec  dummy;
    
    
          cf2_hint_initZero( &dummy );   /* invalid hint map element */
    
          /* ghost bottom */
          cf2_hintmap_insertHint( hintmap,
                                  &font->blues.emBoxBottomEdge,
                                  &dummy );
          /* ghost top */
          cf2_hintmap_insertHint( hintmap,
                                  &dummy,
                                  &font->blues.emBoxTopEdge );
        }
    
        /* insert hints captured by a blue zone or already locked (higher */
        /* priority)                                                      */
        for ( i = 0, maskByte = 0x80; i < bitCount; i++ )
        {
          if ( maskByte & *maskPtr )
          {
            /* expand StemHint into two `CF2_Hint' elements */
            CF2_HintRec  bottomHintEdge, topHintEdge;
    
    
            cf2_hint_init( &bottomHintEdge,
                           hStemHintArray,
                           i,
                           font,
                           hintOrigin,
                           hintmap->scale,
                           TRUE /* bottom */ );
            cf2_hint_init( &topHintEdge,
                           hStemHintArray,
                           i,
                           font,
                           hintOrigin,
                           hintmap->scale,
                           FALSE /* top */ );
    
            if ( cf2_hint_isLocked( &bottomHintEdge ) ||
                 cf2_hint_isLocked( &topHintEdge )    ||
                 cf2_blues_capture( &font->blues,
                                    &bottomHintEdge,
                                    &topHintEdge )   )
            {
              /* insert captured hint into map */
              cf2_hintmap_insertHint( hintmap, &bottomHintEdge, &topHintEdge );
    
              *maskPtr &= ~maskByte;      /* turn off the bit for this hint */
            }
          }
    
          if ( ( i & 7 ) == 7 )
          {
            /* move to next mask byte */
            maskPtr++;
            maskByte = 0x80;
          }
          else
            maskByte >>= 1;
        }
    
        /* initial hint map includes only captured hints plus maybe one at 0 */
    
        /*
         * TODO: There is a problem here because we are trying to build a
         *       single hint map containing all captured hints.  It is
         *       possible for there to be conflicts between captured hints,
         *       either because of darkening or because the hints are in
         *       separate hint zones (we are ignoring hint zones for the
         *       initial map).  An example of the latter is MinionPro-Regular
         *       v2.030 glyph 883 (Greek Capital Alpha with Psili) at 15ppem.
         *       A stem hint for the psili conflicts with the top edge hint
         *       for the base character.  The stem hint gets priority because
         *       of its sort order.  In glyph 884 (Greek Capital Alpha with
         *       Psili and Oxia), the top of the base character gets a stem
         *       hint, and the psili does not.  This creates different initial
         *       maps for the two glyphs resulting in different renderings of
         *       the base character.  Will probably defer this either as not
         *       worth the cost or as a font bug.  I don't think there is any
         *       good reason for an accent to be captured by an alignment
         *       zone.  -darnold 2/12/10
         */
    
        if ( initialMap )
        {
          /* Apply a heuristic that inserts a point for (0,0), unless it's     */
          /* already covered by a mapping.  This locks the baseline for glyphs */
          /* that have no baseline hints.                                      */
    
          if ( hintmap->count == 0                           ||
               hintmap->edge[0].csCoord > 0                  ||
               hintmap->edge[hintmap->count - 1].csCoord < 0 )
          {
            /* all edges are above 0 or all edges are below 0; */
            /* construct a locked edge hint at 0               */
    
            CF2_HintRec  edge, invalid;
    
    
            cf2_hint_initZero( &edge );
    
            edge.flags = CF2_GhostBottom |
                         CF2_Locked      |
                         CF2_Synthetic;
            edge.scale = hintmap->scale;
    
            cf2_hint_initZero( &invalid );
            cf2_hintmap_insertHint( hintmap, &edge, &invalid );
          }
        }
        else
        {
          /* insert remaining hints */
    
          maskPtr = cf2_hintmask_getMaskPtr( &tempHintMask );
    
          for ( i = 0, maskByte = 0x80; i < bitCount; i++ )
          {
            if ( maskByte & *maskPtr )
            {
              CF2_HintRec  bottomHintEdge, topHintEdge;
    
    
              cf2_hint_init( &bottomHintEdge,
                             hStemHintArray,
                             i,
                             font,
                             hintOrigin,
                             hintmap->scale,
                             TRUE /* bottom */ );
              cf2_hint_init( &topHintEdge,
                             hStemHintArray,
                             i,
                             font,
                             hintOrigin,
                             hintmap->scale,
                             FALSE /* top */ );
    
              cf2_hintmap_insertHint( hintmap, &bottomHintEdge, &topHintEdge );
            }
    
            if ( ( i & 7 ) == 7 )
            {
              /* move to next mask byte */
              maskPtr++;
              maskByte = 0x80;
            }
            else
              maskByte >>= 1;
          }
        }
    
        /*
         * Note: The following line is a convenient place to break when
         *       debugging hinting.  Examine `hintmap->edge' for the list of
         *       enabled hints, then step over the call to see the effect of
         *       adjustment.  We stop here first on the recursive call that
         *       creates the initial map, and then on each counter group and
         *       hint zone.
         */
    
        /* adjust positions of hint edges that are not locked to blue zones */
        cf2_hintmap_adjustHints( hintmap );
    
        /* save the position of all hints that were used in this hint map; */
        /* if we use them again, we'll locate them in the same position    */
        if ( !initialMap )
        {
          for ( i = 0; i < hintmap->count; i++ )
          {
            if ( !cf2_hint_isSynthetic( &hintmap->edge[i] ) )
            {
              /* Note: include both valid and invalid edges            */
              /* Note: top and bottom edges are copied back separately */
              CF2_StemHint  stemhint = (CF2_StemHint)
                              cf2_arrstack_getPointer( hStemHintArray,
                                                       hintmap->edge[i].index );
    
    
              if ( cf2_hint_isTop( &hintmap->edge[i] ) )
                stemhint->maxDS = hintmap->edge[i].dsCoord;
              else
                stemhint->minDS = hintmap->edge[i].dsCoord;
    
              stemhint->used = TRUE;
            }
          }
        }
    
        /* hint map is ready to use */
        hintmap->isValid = TRUE;
    
        /* remember this mask has been used */
        cf2_hintmask_setNew( hintMask, FALSE );
      }
    
    
      FT_LOCAL_DEF( void )
      cf2_glyphpath_init( CF2_GlyphPath         glyphpath,
                          CF2_Font              font,
                          CF2_OutlineCallbacks  callbacks,
                          CF2_Fixed             scaleY,
                          /* CF2_Fixed  hShift, */
                          CF2_ArrStack          hStemHintArray,
                          CF2_ArrStack          vStemHintArray,
                          CF2_HintMask          hintMask,
                          CF2_Fixed             hintOriginY,
                          const CF2_Blues       blues,
                          const FT_Vector*      fractionalTranslation )
      {
        FT_ZERO( glyphpath );
    
        glyphpath->font      = font;
        glyphpath->callbacks = callbacks;
    
        cf2_arrstack_init( &glyphpath->hintMoves,
                           font->memory,
                           &font->error,
                           sizeof ( CF2_HintMoveRec ) );
    
        cf2_hintmap_init( &glyphpath->initialHintMap,
                          font,
                          &glyphpath->initialHintMap,
                          &glyphpath->hintMoves,
                          scaleY );
        cf2_hintmap_init( &glyphpath->firstHintMap,
                          font,
                          &glyphpath->initialHintMap,
                          &glyphpath->hintMoves,
                          scaleY );
        cf2_hintmap_init( &glyphpath->hintMap,
                          font,
                          &glyphpath->initialHintMap,
                          &glyphpath->hintMoves,
                          scaleY );
    
        glyphpath->scaleX = font->innerTransform.a;
        glyphpath->scaleC = font->innerTransform.c;
        glyphpath->scaleY = font->innerTransform.d;
    
        glyphpath->fractionalTranslation = *fractionalTranslation;
    
    #if 0
        glyphpath->hShift = hShift;       /* for fauxing */
    #endif
    
        glyphpath->hStemHintArray = hStemHintArray;
        glyphpath->vStemHintArray = vStemHintArray;
        glyphpath->hintMask       = hintMask;      /* ptr to current mask */
        glyphpath->hintOriginY    = hintOriginY;
        glyphpath->blues          = blues;
        glyphpath->darken         = font->darkened; /* TODO: should we make copies? */
        glyphpath->xOffset        = font->darkenX;
        glyphpath->yOffset        = font->darkenY;
        glyphpath->miterLimit     = 2 * FT_MAX(
                                         cf2_fixedAbs( glyphpath->xOffset ),
                                         cf2_fixedAbs( glyphpath->yOffset ) );
    
        /* .1 character space unit */
        glyphpath->snapThreshold = cf2_floatToFixed( 0.1f );
    
        glyphpath->moveIsPending = TRUE;
        glyphpath->pathIsOpen    = FALSE;
        glyphpath->pathIsClosing = FALSE;
        glyphpath->elemIsQueued  = FALSE;
      }
    
    
      FT_LOCAL_DEF( void )
      cf2_glyphpath_finalize( CF2_GlyphPath  glyphpath )
      {
        cf2_arrstack_finalize( &glyphpath->hintMoves );
      }
    
    
      /*
       * Hint point in y-direction and apply outerTransform.
       * Input `current' hint map (which is actually delayed by one element).
       * Input x,y point in Character Space.
       * Output x,y point in Device Space, including translation.
       */
      static void
      cf2_glyphpath_hintPoint( CF2_GlyphPath  glyphpath,
                               CF2_HintMap    hintmap,
                               FT_Vector*     ppt,
                               CF2_Fixed      x,
                               CF2_Fixed      y )
      {
        FT_Vector  pt;   /* hinted point in upright DS */
    
    
        pt.x = FT_MulFix( glyphpath->scaleX, x ) +
                 FT_MulFix( glyphpath->scaleC, y );
        pt.y = cf2_hintmap_map( hintmap, y );
    
        ppt->x = FT_MulFix( glyphpath->font->outerTransform.a, pt.x )   +
                   FT_MulFix( glyphpath->font->outerTransform.c, pt.y ) +
                   glyphpath->fractionalTranslation.x;
        ppt->y = FT_MulFix( glyphpath->font->outerTransform.b, pt.x )   +
                   FT_MulFix( glyphpath->font->outerTransform.d, pt.y ) +
                   glyphpath->fractionalTranslation.y;
      }
    
    
      /*
       * From two line segments, (u1,u2) and (v1,v2), compute a point of
       * intersection on the corresponding lines.
       * Return false if no intersection is found, or if the intersection is
       * too far away from the ends of the line segments, u2 and v1.
       *
       */
      static FT_Bool
      cf2_glyphpath_computeIntersection( CF2_GlyphPath     glyphpath,
                                         const FT_Vector*  u1,
                                         const FT_Vector*  u2,
                                         const FT_Vector*  v1,
                                         const FT_Vector*  v2,
                                         FT_Vector*        intersection )
      {
        /*
         * Let `u' be a zero-based vector from the first segment, `v' from the
         * second segment.
         * Let `w 'be the zero-based vector from `u1' to `v1'.
         * `perp' is the `perpendicular dot product'; see
         * http://mathworld.wolfram.com/PerpDotProduct.html.
         * `s' is the parameter for the parametric line for the first segment
         * (`u').
         *
         * See notation in
         * http://softsurfer.com/Archive/algorithm_0104/algorithm_0104B.htm.
         * Calculations are done in 16.16, but must handle the squaring of
         * line lengths in character space.  We scale all vectors by 1/32 to
         * avoid overflow.  This allows values up to 4095 to be squared.  The
         * scale factor cancels in the divide.
         *
         * TODO: the scale factor could be computed from UnitsPerEm.
         *
         */
    
    #define cf2_perp( a, b )                                    \
              ( FT_MulFix( a.x, b.y ) - FT_MulFix( a.y, b.x ) )
    
      /* round and divide by 32 */
    #define CF2_CS_SCALE( x )         \
              ( ( (x) + 0x10 ) >> 5 )
    
        FT_Vector  u, v, w;      /* scaled vectors */
        CF2_Fixed  denominator, s;
    
    
        u.x = CF2_CS_SCALE( u2->x - u1->x );
        u.y = CF2_CS_SCALE( u2->y - u1->y );
        v.x = CF2_CS_SCALE( v2->x - v1->x );
        v.y = CF2_CS_SCALE( v2->y - v1->y );
        w.x = CF2_CS_SCALE( v1->x - u1->x );
        w.y = CF2_CS_SCALE( v1->y - u1->y );
    
        denominator = cf2_perp( u, v );
    
        if ( denominator == 0 )
          return FALSE;           /* parallel or coincident lines */
    
        s = FT_DivFix( cf2_perp( w, v ), denominator );
    
        intersection->x = u1->x + FT_MulFix( s, u2->x - u1->x );
        intersection->y = u1->y + FT_MulFix( s, u2->y - u1->y );
    
        /*
         * Special case snapping for horizontal and vertical lines.
         * This cleans up intersections and reduces problems with winding
         * order detection.
         * Sample case is sbc cd KozGoPr6N-Medium.otf 20 16685.
         * Note: these calculations are in character space.
         *
         */
    
        if ( u1->x == u2->x                                                     &&
             cf2_fixedAbs( intersection->x - u1->x ) < glyphpath->snapThreshold )
          intersection->x = u1->x;
        if ( u1->y == u2->y                                                     &&
             cf2_fixedAbs( intersection->y - u1->y ) < glyphpath->snapThreshold )
          intersection->y = u1->y;
    
        if ( v1->x == v2->x                                                     &&
             cf2_fixedAbs( intersection->x - v1->x ) < glyphpath->snapThreshold )
          intersection->x = v1->x;
        if ( v1->y == v2->y                                                     &&
             cf2_fixedAbs( intersection->y - v1->y ) < glyphpath->snapThreshold )
          intersection->y = v1->y;
    
        /* limit the intersection distance from midpoint of u2 and v1 */
        if ( cf2_fixedAbs( intersection->x - ( u2->x + v1->x ) / 2 ) >
               glyphpath->miterLimit                                   ||
             cf2_fixedAbs( intersection->y - ( u2->y + v1->y ) / 2 ) >
               glyphpath->miterLimit                                   )
          return FALSE;
    
        return TRUE;
      }
    
    
      /*
       * Push the cached element (glyphpath->prevElem*) to the outline
       * consumer.  When a darkening offset is used, the end point of the
       * cached element may be adjusted to an intersection point or we may
       * synthesize a connecting line to the current element.  If we are
       * closing a subpath, we may also generate a connecting line to the start
       * point.
       *
       * This is where Character Space (CS) is converted to Device Space (DS)
       * using a hint map.  This calculation must use a HintMap that was valid
       * at the time the element was saved.  For the first point in a subpath,
       * that is a saved HintMap.  For most elements, it just means the caller
       * has delayed building a HintMap from the current HintMask.
       *
       * Transform each point with outerTransform and call the outline
       * callbacks.  This is a general 3x3 transform:
       *
       *   x' = a*x + c*y + tx, y' = b*x + d*y + ty
       *
       * but it uses 4 elements from CF2_Font and the translation part
       * from CF2_GlyphPath.
       *
       */
      static void
      cf2_glyphpath_pushPrevElem( CF2_GlyphPath  glyphpath,
                                  CF2_HintMap    hintmap,
                                  FT_Vector*     nextP0,
                                  FT_Vector      nextP1,
                                  FT_Bool        close )
      {
        CF2_CallbackParamsRec  params;
    
        FT_Vector*  prevP0;
        FT_Vector*  prevP1;
    
        FT_Vector  intersection    = { 0, 0 };
        FT_Bool    useIntersection = FALSE;
    
    
        FT_ASSERT( glyphpath->prevElemOp == CF2_PathOpLineTo ||
                   glyphpath->prevElemOp == CF2_PathOpCubeTo );
    
        if ( glyphpath->prevElemOp == CF2_PathOpLineTo )
        {
          prevP0 = &glyphpath->prevElemP0;
          prevP1 = &glyphpath->prevElemP1;
        }
        else
        {
          prevP0 = &glyphpath->prevElemP2;
          prevP1 = &glyphpath->prevElemP3;
        }
    
        /* optimization: if previous and next elements are offset by the same */
        /* amount, then there will be no gap, and no need to compute an       */
        /* intersection.                                                      */
        if ( prevP1->x != nextP0->x || prevP1->y != nextP0->y )
        {
          /* previous element does not join next element:             */
          /* adjust end point of previous element to the intersection */
          useIntersection = cf2_glyphpath_computeIntersection( glyphpath,
                                                               prevP0,
                                                               prevP1,
                                                               nextP0,
                                                               &nextP1,
                                                               &intersection );
          if ( useIntersection )
          {
            /* modify the last point of the cached element (either line or */
            /* curve)                                                      */
            *prevP1 = intersection;
          }
        }
    
        params.pt0 = glyphpath->currentDS;
    
        switch( glyphpath->prevElemOp )
        {
        case CF2_PathOpLineTo:
          params.op = CF2_PathOpLineTo;
    
          /* note: pt2 and pt3 are unused */
    
          if ( close )
          {
            /* use first hint map if closing */
            cf2_glyphpath_hintPoint( glyphpath,
                                     &glyphpath->firstHintMap,
                                     &params.pt1,
                                     glyphpath->prevElemP1.x,
                                     glyphpath->prevElemP1.y );
          }
          else
          {
            cf2_glyphpath_hintPoint( glyphpath,
                                     hintmap,
                                     &params.pt1,
                                     glyphpath->prevElemP1.x,
                                     glyphpath->prevElemP1.y );
          }
    
          /* output only non-zero length lines */
          if ( params.pt0.x != params.pt1.x || params.pt0.y != params.pt1.y )
          {
            glyphpath->callbacks->lineTo( glyphpath->callbacks, &params );
    
            glyphpath->currentDS = params.pt1;
          }
          break;
    
        case CF2_PathOpCubeTo:
          params.op = CF2_PathOpCubeTo;
    
          /* TODO: should we intersect the interior joins (p1-p2 and p2-p3)? */
          cf2_glyphpath_hintPoint( glyphpath,
                                   hintmap,
                                   &params.pt1,
                                   glyphpath->prevElemP1.x,
                                   glyphpath->prevElemP1.y );
          cf2_glyphpath_hintPoint( glyphpath,
                                   hintmap,
                                   &params.pt2,
                                   glyphpath->prevElemP2.x,
                                   glyphpath->prevElemP2.y );
          cf2_glyphpath_hintPoint( glyphpath,
                                   hintmap,
                                   &params.pt3,
                                   glyphpath->prevElemP3.x,
                                   glyphpath->prevElemP3.y );
    
          glyphpath->callbacks->cubeTo( glyphpath->callbacks, &params );
    
          glyphpath->currentDS = params.pt3;
    
          break;
        }
    
        if ( !useIntersection || close )
        {
          /* insert connecting line between end of previous element and start */
          /* of current one                                                   */
          /* note: at the end of a subpath, we might do both, so use `nextP0' */
          /* before we change it, below                                       */
    
          if ( close )
          {
            /* if we are closing the subpath, then nextP0 is in the first     */
            /* hint zone                                                      */
            cf2_glyphpath_hintPoint( glyphpath,
                                     &glyphpath->firstHintMap,
                                     &params.pt1,
                                     nextP0->x,
                                     nextP0->y );
          }
          else
          {
            cf2_glyphpath_hintPoint( glyphpath,
                                     hintmap,
                                     &params.pt1,
                                     nextP0->x,
                                     nextP0->y );
          }
    
          if ( params.pt1.x != glyphpath->currentDS.x ||
               params.pt1.y != glyphpath->currentDS.y )
          {
            /* length is nonzero */
            params.op  = CF2_PathOpLineTo;
            params.pt0 = glyphpath->currentDS;
    
            /* note: pt2 and pt3 are unused */
            glyphpath->callbacks->lineTo( glyphpath->callbacks, &params );
    
            glyphpath->currentDS = params.pt1;
          }
        }
    
        if ( useIntersection )
        {
          /* return intersection point to caller */
          *nextP0 = intersection;
        }
      }
    
    
      /* push a MoveTo element based on current point and offset of current */
      /* element                                                            */
      static void
      cf2_glyphpath_pushMove( CF2_GlyphPath  glyphpath,
                              FT_Vector      start )
      {
        CF2_CallbackParamsRec  params;
    
    
        params.op  = CF2_PathOpMoveTo;
        params.pt0 = glyphpath->currentDS;
    
        /* Test if move has really happened yet; it would have called */
        /* `cf2_hintmap_build' to set `isValid'.                   */
        if ( !cf2_hintmap_isValid( &glyphpath->hintMap ) )
        {
          /* we are here iff first subpath is missing a moveto operator: */
          /* synthesize first moveTo to finish initialization of hintMap */
          cf2_glyphpath_moveTo( glyphpath,
                                glyphpath->start.x,
                                glyphpath->start.y );
        }
    
        cf2_glyphpath_hintPoint( glyphpath,
                                 &glyphpath->hintMap,
                                 &params.pt1,
                                 start.x,
                                 start.y );
    
        /* note: pt2 and pt3 are unused */
        glyphpath->callbacks->moveTo( glyphpath->callbacks, &params );
    
        glyphpath->currentDS    = params.pt1;
        glyphpath->offsetStart0 = start;
      }
    
    
      /*
       * All coordinates are in character space.
       * On input, (x1, y1) and (x2, y2) give line segment.
       * On output, (x, y) give offset vector.
       * We use a piecewise approximation to trig functions.
       *
       * TODO: Offset true perpendicular and proper length
       *       supply the y-translation for hinting here, too,
       *       that adds yOffset unconditionally to *y.
       */
      static void
      cf2_glyphpath_computeOffset( CF2_GlyphPath  glyphpath,
                                   CF2_Fixed      x1,
                                   CF2_Fixed      y1,
                                   CF2_Fixed      x2,
                                   CF2_Fixed      y2,
                                   CF2_Fixed*     x,
                                   CF2_Fixed*     y )
      {
        CF2_Fixed  dx = x2 - x1;
        CF2_Fixed  dy = y2 - y1;
    
    
        /* note: negative offsets don't work here; negate deltas to change */
        /* quadrants, below                                                */
        if ( glyphpath->font->reverseWinding )
        {
          dx = -dx;
          dy = -dy;
        }
    
        *x = *y = 0;
    
        if ( !glyphpath->darken )
            return;
    
        /* add momentum for this path element */
        glyphpath->callbacks->windingMomentum +=
          cf2_getWindingMomentum( x1, y1, x2, y2 );
    
        /* note: allow mixed integer and fixed multiplication here */
        if ( dx >= 0 )
        {
          if ( dy >= 0 )
          {
            /* first quadrant, +x +y */
    
            if ( dx > 2 * dy )
            {
              /* +x */
              *x = 0;
              *y = 0;
            }
            else if ( dy > 2 * dx )
            {
              /* +y */
              *x = glyphpath->xOffset;
              *y = glyphpath->yOffset;
            }
            else
            {
              /* +x +y */
              *x = FT_MulFix( cf2_floatToFixed( 0.7 ),
                              glyphpath->xOffset );
              *y = FT_MulFix( cf2_floatToFixed( 1.0 - 0.7 ),
                              glyphpath->yOffset );
            }
          }
          else
          {
            /* fourth quadrant, +x -y */
    
            if ( dx > -2 * dy )
            {
              /* +x */
              *x = 0;
              *y = 0;
            }
            else if ( -dy > 2 * dx )
            {
              /* -y */
              *x = -glyphpath->xOffset;
              *y = glyphpath->yOffset;
            }
            else
            {
              /* +x -y */
              *x = FT_MulFix( cf2_floatToFixed( -0.7 ),
                              glyphpath->xOffset );
              *y = FT_MulFix( cf2_floatToFixed( 1.0 - 0.7 ),
                              glyphpath->yOffset );
            }
          }
        }
        else
        {
          if ( dy >= 0 )
          {
            /* second quadrant, -x +y */
    
            if ( -dx > 2 * dy )
            {
              /* -x */
              *x = 0;
              *y = 2 * glyphpath->yOffset;
            }
            else if ( dy > -2 * dx )
            {
              /* +y */
              *x = glyphpath->xOffset;
              *y = glyphpath->yOffset;
            }
            else
            {
              /* -x +y */
              *x = FT_MulFix( cf2_floatToFixed( 0.7 ),
                              glyphpath->xOffset );
              *y = FT_MulFix( cf2_floatToFixed( 1.0 + 0.7 ),
                              glyphpath->yOffset );
            }
          }
          else
          {
            /* third quadrant, -x -y */
    
            if ( -dx > -2 * dy )
            {
              /* -x */
              *x = 0;
              *y = 2 * glyphpath->yOffset;
            }
            else if ( -dy > -2 * dx )
            {
              /* -y */
              *x = -glyphpath->xOffset;
              *y = glyphpath->yOffset;
            }
            else
            {
              /* -x -y */
              *x = FT_MulFix( cf2_floatToFixed( -0.7 ),
                              glyphpath->xOffset );
              *y = FT_MulFix( cf2_floatToFixed( 1.0 + 0.7 ),
                              glyphpath->yOffset );
            }
          }
        }
      }
    
    
      /*
       * The functions cf2_glyphpath_{moveTo,lineTo,curveTo,closeOpenPath} are
       * called by the interpreter with Character Space (CS) coordinates.  Each
       * path element is placed into a queue of length one to await the
       * calculation of the following element.  At that time, the darkening
       * offset of the following element is known and joins can be computed,
       * including possible modification of this element, before mapping to
       * Device Space (DS) and passing it on to the outline consumer.
       *
       */
      FT_LOCAL_DEF( void )
      cf2_glyphpath_moveTo( CF2_GlyphPath  glyphpath,
                            CF2_Fixed      x,
                            CF2_Fixed      y )
      {
        cf2_glyphpath_closeOpenPath( glyphpath );
    
        /* save the parameters of the move for later, when we'll know how to */
        /* offset it;                                                        */
        /* also save last move point */
        glyphpath->currentCS.x = glyphpath->start.x = x;
        glyphpath->currentCS.y = glyphpath->start.y = y;
    
        glyphpath->moveIsPending = TRUE;
    
        /* ensure we have a valid map with current mask */
        if ( !cf2_hintmap_isValid( &glyphpath->hintMap ) ||
             cf2_hintmask_isNew( glyphpath->hintMask )   )
          cf2_hintmap_build( &glyphpath->hintMap,
                             glyphpath->hStemHintArray,
                             glyphpath->vStemHintArray,
                             glyphpath->hintMask,
                             glyphpath->hintOriginY,
                             FALSE );
    
        /* save a copy of current HintMap to use when drawing initial point */
        glyphpath->firstHintMap = glyphpath->hintMap;     /* structure copy */
      }
    
    
      FT_LOCAL_DEF( void )
      cf2_glyphpath_lineTo( CF2_GlyphPath  glyphpath,
                            CF2_Fixed      x,
                            CF2_Fixed      y )
      {
        CF2_Fixed  xOffset, yOffset;
        FT_Vector  P0, P1;
        FT_Bool    newHintMap;
    
        /*
         * New hints will be applied after cf2_glyphpath_pushPrevElem has run.
         * In case this is a synthesized closing line, any new hints should be
         * delayed until this path is closed (`cf2_hintmask_isNew' will be
         * called again before the next line or curve).
         */
    
        /* true if new hint map not on close */
        newHintMap = cf2_hintmask_isNew( glyphpath->hintMask ) &&
                     !glyphpath->pathIsClosing;
    
        /*
         * Zero-length lines may occur in the charstring.  Because we cannot
         * compute darkening offsets or intersections from zero-length lines,
         * it is best to remove them and avoid artifacts.  However, zero-length
         * lines in CS at the start of a new hint map can generate non-zero
         * lines in DS due to hint substitution.  We detect a change in hint
         * map here and pass those zero-length lines along.
         */
    
        /*
         * Note: Find explicitly closed paths here with a conditional
         *       breakpoint using
         *
         *         !gp->pathIsClosing && gp->start.x == x && gp->start.y == y
         *
         */
    
        if ( glyphpath->currentCS.x == x &&
             glyphpath->currentCS.y == y &&
             !newHintMap                 )
          /*
           * Ignore zero-length lines in CS where the hint map is the same
           * because the line in DS will also be zero length.
           *
           * Ignore zero-length lines when we synthesize a closing line because
           * the close will be handled in cf2_glyphPath_pushPrevElem.
           */
          return;
    
        cf2_glyphpath_computeOffset( glyphpath,
                                     glyphpath->currentCS.x,
                                     glyphpath->currentCS.y,
                                     x,
                                     y,
                                     &xOffset,
                                     &yOffset );
    
        /* construct offset points */
        P0.x = glyphpath->currentCS.x + xOffset;
        P0.y = glyphpath->currentCS.y + yOffset;
        P1.x = x + xOffset;
        P1.y = y + yOffset;
    
        if ( glyphpath->moveIsPending )
        {
          /* emit offset 1st point as MoveTo */
          cf2_glyphpath_pushMove( glyphpath, P0 );
    
          glyphpath->moveIsPending = FALSE;  /* adjust state machine */
          glyphpath->pathIsOpen    = TRUE;
    
          glyphpath->offsetStart1 = P1;              /* record second point */
        }
    
        if ( glyphpath->elemIsQueued )
        {
          FT_ASSERT( cf2_hintmap_isValid( &glyphpath->hintMap ) ||
                     glyphpath->hintMap.count == 0              );
    
          cf2_glyphpath_pushPrevElem( glyphpath,
                                      &glyphpath->hintMap,
                                      &P0,
                                      P1,
                                      FALSE );
        }
    
        /* queue the current element with offset points */
        glyphpath->elemIsQueued = TRUE;
        glyphpath->prevElemOp   = CF2_PathOpLineTo;
        glyphpath->prevElemP0   = P0;
        glyphpath->prevElemP1   = P1;
    
        /* update current map */
        if ( newHintMap )
          cf2_hintmap_build( &glyphpath->hintMap,
                             glyphpath->hStemHintArray,
                             glyphpath->vStemHintArray,
                             glyphpath->hintMask,
                             glyphpath->hintOriginY,
                             FALSE );
    
        glyphpath->currentCS.x = x;     /* pre-offset current point */
        glyphpath->currentCS.y = y;
      }
    
    
      FT_LOCAL_DEF( void )
      cf2_glyphpath_curveTo( CF2_GlyphPath  glyphpath,
                             CF2_Fixed      x1,
                             CF2_Fixed      y1,
                             CF2_Fixed      x2,
                             CF2_Fixed      y2,
                             CF2_Fixed      x3,
                             CF2_Fixed      y3 )
      {
        CF2_Fixed  xOffset1, yOffset1, xOffset3, yOffset3;
        FT_Vector  P0, P1, P2, P3;
    
    
        /* TODO: ignore zero length portions of curve?? */
        cf2_glyphpath_computeOffset( glyphpath,
                                     glyphpath->currentCS.x,
                                     glyphpath->currentCS.y,
                                     x1,
                                     y1,
                                     &xOffset1,
                                     &yOffset1 );
        cf2_glyphpath_computeOffset( glyphpath,
                                     x2,
                                     y2,
                                     x3,
                                     y3,
                                     &xOffset3,
                                     &yOffset3 );
    
        /* add momentum from the middle segment */
        glyphpath->callbacks->windingMomentum +=
          cf2_getWindingMomentum( x1, y1, x2, y2 );
    
        /* construct offset points */
        P0.x = glyphpath->currentCS.x + xOffset1;
        P0.y = glyphpath->currentCS.y + yOffset1;
        P1.x = x1 + xOffset1;
        P1.y = y1 + yOffset1;
        /* note: preserve angle of final segment by using offset3 at both ends */
        P2.x = x2 + xOffset3;
        P2.y = y2 + yOffset3;
        P3.x = x3 + xOffset3;
        P3.y = y3 + yOffset3;
    
        if ( glyphpath->moveIsPending )
        {
          /* emit offset 1st point as MoveTo */
          cf2_glyphpath_pushMove( glyphpath, P0 );
    
          glyphpath->moveIsPending = FALSE;
          glyphpath->pathIsOpen    = TRUE;
    
          glyphpath->offsetStart1 = P1;              /* record second point */
        }
    
        if ( glyphpath->elemIsQueued )
        {
          FT_ASSERT( cf2_hintmap_isValid( &glyphpath->hintMap ) ||
                     glyphpath->hintMap.count == 0              );
    
          cf2_glyphpath_pushPrevElem( glyphpath,
                                      &glyphpath->hintMap,
                                      &P0,
                                      P1,
                                      FALSE );
        }
    
        /* queue the current element with offset points */
        glyphpath->elemIsQueued = TRUE;
        glyphpath->prevElemOp   = CF2_PathOpCubeTo;
        glyphpath->prevElemP0   = P0;
        glyphpath->prevElemP1   = P1;
        glyphpath->prevElemP2   = P2;
        glyphpath->prevElemP3   = P3;
    
        /* update current map */
        if ( cf2_hintmask_isNew( glyphpath->hintMask ) )
          cf2_hintmap_build( &glyphpath->hintMap,
                             glyphpath->hStemHintArray,
                             glyphpath->vStemHintArray,
                             glyphpath->hintMask,
                             glyphpath->hintOriginY,
                             FALSE );
    
        glyphpath->currentCS.x = x3;       /* pre-offset current point */
        glyphpath->currentCS.y = y3;
      }
    
    
      FT_LOCAL_DEF( void )
      cf2_glyphpath_closeOpenPath( CF2_GlyphPath  glyphpath )
      {
        if ( glyphpath->pathIsOpen )
        {
          /*
           * A closing line in Character Space line is always generated below
           * with `cf2_glyphPath_lineTo'.  It may be ignored later if it turns
           * out to be zero length in Device Space.
           */
          glyphpath->pathIsClosing = TRUE;
    
          cf2_glyphpath_lineTo( glyphpath,
                                glyphpath->start.x,
                                glyphpath->start.y );
    
          /* empty the final element from the queue and close the path */
          if ( glyphpath->elemIsQueued )
            cf2_glyphpath_pushPrevElem( glyphpath,
                                        &glyphpath->hintMap,
                                        &glyphpath->offsetStart0,
                                        glyphpath->offsetStart1,
                                        TRUE );
    
          /* reset state machine */
          glyphpath->moveIsPending = TRUE;
          glyphpath->pathIsOpen    = FALSE;
          glyphpath->pathIsClosing = FALSE;
          glyphpath->elemIsQueued  = FALSE;
        }
      }
    
    
    /* END */