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kc3-lang/freetype/src/autofit/aflatin.c

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  • Author : luz paz
    Date : 2024-08-13 23:29:13
    Hash : f92c9655
    Message : Fix various typos.

  • src/autofit/aflatin.c
  • /****************************************************************************
     *
     * aflatin.c
     *
     *   Auto-fitter hinting routines for latin writing system (body).
     *
     * Copyright (C) 2003-2024 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 <freetype/ftadvanc.h>
    #include <freetype/internal/ftdebug.h>
    
    #include "afglobal.h"
    #include "aflatin.h"
    #include "aferrors.h"
    
    
      /**************************************************************************
       *
       * The macro FT_COMPONENT is used in trace mode.  It is an implicit
       * parameter of the FT_TRACE() and FT_ERROR() macros, used to print/log
       * messages during execution.
       */
    #undef  FT_COMPONENT
    #define FT_COMPONENT  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" ));
        FT_TRACE5(( "latin standard widths computation (style `%s')\n",
                    af_style_names[metrics->root.style_class->style] ));
        FT_TRACE5(( "=====================================================\n" ));
        FT_TRACE5(( "\n" ));
    
        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;
    
          AF_StyleClass   style_class  = metrics->root.style_class;
          AF_ScriptClass  script_class = af_script_classes[style_class->script];
    
          /* If HarfBuzz is not available, we need a pointer to a single */
          /* unsigned long value.                                        */
    #ifdef FT_CONFIG_OPTION_USE_HARFBUZZ
          void*     shaper_buf;
    #else
          FT_ULong  shaper_buf_;
          void*     shaper_buf = &shaper_buf_;
    #endif
    
          const char*  p;
    
    #ifdef FT_DEBUG_LEVEL_TRACE
          FT_ULong  ch = 0;
    #endif
    
    
          p = script_class->standard_charstring;
    
    #ifdef FT_CONFIG_OPTION_USE_HARFBUZZ
          shaper_buf = af_shaper_buf_create( face );
    #endif
          /*
           * 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 )
          {
            FT_TRACE5(( "standard character missing;"
                        " using fallback stem widths\n" ));
            goto Exit;
          }
    
          FT_TRACE5(( "standard character: U+%04lX (glyph index %ld)\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 = FT_OFFSET( 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(( "  %ld (standard)", axis->standard_width ));
              for ( i = 1; i < axis->width_count; i++ )
                FT_TRACE5(( " %ld", 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 int
      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 );
    
        /* If HarfBuzz is not available, we need a pointer to a single */
        /* unsigned long value.                                        */
    #ifdef FT_CONFIG_OPTION_USE_HARFBUZZ
        void*     shaper_buf;
    #else
        FT_ULong  shaper_buf_;
        void*     shaper_buf = &shaper_buf_;
    #endif
    
    
        /* 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" ));
        FT_TRACE5(( "============================\n" ));
        FT_TRACE5(( "\n" ));
    
    #ifdef FT_CONFIG_OPTION_USE_HARFBUZZ
        shaper_buf = af_shaper_buf_create( face );
    #endif
    
        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_contour_first = -1;
              best_contour_last  = -1;
              best_y             = 0;  /* make compiler happy */
    
              {
                FT_Int  nn;
                FT_Int  pp, first, last;
    
    
                last = -1;
                for ( nn = 0; nn < outline.n_contours; nn++ )
                {
                  first = last + 1;
                  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 > best_contour_last )
                  {
                    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", *blue_ref ));
          FT_TRACE5(( "       overshoot = %ld\n", *blue_shoot ));
    
        } /* end for loop */
    
        af_shaper_buf_destroy( face, shaper_buf );
    
        if ( axis->blue_count )
        {
          /* we finally check whether blue zones are ordered;            */
          /* `ref' and `shoot' values of two blue zones must not overlap */
    
          FT_UInt       i;
          AF_LatinBlue  blue_sorted[AF_BLUE_STRINGSET_MAX_LEN];
    
    
          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 %td to %ld\n",
                          a_is_top ? "overshoot" : "reference",
                          blue_sorted[i] - axis->blues,
                          *a ));
            }
          }
    
          FT_TRACE5(( "\n" ));
    
          return 0;
        }
        else
        {
          /* disable hinting for the current style if there are no blue zones */
    
          AF_FaceGlobals  globals = metrics->root.globals;
          FT_UShort*      gstyles = globals->glyph_styles;
    
          FT_UInt  i;
    
    
          FT_TRACE5(( "no blue zones found:"
                      " hinting disabled for this style\n" ));
    
          for ( i = 0; i < globals->glyph_count; i++ )
          {
            if ( ( gstyles[i] & AF_STYLE_MASK ) == sc->style )
              gstyles[i] = AF_STYLE_NONE_DFLT;
          }
    
          FT_TRACE5(( "\n" ));
    
          return 1;
        }
      }
    
    
      /* 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_Long  advance = 0, old_advance = 0;
    
        /* If HarfBuzz is not available, we need a pointer to a single */
        /* unsigned long value.                                        */
    #ifdef FT_CONFIG_OPTION_USE_HARFBUZZ
        void*     shaper_buf;
    #else
        FT_ULong  shaper_buf_;
        void*     shaper_buf = &shaper_buf_;
    #endif
    
        /* 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;
    
    #ifdef FT_CONFIG_OPTION_USE_HARFBUZZ
        shaper_buf = af_shaper_buf_create( face );
    #endif
    
        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_StyleMetrics  metrics_,   /* AF_LatinMetrics */
                             FT_Face          face )
      {
        AF_LatinMetrics  metrics = (AF_LatinMetrics)metrics_;
    
        FT_Error  error = FT_Err_Ok;
    
        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 );
          if ( af_latin_metrics_init_blues( metrics, face ) )
          {
            /* use internal error code to indicate missing blue zones */
            error = -1;
            goto Exit;
          }
          af_latin_metrics_check_digits( metrics, face );
        }
    
      Exit:
        face->charmap = oldmap;
        return error;
      }
    
    
      /* 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_MulFix( max_height, new_scale - scale );
    
                if ( -128 < dist && dist < 128 )
                {
                  FT_TRACE5(( "af_latin_metrics_scale_dim:"
                              " x height alignment (style `%s'):\n",
                              af_style_names[metrics->root.style_class->style] ));
                  FT_TRACE5(( "                           "
                              " vertical scaling changed"
                              " from %.5f to %.5f (by %ld%%)\n",
                              (double)scale / 65536,
                              (double)new_scale / 65536,
                              ( fitted - scaled ) * 100 / scaled ));
                  FT_TRACE5(( "\n" ));
    
                  scale = new_scale;
                }
    #ifdef FT_DEBUG_LEVEL_TRACE
                else
                {
                  FT_TRACE5(( "af_latin_metrics_scale_dim:"
                              " x height alignment (style `%s'):\n",
                              af_style_names[metrics->root.style_class->style] ));
                  FT_TRACE5(( "                           "
                              " excessive vertical scaling abandoned\n" ));
                  FT_TRACE5(( "\n" ));
                }
    #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(( "  %ld scaled to %.2f\n",
                      width->org,
                      (double)width->cur / 64 ));
        }
    
        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",
                      af_style_names[metrics->root.style_class->style] ));
          FT_TRACE5(( "\n" ));
        }
    #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: %ld scaled to %.2f%s\n",
                        nn,
                        blue->ref.org,
                        (double)blue->ref.fit / 64,
                        ( blue->flags & AF_LATIN_BLUE_ACTIVE ) ? ""
                                                               : " (inactive)" ));
            FT_TRACE5(( "  overshoot %d: %ld scaled to %.2f%s\n",
                        nn,
                        blue->shoot.org,
                        (double)blue->shoot.fit / 64,
                        ( blue->flags & AF_LATIN_BLUE_ACTIVE ) ? ""
                                                               : " (inactive)" ));
          }
    #endif
        }
      }
    
    
      /* Scale global values in both directions. */
    
      FT_LOCAL_DEF( void )
      af_latin_metrics_scale( AF_StyleMetrics  metrics_,   /* AF_LatinMetrics */
                              AF_Scaler        scaler )
      {
        AF_LatinMetrics  metrics = (AF_LatinMetrics)metrics_;
    
    
        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_CALLBACK_DEF( void )
      af_latin_get_standard_widths( AF_StyleMetrics  metrics_, /* AF_LatinMetrics */
                                    FT_Pos*          stdHW,
                                    FT_Pos*          stdVW )
      {
        AF_LatinMetrics  metrics = (AF_LatinMetrics)metrics_;
    
    
        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 );
                    prev_segment->delta = (FT_Short)( ( max_pos -
                                                        min_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 );
                      prev_segment->delta = (FT_Short)( ( prev_max_pos -
                                                          prev_min_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 );
                      segment->delta = (FT_Short)( ( max_pos - min_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                  ) )
            {
              /*
               * For efficiency, we restrict the number of segments to 1000,
               * which is a heuristic value: it is very unlikely that a glyph
               * with so many segments can be hinted in a sensible way.
               * Reasons:
               *
               * - The glyph has really 1000 segments; this implies that it has
               *   at least 2000 outline points.  Assuming 'normal' fonts that
               *   have superfluous points optimized away, viewing such a glyph
               *   only makes sense at large magnifications where hinting
               *   isn't applied anyway.
               *
               * - We have a broken glyph.  Hinting doesn't make sense in this
               *   case either.
               */
              if ( axis->num_segments > 1000 )
              {
                FT_TRACE0(( "af_latin_hints_compute_segments:"
                            " more than 1000 segments in this glyph;\n" ));
                FT_TRACE0(( "                                "
                            " hinting is suppressed\n" ));
                axis->num_segments = 0;
                return FT_Err_Ok;
              }
    
              /* 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 = FT_OFFSET( 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 = FT_OFFSET( 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 */
              /* (that 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.
                 *
                 * - The less overlapping along the main axis, the worse it
                 *   is, causing a larger demerit.
                 *
                 * - 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  = NULL;
              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];
    
        AF_StyleClass   style_class  = hints->metrics->style_class;
        AF_ScriptClass  script_class = af_script_classes[style_class->script];
    
        FT_Bool  top_to_bottom_hinting = 0;
    
        AF_Segment    segments      = axis->segments;
        AF_Segment    segment_limit = FT_OFFSET( 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_UInt  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_UInt  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 = FT_OFFSET( 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 = FT_OFFSET( 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;
          }
        }
      }
    
    
      /* Initialize hinting engine. */
    
      static FT_Error
      af_latin_hints_init( AF_GlyphHints    hints,
                           AF_StyleMetrics  metrics_ )   /* AF_LatinMetrics */
      {
        AF_LatinMetrics  metrics = (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;
    
        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;
    
        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 %td (opos=%.2f) linked to %.2f,"
                    " dist was %.2f, now %.2f\n",
                    stem_edge - hints->axis[dim].edges,
                    (double)stem_edge->opos / 64, (double)stem_edge->pos / 64,
                    (double)dist / 64, (double)fitted_width / 64 ));
      }
    
    
      /* 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 = FT_OFFSET( edges, axis->num_edges );
        FT_PtrDist    n_edges;
        AF_Edge       edge;
        AF_Edge       anchor     = NULL;
        FT_Int        has_serifs = 0;
    
        AF_StyleClass   style_class  = hints->metrics->style_class;
        AF_ScriptClass  script_class = af_script_classes[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 %td (opos=%.2f) snapped to %.2f,"
                          " was %.2f (anchor=edge %td)\n",
                          edge1 - edges,
                          (double)edge1->opos / 64, (double)blue->fit / 64,
                          (double)edge1->pos / 64, edge - edges ));
            else
              FT_TRACE5(( "  BLUE: edge %td (opos=%.2f) snapped to %.2f,"
                          " was %.2f\n",
                          edge1 - edges,
                          (double)edge1->opos / 64, (double)blue->fit / 64,
                          (double)edge1->pos / 64 ));
    
            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 %td\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 %td (opos=%.2f) and %td (opos=%.2f)"
                        " snapped to %.2f and %.2f\n",
                        edge - edges, (double)edge->opos / 64,
                        edge2 - edges, (double)edge2->opos / 64,
                        (double)edge->pos / 64, (double)edge2->pos / 64 ));
    
            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 %td (pos=%.2f) moved to %.2f\n",
                          edge - edges, (double)edge->pos / 64,
                          (double)( edge2->pos - cur_len ) / 64 ));
    
              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 %td (opos=%.2f) linked to %td (opos=%.2f)"
                          " snapped to %.2f and %.2f\n",
                          edge - edges, (double)edge->opos / 64,
                          edge2 - edges, (double)edge2->opos / 64,
                          (double)edge->pos / 64, (double)edge2->pos / 64 ));
            }
    
            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 %td (opos=%.2f) linked to %td (opos=%.2f)"
                          " snapped to %.2f and %.2f\n",
                          edge - edges, (double)edge->opos / 64,
                          edge2 - edges, (double)edge2->opos / 64,
                          (double)edge->pos / 64, (double)edge2->pos / 64 ));
            }
    
    #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 %td (pos=%.2f) moved to %.2f\n",
                            edge - edges,
                            (double)edge->pos / 64,
                            (double)edge[-1].pos / 64 ));
    
                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 %td (opos=%.2f) serif to %td (opos=%.2f)"
                          " aligned to %.2f\n",
                          edge - edges, (double)edge->opos / 64,
                          edge->serif - edges, (double)edge->serif->opos / 64,
                          (double)edge->pos / 64 ));
            }
            else if ( !anchor )
            {
              edge->pos = FT_PIX_ROUND( edge->opos );
              anchor    = edge;
              FT_TRACE5(( "  SERIF_ANCHOR: edge %td (opos=%.2f)"
                          " snapped to %.2f\n",
                          edge - edges,
                          (double)edge->opos / 64, (double)edge->pos / 64 ));
            }
            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 %td (opos=%.2f) snapped to %.2f"
                            " from %td (opos=%.2f)\n",
                            edge - edges, (double)edge->opos / 64,
                            (double)edge->pos / 64,
                            before - edges, (double)before->opos / 64 ));
              }
              else
              {
                edge->pos = anchor->pos +
                            ( ( edge->opos - anchor->opos + 16 ) & ~31 );
                FT_TRACE5(( "  SERIF_LINK2: edge %td (opos=%.2f)"
                            " snapped to %.2f\n",
                            edge - edges,
                            (double)edge->opos / 64, (double)edge->pos / 64 ));
              }
            }
    
    #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 %td (pos=%.2f) moved to %.2f\n",
                            edge - edges,
                            (double)edge->pos / 64,
                            (double)edge[-1].pos / 64 ));
    
                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 %td (pos=%.2f) moved to %.2f\n",
                            edge - edges,
                            (double)edge->pos / 64,
                            (double)edge[1].pos / 64 ));
    
                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_StyleMetrics  metrics_ )    /* AF_LatinMetrics */
      {
        AF_LatinMetrics  metrics = (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++ )
        {
          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 */