text: /***************************************************************************/
  /*                                                                         */
  /*  aflatin.c                                                              */
  /*                                                                         */
  /*    Auto-fitter hinting routines for latin writing system (body).        */
  /*                                                                         */
  /*  Copyright 2003-2017 by                                                 */
  /*  David Turner, Robert Wilhelm, and Werner Lemberg.                      */
  /*                                                                         */
  /*  This file is part of the FreeType project, and may only be used,       */
  /*  modified, and distributed under the terms of the FreeType project      */
  /*  license, LICENSE.TXT.  By continuing to use, modify, or distribute     */
  /*  this file you indicate that you have read the license and              */
  /*  understand and accept it fully.                                        */
  /*                                                                         */
  /***************************************************************************/
  
  
  #include <ft2build.h>
  #include FT_ADVANCES_H
  #include FT_INTERNAL_DEBUG_H
  
  #include "afglobal.h"
  #include "afpic.h"
  #include "aflatin.h"
  #include "aferrors.h"
  
  
  #ifdef AF_CONFIG_OPTION_USE_WARPER
  #include "afwarp.h"
  #endif
  
  
    /*************************************************************************/
    /*                                                                       */
    /* 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_aflatin
  
  
    /* needed for computation of round vs. flat segments */
  #define FLAT_THRESHOLD( x )  ( x / 14 )
  
  
    /*************************************************************************/
    /*************************************************************************/
    /*****                                                               *****/
    /*****            L A T I N   G L O B A L   M E T R I C S            *****/
    /*****                                                               *****/
    /*************************************************************************/
    /*************************************************************************/
  
  
    /* Find segments and links, compute all stem widths, and initialize */
    /* standard width and height for the glyph with given charcode.     */
  
    FT_LOCAL_DEF( void )
    af_latin_metrics_init_widths( AF_LatinMetrics  metrics,
                                  FT_Face          face )
    {
      /* scan the array of segments in each direction */
      AF_GlyphHintsRec  hints[1];
  
  
      FT_TRACE5(( "\n"
                  "latin standard widths computation (style `%s')\n"
                  "=====================================================\n"
                  "\n",
                  af_style_names[metrics->root.style_class->style] ));
  
      af_glyph_hints_init( hints, face->memory );
  
      metrics->axis[AF_DIMENSION_HORZ].width_count = 0;
      metrics->axis[AF_DIMENSION_VERT].width_count = 0;
  
      {
        FT_Error            error;
        FT_ULong            glyph_index;
        int                 dim;
        AF_LatinMetricsRec  dummy[1];
        AF_Scaler           scaler = &dummy->root.scaler;
  
  #ifdef FT_CONFIG_OPTION_PIC
        AF_FaceGlobals  globals = metrics->root.globals;
  #endif
  
        AF_StyleClass   style_class  = metrics->root.style_class;
        AF_ScriptClass  script_class = AF_SCRIPT_CLASSES_GET
                                         [style_class->script];
  
        void*        shaper_buf;
        const char*  p;
  
  #ifdef FT_DEBUG_LEVEL_TRACE
        FT_ULong  ch = 0;
  #endif
  
        p          = script_class->standard_charstring;
        shaper_buf = af_shaper_buf_create( face );
  
        /*
         * We check a list of standard characters to catch features like
         * `c2sc' (small caps from caps) that don't contain lowercase letters
         * by definition, or other features that mainly operate on numerals.
         * The first match wins.
         */
  
        glyph_index = 0;
        while ( *p )
        {
          unsigned int  num_idx;
  
  #ifdef FT_DEBUG_LEVEL_TRACE
          const char*  p_old;
  #endif
  
  
          while ( *p == ' ' )
            p++;
  
  #ifdef FT_DEBUG_LEVEL_TRACE
          p_old = p;
          GET_UTF8_CHAR( ch, p_old );
  #endif
  
          /* reject input that maps to more than a single glyph */
          p = af_shaper_get_cluster( p, &metrics->root, shaper_buf, &num_idx );
          if ( num_idx > 1 )
            continue;
  
          /* otherwise exit loop if we have a result */
          glyph_index = af_shaper_get_elem( &metrics->root,
                                            shaper_buf,
                                            0,
                                            NULL,
                                            NULL );
          if ( glyph_index )
            break;
        }
  
        af_shaper_buf_destroy( face, shaper_buf );
  
        if ( !glyph_index )
          goto Exit;
  
        FT_TRACE5(( "standard character: U+%04lX (glyph index %d)\n",
                    ch, glyph_index ));
  
        error = FT_Load_Glyph( face, glyph_index, FT_LOAD_NO_SCALE );
        if ( error || face->glyph->outline.n_points <= 0 )
          goto Exit;
  
        FT_ZERO( dummy );
  
        dummy->units_per_em = metrics->units_per_em;
  
        scaler->x_scale = 0x10000L;
        scaler->y_scale = 0x10000L;
        scaler->x_delta = 0;
        scaler->y_delta = 0;
  
        scaler->face        = face;
        scaler->render_mode = FT_RENDER_MODE_NORMAL;
        scaler->flags       = 0;
  
        af_glyph_hints_rescale( hints, (AF_StyleMetrics)dummy );
  
        error = af_glyph_hints_reload( hints, &face->glyph->outline );
        if ( error )
          goto Exit;
  
        for ( dim = 0; dim < AF_DIMENSION_MAX; dim++ )
        {
          AF_LatinAxis  axis    = &metrics->axis[dim];
          AF_AxisHints  axhints = &hints->axis[dim];
          AF_Segment    seg, limit, link;
          FT_UInt       num_widths = 0;
  
  
          error = af_latin_hints_compute_segments( hints,
                                                   (AF_Dimension)dim );
          if ( error )
            goto Exit;
  
          /*
           *  We assume that the glyphs selected for the stem width
           *  computation are `featureless' enough so that the linking
           *  algorithm works fine without adjustments of its scoring
           *  function.
           */
          af_latin_hints_link_segments( hints,
                                        0,
                                        NULL,
                                        (AF_Dimension)dim );
  
          seg   = axhints->segments;
          limit = seg + axhints->num_segments;
  
          for ( ; seg < limit; seg++ )
          {
            link = seg->link;
  
            /* we only consider stem segments there! */
            if ( link && link->link == seg && link > seg )
            {
              FT_Pos  dist;
  
  
              dist = seg->pos - link->pos;
              if ( dist < 0 )
                dist = -dist;
  
              if ( num_widths < AF_LATIN_MAX_WIDTHS )
                axis->widths[num_widths++].org = dist;
            }
          }
  
          /* this also replaces multiple almost identical stem widths */
          /* with a single one (the value 100 is heuristic)           */
          af_sort_and_quantize_widths( &num_widths, axis->widths,
                                       dummy->units_per_em / 100 );
          axis->width_count = num_widths;
        }
  
      Exit:
        for ( dim = 0; dim < AF_DIMENSION_MAX; dim++ )
        {
          AF_LatinAxis  axis = &metrics->axis[dim];
          FT_Pos        stdw;
  
  
          stdw = ( axis->width_count > 0 ) ? axis->widths[0].org
                                           : AF_LATIN_CONSTANT( metrics, 50 );
  
          /* let's try 20% of the smallest width */
          axis->edge_distance_threshold = stdw / 5;
          axis->standard_width          = stdw;
          axis->extra_light             = 0;
  
  #ifdef FT_DEBUG_LEVEL_TRACE
          {
            FT_UInt  i;
  
  
            FT_TRACE5(( "%s widths:\n",
                        dim == AF_DIMENSION_VERT ? "horizontal"
                                                 : "vertical" ));
  
            FT_TRACE5(( "  %d (standard)", axis->standard_width ));
            for ( i = 1; i < axis->width_count; i++ )
              FT_TRACE5(( " %d", axis->widths[i].org ));
  
            FT_TRACE5(( "\n" ));
          }
  #endif
        }
      }
  
      FT_TRACE5(( "\n" ));
  
      af_glyph_hints_done( hints );
    }
  
  
    static void
    af_latin_sort_blue( FT_UInt        count,
                        AF_LatinBlue*  table )
    {
      FT_UInt       i, j;
      AF_LatinBlue  swap;
  
  
      /* we sort from bottom to top */
      for ( i = 1; i < count; i++ )
      {
        for ( j = i; j > 0; j-- )
        {
          FT_Pos  a, b;
  
  
          if ( table[j - 1]->flags & ( AF_LATIN_BLUE_TOP     |
                                       AF_LATIN_BLUE_SUB_TOP ) )
            a = table[j - 1]->ref.org;
          else
            a = table[j - 1]->shoot.org;
  
          if ( table[j]->flags & ( AF_LATIN_BLUE_TOP     |
                                   AF_LATIN_BLUE_SUB_TOP ) )
            b = table[j]->ref.org;
          else
            b = table[j]->shoot.org;
  
          if ( b >= a )
            break;
  
          swap         = table[j];
          table[j]     = table[j - 1];
          table[j - 1] = swap;
        }
      }
    }
  
  
    /* Find all blue zones.  Flat segments give the reference points, */
    /* round segments the overshoot positions.                        */
  
    static void
    af_latin_metrics_init_blues( AF_LatinMetrics  metrics,
                                 FT_Face          face )
    {
      FT_Pos        flats [AF_BLUE_STRING_MAX_LEN];
      FT_Pos        rounds[AF_BLUE_STRING_MAX_LEN];
  
      FT_UInt       num_flats;
      FT_UInt       num_rounds;
  
      AF_LatinBlue  blue;
      FT_Error      error;
      AF_LatinAxis  axis = &metrics->axis[AF_DIMENSION_VERT];
      FT_Outline    outline;
  
      AF_StyleClass  sc = metrics->root.style_class;
  
      AF_Blue_Stringset         bss = sc->blue_stringset;
      const AF_Blue_StringRec*  bs  = &af_blue_stringsets[bss];
  
      FT_Pos  flat_threshold = FLAT_THRESHOLD( metrics->units_per_em );
  
      void*  shaper_buf;
  
  
      /* we walk over the blue character strings as specified in the */
      /* style's entry in the `af_blue_stringset' array              */
  
      FT_TRACE5(( "latin blue zones computation\n"
                  "============================\n"
                  "\n" ));
  
      shaper_buf = af_shaper_buf_create( face );
  
      for ( ; bs->string != AF_BLUE_STRING_MAX; bs++ )
      {
        const char*  p = &af_blue_strings[bs->string];
        FT_Pos*      blue_ref;
        FT_Pos*      blue_shoot;
        FT_Pos       ascender;
        FT_Pos       descender;
  
  
  #ifdef FT_DEBUG_LEVEL_TRACE
        {
          FT_Bool  have_flag = 0;
  
  
          FT_TRACE5(( "blue zone %d", axis->blue_count ));
  
          if ( bs->properties )
          {
            FT_TRACE5(( " (" ));
  
            if ( AF_LATIN_IS_TOP_BLUE( bs ) )
            {
              FT_TRACE5(( "top" ));
              have_flag = 1;
            }
            else if ( AF_LATIN_IS_SUB_TOP_BLUE( bs ) )
            {
              FT_TRACE5(( "sub top" ));
              have_flag = 1;
            }
  
            if ( AF_LATIN_IS_NEUTRAL_BLUE( bs ) )
            {
              if ( have_flag )
                FT_TRACE5(( ", " ));
              FT_TRACE5(( "neutral" ));
              have_flag = 1;
            }
  
            if ( AF_LATIN_IS_X_HEIGHT_BLUE( bs ) )
            {
              if ( have_flag )
                FT_TRACE5(( ", " ));
              FT_TRACE5(( "small top" ));
              have_flag = 1;
            }
  
            if ( AF_LATIN_IS_LONG_BLUE( bs ) )
            {
              if ( have_flag )
                FT_TRACE5(( ", " ));
              FT_TRACE5(( "long" ));
            }
  
            FT_TRACE5(( ")" ));
          }
  
          FT_TRACE5(( ":\n" ));
        }
  #endif /* FT_DEBUG_LEVEL_TRACE */
  
        num_flats  = 0;
        num_rounds = 0;
        ascender   = 0;
        descender  = 0;
  
        while ( *p )
        {
          FT_ULong    glyph_index;
          FT_Long     y_offset;
          FT_Int      best_point, best_contour_first, best_contour_last;
          FT_Vector*  points;
  
          FT_Pos   best_y_extremum;                      /* same as points.y */
          FT_Bool  best_round = 0;
  
          unsigned int  i, num_idx;
  
  #ifdef FT_DEBUG_LEVEL_TRACE
          const char*  p_old;
          FT_ULong     ch;
  #endif
  
  
          while ( *p == ' ' )
            p++;
  
  #ifdef FT_DEBUG_LEVEL_TRACE
          p_old = p;
          GET_UTF8_CHAR( ch, p_old );
  #endif
  
          p = af_shaper_get_cluster( p, &metrics->root, shaper_buf, &num_idx );
  
          if ( !num_idx )
          {
            FT_TRACE5(( "  U+%04lX unavailable\n", ch ));
            continue;
          }
  
          if ( AF_LATIN_IS_TOP_BLUE( bs ) )
            best_y_extremum = FT_INT_MIN;
          else
            best_y_extremum = FT_INT_MAX;
  
          /* iterate over all glyph elements of the character cluster */
          /* and get the data of the `biggest' one                    */
          for ( i = 0; i < num_idx; i++ )
          {
            FT_Pos   best_y;
            FT_Bool  round = 0;
  
  
            /* load the character in the face -- skip unknown or empty ones */
            glyph_index = af_shaper_get_elem( &metrics->root,
                                              shaper_buf,
                                              i,
                                              NULL,
                                              &y_offset );
            if ( glyph_index == 0 )
            {
              FT_TRACE5(( "  U+%04lX unavailable\n", ch ));
              continue;
            }
  
            error   = FT_Load_Glyph( face, glyph_index, FT_LOAD_NO_SCALE );
            outline = face->glyph->outline;
            /* reject glyphs that don't produce any rendering */
            if ( error || outline.n_points <= 2 )
            {
  #ifdef FT_DEBUG_LEVEL_TRACE
              if ( num_idx == 1 )
                FT_TRACE5(( "  U+%04lX contains no (usable) outlines\n", ch ));
              else
                FT_TRACE5(( "  component %d of cluster starting with U+%04lX"
                            " contains no (usable) outlines\n", i, ch ));
  #endif
              continue;
            }
  
            /* now compute min or max point indices and coordinates */
            points             = outline.points;
            best_point         = -1;
            best_y             = 0;  /* make compiler happy */
            best_contour_first = 0;  /* ditto */
            best_contour_last  = 0;  /* ditto */
  
            {
              FT_Int  nn;
              FT_Int  first = 0;
              FT_Int  last  = -1;
  
  
              for ( nn = 0; nn < outline.n_contours; first = last + 1, nn++ )
              {
                FT_Int  old_best_point = best_point;
                FT_Int  pp;
  
  
                last = outline.contours[nn];
  
                /* Avoid single-point contours since they are never      */
                /* rasterized.  In some fonts, they correspond to mark   */
                /* attachment points that are way outside of the glyph's */
                /* real outline.                                         */
                if ( last <= first )
                  continue;
  
                if ( AF_LATIN_IS_TOP_BLUE( bs )     ||
                     AF_LATIN_IS_SUB_TOP_BLUE( bs ) )
                {
                  for ( pp = first; pp <= last; pp++ )
                  {
                    if ( best_point < 0 || points[pp].y > best_y )
                    {
                      best_point = pp;
                      best_y     = points[pp].y;
                      ascender   = FT_MAX( ascender, best_y + y_offset );
                    }
                    else
                      descender = FT_MIN( descender, points[pp].y + y_offset );
                  }
                }
                else
                {
                  for ( pp = first; pp <= last; pp++ )
                  {
                    if ( best_point < 0 || points[pp].y < best_y )
                    {
                      best_point = pp;
                      best_y     = points[pp].y;
                      descender  = FT_MIN( descender, best_y + y_offset );
                    }
                    else
                      ascender = FT_MAX( ascender, points[pp].y + y_offset );
                  }
                }
  
                if ( best_point != old_best_point )
                {
                  best_contour_first = first;
                  best_contour_last  = last;
                }
              }
            }
  
            /* now check whether the point belongs to a straight or round   */
            /* segment; we first need to find in which contour the extremum */
            /* lies, then inspect its previous and next points              */
            if ( best_point >= 0 )
            {
              FT_Pos  best_x = points[best_point].x;
              FT_Int  prev, next;
              FT_Int  best_segment_first, best_segment_last;
              FT_Int  best_on_point_first, best_on_point_last;
              FT_Pos  dist;
  
  
              best_segment_first = best_point;
              best_segment_last  = best_point;
  
              if ( FT_CURVE_TAG( outline.tags[best_point] ) == FT_CURVE_TAG_ON )
              {
                best_on_point_first = best_point;
                best_on_point_last  = best_point;
              }
              else
              {
                best_on_point_first = -1;
                best_on_point_last  = -1;
              }
  
              /* look for the previous and next points on the contour  */
              /* that are not on the same Y coordinate, then threshold */
              /* the `closeness'...                                    */
              prev = best_point;
              next = prev;
  
              do
              {
                if ( prev > best_contour_first )
                  prev--;
                else
                  prev = best_contour_last;
  
                dist = FT_ABS( points[prev].y - best_y );
                /* accept a small distance or a small angle (both values are */
                /* heuristic; value 20 corresponds to approx. 2.9 degrees)   */
                if ( dist > 5 )
                  if ( FT_ABS( points[prev].x - best_x ) <= 20 * dist )
                    break;
  
                best_segment_first = prev;
  
                if ( FT_CURVE_TAG( outline.tags[prev] ) == FT_CURVE_TAG_ON )
                {
                  best_on_point_first = prev;
                  if ( best_on_point_last < 0 )
                    best_on_point_last = prev;
                }
  
              } while ( prev != best_point );
  
              do
              {
                if ( next < best_contour_last )
                  next++;
                else
                  next = best_contour_first;
  
                dist = FT_ABS( points[next].y - best_y );
                if ( dist > 5 )
                  if ( FT_ABS( points[next].x - best_x ) <= 20 * dist )
                    break;
  
                best_segment_last = next;
  
                if ( FT_CURVE_TAG( outline.tags[next] ) == FT_CURVE_TAG_ON )
                {
                  best_on_point_last = next;
                  if ( best_on_point_first < 0 )
                    best_on_point_first = next;
                }
  
              } while ( next != best_point );
  
              if ( AF_LATIN_IS_LONG_BLUE( bs ) )
              {
                /* If this flag is set, we have an additional constraint to  */
                /* get the blue zone distance: Find a segment of the topmost */
                /* (or bottommost) contour that is longer than a heuristic   */
                /* threshold.  This ensures that small bumps in the outline  */
                /* are ignored (for example, the `vertical serifs' found in  */
                /* many Hebrew glyph designs).                               */
  
                /* If this segment is long enough, we are done.  Otherwise,  */
                /* search the segment next to the extremum that is long      */
                /* enough, has the same direction, and a not too large       */
                /* vertical distance from the extremum.  Note that the       */
                /* algorithm doesn't check whether the found segment is      */
                /* actually the one (vertically) nearest to the extremum.    */
  
                /* heuristic threshold value */
                FT_Pos  length_threshold = metrics->units_per_em / 25;
  
  
                dist = FT_ABS( points[best_segment_last].x -
                                 points[best_segment_first].x );
  
                if ( dist < length_threshold                       &&
                     best_segment_last - best_segment_first + 2 <=
                       best_contour_last - best_contour_first      )
                {
                  /* heuristic threshold value */
                  FT_Pos  height_threshold = metrics->units_per_em / 4;
  
                  FT_Int   first;
                  FT_Int   last;
                  FT_Bool  hit;
  
                  /* we intentionally declare these two variables        */
                  /* outside of the loop since various compilers emit    */
                  /* incorrect warning messages otherwise, talking about */
                  /* `possibly uninitialized variables'                  */
                  FT_Int  p_first = 0;            /* make compiler happy */
                  FT_Int  p_last  = 0;
  
                  FT_Bool  left2right;
  
  
                  /* compute direction */
                  prev = best_point;
  
                  do
                  {
                    if ( prev > best_contour_first )
                      prev--;
                    else
                      prev = best_contour_last;
  
                    if ( points[prev].x != best_x )
                      break;
  
                  } while ( prev != best_point );
  
                  /* skip glyph for the degenerate case */
                  if ( prev == best_point )
                    continue;
  
                  left2right = FT_BOOL( points[prev].x < points[best_point].x );
  
                  first = best_segment_last;
                  last  = first;
                  hit   = 0;
  
                  do
                  {
                    FT_Bool  l2r;
                    FT_Pos   d;
  
  
                    if ( !hit )
                    {
                      /* no hit; adjust first point */
                      first = last;
  
                      /* also adjust first and last on point */
                      if ( FT_CURVE_TAG( outline.tags[first] ) ==
                             FT_CURVE_TAG_ON )
                      {
                        p_first = first;
                        p_last  = first;
                      }
                      else
                      {
                        p_first = -1;
                        p_last  = -1;
                      }
  
                      hit = 1;
                    }
  
                    if ( last < best_contour_last )
                      last++;
                    else
                      last = best_contour_first;
  
                    if ( FT_ABS( best_y - points[first].y ) > height_threshold )
                    {
                      /* vertical distance too large */
                      hit = 0;
                      continue;
                    }
  
                    /* same test as above */
                    dist = FT_ABS( points[last].y - points[first].y );
                    if ( dist > 5 )
                      if ( FT_ABS( points[last].x - points[first].x ) <=
                             20 * dist )
                      {
                        hit = 0;
                        continue;
                      }
  
                    if ( FT_CURVE_TAG( outline.tags[last] ) == FT_CURVE_TAG_ON )
                    {
                      p_last = last;
                      if ( p_first < 0 )
                        p_first = last;
                    }
  
                    l2r = FT_BOOL( points[first].x < points[last].x );
                    d   = FT_ABS( points[last].x - points[first].x );
  
                    if ( l2r == left2right     &&
                         d >= length_threshold )
                    {
                      /* all constraints are met; update segment after */
                      /* finding its end                               */
                      do
                      {
                        if ( last < best_contour_last )
                          last++;
                        else
                          last = best_contour_first;
  
                        d = FT_ABS( points[last].y - points[first].y );
                        if ( d > 5 )
                          if ( FT_ABS( points[next].x - points[first].x ) <=
                                 20 * dist )
                          {
                            if ( last > best_contour_first )
                              last--;
                            else
                              last = best_contour_last;
                            break;
                          }
  
                        p_last = last;
  
                        if ( FT_CURVE_TAG( outline.tags[last] ) ==
                               FT_CURVE_TAG_ON )
                        {
                          p_last = last;
                          if ( p_first < 0 )
                            p_first = last;
                        }
  
                      } while ( last != best_segment_first );
  
                      best_y = points[first].y;
  
                      best_segment_first = first;
                      best_segment_last  = last;
  
                      best_on_point_first = p_first;
                      best_on_point_last  = p_last;
  
                      break;
                    }
  
                  } while ( last != best_segment_first );
                }
              }
  
              /* for computing blue zones, we add the y offset as returned */
              /* by the currently used OpenType feature -- for example,    */
              /* superscript glyphs might be identical to subscript glyphs */
              /* with a vertical shift                                     */
              best_y += y_offset;
  
  #ifdef FT_DEBUG_LEVEL_TRACE
              if ( num_idx == 1 )
                FT_TRACE5(( "  U+%04lX: best_y = %5ld", ch, best_y ));
              else
                FT_TRACE5(( "  component %d of cluster starting with U+%04lX:"
                            " best_y = %5ld", i, ch, best_y ));
  #endif
  
              /* now set the `round' flag depending on the segment's kind: */
              /*                                                           */
              /* - if the horizontal distance between the first and last   */
              /*   `on' point is larger than a heuristic threshold         */
              /*   we have a flat segment                                  */
              /* - if either the first or the last point of the segment is */
              /*   an `off' point, the segment is round, otherwise it is   */
              /*   flat                                                    */
              if ( best_on_point_first >= 0                               &&
                   best_on_point_last >= 0                                &&
                   ( FT_ABS( points[best_on_point_last].x -
                             points[best_on_point_first].x ) ) >
                     flat_threshold                                       )
                round = 0;
              else
                round = FT_BOOL(
                          FT_CURVE_TAG( outline.tags[best_segment_first] ) !=
                            FT_CURVE_TAG_ON                                   ||
                          FT_CURVE_TAG( outline.tags[best_segment_last]  ) !=
                            FT_CURVE_TAG_ON                                   );
  
              if ( round && AF_LATIN_IS_NEUTRAL_BLUE( bs ) )
              {
                /* only use flat segments for a neutral blue zone */
                FT_TRACE5(( " (round, skipped)\n" ));
                continue;
              }
  
              FT_TRACE5(( " (%s)\n", round ? "round" : "flat" ));
            }
  
            if ( AF_LATIN_IS_TOP_BLUE( bs ) )
            {
              if ( best_y > best_y_extremum )
              {
                best_y_extremum = best_y;
                best_round      = round;
              }
            }
            else
            {
              if ( best_y < best_y_extremum )
              {
                best_y_extremum = best_y;
                best_round      = round;
              }
            }
  
          } /* end for loop */
  
          if ( !( best_y_extremum == FT_INT_MIN ||
                  best_y_extremum == FT_INT_MAX ) )
          {
            if ( best_round )
              rounds[num_rounds++] = best_y_extremum;
            else
              flats[num_flats++]   = best_y_extremum;
          }
  
        } /* end while loop */
  
        if ( num_flats == 0 && num_rounds == 0 )
        {
          /*
           *  we couldn't find a single glyph to compute this blue zone,
           *  we will simply ignore it then
           */
          FT_TRACE5(( "  empty\n" ));
          continue;
        }
  
        /* we have computed the contents of the `rounds' and `flats' tables, */
        /* now determine the reference and overshoot position of the blue -- */
        /* we simply take the median value after a simple sort               */
        af_sort_pos( num_rounds, rounds );
        af_sort_pos( num_flats,  flats );
  
        blue       = &axis->blues[axis->blue_count];
        blue_ref   = &blue->ref.org;
        blue_shoot = &blue->shoot.org;
  
        axis->blue_count++;
  
        if ( num_flats == 0 )
        {
          *blue_ref   =
          *blue_shoot = rounds[num_rounds / 2];
        }
        else if ( num_rounds == 0 )
        {
          *blue_ref   =
          *blue_shoot = flats[num_flats / 2];
        }
        else
        {
          *blue_ref   = flats [num_flats  / 2];
          *blue_shoot = rounds[num_rounds / 2];
        }
  
        /* there are sometimes problems: if the overshoot position of top     */
        /* zones is under its reference position, or the opposite for bottom  */
        /* zones.  We must thus check everything there and correct the errors */
        if ( *blue_shoot != *blue_ref )
        {
          FT_Pos   ref      = *blue_ref;
          FT_Pos   shoot    = *blue_shoot;
          FT_Bool  over_ref = FT_BOOL( shoot > ref );
  
  
          if ( ( AF_LATIN_IS_TOP_BLUE( bs )    ||
                 AF_LATIN_IS_SUB_TOP_BLUE( bs) ) ^ over_ref )
          {
            *blue_ref   =
            *blue_shoot = ( shoot + ref ) / 2;
  
            FT_TRACE5(( "  [overshoot smaller than reference,"
                        " taking mean value]\n" ));
          }
        }
  
        blue->ascender  = ascender;
        blue->descender = descender;
  
        blue->flags = 0;
        if ( AF_LATIN_IS_TOP_BLUE( bs ) )
          blue->flags |= AF_LATIN_BLUE_TOP;
        if ( AF_LATIN_IS_SUB_TOP_BLUE( bs ) )
          blue->flags |= AF_LATIN_BLUE_SUB_TOP;
        if ( AF_LATIN_IS_NEUTRAL_BLUE( bs ) )
          blue->flags |= AF_LATIN_BLUE_NEUTRAL;
  
        /*
         * The following flag is used later to adjust the y and x scales
         * in order to optimize the pixel grid alignment of the top of small
         * letters.
         */
        if ( AF_LATIN_IS_X_HEIGHT_BLUE( bs ) )
          blue->flags |= AF_LATIN_BLUE_ADJUSTMENT;
  
        FT_TRACE5(( "    -> reference = %ld\n"
                    "       overshoot = %ld\n",
                    *blue_ref, *blue_shoot ));
  
      } /* end for loop */
  
      af_shaper_buf_destroy( face, shaper_buf );
  
      /* we finally check whether blue zones are ordered; */
      /* `ref' and `shoot' values of two blue zones must not overlap */
      if ( axis->blue_count )
      {
        FT_UInt       i;
        AF_LatinBlue  blue_sorted[AF_BLUE_STRINGSET_MAX_LEN + 2];
  
  
        for ( i = 0; i < axis->blue_count; i++ )
          blue_sorted[i] = &axis->blues[i];
  
        /* sort bottoms of blue zones... */
        af_latin_sort_blue( axis->blue_count, blue_sorted );
  
        /* ...and adjust top values if necessary */
        for ( i = 0; i < axis->blue_count - 1; i++ )
        {
          FT_Pos*  a;
          FT_Pos*  b;
  
  #ifdef FT_DEBUG_LEVEL_TRACE
          FT_Bool  a_is_top = 0;
  #endif
  
  
          if ( blue_sorted[i]->flags & ( AF_LATIN_BLUE_TOP     |
                                         AF_LATIN_BLUE_SUB_TOP ) )
          {
            a = &blue_sorted[i]->shoot.org;
  #ifdef FT_DEBUG_LEVEL_TRACE
            a_is_top = 1;
  #endif
          }
          else
            a = &blue_sorted[i]->ref.org;
  
          if ( blue_sorted[i + 1]->flags & ( AF_LATIN_BLUE_TOP     |
                                             AF_LATIN_BLUE_SUB_TOP ) )
            b = &blue_sorted[i + 1]->shoot.org;
          else
            b = &blue_sorted[i + 1]->ref.org;
  
          if ( *a > *b )
          {
            *a = *b;
            FT_TRACE5(( "blue zone overlap:"
                        " adjusting %s %d to %ld\n",
                        a_is_top ? "overshoot" : "reference",
                        blue_sorted[i] - axis->blues,
                        *a ));
          }
        }
      }
  
      FT_TRACE5(( "\n" ));
  
      return;
    }
  
  
    /* Check whether all ASCII digits have the same advance width. */
  
    FT_LOCAL_DEF( void )
    af_latin_metrics_check_digits( AF_LatinMetrics  metrics,
                                   FT_Face          face )
    {
      FT_Bool   started = 0, same_width = 1;
      FT_Fixed  advance = 0, old_advance = 0;
  
      void*  shaper_buf;
  
      /* in all supported charmaps, digits have character codes 0x30-0x39 */
      const char   digits[] = "0 1 2 3 4 5 6 7 8 9";
      const char*  p;
  
  
      p          = digits;
      shaper_buf = af_shaper_buf_create( face );
  
      while ( *p )
      {
        FT_ULong      glyph_index;
        unsigned int  num_idx;
  
  
        /* reject input that maps to more than a single glyph */
        p = af_shaper_get_cluster( p, &metrics->root, shaper_buf, &num_idx );
        if ( num_idx > 1 )
          continue;
  
        glyph_index = af_shaper_get_elem( &metrics->root,
                                          shaper_buf,
                                          0,
                                          &advance,
                                          NULL );
        if ( !glyph_index )
          continue;
  
        if ( started )
        {
          if ( advance != old_advance )
          {
            same_width = 0;
            break;
          }
        }
        else
        {
          old_advance = advance;
          started     = 1;
        }
      }
  
      af_shaper_buf_destroy( face, shaper_buf );
  
      metrics->root.digits_have_same_width = same_width;
    }
  
  
    /* Initialize global metrics. */
  
    FT_LOCAL_DEF( FT_Error )
    af_latin_metrics_init( AF_LatinMetrics  metrics,
                           FT_Face          face )
    {
      FT_CharMap  oldmap = face->charmap;
  
  
      metrics->units_per_em = face->units_per_EM;
  
      if ( !FT_Select_Charmap( face, FT_ENCODING_UNICODE ) )
      {
        af_latin_metrics_init_widths( metrics, face );
        af_latin_metrics_init_blues( metrics, face );
        af_latin_metrics_check_digits( metrics, face );
      }
  
      FT_Set_Charmap( face, oldmap );
      return FT_Err_Ok;
    }
  
  
    /* Adjust scaling value, then scale and shift widths   */
    /* and blue zones (if applicable) for given dimension. */
  
    static void
    af_latin_metrics_scale_dim( AF_LatinMetrics  metrics,
                                AF_Scaler        scaler,
                                AF_Dimension     dim )
    {
      FT_Fixed      scale;
      FT_Pos        delta;
      AF_LatinAxis  axis;
      FT_UInt       nn;
  
  
      if ( dim == AF_DIMENSION_HORZ )
      {
        scale = scaler->x_scale;
        delta = scaler->x_delta;
      }
      else
      {
        scale = scaler->y_scale;
        delta = scaler->y_delta;
      }
  
      axis = &metrics->axis[dim];
  
      if ( axis->org_scale == scale && axis->org_delta == delta )
        return;
  
      axis->org_scale = scale;
      axis->org_delta = delta;
  
      /*
       * correct X and Y scale to optimize the alignment of the top of small
       * letters to the pixel grid
       */
      {
        AF_LatinAxis  Axis = &metrics->axis[AF_DIMENSION_VERT];
        AF_LatinBlue  blue = NULL;
  
  
        for ( nn = 0; nn < Axis->blue_count; nn++ )
        {
          if ( Axis->blues[nn].flags & AF_LATIN_BLUE_ADJUSTMENT )
          {
            blue = &Axis->blues[nn];
            break;
          }
        }
  
        if ( blue )
        {
          FT_Pos   scaled;
          FT_Pos   threshold;
          FT_Pos   fitted;
          FT_UInt  limit;
          FT_UInt  ppem;
  
  
          scaled    = FT_MulFix( blue->shoot.org, scale );
          ppem      = metrics->root.scaler.face->size->metrics.x_ppem;
          limit     = metrics->root.globals->increase_x_height;
          threshold = 40;
  
          /* if the `increase-x-height' property is active, */
          /* we round up much more often                    */
          if ( limit                                 &&
               ppem <= limit                         &&
               ppem >= AF_PROP_INCREASE_X_HEIGHT_MIN )
            threshold = 52;
  
          fitted = ( scaled + threshold ) & ~63;
  
          if ( scaled != fitted )
          {
  #if 0
            if ( dim == AF_DIMENSION_HORZ )
            {
              if ( fitted < scaled )
                scale -= scale / 50;  /* scale *= 0.98 */
            }
            else
  #endif
            if ( dim == AF_DIMENSION_VERT )
            {
              FT_Pos    max_height;
              FT_Pos    dist;
              FT_Fixed  new_scale;
  
  
              new_scale = FT_MulDiv( scale, fitted, scaled );
  
              /* the scaling should not change the result by more than two pixels */
              max_height = metrics->units_per_em;
  
              for ( nn = 0; nn < Axis->blue_count; nn++ )
              {
                max_height = FT_MAX( max_height, Axis->blues[nn].ascender );
                max_height = FT_MAX( max_height, -Axis->blues[nn].descender );
              }
  
              dist  = FT_ABS( FT_MulFix( max_height, new_scale - scale ) );
              dist &= ~127;
  
              if ( dist == 0 )
              {
                FT_TRACE5((
                  "af_latin_metrics_scale_dim:"
                  " x height alignment (style `%s'):\n"
                  "                           "
                  " vertical scaling changed from %.5f to %.5f (by %d%%)\n"
                  "\n",
                  af_style_names[metrics->root.style_class->style],
                  scale / 65536.0,
                  new_scale / 65536.0,
                  ( fitted - scaled ) * 100 / scaled ));
  
                scale = new_scale;
              }
  #ifdef FT_DEBUG_LEVEL_TRACE
              else
              {
                FT_TRACE5((
                  "af_latin_metrics_scale_dim:"
                  " x height alignment (style `%s'):\n"
                  "                           "
                  " excessive vertical scaling abandoned\n"
                  "\n",
                  af_style_names[metrics->root.style_class->style] ));
              }
  #endif
            }
          }
        }
      }
  
      axis->scale = scale;
      axis->delta = delta;
  
      if ( dim == AF_DIMENSION_HORZ )
      {
        metrics->root.scaler.x_scale = scale;
        metrics->root.scaler.x_delta = delta;
      }
      else
      {
        metrics->root.scaler.y_scale = scale;
        metrics->root.scaler.y_delta = delta;
      }
  
      FT_TRACE5(( "%s widths (style `%s')\n",
                  dim == AF_DIMENSION_HORZ ? "horizontal" : "vertical",
                  af_style_names[metrics->root.style_class->style] ));
  
      /* scale the widths */
      for ( nn = 0; nn < axis->width_count; nn++ )
      {
        AF_Width  width = axis->widths + nn;
  
  
        width->cur = FT_MulFix( width->org, scale );
        width->fit = width->cur;
  
        FT_TRACE5(( "  %d scaled to %.2f\n",
                    width->org,
                    width->cur / 64.0 ));
      }
  
      FT_TRACE5(( "\n" ));
  
      /* an extra-light axis corresponds to a standard width that is */
      /* smaller than 5/8 pixels                                     */
      axis->extra_light =
        (FT_Bool)( FT_MulFix( axis->standard_width, scale ) < 32 + 8 );
  
  #ifdef FT_DEBUG_LEVEL_TRACE
      if ( axis->extra_light )
        FT_TRACE5(( "`%s' style is extra light (at current resolution)\n"
                    "\n",
                    af_style_names[metrics->root.style_class->style] ));
  #endif
  
      if ( dim == AF_DIMENSION_VERT )
      {
  #ifdef FT_DEBUG_LEVEL_TRACE
        if ( axis->blue_count )
          FT_TRACE5(( "blue zones (style `%s')\n",
                      af_style_names[metrics->root.style_class->style] ));
  #endif
  
        /* scale the blue zones */
        for ( nn = 0; nn < axis->blue_count; nn++ )
        {
          AF_LatinBlue  blue = &axis->blues[nn];
          FT_Pos        dist;
  
  
          blue->ref.cur   = FT_MulFix( blue->ref.org, scale ) + delta;
          blue->ref.fit   = blue->ref.cur;
          blue->shoot.cur = FT_MulFix( blue->shoot.org, scale ) + delta;
          blue->shoot.fit = blue->shoot.cur;
          blue->flags    &= ~AF_LATIN_BLUE_ACTIVE;
  
          /* a blue zone is only active if it is less than 3/4 pixels tall */
          dist = FT_MulFix( blue->ref.org - blue->shoot.org, scale );
          if ( dist <= 48 && dist >= -48 )
          {
  #if 0
            FT_Pos  delta1;
  #endif
            FT_Pos  delta2;
  
  
            /* use discrete values for blue zone widths */
  
  #if 0
  
            /* generic, original code */
            delta1 = blue->shoot.org - blue->ref.org;
            delta2 = delta1;
            if ( delta1 < 0 )
              delta2 = -delta2;
  
            delta2 = FT_MulFix( delta2, scale );
  
            if ( delta2 < 32 )
              delta2 = 0;
            else if ( delta2 < 64 )
              delta2 = 32 + ( ( ( delta2 - 32 ) + 16 ) & ~31 );
            else
              delta2 = FT_PIX_ROUND( delta2 );
  
            if ( delta1 < 0 )
              delta2 = -delta2;
  
            blue->ref.fit   = FT_PIX_ROUND( blue->ref.cur );
            blue->shoot.fit = blue->ref.fit + delta2;
  
  #else
  
            /* simplified version due to abs(dist) <= 48 */
            delta2 = dist;
            if ( dist < 0 )
              delta2 = -delta2;
  
            if ( delta2 < 32 )
              delta2 = 0;
            else if ( delta2 < 48 )
              delta2 = 32;
            else
              delta2 = 64;
  
            if ( dist < 0 )
              delta2 = -delta2;
  
            blue->ref.fit   = FT_PIX_ROUND( blue->ref.cur );
            blue->shoot.fit = blue->ref.fit - delta2;
  
  #endif
  
            blue->flags |= AF_LATIN_BLUE_ACTIVE;
          }
        }
  
        /* use sub-top blue zone only if it doesn't overlap with */
        /* another (non-sup-top) blue zone; otherwise, the       */
        /* effect would be similar to a neutral blue zone, which */
        /* is not desired here                                   */
        for ( nn = 0; nn < axis->blue_count; nn++ )
        {
          AF_LatinBlue  blue = &axis->blues[nn];
          FT_UInt       i;
  
  
          if ( !( blue->flags & AF_LATIN_BLUE_SUB_TOP ) )
            continue;
          if ( !( blue->flags & AF_LATIN_BLUE_ACTIVE ) )
            continue;
  
          for ( i = 0; i < axis->blue_count; i++ )
          {
            AF_LatinBlue  b = &axis->blues[i];
  
  
            if ( b->flags & AF_LATIN_BLUE_SUB_TOP )
              continue;
            if ( !( b->flags & AF_LATIN_BLUE_ACTIVE ) )
              continue;
  
            if ( b->ref.fit <= blue->shoot.fit &&
                 b->shoot.fit >= blue->ref.fit )
            {
              blue->flags &= ~AF_LATIN_BLUE_ACTIVE;
              break;
            }
          }
        }
  
  #ifdef FT_DEBUG_LEVEL_TRACE
        for ( nn = 0; nn < axis->blue_count; nn++ )
        {
          AF_LatinBlue  blue = &axis->blues[nn];
  
  
          FT_TRACE5(( "  reference %d: %d scaled to %.2f%s\n"
                      "  overshoot %d: %d scaled to %.2f%s\n",
                      nn,
                      blue->ref.org,
                      blue->ref.fit / 64.0,
                      blue->flags & AF_LATIN_BLUE_ACTIVE ? ""
                                                         : " (inactive)",
                      nn,
                      blue->shoot.org,
                      blue->shoot.fit / 64.0,
                      blue->flags & AF_LATIN_BLUE_ACTIVE ? ""
                                                         : " (inactive)" ));
        }
  #endif
      }
    }
  
  
    /* Scale global values in both directions. */
  
    FT_LOCAL_DEF( void )
    af_latin_metrics_scale( AF_LatinMetrics  metrics,
                            AF_Scaler        scaler )
    {
      metrics->root.scaler.render_mode = scaler->render_mode;
      metrics->root.scaler.face        = scaler->face;
      metrics->root.scaler.flags       = scaler->flags;
  
      af_latin_metrics_scale_dim( metrics, scaler, AF_DIMENSION_HORZ );
      af_latin_metrics_scale_dim( metrics, scaler, AF_DIMENSION_VERT );
    }
  
  
    /* Extract standard_width from writing system/script specific */
    /* metrics class.                                             */
  
    FT_LOCAL_DEF( void )
    af_latin_get_standard_widths( AF_LatinMetrics  metrics,
                                  FT_Pos*          stdHW,
                                  FT_Pos*          stdVW )
    {
      if ( stdHW )
        *stdHW = metrics->axis[AF_DIMENSION_VERT].standard_width;
  
      if ( stdVW )
        *stdVW = metrics->axis[AF_DIMENSION_HORZ].standard_width;
    }
  
  
    /*************************************************************************/
    /*************************************************************************/
    /*****                                                               *****/
    /*****           L A T I N   G L Y P H   A N A L Y S I S             *****/
    /*****                                                               *****/
    /*************************************************************************/
    /*************************************************************************/
  
  
    /* Walk over all contours and compute its segments. */
  
    FT_LOCAL_DEF( FT_Error )
    af_latin_hints_compute_segments( AF_GlyphHints  hints,
                                     AF_Dimension   dim )
    {
      AF_LatinMetrics  metrics       = (AF_LatinMetrics)hints->metrics;
      AF_AxisHints     axis          = &hints->axis[dim];
      FT_Memory        memory        = hints->memory;
      FT_Error         error         = FT_Err_Ok;
      AF_Segment       segment       = NULL;
      AF_SegmentRec    seg0;
      AF_Point*        contour       = hints->contours;
      AF_Point*        contour_limit = contour + hints->num_contours;
      AF_Direction     major_dir, segment_dir;
  
      FT_Pos  flat_threshold = FLAT_THRESHOLD( metrics->units_per_em );
  
  
      FT_ZERO( &seg0 );
      seg0.score = 32000;
      seg0.flags = AF_EDGE_NORMAL;
  
      major_dir   = (AF_Direction)FT_ABS( axis->major_dir );
      segment_dir = major_dir;
  
      axis->num_segments = 0;
  
      /* set up (u,v) in each point */
      if ( dim == AF_DIMENSION_HORZ )
      {
        AF_Point  point = hints->points;
        AF_Point  limit = point + hints->num_points;
  
  
        for ( ; point < limit; point++ )
        {
          point->u = point->fx;
          point->v = point->fy;
        }
      }
      else
      {
        AF_Point  point = hints->points;
        AF_Point  limit = point + hints->num_points;
  
  
        for ( ; point < limit; point++ )
        {
          point->u = point->fy;
          point->v = point->fx;
        }
      }
  
      /* do each contour separately */
      for ( ; contour < contour_limit; contour++ )
      {
        AF_Point  point   = contour[0];
        AF_Point  last    = point->prev;
        int       on_edge = 0;
  
        /* we call values measured along a segment (point->v)    */
        /* `coordinates', and values orthogonal to it (point->u) */
        /* `positions'                                           */
        FT_Pos     min_pos      =  32000;
        FT_Pos     max_pos      = -32000;
        FT_Pos     min_coord    =  32000;
        FT_Pos     max_coord    = -32000;
        FT_UShort  min_flags    =  AF_FLAG_NONE;
        FT_UShort  max_flags    =  AF_FLAG_NONE;
        FT_Pos     min_on_coord =  32000;
        FT_Pos     max_on_coord = -32000;
  
        FT_Bool  passed;
  
        AF_Segment  prev_segment = NULL;
  
        FT_Pos     prev_min_pos      = min_pos;
        FT_Pos     prev_max_pos      = max_pos;
        FT_Pos     prev_min_coord    = min_coord;
        FT_Pos     prev_max_coord    = max_coord;
        FT_UShort  prev_min_flags    = min_flags;
        FT_UShort  prev_max_flags    = max_flags;
        FT_Pos     prev_min_on_coord = min_on_coord;
        FT_Pos     prev_max_on_coord = max_on_coord;
  
  
        if ( FT_ABS( last->out_dir )  == major_dir &&
             FT_ABS( point->out_dir ) == major_dir )
        {
          /* we are already on an edge, try to locate its start */
          last = point;
  
          for (;;)
          {
            point = point->prev;
            if ( FT_ABS( point->out_dir ) != major_dir )
            {
              point = point->next;
              break;
            }
            if ( point == last )
              break;
          }
        }
  
        last   = point;
        passed = 0;
  
        for (;;)
        {
          FT_Pos  u, v;
  
  
          if ( on_edge )
          {
            /* get minimum and maximum position */
            u = point->u;
            if ( u < min_pos )
              min_pos = u;
            if ( u > max_pos )
              max_pos = u;
  
            /* get minimum and maximum coordinate together with flags */
            v = point->v;
            if ( v < min_coord )
            {
              min_coord = v;
              min_flags = point->flags;
            }
            if ( v > max_coord )
            {
              max_coord = v;
              max_flags = point->flags;
            }
  
            /* get minimum and maximum coordinate of `on' points */
            if ( !( point->flags & AF_FLAG_CONTROL ) )
            {
              v = point->v;
              if ( v < min_on_coord )
                min_on_coord = v;
              if ( v > max_on_coord )
                max_on_coord = v;
            }
  
            if ( point->out_dir != segment_dir || point == last )
            {
              /* check whether the new segment's start point is identical to */
              /* the previous segment's end point; for example, this might   */
              /* happen for spikes                                           */
  
              if ( !prev_segment || segment->first != prev_segment->last )
              {
                /* points are different: we are just leaving an edge, thus */
                /* record a new segment                                    */
  
                segment->last  = point;
                segment->pos   = (FT_Short)( ( min_pos + max_pos ) >> 1 );
                segment->delta = (FT_Short)( ( max_pos - min_pos ) >> 1 );
  
                /* a segment is round if either its first or last point */
                /* is a control point, and the length of the on points  */
                /* inbetween doesn't exceed a heuristic limit           */
                if ( ( min_flags | max_flags ) & AF_FLAG_CONTROL      &&
                     ( max_on_coord - min_on_coord ) < flat_threshold )
                  segment->flags |= AF_EDGE_ROUND;
  
                segment->min_coord = (FT_Short)min_coord;
                segment->max_coord = (FT_Short)max_coord;
                segment->height    = segment->max_coord - segment->min_coord;
  
                prev_segment      = segment;
                prev_min_pos      = min_pos;
                prev_max_pos      = max_pos;
                prev_min_coord    = min_coord;
                prev_max_coord    = max_coord;
                prev_min_flags    = min_flags;
                prev_max_flags    = max_flags;
                prev_min_on_coord = min_on_coord;
                prev_max_on_coord = max_on_coord;
              }
              else
              {
                /* points are the same: we don't create a new segment but */
                /* merge the current segment with the previous one        */
  
                if ( prev_segment->last->in_dir == point->in_dir )
                {
                  /* we have identical directions (this can happen for       */
                  /* degenerate outlines that move zig-zag along the main    */
                  /* axis without changing the coordinate value of the other */
                  /* axis, and where the segments have just been merged):    */
                  /* unify segments                                          */
  
                  /* update constraints */
  
                  if ( prev_min_pos < min_pos )
                    min_pos = prev_min_pos;
                  if ( prev_max_pos > max_pos )
                    max_pos = prev_max_pos;
  
                  if ( prev_min_coord < min_coord )
                  {
                    min_coord = prev_min_coord;
                    min_flags = prev_min_flags;
                  }
                  if ( prev_max_coord > max_coord )
                  {
                    max_coord = prev_max_coord;
                    max_flags = prev_max_flags;
                  }
  
                  if ( prev_min_on_coord < min_on_coord )
                    min_on_coord = prev_min_on_coord;
                  if ( prev_max_on_coord > max_on_coord )
                    max_on_coord = prev_max_on_coord;
  
                  prev_segment->last = point;
                  prev_segment->pos  = (FT_Short)( ( min_pos +
                                                     max_pos ) >> 1 );
  
                  if ( ( min_flags | max_flags ) & AF_FLAG_CONTROL      &&
                       ( max_on_coord - min_on_coord ) < flat_threshold )
                    prev_segment->flags |= AF_EDGE_ROUND;
                  else
                    prev_segment->flags &= ~AF_EDGE_ROUND;
  
                  prev_segment->min_coord = (FT_Short)min_coord;
                  prev_segment->max_coord = (FT_Short)max_coord;
                  prev_segment->height    = prev_segment->max_coord -
                                            prev_segment->min_coord;
                }
                else
                {
                  /* we have different directions; use the properties of the */
                  /* longer segment and discard the other one                */
  
                  if ( FT_ABS( prev_max_coord - prev_min_coord ) >
                       FT_ABS( max_coord - min_coord ) )
                  {
                    /* discard current segment */
  
                    if ( min_pos < prev_min_pos )
                      prev_min_pos = min_pos;
                    if ( max_pos > prev_max_pos )
                      prev_max_pos = max_pos;
  
                    prev_segment->last = point;
                    prev_segment->pos  = (FT_Short)( ( prev_min_pos +
                                                       prev_max_pos ) >> 1 );
                  }
                  else
                  {
                    /* discard previous segment */
  
                    if ( prev_min_pos < min_pos )
                      min_pos = prev_min_pos;
                    if ( prev_max_pos > max_pos )
                      max_pos = prev_max_pos;
  
                    segment->last = point;
                    segment->pos  = (FT_Short)( ( min_pos + max_pos ) >> 1 );
  
                    if ( ( min_flags | max_flags ) & AF_FLAG_CONTROL      &&
                         ( max_on_coord - min_on_coord ) < flat_threshold )
                      segment->flags |= AF_EDGE_ROUND;
  
                    segment->min_coord = (FT_Short)min_coord;
                    segment->max_coord = (FT_Short)max_coord;
                    segment->height    = segment->max_coord -
                                         segment->min_coord;
  
                    *prev_segment = *segment;
  
                    prev_min_pos      = min_pos;
                    prev_max_pos      = max_pos;
                    prev_min_coord    = min_coord;
                    prev_max_coord    = max_coord;
                    prev_min_flags    = min_flags;
                    prev_max_flags    = max_flags;
                    prev_min_on_coord = min_on_coord;
                    prev_max_on_coord = max_on_coord;
                  }
                }
  
                axis->num_segments--;
              }
  
              on_edge = 0;
              segment = NULL;
  
              /* fall through */
            }
          }
  
          /* now exit if we are at the start/end point */
          if ( point == last )
          {
            if ( passed )
              break;
            passed = 1;
          }
  
          /* if we are not on an edge, check whether the major direction */
          /* coincides with the current point's `out' direction, or      */
          /* whether we have a single-point contour                      */
          if ( !on_edge                                  &&
               ( FT_ABS( point->out_dir ) == major_dir ||
                 point == point->prev                  ) )
          {
            /* this is the start of a new segment! */
            segment_dir = (AF_Direction)point->out_dir;
  
            error = af_axis_hints_new_segment( axis, memory, &segment );
            if ( error )
              goto Exit;
  
            /* clear all segment fields */
            segment[0] = seg0;
  
            segment->dir   = (FT_Char)segment_dir;
            segment->first = point;
            segment->last  = point;
  
            /* `af_axis_hints_new_segment' reallocates memory,    */
            /* thus we have to refresh the `prev_segment' pointer */
            if ( prev_segment )
              prev_segment = segment - 1;
  
            min_pos   = max_pos   = point->u;
            min_coord = max_coord = point->v;
            min_flags = max_flags = point->flags;
  
            if ( point->flags & AF_FLAG_CONTROL )
            {
              min_on_coord =  32000;
              max_on_coord = -32000;
            }
            else
              min_on_coord = max_on_coord = point->v;
  
            on_edge = 1;
  
            if ( point == point->prev )
            {
              /* we have a one-point segment: this is a one-point */
              /* contour with `in' and `out' direction set to     */
              /* AF_DIR_NONE                                      */
              segment->pos = (FT_Short)min_pos;
  
              if (point->flags & AF_FLAG_CONTROL)
                segment->flags |= AF_EDGE_ROUND;
  
              segment->min_coord = (FT_Short)point->v;
              segment->max_coord = (FT_Short)point->v;
              segment->height = 0;
  
              on_edge = 0;
              segment = NULL;
            }
          }
  
          point = point->next;
        }
  
      } /* contours */
  
  
      /* now slightly increase the height of segments if this makes */
      /* sense -- this is used to better detect and ignore serifs   */
      {
        AF_Segment  segments     = axis->segments;
        AF_Segment  segments_end = segments + axis->num_segments;
  
  
        for ( segment = segments; segment < segments_end; segment++ )
        {
          AF_Point  first   = segment->first;
          AF_Point  last    = segment->last;
          FT_Pos    first_v = first->v;
          FT_Pos    last_v  = last->v;
  
  
          if ( first_v < last_v )
          {
            AF_Point  p;
  
  
            p = first->prev;
            if ( p->v < first_v )
              segment->height = (FT_Short)( segment->height +
                                            ( ( first_v - p->v ) >> 1 ) );
  
            p = last->next;
            if ( p->v > last_v )
              segment->height = (FT_Short)( segment->height +
                                            ( ( p->v - last_v ) >> 1 ) );
          }
          else
          {
            AF_Point  p;
  
  
            p = first->prev;
            if ( p->v > first_v )
              segment->height = (FT_Short)( segment->height +
                                            ( ( p->v - first_v ) >> 1 ) );
  
            p = last->next;
            if ( p->v < last_v )
              segment->height = (FT_Short)( segment->height +
                                            ( ( last_v - p->v ) >> 1 ) );
          }
        }
      }
  
    Exit:
      return error;
    }
  
  
    /* Link segments to form stems and serifs.  If `width_count' and      */
    /* `widths' are non-zero, use them to fine-tune the scoring function. */
  
    FT_LOCAL_DEF( void )
    af_latin_hints_link_segments( AF_GlyphHints  hints,
                                  FT_UInt        width_count,
                                  AF_WidthRec*   widths,
                                  AF_Dimension   dim )
    {
      AF_AxisHints  axis          = &hints->axis[dim];
      AF_Segment    segments      = axis->segments;
      AF_Segment    segment_limit = segments + axis->num_segments;
      FT_Pos        len_threshold, len_score, dist_score, max_width;
      AF_Segment    seg1, seg2;
  
  
      if ( width_count )
        max_width = widths[width_count - 1].org;
      else
        max_width = 0;
  
      /* a heuristic value to set up a minimum value for overlapping */
      len_threshold = AF_LATIN_CONSTANT( hints->metrics, 8 );
      if ( len_threshold == 0 )
        len_threshold = 1;
  
      /* a heuristic value to weight lengths */
      len_score = AF_LATIN_CONSTANT( hints->metrics, 6000 );
  
      /* a heuristic value to weight distances (no call to    */
      /* AF_LATIN_CONSTANT needed, since we work on multiples */
      /* of the stem width)                                   */
      dist_score = 3000;
  
      /* now compare each segment to the others */
      for ( seg1 = segments; seg1 < segment_limit; seg1++ )
      {
        if ( seg1->dir != axis->major_dir )
          continue;
  
        /* search for stems having opposite directions, */
        /* with seg1 to the `left' of seg2              */
        for ( seg2 = segments; seg2 < segment_limit; seg2++ )
        {
          FT_Pos  pos1 = seg1->pos;
          FT_Pos  pos2 = seg2->pos;
  
  
          if ( seg1->dir + seg2->dir == 0 && pos2 > pos1 )
          {
            /* compute distance between the two segments */
            FT_Pos  min = seg1->min_coord;
            FT_Pos  max = seg1->max_coord;
            FT_Pos  len;
  
  
            if ( min < seg2->min_coord )
              min = seg2->min_coord;
  
            if ( max > seg2->max_coord )
              max = seg2->max_coord;
  
            /* compute maximum coordinate difference of the two segments */
            /* (this is, how much they overlap)                          */
            len = max - min;
            if ( len >= len_threshold )
            {
              /*
               *  The score is the sum of two demerits indicating the
               *  `badness' of a fit, measured along the segments' main axis
               *  and orthogonal to it, respectively.
               *
               *  o The less overlapping along the main axis, the worse it
               *    is, causing a larger demerit.
               *
               *  o The nearer the orthogonal distance to a stem width, the
               *    better it is, causing a smaller demerit.  For simplicity,
               *    however, we only increase the demerit for values that
               *    exceed the largest stem width.
               */
  
              FT_Pos  dist = pos2 - pos1;
  
              FT_Pos  dist_demerit, score;
  
  
              if ( max_width )
              {
                /* distance demerits are based on multiples of `max_width'; */
                /* we scale by 1024 for getting more precision              */
                FT_Pos  delta = ( dist << 10 ) / max_width - ( 1 << 10 );
  
  
                if ( delta > 10000 )
                  dist_demerit = 32000;
                else if ( delta > 0 )
                  dist_demerit = delta * delta / dist_score;
                else
                  dist_demerit = 0;
              }
              else
                dist_demerit = dist; /* default if no widths available */
  
              score = dist_demerit + len_score / len;
  
              /* and we search for the smallest score */
              if ( score < seg1->score )
              {
                seg1->score = score;
                seg1->link  = seg2;
              }
  
              if ( score < seg2->score )
              {
                seg2->score = score;
                seg2->link  = seg1;
              }
            }
          }
        }
      }
  
      /* now compute the `serif' segments, cf. explanations in `afhints.h' */
      for ( seg1 = segments; seg1 < segment_limit; seg1++ )
      {
        seg2 = seg1->link;
  
        if ( seg2 )
        {
          if ( seg2->link != seg1 )
          {
            seg1->link  = 0;
            seg1->serif = seg2->link;
          }
        }
      }
    }
  
  
    /* Link segments to edges, using feature analysis for selection. */
  
    FT_LOCAL_DEF( FT_Error )
    af_latin_hints_compute_edges( AF_GlyphHints  hints,
                                  AF_Dimension   dim )
    {
      AF_AxisHints  axis   = &hints->axis[dim];
      FT_Error      error  = FT_Err_Ok;
      FT_Memory     memory = hints->memory;
      AF_LatinAxis  laxis  = &((AF_LatinMetrics)hints->metrics)->axis[dim];
  
  #ifdef FT_CONFIG_OPTION_PIC
      AF_FaceGlobals  globals = hints->metrics->globals;
  #endif
  
      AF_StyleClass   style_class  = hints->metrics->style_class;
      AF_ScriptClass  script_class = AF_SCRIPT_CLASSES_GET
                                       [style_class->script];
  
      FT_Bool  top_to_bottom_hinting = 0;
  
      AF_Segment    segments      = axis->segments;
      AF_Segment    segment_limit = segments + axis->num_segments;
      AF_Segment    seg;
  
  #if 0
      AF_Direction  up_dir;
  #endif
      FT_Fixed      scale;
      FT_Pos        edge_distance_threshold;
      FT_Pos        segment_length_threshold;
      FT_Pos        segment_width_threshold;
  
  
      axis->num_edges = 0;
  
      scale = ( dim == AF_DIMENSION_HORZ ) ? hints->x_scale
                                           : hints->y_scale;
  
  #if 0
      up_dir = ( dim == AF_DIMENSION_HORZ ) ? AF_DIR_UP
                                            : AF_DIR_RIGHT;
  #endif
  
      if ( dim == AF_DIMENSION_VERT )
        top_to_bottom_hinting = script_class->top_to_bottom_hinting;
  
      /*
       *  We ignore all segments that are less than 1 pixel in length
       *  to avoid many problems with serif fonts.  We compute the
       *  corresponding threshold in font units.
       */
      if ( dim == AF_DIMENSION_HORZ )
        segment_length_threshold = FT_DivFix( 64, hints->y_scale );
      else
        segment_length_threshold = 0;
  
      /*
       *  Similarly, we ignore segments that have a width delta
       *  larger than 0.5px (i.e., a width larger than 1px).
       */
      segment_width_threshold = FT_DivFix( 32, scale );
  
      /*********************************************************************/
      /*                                                                   */
      /* We begin by generating a sorted table of edges for the current    */
      /* direction.  To do so, we simply scan each segment and try to find */
      /* an edge in our table that corresponds to its position.            */
      /*                                                                   */
      /* If no edge is found, we create and insert a new edge in the       */
      /* sorted table.  Otherwise, we simply add the segment to the edge's */
      /* list which gets processed in the second step to compute the       */
      /* edge's properties.                                                */
      /*                                                                   */
      /* Note that the table of edges is sorted along the segment/edge     */
      /* position.                                                         */
      /*                                                                   */
      /*********************************************************************/
  
      /* assure that edge distance threshold is at most 0.25px */
      edge_distance_threshold = FT_MulFix( laxis->edge_distance_threshold,
                                           scale );
      if ( edge_distance_threshold > 64 / 4 )
        edge_distance_threshold = 64 / 4;
  
      edge_distance_threshold = FT_DivFix( edge_distance_threshold,
                                           scale );
  
      for ( seg = segments; seg < segment_limit; seg++ )
      {
        AF_Edge  found = NULL;
        FT_Int   ee;
  
  
        /* ignore too short segments, too wide ones, and, in this loop, */
        /* one-point segments without a direction                       */
        if ( seg->height < segment_length_threshold ||
             seg->delta > segment_width_threshold   ||
             seg->dir == AF_DIR_NONE                )
          continue;
  
        /* A special case for serif edges: If they are smaller than */
        /* 1.5 pixels we ignore them.                               */
        if ( seg->serif                                     &&
             2 * seg->height < 3 * segment_length_threshold )
          continue;
  
        /* look for an edge corresponding to the segment */
        for ( ee = 0; ee < axis->num_edges; ee++ )
        {
          AF_Edge  edge = axis->edges + ee;
          FT_Pos   dist;
  
  
          dist = seg->pos - edge->fpos;
          if ( dist < 0 )
            dist = -dist;
  
          if ( dist < edge_distance_threshold && edge->dir == seg->dir )
          {
            found = edge;
            break;
          }
        }
  
        if ( !found )
        {
          AF_Edge  edge;
  
  
          /* insert a new edge in the list and */
          /* sort according to the position    */
          error = af_axis_hints_new_edge( axis, seg->pos,
                                          (AF_Direction)seg->dir,
                                          top_to_bottom_hinting,
                                          memory, &edge );
          if ( error )
            goto Exit;
  
          /* add the segment to the new edge's list */
          FT_ZERO( edge );
  
          edge->first    = seg;
          edge->last     = seg;
          edge->dir      = seg->dir;
          edge->fpos     = seg->pos;
          edge->opos     = FT_MulFix( seg->pos, scale );
          edge->pos      = edge->opos;
          seg->edge_next = seg;
        }
        else
        {
          /* if an edge was found, simply add the segment to the edge's */
          /* list                                                       */
          seg->edge_next         = found->first;
          found->last->edge_next = seg;
          found->last            = seg;
        }
      }
  
      /* we loop again over all segments to catch one-point segments   */
      /* without a direction: if possible, link them to existing edges */
      for ( seg = segments; seg < segment_limit; seg++ )
      {
        AF_Edge  found = NULL;
        FT_Int   ee;
  
  
        if ( seg->dir != AF_DIR_NONE )
          continue;
  
        /* look for an edge corresponding to the segment */
        for ( ee = 0; ee < axis->num_edges; ee++ )
        {
          AF_Edge  edge = axis->edges + ee;
          FT_Pos   dist;
  
  
          dist = seg->pos - edge->fpos;
          if ( dist < 0 )
            dist = -dist;
  
          if ( dist < edge_distance_threshold )
          {
            found = edge;
            break;
          }
        }
  
        /* one-point segments without a match are ignored */
        if ( found )
        {
          seg->edge_next         = found->first;
          found->last->edge_next = seg;
          found->last            = seg;
        }
      }
  
  
      /******************************************************************/
      /*                                                                */
      /* Good, we now compute each edge's properties according to the   */
      /* segments found on its position.  Basically, these are          */
      /*                                                                */
      /*  - the edge's main direction                                   */
      /*  - stem edge, serif edge or both (which defaults to stem then) */
      /*  - rounded edge, straight or both (which defaults to straight) */
      /*  - link for edge                                               */
      /*                                                                */
      /******************************************************************/
  
      /* first of all, set the `edge' field in each segment -- this is */
      /* required in order to compute edge links                       */
  
      /*
       * Note that removing this loop and setting the `edge' field of each
       * segment directly in the code above slows down execution speed for
       * some reasons on platforms like the Sun.
       */
      {
        AF_Edge  edges      = axis->edges;
        AF_Edge  edge_limit = edges + axis->num_edges;
        AF_Edge  edge;
  
  
        for ( edge = edges; edge < edge_limit; edge++ )
        {
          seg = edge->first;
          if ( seg )
            do
            {
              seg->edge = edge;
              seg       = seg->edge_next;
  
            } while ( seg != edge->first );
        }
  
        /* now compute each edge properties */
        for ( edge = edges; edge < edge_limit; edge++ )
        {
          FT_Int  is_round    = 0;  /* does it contain round segments?    */
          FT_Int  is_straight = 0;  /* does it contain straight segments? */
  #if 0
          FT_Pos  ups         = 0;  /* number of upwards segments         */
          FT_Pos  downs       = 0;  /* number of downwards segments       */
  #endif
  
  
          seg = edge->first;
  
          do
          {
            FT_Bool  is_serif;
  
  
            /* check for roundness of segment */
            if ( seg->flags & AF_EDGE_ROUND )
              is_round++;
            else
              is_straight++;
  
  #if 0
            /* check for segment direction */
            if ( seg->dir == up_dir )
              ups   += seg->max_coord - seg->min_coord;
            else
              downs += seg->max_coord - seg->min_coord;
  #endif
  
            /* check for links -- if seg->serif is set, then seg->link must */
            /* be ignored                                                   */
            is_serif = (FT_Bool)( seg->serif               &&
                                  seg->serif->edge         &&
                                  seg->serif->edge != edge );
  
            if ( ( seg->link && seg->link->edge ) || is_serif )
            {
              AF_Edge     edge2;
              AF_Segment  seg2;
  
  
              edge2 = edge->link;
              seg2  = seg->link;
  
              if ( is_serif )
              {
                seg2  = seg->serif;
                edge2 = edge->serif;
              }
  
              if ( edge2 )
              {
                FT_Pos  edge_delta;
                FT_Pos  seg_delta;
  
  
                edge_delta = edge->fpos - edge2->fpos;
                if ( edge_delta < 0 )
                  edge_delta = -edge_delta;
  
                seg_delta = seg->pos - seg2->pos;
                if ( seg_delta < 0 )
                  seg_delta = -seg_delta;
  
                if ( seg_delta < edge_delta )
                  edge2 = seg2->edge;
              }
              else
                edge2 = seg2->edge;
  
              if ( is_serif )
              {
                edge->serif   = edge2;
                edge2->flags |= AF_EDGE_SERIF;
              }
              else
                edge->link  = edge2;
            }
  
            seg = seg->edge_next;
  
          } while ( seg != edge->first );
  
          /* set the round/straight flags */
          edge->flags = AF_EDGE_NORMAL;
  
          if ( is_round > 0 && is_round >= is_straight )
            edge->flags |= AF_EDGE_ROUND;
  
  #if 0
          /* set the edge's main direction */
          edge->dir = AF_DIR_NONE;
  
          if ( ups > downs )
            edge->dir = (FT_Char)up_dir;
  
          else if ( ups < downs )
            edge->dir = (FT_Char)-up_dir;
  
          else if ( ups == downs )
            edge->dir = 0;  /* both up and down! */
  #endif
  
          /* get rid of serifs if link is set                 */
          /* XXX: This gets rid of many unpleasant artefacts! */
          /*      Example: the `c' in cour.pfa at size 13     */
  
          if ( edge->serif && edge->link )
            edge->serif = NULL;
        }
      }
  
    Exit:
      return error;
    }
  
  
    /* Detect segments and edges for given dimension. */
  
    FT_LOCAL_DEF( FT_Error )
    af_latin_hints_detect_features( AF_GlyphHints  hints,
                                    FT_UInt        width_count,
                                    AF_WidthRec*   widths,
                                    AF_Dimension   dim )
    {
      FT_Error  error;
  
  
      error = af_latin_hints_compute_segments( hints, dim );
      if ( !error )
      {
        af_latin_hints_link_segments( hints, width_count, widths, dim );
  
        error = af_latin_hints_compute_edges( hints, dim );
      }
  
      return error;
    }
  
  
    /* Compute all edges which lie within blue zones. */
  
    static void
    af_latin_hints_compute_blue_edges( AF_GlyphHints    hints,
                                       AF_LatinMetrics  metrics )
    {
      AF_AxisHints  axis       = &hints->axis[AF_DIMENSION_VERT];
      AF_Edge       edge       = axis->edges;
      AF_Edge       edge_limit = edge + axis->num_edges;
      AF_LatinAxis  latin      = &metrics->axis[AF_DIMENSION_VERT];
      FT_Fixed      scale      = latin->scale;
  
  
      /* compute which blue zones are active, i.e. have their scaled */
      /* size < 3/4 pixels                                           */
  
      /* for each horizontal edge search the blue zone which is closest */
      for ( ; edge < edge_limit; edge++ )
      {
        FT_UInt   bb;
        AF_Width  best_blue            = NULL;
        FT_Bool   best_blue_is_neutral = 0;
        FT_Pos    best_dist;                 /* initial threshold */
  
  
        /* compute the initial threshold as a fraction of the EM size */
        /* (the value 40 is heuristic)                                */
        best_dist = FT_MulFix( metrics->units_per_em / 40, scale );
  
        /* assure a minimum distance of 0.5px */
        if ( best_dist > 64 / 2 )
          best_dist = 64 / 2;
  
        for ( bb = 0; bb < latin->blue_count; bb++ )
        {
          AF_LatinBlue  blue = latin->blues + bb;
          FT_Bool       is_top_blue, is_neutral_blue, is_major_dir;
  
  
          /* skip inactive blue zones (i.e., those that are too large) */
          if ( !( blue->flags & AF_LATIN_BLUE_ACTIVE ) )
            continue;
  
          /* if it is a top zone, check for right edges (against the major */
          /* direction); if it is a bottom zone, check for left edges (in  */
          /* the major direction) -- this assumes the TrueType convention  */
          /* for the orientation of contours                               */
          is_top_blue =
            (FT_Byte)( ( blue->flags & ( AF_LATIN_BLUE_TOP     |
                                         AF_LATIN_BLUE_SUB_TOP ) ) != 0 );
          is_neutral_blue =
            (FT_Byte)( ( blue->flags & AF_LATIN_BLUE_NEUTRAL ) != 0);
          is_major_dir =
            FT_BOOL( edge->dir == axis->major_dir );
  
          /* neutral blue zones are handled for both directions */
          if ( is_top_blue ^ is_major_dir || is_neutral_blue )
          {
            FT_Pos  dist;
  
  
            /* first of all, compare it to the reference position */
            dist = edge->fpos - blue->ref.org;
            if ( dist < 0 )
              dist = -dist;
  
            dist = FT_MulFix( dist, scale );
            if ( dist < best_dist )
            {
              best_dist            = dist;
              best_blue            = &blue->ref;
              best_blue_is_neutral = is_neutral_blue;
            }
  
            /* now compare it to the overshoot position and check whether */
            /* the edge is rounded, and whether the edge is over the      */
            /* reference position of a top zone, or under the reference   */
            /* position of a bottom zone (provided we don't have a        */
            /* neutral blue zone)                                         */
            if ( edge->flags & AF_EDGE_ROUND &&
                 dist != 0                   &&
                 !is_neutral_blue            )
            {
              FT_Bool  is_under_ref = FT_BOOL( edge->fpos < blue->ref.org );
  
  
              if ( is_top_blue ^ is_under_ref )
              {
                dist = edge->fpos - blue->shoot.org;
                if ( dist < 0 )
                  dist = -dist;
  
                dist = FT_MulFix( dist, scale );
                if ( dist < best_dist )
                {
                  best_dist            = dist;
                  best_blue            = &blue->shoot;
                  best_blue_is_neutral = is_neutral_blue;
                }
              }
            }
          }
        }
  
        if ( best_blue )
        {
          edge->blue_edge = best_blue;
          if ( best_blue_is_neutral )
            edge->flags |= AF_EDGE_NEUTRAL;
        }
      }
    }
  
  
    /* Initalize hinting engine. */
  
    static FT_Error
    af_latin_hints_init( AF_GlyphHints    hints,
                         AF_LatinMetrics  metrics )
    {
      FT_Render_Mode  mode;
      FT_UInt32       scaler_flags, other_flags;
      FT_Face         face = metrics->root.scaler.face;
  
  
      af_glyph_hints_rescale( hints, (AF_StyleMetrics)metrics );
  
      /*
       *  correct x_scale and y_scale if needed, since they may have
       *  been modified by `af_latin_metrics_scale_dim' above
       */
      hints->x_scale = metrics->axis[AF_DIMENSION_HORZ].scale;
      hints->x_delta = metrics->axis[AF_DIMENSION_HORZ].delta;
      hints->y_scale = metrics->axis[AF_DIMENSION_VERT].scale;
      hints->y_delta = metrics->axis[AF_DIMENSION_VERT].delta;
  
      /* compute flags depending on render mode, etc. */
      mode = metrics->root.scaler.render_mode;
  
  #if 0 /* #ifdef AF_CONFIG_OPTION_USE_WARPER */
      if ( mode == FT_RENDER_MODE_LCD || mode == FT_RENDER_MODE_LCD_V )
        metrics->root.scaler.render_mode = mode = FT_RENDER_MODE_NORMAL;
  #endif
  
      scaler_flags = hints->scaler_flags;
      other_flags  = 0;
  
      /*
       *  We snap the width of vertical stems for the monochrome and
       *  horizontal LCD rendering targets only.
       */
      if ( mode == FT_RENDER_MODE_MONO || mode == FT_RENDER_MODE_LCD )
        other_flags |= AF_LATIN_HINTS_HORZ_SNAP;
  
      /*
       *  We snap the width of horizontal stems for the monochrome and
       *  vertical LCD rendering targets only.
       */
      if ( mode == FT_RENDER_MODE_MONO || mode == FT_RENDER_MODE_LCD_V )
        other_flags |= AF_LATIN_HINTS_VERT_SNAP;
  
      /*
       *  We adjust stems to full pixels unless in `light' or `lcd' mode.
       */
      if ( mode != FT_RENDER_MODE_LIGHT && mode != FT_RENDER_MODE_LCD )
        other_flags |= AF_LATIN_HINTS_STEM_ADJUST;
  
      if ( mode == FT_RENDER_MODE_MONO )
        other_flags |= AF_LATIN_HINTS_MONO;
  
      /*
       *  In `light' or `lcd' mode we disable horizontal hinting completely.
       *  We also do it if the face is italic.
       *
       *  However, if warping is enabled (which only works in `light' hinting
       *  mode), advance widths get adjusted, too.
       */
      if ( mode == FT_RENDER_MODE_LIGHT || mode == FT_RENDER_MODE_LCD ||
           ( face->style_flags & FT_STYLE_FLAG_ITALIC ) != 0          )
        scaler_flags |= AF_SCALER_FLAG_NO_HORIZONTAL;
  
  #ifdef AF_CONFIG_OPTION_USE_WARPER
      /* get (global) warper flag */
      if ( !metrics->root.globals->module->warping )
        scaler_flags |= AF_SCALER_FLAG_NO_WARPER;
  #endif
  
      hints->scaler_flags = scaler_flags;
      hints->other_flags  = other_flags;
  
      return FT_Err_Ok;
    }
  
  
    /*************************************************************************/
    /*************************************************************************/
    /*****                                                               *****/
    /*****        L A T I N   G L Y P H   G R I D - F I T T I N G        *****/
    /*****                                                               *****/
    /*************************************************************************/
    /*************************************************************************/
  
    /* Snap a given width in scaled coordinates to one of the */
    /* current standard widths.                               */
  
    static FT_Pos
    af_latin_snap_width( AF_Width  widths,
                         FT_UInt   count,
                         FT_Pos    width )
    {
      FT_UInt  n;
      FT_Pos   best      = 64 + 32 + 2;
      FT_Pos   reference = width;
      FT_Pos   scaled;
  
  
      for ( n = 0; n < count; n++ )
      {
        FT_Pos  w;
        FT_Pos  dist;
  
  
        w = widths[n].cur;
        dist = width - w;
        if ( dist < 0 )
          dist = -dist;
        if ( dist < best )
        {
          best      = dist;
          reference = w;
        }
      }
  
      scaled = FT_PIX_ROUND( reference );
  
      if ( width >= reference )
      {
        if ( width < scaled + 48 )
          width = reference;
      }
      else
      {
        if ( width > scaled - 48 )
          width = reference;
      }
  
      return width;
    }
  
  
    /* Compute the snapped width of a given stem, ignoring very thin ones. */
    /* There is a lot of voodoo in this function; changing the hard-coded  */
    /* parameters influence the whole hinting process.                     */
  
    static FT_Pos
    af_latin_compute_stem_width( AF_GlyphHints  hints,
                                 AF_Dimension   dim,
                                 FT_Pos         width,
                                 FT_Pos         base_delta,
                                 FT_UInt        base_flags,
                                 FT_UInt        stem_flags )
    {
      AF_LatinMetrics  metrics  = (AF_LatinMetrics)hints->metrics;
      AF_LatinAxis     axis     = &metrics->axis[dim];
      FT_Pos           dist     = width;
      FT_Int           sign     = 0;
      FT_Int           vertical = ( dim == AF_DIMENSION_VERT );
  
  
      if ( !AF_LATIN_HINTS_DO_STEM_ADJUST( hints ) ||
           axis->extra_light                       )
        return width;
  
      if ( dist < 0 )
      {
        dist = -width;
        sign = 1;
      }
  
      if ( (  vertical && !AF_LATIN_HINTS_DO_VERT_SNAP( hints ) ) ||
           ( !vertical && !AF_LATIN_HINTS_DO_HORZ_SNAP( hints ) ) )
      {
        /* smooth hinting process: very lightly quantize the stem width */
  
        /* leave the widths of serifs alone */
        if ( ( stem_flags & AF_EDGE_SERIF ) &&
             vertical                       &&
             ( dist < 3 * 64 )              )
          goto Done_Width;
  
        else if ( base_flags & AF_EDGE_ROUND )
        {
          if ( dist < 80 )
            dist = 64;
        }
        else if ( dist < 56 )
          dist = 56;
  
        if ( axis->width_count > 0 )
        {
          FT_Pos  delta;
  
  
          /* compare to standard width */
          delta = dist - axis->widths[0].cur;
  
          if ( delta < 0 )
            delta = -delta;
  
          if ( delta < 40 )
          {
            dist = axis->widths[0].cur;
            if ( dist < 48 )
              dist = 48;
  
            goto Done_Width;
          }
  
          if ( dist < 3 * 64 )
          {
            delta  = dist & 63;
            dist  &= -64;
  
            if ( delta < 10 )
              dist += delta;
  
            else if ( delta < 32 )
              dist += 10;
  
            else if ( delta < 54 )
              dist += 54;
  
            else
              dist += delta;
          }
          else
          {
            /* A stem's end position depends on two values: the start        */
            /* position and the stem length.  The former gets usually        */
            /* rounded to the grid, while the latter gets rounded also if it */
            /* exceeds a certain length (see below in this function).  This  */
            /* `double rounding' can lead to a great difference to the       */
            /* original, unhinted position; this normally doesn't matter for */
            /* large PPEM values, but for small sizes it can easily make     */
            /* outlines collide.  For this reason, we adjust the stem length */
            /* by a small amount depending on the PPEM value in case the     */
            /* former and latter rounding both point into the same           */
            /* direction.                                                    */
  
            FT_Pos  bdelta = 0;
  
  
            if ( ( ( width > 0 ) && ( base_delta > 0 ) ) ||
                 ( ( width < 0 ) && ( base_delta < 0 ) ) )
            {
              FT_UInt  ppem = metrics->root.scaler.face->size->metrics.x_ppem;
  
  
              if ( ppem < 10 )
                bdelta = base_delta;
              else if ( ppem < 30 )
                bdelta = ( base_delta * (FT_Pos)( 30 - ppem ) ) / 20;
  
              if ( bdelta < 0 )
                bdelta = -bdelta;
            }
  
            dist = ( dist - bdelta + 32 ) & ~63;
          }
        }
      }
      else
      {
        /* strong hinting process: snap the stem width to integer pixels */
  
        FT_Pos  org_dist = dist;
  
  
        dist = af_latin_snap_width( axis->widths, axis->width_count, dist );
  
        if ( vertical )
        {
          /* in the case of vertical hinting, always round */
          /* the stem heights to integer pixels            */
  
          if ( dist >= 64 )
            dist = ( dist + 16 ) & ~63;
          else
            dist = 64;
        }
        else
        {
          if ( AF_LATIN_HINTS_DO_MONO( hints ) )
          {
            /* monochrome horizontal hinting: snap widths to integer pixels */
            /* with a different threshold                                   */
  
            if ( dist < 64 )
              dist = 64;
            else
              dist = ( dist + 32 ) & ~63;
          }
          else
          {
            /* for horizontal anti-aliased hinting, we adopt a more subtle */
            /* approach: we strengthen small stems, round stems whose size */
            /* is between 1 and 2 pixels to an integer, otherwise nothing  */
  
            if ( dist < 48 )
              dist = ( dist + 64 ) >> 1;
  
            else if ( dist < 128 )
            {
              /* We only round to an integer width if the corresponding */
              /* distortion is less than 1/4 pixel.  Otherwise this     */
              /* makes everything worse since the diagonals, which are  */
              /* not hinted, appear a lot bolder or thinner than the    */
              /* vertical stems.                                        */
  
              FT_Pos  delta;
  
  
              dist = ( dist + 22 ) & ~63;
              delta = dist - org_dist;
              if ( delta < 0 )
                delta = -delta;
  
              if ( delta >= 16 )
              {
                dist = org_dist;
                if ( dist < 48 )
                  dist = ( dist + 64 ) >> 1;
              }
            }
            else
              /* round otherwise to prevent color fringes in LCD mode */
              dist = ( dist + 32 ) & ~63;
          }
        }
      }
  
    Done_Width:
      if ( sign )
        dist = -dist;
  
      return dist;
    }
  
  
    /* Align one stem edge relative to the previous stem edge. */
  
    static void
    af_latin_align_linked_edge( AF_GlyphHints  hints,
                                AF_Dimension   dim,
                                AF_Edge        base_edge,
                                AF_Edge        stem_edge )
    {
      FT_Pos  dist, base_delta;
      FT_Pos  fitted_width;
  
  
      dist       = stem_edge->opos - base_edge->opos;
      base_delta = base_edge->pos - base_edge->opos;
  
      fitted_width = af_latin_compute_stem_width( hints, dim,
                                                  dist, base_delta,
                                                  base_edge->flags,
                                                  stem_edge->flags );
  
  
      stem_edge->pos = base_edge->pos + fitted_width;
  
      FT_TRACE5(( "  LINK: edge %d (opos=%.2f) linked to %.2f,"
                  " dist was %.2f, now %.2f\n",
                  stem_edge - hints->axis[dim].edges, stem_edge->opos / 64.0,
                  stem_edge->pos / 64.0, dist / 64.0, fitted_width / 64.0 ));
    }
  
  
    /* Shift the coordinates of the `serif' edge by the same amount */
    /* as the corresponding `base' edge has been moved already.     */
  
    static void
    af_latin_align_serif_edge( AF_GlyphHints  hints,
                               AF_Edge        base,
                               AF_Edge        serif )
    {
      FT_UNUSED( hints );
  
      serif->pos = base->pos + ( serif->opos - base->opos );
    }
  
  
    /*************************************************************************/
    /*************************************************************************/
    /*************************************************************************/
    /****                                                                 ****/
    /****                    E D G E   H I N T I N G                      ****/
    /****                                                                 ****/
    /*************************************************************************/
    /*************************************************************************/
    /*************************************************************************/
  
  
    /* The main grid-fitting routine. */
  
    static void
    af_latin_hint_edges( AF_GlyphHints  hints,
                         AF_Dimension   dim )
    {
      AF_AxisHints  axis       = &hints->axis[dim];
      AF_Edge       edges      = axis->edges;
      AF_Edge       edge_limit = edges + axis->num_edges;
      FT_PtrDist    n_edges;
      AF_Edge       edge;
      AF_Edge       anchor     = NULL;
      FT_Int        has_serifs = 0;
  
  #ifdef FT_CONFIG_OPTION_PIC
      AF_FaceGlobals  globals = hints->metrics->globals;
  #endif
  
      AF_StyleClass   style_class  = hints->metrics->style_class;
      AF_ScriptClass  script_class = AF_SCRIPT_CLASSES_GET
                                       [style_class->script];
  
      FT_Bool  top_to_bottom_hinting = 0;
  
  #ifdef FT_DEBUG_LEVEL_TRACE
      FT_UInt  num_actions = 0;
  #endif
  
  
      FT_TRACE5(( "latin %s edge hinting (style `%s')\n",
                  dim == AF_DIMENSION_VERT ? "horizontal" : "vertical",
                  af_style_names[hints->metrics->style_class->style] ));
  
      if ( dim == AF_DIMENSION_VERT )
        top_to_bottom_hinting = script_class->top_to_bottom_hinting;
  
      /* we begin by aligning all stems relative to the blue zone */
      /* if needed -- that's only for horizontal edges            */
  
      if ( dim == AF_DIMENSION_VERT && AF_HINTS_DO_BLUES( hints ) )
      {
        for ( edge = edges; edge < edge_limit; edge++ )
        {
          AF_Width  blue;
          AF_Edge   edge1, edge2; /* these edges form the stem to check */
  
  
          if ( edge->flags & AF_EDGE_DONE )
            continue;
  
          edge1 = NULL;
          edge2 = edge->link;
  
          /*
           *  If a stem contains both a neutral and a non-neutral blue zone,
           *  skip the neutral one.  Otherwise, outlines with different
           *  directions might be incorrectly aligned at the same vertical
           *  position.
           *
           *  If we have two neutral blue zones, skip one of them.
           *
           */
          if ( edge->blue_edge && edge2 && edge2->blue_edge )
          {
            FT_Byte  neutral  = edge->flags  & AF_EDGE_NEUTRAL;
            FT_Byte  neutral2 = edge2->flags & AF_EDGE_NEUTRAL;
  
  
            if ( neutral2 )
            {
              edge2->blue_edge = NULL;
              edge2->flags    &= ~AF_EDGE_NEUTRAL;
            }
            else if ( neutral )
            {
              edge->blue_edge = NULL;
              edge->flags    &= ~AF_EDGE_NEUTRAL;
            }
          }
  
          blue = edge->blue_edge;
          if ( blue )
            edge1 = edge;
  
          /* flip edges if the other edge is aligned to a blue zone */
          else if ( edge2 && edge2->blue_edge )
          {
            blue  = edge2->blue_edge;
            edge1 = edge2;
            edge2 = edge;
          }
  
          if ( !edge1 )
            continue;
  
  #ifdef FT_DEBUG_LEVEL_TRACE
          if ( !anchor )
            FT_TRACE5(( "  BLUE_ANCHOR: edge %d (opos=%.2f) snapped to %.2f,"
                        " was %.2f (anchor=edge %d)\n",
                        edge1 - edges, edge1->opos / 64.0, blue->fit / 64.0,
                        edge1->pos / 64.0, edge - edges ));
          else
            FT_TRACE5(( "  BLUE: edge %d (opos=%.2f) snapped to %.2f,"
                        " was %.2f\n",
                        edge1 - edges, edge1->opos / 64.0, blue->fit / 64.0,
                        edge1->pos / 64.0 ));
  
          num_actions++;
  #endif
  
          edge1->pos    = blue->fit;
          edge1->flags |= AF_EDGE_DONE;
  
          if ( edge2 && !edge2->blue_edge )
          {
            af_latin_align_linked_edge( hints, dim, edge1, edge2 );
            edge2->flags |= AF_EDGE_DONE;
  
  #ifdef FT_DEBUG_LEVEL_TRACE
            num_actions++;
  #endif
          }
  
          if ( !anchor )
            anchor = edge;
        }
      }
  
      /* now we align all other stem edges, trying to maintain the */
      /* relative order of stems in the glyph                      */
      for ( edge = edges; edge < edge_limit; edge++ )
      {
        AF_Edge  edge2;
  
  
        if ( edge->flags & AF_EDGE_DONE )
          continue;
  
        /* skip all non-stem edges */
        edge2 = edge->link;
        if ( !edge2 )
        {
          has_serifs++;
          continue;
        }
  
        /* now align the stem */
  
        /* this should not happen, but it's better to be safe */
        if ( edge2->blue_edge )
        {
          FT_TRACE5(( "  ASSERTION FAILED for edge %d\n", edge2 - edges ));
  
          af_latin_align_linked_edge( hints, dim, edge2, edge );
          edge->flags |= AF_EDGE_DONE;
  
  #ifdef FT_DEBUG_LEVEL_TRACE
          num_actions++;
  #endif
          continue;
        }
  
        if ( !anchor )
        {
          /* if we reach this if clause, no stem has been aligned yet */
  
          FT_Pos  org_len, org_center, cur_len;
          FT_Pos  cur_pos1, error1, error2, u_off, d_off;
  
  
          org_len = edge2->opos - edge->opos;
          cur_len = af_latin_compute_stem_width( hints, dim,
                                                 org_len, 0,
                                                 edge->flags,
                                                 edge2->flags );
  
          /* some voodoo to specially round edges for small stem widths; */
          /* the idea is to align the center of a stem, then shifting    */
          /* the stem edges to suitable positions                        */
          if ( cur_len <= 64 )
          {
            /* width <= 1px */
            u_off = 32;
            d_off = 32;
          }
          else
          {
            /* 1px < width < 1.5px */
            u_off = 38;
            d_off = 26;
          }
  
          if ( cur_len < 96 )
          {
            org_center = edge->opos + ( org_len >> 1 );
            cur_pos1   = FT_PIX_ROUND( org_center );
  
            error1 = org_center - ( cur_pos1 - u_off );
            if ( error1 < 0 )
              error1 = -error1;
  
            error2 = org_center - ( cur_pos1 + d_off );
            if ( error2 < 0 )
              error2 = -error2;
  
            if ( error1 < error2 )
              cur_pos1 -= u_off;
            else
              cur_pos1 += d_off;
  
            edge->pos  = cur_pos1 - cur_len / 2;
            edge2->pos = edge->pos + cur_len;
          }
          else
            edge->pos = FT_PIX_ROUND( edge->opos );
  
          anchor       = edge;
          edge->flags |= AF_EDGE_DONE;
  
          FT_TRACE5(( "  ANCHOR: edge %d (opos=%.2f) and %d (opos=%.2f)"
                      " snapped to %.2f and %.2f\n",
                      edge - edges, edge->opos / 64.0,
                      edge2 - edges, edge2->opos / 64.0,
                      edge->pos / 64.0, edge2->pos / 64.0 ));
  
          af_latin_align_linked_edge( hints, dim, edge, edge2 );
  
  #ifdef FT_DEBUG_LEVEL_TRACE
          num_actions += 2;
  #endif
        }
        else
        {
          FT_Pos  org_pos, org_len, org_center, cur_len;
          FT_Pos  cur_pos1, cur_pos2, delta1, delta2;
  
  
          org_pos    = anchor->pos + ( edge->opos - anchor->opos );
          org_len    = edge2->opos - edge->opos;
          org_center = org_pos + ( org_len >> 1 );
  
          cur_len = af_latin_compute_stem_width( hints, dim,
                                                 org_len, 0,
                                                 edge->flags,
                                                 edge2->flags );
  
          if ( edge2->flags & AF_EDGE_DONE )
          {
            FT_TRACE5(( "  ADJUST: edge %d (pos=%.2f) moved to %.2f\n",
                        edge - edges, edge->pos / 64.0,
                        ( edge2->pos - cur_len ) / 64.0 ));
  
            edge->pos = edge2->pos - cur_len;
          }
  
          else if ( cur_len < 96 )
          {
            FT_Pos  u_off, d_off;
  
  
            cur_pos1 = FT_PIX_ROUND( org_center );
  
            if ( cur_len <= 64 )
            {
              u_off = 32;
              d_off = 32;
            }
            else
            {
              u_off = 38;
              d_off = 26;
            }
  
            delta1 = org_center - ( cur_pos1 - u_off );
            if ( delta1 < 0 )
              delta1 = -delta1;
  
            delta2 = org_center - ( cur_pos1 + d_off );
            if ( delta2 < 0 )
              delta2 = -delta2;
  
            if ( delta1 < delta2 )
              cur_pos1 -= u_off;
            else
              cur_pos1 += d_off;
  
            edge->pos  = cur_pos1 - cur_len / 2;
            edge2->pos = cur_pos1 + cur_len / 2;
  
            FT_TRACE5(( "  STEM: edge %d (opos=%.2f) linked to %d (opos=%.2f)"
                        " snapped to %.2f and %.2f\n",
                        edge - edges, edge->opos / 64.0,
                        edge2 - edges, edge2->opos / 64.0,
                        edge->pos / 64.0, edge2->pos / 64.0 ));
          }
  
          else
          {
            org_pos    = anchor->pos + ( edge->opos - anchor->opos );
            org_len    = edge2->opos - edge->opos;
            org_center = org_pos + ( org_len >> 1 );
  
            cur_len    = af_latin_compute_stem_width( hints, dim,
                                                      org_len, 0,
                                                      edge->flags,
                                                      edge2->flags );
  
            cur_pos1 = FT_PIX_ROUND( org_pos );
            delta1   = cur_pos1 + ( cur_len >> 1 ) - org_center;
            if ( delta1 < 0 )
              delta1 = -delta1;
  
            cur_pos2 = FT_PIX_ROUND( org_pos + org_len ) - cur_len;
            delta2   = cur_pos2 + ( cur_len >> 1 ) - org_center;
            if ( delta2 < 0 )
              delta2 = -delta2;
  
            edge->pos  = ( delta1 < delta2 ) ? cur_pos1 : cur_pos2;
            edge2->pos = edge->pos + cur_len;
  
            FT_TRACE5(( "  STEM: edge %d (opos=%.2f) linked to %d (opos=%.2f)"
                        " snapped to %.2f and %.2f\n",
                        edge - edges, edge->opos / 64.0,
                        edge2 - edges, edge2->opos / 64.0,
                        edge->pos / 64.0, edge2->pos / 64.0 ));
          }
  
  #ifdef FT_DEBUG_LEVEL_TRACE
          num_actions++;
  #endif
  
          edge->flags  |= AF_EDGE_DONE;
          edge2->flags |= AF_EDGE_DONE;
  
          if ( edge > edges                                             &&
               ( top_to_bottom_hinting ? ( edge->pos > edge[-1].pos )
                                       : ( edge->pos < edge[-1].pos ) ) )
          {
            /* don't move if stem would (almost) disappear otherwise; */
            /* the ad-hoc value 16 corresponds to 1/4px               */
            if ( edge->link && FT_ABS( edge->link->pos - edge[-1].pos ) > 16 )
            {
  #ifdef FT_DEBUG_LEVEL_TRACE
              FT_TRACE5(( "  BOUND: edge %d (pos=%.2f) moved to %.2f\n",
                          edge - edges,
                          edge->pos / 64.0,
                          edge[-1].pos / 64.0 ));
  
              num_actions++;
  #endif
  
              edge->pos = edge[-1].pos;
            }
          }
        }
      }
  
      /* make sure that lowercase m's maintain their symmetry */
  
      /* In general, lowercase m's have six vertical edges if they are sans */
      /* serif, or twelve if they are with serifs.  This implementation is  */
      /* based on that assumption, and seems to work very well with most    */
      /* faces.  However, if for a certain face this assumption is not      */
      /* true, the m is just rendered like before.  In addition, any stem   */
      /* correction will only be applied to symmetrical glyphs (even if the */
      /* glyph is not an m), so the potential for unwanted distortion is    */
      /* relatively low.                                                    */
  
      /* We don't handle horizontal edges since we can't easily assure that */
      /* the third (lowest) stem aligns with the base line; it might end up */
      /* one pixel higher or lower.                                         */
  
      n_edges = edge_limit - edges;
      if ( dim == AF_DIMENSION_HORZ && ( n_edges == 6 || n_edges == 12 ) )
      {
        AF_Edge  edge1, edge2, edge3;
        FT_Pos   dist1, dist2, span, delta;
  
  
        if ( n_edges == 6 )
        {
          edge1 = edges;
          edge2 = edges + 2;
          edge3 = edges + 4;
        }
        else
        {
          edge1 = edges + 1;
          edge2 = edges + 5;
          edge3 = edges + 9;
        }
  
        dist1 = edge2->opos - edge1->opos;
        dist2 = edge3->opos - edge2->opos;
  
        span = dist1 - dist2;
        if ( span < 0 )
          span = -span;
  
        if ( span < 8 )
        {
          delta = edge3->pos - ( 2 * edge2->pos - edge1->pos );
          edge3->pos -= delta;
          if ( edge3->link )
            edge3->link->pos -= delta;
  
          /* move the serifs along with the stem */
          if ( n_edges == 12 )
          {
            ( edges + 8 )->pos -= delta;
            ( edges + 11 )->pos -= delta;
          }
  
          edge3->flags |= AF_EDGE_DONE;
          if ( edge3->link )
            edge3->link->flags |= AF_EDGE_DONE;
        }
      }
  
      if ( has_serifs || !anchor )
      {
        /*
         *  now hint the remaining edges (serifs and single) in order
         *  to complete our processing
         */
        for ( edge = edges; edge < edge_limit; edge++ )
        {
          FT_Pos  delta;
  
  
          if ( edge->flags & AF_EDGE_DONE )
            continue;
  
          delta = 1000;
  
          if ( edge->serif )
          {
            delta = edge->serif->opos - edge->opos;
            if ( delta < 0 )
              delta = -delta;
          }
  
          if ( delta < 64 + 16 )
          {
            af_latin_align_serif_edge( hints, edge->serif, edge );
            FT_TRACE5(( "  SERIF: edge %d (opos=%.2f) serif to %d (opos=%.2f)"
                        " aligned to %.2f\n",
                        edge - edges, edge->opos / 64.0,
                        edge->serif - edges, edge->serif->opos / 64.0,
                        edge->pos / 64.0 ));
          }
          else if ( !anchor )
          {
            edge->pos = FT_PIX_ROUND( edge->opos );
            anchor    = edge;
            FT_TRACE5(( "  SERIF_ANCHOR: edge %d (opos=%.2f)"
                        " snapped to %.2f\n",
                        edge-edges, edge->opos / 64.0, edge->pos / 64.0 ));
          }
          else
          {
            AF_Edge  before, after;
  
  
            for ( before = edge - 1; before >= edges; before-- )
              if ( before->flags & AF_EDGE_DONE )
                break;
  
            for ( after = edge + 1; after < edge_limit; after++ )
              if ( after->flags & AF_EDGE_DONE )
                break;
  
            if ( before >= edges && before < edge   &&
                 after < edge_limit && after > edge )
            {
              if ( after->opos == before->opos )
                edge->pos = before->pos;
              else
                edge->pos = before->pos +
                            FT_MulDiv( edge->opos - before->opos,
                                       after->pos - before->pos,
                                       after->opos - before->opos );
  
              FT_TRACE5(( "  SERIF_LINK1: edge %d (opos=%.2f) snapped to %.2f"
                          " from %d (opos=%.2f)\n",
                          edge - edges, edge->opos / 64.0,
                          edge->pos / 64.0,
                          before - edges, before->opos / 64.0 ));
            }
            else
            {
              edge->pos = anchor->pos +
                          ( ( edge->opos - anchor->opos + 16 ) & ~31 );
              FT_TRACE5(( "  SERIF_LINK2: edge %d (opos=%.2f)"
                          " snapped to %.2f\n",
                          edge - edges, edge->opos / 64.0, edge->pos / 64.0 ));
            }
          }
  
  #ifdef FT_DEBUG_LEVEL_TRACE
          num_actions++;
  #endif
          edge->flags |= AF_EDGE_DONE;
  
          if ( edge > edges                                             &&
               ( top_to_bottom_hinting ? ( edge->pos > edge[-1].pos )
                                       : ( edge->pos < edge[-1].pos ) ) )
          {
            /* don't move if stem would (almost) disappear otherwise; */
            /* the ad-hoc value 16 corresponds to 1/4px               */
            if ( edge->link && FT_ABS( edge->link->pos - edge[-1].pos ) > 16 )
            {
  #ifdef FT_DEBUG_LEVEL_TRACE
              FT_TRACE5(( "  BOUND: edge %d (pos=%.2f) moved to %.2f\n",
                          edge - edges,
                          edge->pos / 64.0,
                          edge[-1].pos / 64.0 ));
  
              num_actions++;
  #endif
              edge->pos = edge[-1].pos;
            }
          }
  
          if ( edge + 1 < edge_limit                                   &&
               edge[1].flags & AF_EDGE_DONE                            &&
               ( top_to_bottom_hinting ? ( edge->pos < edge[1].pos )
                                       : ( edge->pos > edge[1].pos ) ) )
          {
            /* don't move if stem would (almost) disappear otherwise; */
            /* the ad-hoc value 16 corresponds to 1/4px               */
            if ( edge->link && FT_ABS( edge->link->pos - edge[-1].pos ) > 16 )
            {
  #ifdef FT_DEBUG_LEVEL_TRACE
              FT_TRACE5(( "  BOUND: edge %d (pos=%.2f) moved to %.2f\n",
                          edge - edges,
                          edge->pos / 64.0,
                          edge[1].pos / 64.0 ));
  
              num_actions++;
  #endif
  
              edge->pos = edge[1].pos;
            }
          }
        }
      }
  
  #ifdef FT_DEBUG_LEVEL_TRACE
      if ( !num_actions )
        FT_TRACE5(( "  (none)\n" ));
      FT_TRACE5(( "\n" ));
  #endif
    }
  
  
    /* Apply the complete hinting algorithm to a latin glyph. */
  
    static FT_Error
    af_latin_hints_apply( FT_UInt          glyph_index,
                          AF_GlyphHints    hints,
                          FT_Outline*      outline,
                          AF_LatinMetrics  metrics )
    {
      FT_Error  error;
      int       dim;
  
      AF_LatinAxis  axis;
  
  
      error = af_glyph_hints_reload( hints, outline );
      if ( error )
        goto Exit;
  
      /* analyze glyph outline */
      if ( AF_HINTS_DO_HORIZONTAL( hints ) )
      {
        axis  = &metrics->axis[AF_DIMENSION_HORZ];
        error = af_latin_hints_detect_features( hints,
                                                axis->width_count,
                                                axis->widths,
                                                AF_DIMENSION_HORZ );
        if ( error )
          goto Exit;
      }
  
      if ( AF_HINTS_DO_VERTICAL( hints ) )
      {
        axis  = &metrics->axis[AF_DIMENSION_VERT];
        error = af_latin_hints_detect_features( hints,
                                                axis->width_count,
                                                axis->widths,
                                                AF_DIMENSION_VERT );
        if ( error )
          goto Exit;
  
        /* apply blue zones to base characters only */
        if ( !( metrics->root.globals->glyph_styles[glyph_index] & AF_NONBASE ) )
          af_latin_hints_compute_blue_edges( hints, metrics );
      }
  
      /* grid-fit the outline */
      for ( dim = 0; dim < AF_DIMENSION_MAX; dim++ )
      {
  #ifdef AF_CONFIG_OPTION_USE_WARPER
        if ( dim == AF_DIMENSION_HORZ                                  &&
             metrics->root.scaler.render_mode == FT_RENDER_MODE_NORMAL &&
             AF_HINTS_DO_WARP( hints )                                 )
        {
          AF_WarperRec  warper;
          FT_Fixed      scale;
          FT_Pos        delta;
  
  
          af_warper_compute( &warper, hints, (AF_Dimension)dim,
                             &scale, &delta );
          af_glyph_hints_scale_dim( hints, (AF_Dimension)dim,
                                    scale, delta );
          continue;
        }
  #endif /* AF_CONFIG_OPTION_USE_WARPER */
  
        if ( ( dim == AF_DIMENSION_HORZ && AF_HINTS_DO_HORIZONTAL( hints ) ) ||
             ( dim == AF_DIMENSION_VERT && AF_HINTS_DO_VERTICAL( hints ) )   )
        {
          af_latin_hint_edges( hints, (AF_Dimension)dim );
          af_glyph_hints_align_edge_points( hints, (AF_Dimension)dim );
          af_glyph_hints_align_strong_points( hints, (AF_Dimension)dim );
          af_glyph_hints_align_weak_points( hints, (AF_Dimension)dim );
        }
      }
  
      af_glyph_hints_save( hints, outline );
  
    Exit:
      return error;
    }
  
  
    /*************************************************************************/
    /*************************************************************************/
    /*****                                                               *****/
    /*****              L A T I N   S C R I P T   C L A S S              *****/
    /*****                                                               *****/
    /*************************************************************************/
    /*************************************************************************/
  
  
    AF_DEFINE_WRITING_SYSTEM_CLASS(
      af_latin_writing_system_class,
  
      AF_WRITING_SYSTEM_LATIN,
  
      sizeof ( AF_LatinMetricsRec ),
  
      (AF_WritingSystem_InitMetricsFunc) af_latin_metrics_init,        /* style_metrics_init    */
      (AF_WritingSystem_ScaleMetricsFunc)af_latin_metrics_scale,       /* style_metrics_scale   */
      (AF_WritingSystem_DoneMetricsFunc) NULL,                         /* style_metrics_done    */
      (AF_WritingSystem_GetStdWidthsFunc)af_latin_get_standard_widths, /* style_metrics_getstdw */
  
      (AF_WritingSystem_InitHintsFunc)   af_latin_hints_init,          /* style_hints_init      */
      (AF_WritingSystem_ApplyHintsFunc)  af_latin_hints_apply          /* style_hints_apply     */
    )
  
  
  /* END */
  