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+/***************************************************************************/
+/*                                                                         */
+/*  pshints.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    */
+/*  license to make, have made, use, offer to sell, sell, import, and      */
+/*  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      */
+/*  (including a cross-claim or counterclaim in a lawsuit) alleging that   */
+/*  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  */
+/*  the date such litigation is filed.                                     */
+/*                                                                         */
+/*  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 "psft.h"
+#include FT_INTERNAL_DEBUG_H
+
+#include "psglue.h"
+#include "psfont.h"
+#include "pshints_.h"
+#include "psintrp.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 ) * ( SUB_INT32( y2, y1 ) >> 16 ) -
+           ( y1 >> 16 ) * ( SUB_INT32( 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 = SUB_INT32( 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 = ADD_INT32( hint->csCoord, 2 * font->darkenY );
+
+    hint->csCoord = ADD_INT32( 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;
+  }
+
+
+  static void
+  cf2_hintmap_dump( CF2_HintMap  hintmap )
+  {
+#ifdef FT_DEBUG_LEVEL_TRACE
+    CF2_UInt  i;
+
+
+    FT_TRACE6(( "  index  csCoord  dsCoord  scale  flags\n" ));
+
+    for ( i = 0; i < hintmap->count; i++ )
+    {
+      CF2_Hint  hint = &hintmap->edge[i];
+
+
+      FT_TRACE6(( "  %3d    %7.2f  %7.2f  %5d  %s%s%s%s\n",
+                  hint->index,
+                  hint->csCoord / 65536.0,
+                  hint->dsCoord / ( hint->scale * 1.0 ),
+                  hint->scale,
+                  ( cf2_hint_isPair( hint ) ? "p" : "g" ),
+                  ( cf2_hint_isTop( hint ) ? "t" : "b" ),
+                  ( cf2_hint_isLocked( hint ) ? "L" : ""),
+                  ( cf2_hint_isSynthetic( hint ) ? "S" : "" ) ));
+    }
+#else
+    FT_UNUSED( hintmap );
+#endif
+  }
+
+
+  /* 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 ADD_INT32( FT_MulFix( SUB_INT32( 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 ADD_INT32( FT_MulFix( SUB_INT32( 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 >=
+               ADD_INT32( 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 <=
+                 ADD_INT32( 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 <=
+                 ADD_INT32( 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 = ADD_INT32( hintmap->edge[i].dsCoord,
+                                              move );
+        if ( isPair )
+          hintmap->edge[j].dsCoord = ADD_INT32( 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( SUB_INT32( hintmap->edge[i].dsCoord,
+                                  hintmap->edge[i - 1].dsCoord ),
+                       SUB_INT32( 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( SUB_INT32( hintmap->edge[j].dsCoord,
+                                  hintmap->edge[j - 1].dsCoord ),
+                       SUB_INT32( 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 >=
+             ADD_INT32( hintmap->edge[j].dsCoord,
+                        hintMove->moveUp + CF2_MIN_COUNTER ) )
+      {
+        /* there is more room now, move edge up */
+        hintmap->edge[j].dsCoord = ADD_INT32( hintmap->edge[j].dsCoord,
+                                              hintMove->moveUp );
+
+        if ( cf2_hint_isPair( &hintmap->edge[j] ) )
+        {
+          FT_ASSERT( j > 0 );
+          hintmap->edge[j - 1].dsCoord =
+            ADD_INT32( 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;
+    }
+
+    FT_TRACE7(( "  Got hint at %.2f (%.2f)\n",
+                firstHintEdge->csCoord / 65536.0,
+                firstHintEdge->dsCoord / 65536.0 ));
+    if ( isPair )
+      FT_TRACE7(( "  Got hint at %.2f (%.2f)\n",
+                  secondHintEdge->csCoord / 65536.0,
+                  secondHintEdge->dsCoord / 65536.0 ));
+
+    /*
+     * 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,
+                       ADD_INT32( secondHintEdge->csCoord,
+                                  firstHintEdge->csCoord ) / 2 );
+        CF2_Fixed  halfWidth =
+                     FT_MulFix( SUB_INT32( secondHintEdge->csCoord,
+                                           firstHintEdge->csCoord ) / 2,
+                                hintmap->scale );
+
+
+        firstHintEdge->dsCoord  = SUB_INT32( midpoint, halfWidth );
+        secondHintEdge->dsCoord = ADD_INT32( 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;
+
+      FT_TRACE7(( "  Inserting hint %.2f (%.2f)\n",
+                  firstHintEdge->csCoord / 65536.0,
+                  firstHintEdge->dsCoord / 65536.0 ));
+
+      if ( isPair )
+      {
+        /* insert second edge */
+        hintmap->edge[indexInsert + 1] = *secondHintEdge;  /* copy struct */
+        hintmap->count                += 1;
+
+        FT_TRACE7(( "  Inserting hint %.2f (%.2f)\n",
+                    secondHintEdge->csCoord / 65536.0,
+                    secondHintEdge->dsCoord / 65536.0 ));
+
+      }
+    }
+
+    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 ) )
+      {
+        if ( font->isT1 )
+        {
+          /* no error, just continue unhinted */
+          *hintMask->error = FT_Err_Ok;
+          hintmap->hinted  = FALSE;
+        }
+        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;
+      }
+    }
+
+    FT_TRACE6(( initialMap ? "flags: [p]air [g]host [t]op "
+                             "[b]ottom [L]ocked [S]ynthetic\n"
+                             "Initial hintmap\n"
+                           : "Hints:\n" ));
+    cf2_hintmap_dump( hintmap );
+
+    /*
+     * 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 );
+
+    FT_TRACE6(( "(adjusted)\n" ));
+    cf2_hintmap_dump( 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_doubleToFixed( 0.1 );
+
+    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 = ADD_INT32( FT_MulFix( glyphpath->scaleX, x ),
+                      FT_MulFix( glyphpath->scaleC, y ) );
+    pt.y = cf2_hintmap_map( hintmap, y );
+
+    ppt->x = ADD_INT32(
+               FT_MulFix( glyphpath->font->outerTransform.a, pt.x ),
+               ADD_INT32(
+                 FT_MulFix( glyphpath->font->outerTransform.c, pt.y ),
+                 glyphpath->fractionalTranslation.x ) );
+    ppt->y = ADD_INT32(
+               FT_MulFix( glyphpath->font->outerTransform.b, pt.x ),
+               ADD_INT32(
+                 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
+     * https://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( SUB_INT32( u2->x, u1->x ) );
+    u.y = CF2_CS_SCALE( SUB_INT32( u2->y, u1->y ) );
+    v.x = CF2_CS_SCALE( SUB_INT32( v2->x, v1->x ) );
+    v.y = CF2_CS_SCALE( SUB_INT32( v2->y, v1->y ) );
+    w.x = CF2_CS_SCALE( SUB_INT32( v1->x, u1->x ) );
+    w.y = CF2_CS_SCALE( SUB_INT32( 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 = ADD_INT32( u1->x,
+                                 FT_MulFix( s, SUB_INT32( u2->x, u1->x ) ) );
+    intersection->y = ADD_INT32( u1->y,
+                                 FT_MulFix( s, SUB_INT32( 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( SUB_INT32( intersection->x,
+                                  u1->x ) ) < glyphpath->snapThreshold )
+      intersection->x = u1->x;
+    if ( u1->y == u2->y                                                &&
+         cf2_fixedAbs( SUB_INT32( intersection->y,
+                                  u1->y ) ) < glyphpath->snapThreshold )
+      intersection->y = u1->y;
+
+    if ( v1->x == v2->x                                                &&
+         cf2_fixedAbs( SUB_INT32( intersection->x,
+                                  v1->x ) ) < glyphpath->snapThreshold )
+      intersection->x = v1->x;
+    if ( v1->y == v2->y                                                &&
+         cf2_fixedAbs( SUB_INT32( 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 - ADD_INT32( u2->x, v1->x ) / 2 ) >
+           glyphpath->miterLimit                                           ||
+         cf2_fixedAbs( intersection->y - ADD_INT32( 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 = SUB_INT32( x2, x1 );
+    CF2_Fixed  dy = SUB_INT32( y2, y1 );
+
+
+    /* note: negative offsets don't work here; negate deltas to change */
+    /* quadrants, below                                                */
+    if ( glyphpath->font->reverseWinding )
+    {
+      dx = NEG_INT32( dx );
+      dy = NEG_INT32( dy );
+    }
+
+    *x = *y = 0;
+
+    if ( !glyphpath->darken )
+        return;
+
+    /* add momentum for this path element */
+    glyphpath->callbacks->windingMomentum =
+      ADD_INT32( 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 > MUL_INT32( 2, dy ) )
+        {
+          /* +x */
+          *x = 0;
+          *y = 0;
+        }
+        else if ( dy > MUL_INT32( 2, dx ) )
+        {
+          /* +y */
+          *x = glyphpath->xOffset;
+          *y = glyphpath->yOffset;
+        }
+        else
+        {
+          /* +x +y */
+          *x = FT_MulFix( cf2_doubleToFixed( 0.7 ),
+                          glyphpath->xOffset );
+          *y = FT_MulFix( cf2_doubleToFixed( 1.0 - 0.7 ),
+                          glyphpath->yOffset );
+        }
+      }
+      else
+      {
+        /* fourth quadrant, +x -y */
+
+        if ( dx > MUL_INT32( -2, dy ) )
+        {
+          /* +x */
+          *x = 0;
+          *y = 0;
+        }
+        else if ( NEG_INT32( dy ) > MUL_INT32( 2, dx ) )
+        {
+          /* -y */
+          *x = NEG_INT32( glyphpath->xOffset );
+          *y = glyphpath->yOffset;
+        }
+        else
+        {
+          /* +x -y */
+          *x = FT_MulFix( cf2_doubleToFixed( -0.7 ),
+                          glyphpath->xOffset );
+          *y = FT_MulFix( cf2_doubleToFixed( 1.0 - 0.7 ),
+                          glyphpath->yOffset );
+        }
+      }
+    }
+    else
+    {
+      if ( dy >= 0 )
+      {
+        /* second quadrant, -x +y */
+
+        if ( NEG_INT32( dx ) > MUL_INT32( 2, dy ) )
+        {
+          /* -x */
+          *x = 0;
+          *y = MUL_INT32( 2, glyphpath->yOffset );
+        }
+        else if ( dy > MUL_INT32( -2, dx ) )
+        {
+          /* +y */
+          *x = glyphpath->xOffset;
+          *y = glyphpath->yOffset;
+        }
+        else
+        {
+          /* -x +y */
+          *x = FT_MulFix( cf2_doubleToFixed( 0.7 ),
+                          glyphpath->xOffset );
+          *y = FT_MulFix( cf2_doubleToFixed( 1.0 + 0.7 ),
+                          glyphpath->yOffset );
+        }
+      }
+      else
+      {
+        /* third quadrant, -x -y */
+
+        if ( NEG_INT32( dx ) > MUL_INT32( -2, dy ) )
+        {
+          /* -x */
+          *x = 0;
+          *y = MUL_INT32( 2, glyphpath->yOffset );
+        }
+        else if ( NEG_INT32( dy ) > MUL_INT32( -2, dx ) )
+        {
+          /* -y */
+          *x = NEG_INT32( glyphpath->xOffset );
+          *y = glyphpath->yOffset;
+        }
+        else
+        {
+          /* -x -y */
+          *x = FT_MulFix( cf2_doubleToFixed( -0.7 ),
+                          glyphpath->xOffset );
+          *y = FT_MulFix( cf2_doubleToFixed( 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 */
+    ft_memcpy(&glyphpath->firstHintMap, &glyphpath->hintMap, sizeof(glyphpath->hintMap));
+  }
+
+
+  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 = ADD_INT32( glyphpath->currentCS.x, xOffset );
+    P0.y = ADD_INT32( glyphpath->currentCS.y, yOffset );
+    P1.x = ADD_INT32( x, xOffset );
+    P1.y = ADD_INT32( 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 =
+      ADD_INT32( glyphpath->callbacks->windingMomentum,
+                 cf2_getWindingMomentum( x1, y1, x2, y2 ) );
+
+    /* construct offset points */
+    P0.x = ADD_INT32( glyphpath->currentCS.x, xOffset1 );
+    P0.y = ADD_INT32( glyphpath->currentCS.y, yOffset1 );
+    P1.x = ADD_INT32( x1, xOffset1 );
+    P1.y = ADD_INT32( y1, yOffset1 );
+    /* note: preserve angle of final segment by using offset3 at both ends */
+    P2.x = ADD_INT32( x2, xOffset3 );
+    P2.y = ADD_INT32( y2, yOffset3 );
+    P3.x = ADD_INT32( x3, xOffset3 );
+    P3.y = ADD_INT32( 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 */