/* get scaling and hint flag from GlyphSlot */
  static void
  cf2_getScaleAndHintFlag( CFF_Decoder*  decoder,
                           CF2_Fixed*    x_scale,
                           CF2_Fixed*    y_scale,
                           FT_Bool*      hinted,
                           FT_Bool*      scaled )
  {
    FT_ASSERT( decoder && decoder->builder.glyph );

    /* note: FreeType scale includes a factor of 64 */
    *hinted = decoder->builder.glyph->hint;
    *scaled = decoder->builder.glyph->scaled;

    if ( *hinted )
    {
      *x_scale = FT_DivFix( decoder->builder.glyph->x_scale,
                            cf2_intToFixed( 64 ) );
      *y_scale = FT_DivFix( decoder->builder.glyph->y_scale,
                            cf2_intToFixed( 64 ) );
    }
    else
    {
      /* for unhinted outlines, `cff_slot_load' does the scaling, */
      /* thus render at `unity' scale                             */

      *x_scale = 0x0400;   /* 1/64 as 16.16 */
      *y_scale = 0x0400;
    }
  }

  FT_Matrix_Invert( FT_Matrix*  matrix )
  {
    FT_Pos  delta, xx, yy;


    if ( !matrix )
      return FT_Err_Invalid_Argument;

    /* compute discriminant */
    delta = FT_MulFix( matrix->xx, matrix->yy ) -
            FT_MulFix( matrix->xy, matrix->yx );

    if ( !delta )
      return FT_Err_Invalid_Argument;  /* matrix can't be inverted */

    matrix->xy = - FT_DivFix( matrix->xy, delta );
    matrix->yx = - FT_DivFix( matrix->yx, delta );

    xx = matrix->xx;
    yy = matrix->yy;

    matrix->xx = FT_DivFix( yy, delta );
    matrix->yy = FT_DivFix( xx, delta );

    return FT_Err_Ok;
  }

  static FT_Error
  Set_Char_Sizes( FT_Size     ttsize,       /* TT_Size */
                  FT_F26Dot6  char_width,
                  FT_F26Dot6  char_height,
                  FT_UInt     horz_resolution,
                  FT_UInt     vert_resolution )
  {
    TT_Size           size     = (TT_Size)ttsize;
    FT_Size_Metrics*  metrics  = &size->root.metrics;
    FT_Size_Metrics*  metrics2 = &size->metrics;
    TT_Face           face     = (TT_Face)size->root.face;
    FT_Long           dim_x, dim_y;


    *metrics2 = *metrics;

    /* This bit flag, when set, indicates that the pixel size must be */
    /* truncated to an integer.  Nearly all TrueType fonts have this  */
    /* bit set, as hinting won't work really well otherwise.          */
    /*                                                                */
    if ( ( face->header.Flags & 8 ) != 0 )
    {
     /* we need to use rounding in the following computations. Otherwise,
      * the resulting hinted outlines will be very slightly distorted
      */
      dim_x = ( ( char_width  * horz_resolution + (36+32*72) ) / 72 ) & ~63;
      dim_y = ( ( char_height * vert_resolution + (36+32*72) ) / 72 ) & ~63;
    }
    else
    {
      dim_x = ( ( char_width  * horz_resolution + 36 ) / 72 );
      dim_y = ( ( char_height * vert_resolution + 36 ) / 72 );
    }

    /* we only modify "metrics2", not "metrics", so these changes have */
    /* no effect on the result of the auto-hinter when it is used      */
    /*                                                                 */
    metrics2->x_ppem  = (FT_UShort)( dim_x >> 6 );
    metrics2->y_ppem  = (FT_UShort)( dim_y >> 6 );
    metrics2->x_scale = FT_DivFix( dim_x, face->root.units_per_EM );
    metrics2->y_scale = FT_DivFix( dim_y, face->root.units_per_EM );

    size->ttmetrics.valid = FALSE;
#ifdef TT_CONFIG_OPTION_EMBEDDED_BITMAPS
    size->strike_index    = 0xFFFFU;
#endif

    return tt_size_reset( size );
  }

  /*
   * This check should avoid most internal overflow cases.  Clients should
   * generally respond to `Glyph_Too_Big' by getting a glyph outline
   * at EM size, scaling it and filling it as a graphics operation.
   *
   */
  static FT_Error
  cf2_checkTransform( const CF2_Matrix*  transform,
                      CF2_Int            unitsPerEm )
  {
    CF2_Fixed  maxScale;


    FT_ASSERT( unitsPerEm > 0 );

    if ( transform->a <= 0 || transform->d <= 0 )
      return FT_THROW( Invalid_Size_Handle );

    FT_ASSERT( transform->b == 0 && transform->c == 0 );
    FT_ASSERT( transform->tx == 0 && transform->ty == 0 );

    if ( unitsPerEm > 0x7FFF )
      return FT_THROW( Glyph_Too_Big );

    maxScale = FT_DivFix( CF2_MAX_SIZE, cf2_intToFixed( unitsPerEm ) );

    if ( transform->a > maxScale || transform->d > maxScale )
      return FT_THROW( Glyph_Too_Big );

    return FT_Err_Ok;
  }

  static void
  t42_parse_font_matrix( T42_Face    face,
                         T42_Loader  loader )
  {
    T42_Parser  parser = &loader->parser;
    FT_Matrix*  matrix = &face->type1.font_matrix;
    FT_Vector*  offset = &face->type1.font_offset;
    FT_Face     root   = (FT_Face)&face->root;
    FT_Fixed    temp[6];
    FT_Fixed    temp_scale;


    (void)T1_ToFixedArray( parser, 6, temp, 3 );

    temp_scale = FT_ABS( temp[3] );

    /* Set Units per EM based on FontMatrix values.  We set the value to */
    /* 1000 / temp_scale, because temp_scale was already multiplied by   */
    /* 1000 (in t1_tofixed, from psobjs.c).                              */

    root->units_per_EM = (FT_UShort)( FT_DivFix( 1000 * 0x10000L,
                                                 temp_scale ) >> 16 );

    /* we need to scale the values by 1.0/temp_scale */
    if ( temp_scale != 0x10000L )
    {
      temp[0] = FT_DivFix( temp[0], temp_scale );
      temp[1] = FT_DivFix( temp[1], temp_scale );
      temp[2] = FT_DivFix( temp[2], temp_scale );
      temp[4] = FT_DivFix( temp[4], temp_scale );
      temp[5] = FT_DivFix( temp[5], temp_scale );
      temp[3] = 0x10000L;
    }

    matrix->xx = temp[0];
    matrix->yx = temp[1];
    matrix->xy = temp[2];
    matrix->yy = temp[3];

    /* note that the offsets must be expressed in integer font units */
    offset->x = temp[4] >> 16;
    offset->y = temp[5] >> 16;
  }

  cid_parse_font_matrix( CID_Face     face,
                         CID_Parser*  parser )
  {
    CID_FaceDict  dict;
    FT_Face       root = (FT_Face)&face->root;
    FT_Fixed      temp[6];
    FT_Fixed      temp_scale;


    if ( parser->num_dict >= 0 && parser->num_dict < face->cid.num_dicts )
    {
      FT_Matrix*  matrix;
      FT_Vector*  offset;
      FT_Int      result;


      dict   = face->cid.font_dicts + parser->num_dict;
      matrix = &dict->font_matrix;
      offset = &dict->font_offset;

      result = cid_parser_to_fixed_array( parser, 6, temp, 3 );

      if ( result < 6 )
        return FT_THROW( Invalid_File_Format );

      temp_scale = FT_ABS( temp[3] );

      if ( temp_scale == 0 )
      {
        FT_ERROR(( "cid_parse_font_matrix: invalid font matrix\n" ));
        return FT_THROW( Invalid_File_Format );
      }

      /* Set Units per EM based on FontMatrix values.  We set the value to */
      /* 1000 / temp_scale, because temp_scale was already multiplied by   */
      /* 1000 (in t1_tofixed, from psobjs.c).                              */

      root->units_per_EM = (FT_UShort)FT_DivFix( 1000, temp_scale );

      /* we need to scale the values by 1.0/temp[3] */
      if ( temp_scale != 0x10000L )
      {
        temp[0] = FT_DivFix( temp[0], temp_scale );
        temp[1] = FT_DivFix( temp[1], temp_scale );
        temp[2] = FT_DivFix( temp[2], temp_scale );
        temp[4] = FT_DivFix( temp[4], temp_scale );
        temp[5] = FT_DivFix( temp[5], temp_scale );
        temp[3] = temp[3] < 0 ? -0x10000L : 0x10000L;
      }

      matrix->xx = temp[0];
      matrix->yx = temp[1];
      matrix->xy = temp[2];
      matrix->yy = temp[3];

      /* note that the font offsets are expressed in integer font units */
      offset->x  = temp[4] >> 16;
      offset->y  = temp[5] >> 16;
    }

  pfr_get_metrics( FT_Face    pfrface,      /* PFR_Face */
                   FT_UInt   *anoutline_resolution,
                   FT_UInt   *ametrics_resolution,
                   FT_Fixed  *ametrics_x_scale,
                   FT_Fixed  *ametrics_y_scale )
  {
    PFR_Face     face = (PFR_Face)pfrface;
    PFR_PhyFont  phys = &face->phy_font;
    FT_Fixed     x_scale, y_scale;
    FT_Size      size = face->root.size;


    if ( anoutline_resolution )
      *anoutline_resolution = phys->outline_resolution;

    if ( ametrics_resolution )
      *ametrics_resolution = phys->metrics_resolution;

    x_scale = 0x10000L;
    y_scale = 0x10000L;

    if ( size )
    {
      x_scale = FT_DivFix( size->metrics.x_ppem << 6,
                           phys->metrics_resolution );

      y_scale = FT_DivFix( size->metrics.y_ppem << 6,
                           phys->metrics_resolution );
    }

    if ( ametrics_x_scale )
      *ametrics_x_scale = x_scale;

    if ( ametrics_y_scale )
      *ametrics_y_scale = y_scale;

    return PFR_Err_Ok;
  }

  static FT_Error
  pfr_get_metrics( PFR_Face   face,
                   FT_UInt   *aoutline_resolution,
                   FT_UInt   *ametrics_resolution,
                   FT_Fixed  *ametrics_x_scale,
                   FT_Fixed  *ametrics_y_scale )
  {
    PFR_PhyFont  phys  = &face->phy_font;
    FT_Fixed     x_scale, y_scale;
    FT_Size      size = face->root.size;

    if ( aoutline_resolution )
      *aoutline_resolution = phys->outline_resolution;

    if ( ametrics_resolution )
      *ametrics_resolution = phys->metrics_resolution;

    x_scale = 0x10000L;
    y_scale = 0x10000L;

    if ( size )
    {
      x_scale = FT_DivFix( size->metrics.x_ppem << 6,
                           phys->metrics_resolution );

      y_scale = FT_DivFix( size->metrics.y_ppem << 6,
                           phys->metrics_resolution );
    }

    if ( ametrics_x_scale )
      *ametrics_x_scale = x_scale;

    if ( ametrics_y_scale )
      *ametrics_y_scale = y_scale;

    return 0;
  }

  cid_parse_font_matrix( CID_Face     face,
                         CID_Parser*  parser )
  {
    CID_FaceDict  dict;
    FT_Face       root = (FT_Face)&face->root;
    FT_Fixed      temp[6];
    FT_Fixed      temp_scale;


    if ( parser->num_dict >= 0 && parser->num_dict < face->cid.num_dicts )
    {
      FT_Matrix*  matrix;
      FT_Vector*  offset;
      FT_Int      result;


      dict   = face->cid.font_dicts + parser->num_dict;
      matrix = &dict->font_matrix;
      offset = &dict->font_offset;

      /* input is scaled by 1000 to accommodate default FontMatrix */
      result = cid_parser_to_fixed_array( parser, 6, temp, 3 );

      if ( result < 6 )
        return FT_THROW( Invalid_File_Format );

      temp_scale = FT_ABS( temp[3] );

      if ( temp_scale == 0 )
      {
        FT_ERROR(( "cid_parse_font_matrix: invalid font matrix\n" ));
        return FT_THROW( Invalid_File_Format );
      }

      /* atypical case */
      if ( temp_scale != 0x10000L )
      {
        /* set units per EM based on FontMatrix values */
        root->units_per_EM = (FT_UShort)FT_DivFix( 1000, temp_scale );

        temp[0] = FT_DivFix( temp[0], temp_scale );
        temp[1] = FT_DivFix( temp[1], temp_scale );
        temp[2] = FT_DivFix( temp[2], temp_scale );
        temp[4] = FT_DivFix( temp[4], temp_scale );
        temp[5] = FT_DivFix( temp[5], temp_scale );
        temp[3] = temp[3] < 0 ? -0x10000L : 0x10000L;
      }

      matrix->xx = temp[0];
      matrix->yx = temp[1];
      matrix->xy = temp[2];
      matrix->yy = temp[3];

      /* note that the font offsets are expressed in integer font units */
      offset->x  = temp[4] >> 16;
      offset->y  = temp[5] >> 16;
    }

  static void
  t42_parse_font_matrix( T42_Face    face,
                         T42_Loader  loader )
  {
    T42_Parser  parser = &loader->parser;
    FT_Matrix*  matrix = &face->type1.font_matrix;
    FT_Vector*  offset = &face->type1.font_offset;
    FT_Face     root   = (FT_Face)&face->root;
    FT_Fixed    temp[6];
    FT_Fixed    temp_scale;
    FT_Int      result;


    result = T1_ToFixedArray( parser, 6, temp, 3 );

    if ( result < 6 )
    {
      parser->root.error = FT_THROW( Invalid_File_Format );
      return;
    }

    temp_scale = FT_ABS( temp[3] );

    if ( temp_scale == 0 )
    {
      FT_ERROR(( "t1_parse_font_matrix: invalid font matrix\n" ));
      parser->root.error = FT_THROW( Invalid_File_Format );
      return;
    }

    /* Set Units per EM based on FontMatrix values.  We set the value to */
    /* 1000 / temp_scale, because temp_scale was already multiplied by   */
    /* 1000 (in t1_tofixed, from psobjs.c).                              */

    root->units_per_EM = (FT_UShort)FT_DivFix( 1000, temp_scale );

    /* we need to scale the values by 1.0/temp_scale */
    if ( temp_scale != 0x10000L )
    {
      temp[0] = FT_DivFix( temp[0], temp_scale );
      temp[1] = FT_DivFix( temp[1], temp_scale );
      temp[2] = FT_DivFix( temp[2], temp_scale );
      temp[4] = FT_DivFix( temp[4], temp_scale );
      temp[5] = FT_DivFix( temp[5], temp_scale );
      temp[3] = temp[3] < 0 ? -0x10000L : 0x10000L;
    }

    matrix->xx = temp[0];
    matrix->yx = temp[1];
    matrix->xy = temp[2];
    matrix->yy = temp[3];

    /* note that the offsets must be expressed in integer font units */
    offset->x = temp[4] >> 16;
    offset->y = temp[5] >> 16;
  }

  cf2_getBlueMetrics( CFF_Decoder*  decoder,
                      CF2_Fixed*    blueScale,
                      CF2_Fixed*    blueShift,
                      CF2_Fixed*    blueFuzz )
  {
    FT_ASSERT( decoder && decoder->current_subfont );

    *blueScale = FT_DivFix(
                   decoder->current_subfont->private_dict.blue_scale,
                   cf2_intToFixed( 1000 ) );
    *blueShift = cf2_intToFixed(
                   decoder->current_subfont->private_dict.blue_shift );
    *blueFuzz  = cf2_intToFixed(
                   decoder->current_subfont->private_dict.blue_fuzz );
  }

  parse_font_matrix( CID_Face     face,
                     CID_Parser*  parser )
  {
    FT_Matrix*    matrix;
    FT_Vector*    offset;
    CID_FaceDict  dict;
    FT_Face       root = (FT_Face)&face->root;
    FT_Fixed      temp[6];
    FT_Fixed      temp_scale;


    if ( parser->num_dict >= 0 )
    {
      dict   = face->cid.font_dicts + parser->num_dict;
      matrix = &dict->font_matrix;
      offset = &dict->font_offset;

      (void)cid_parser_to_fixed_array( parser, 6, temp, 3 );

      temp_scale = FT_ABS( temp[3] );

      /* Set units per EM based on FontMatrix values.  We set the value to */
      /* `1000/temp_scale', because temp_scale was already multiplied by   */
      /* 1000 (in `t1_tofixed', from psobjs.c).                            */
      root->units_per_EM = (FT_UShort)( FT_DivFix( 0x10000L,
                                        FT_DivFix( temp_scale, 1000 ) ) );

      /* we need to scale the values by 1.0/temp[3] */
      if ( temp_scale != 0x10000L )
      {
        temp[0] = FT_DivFix( temp[0], temp_scale );
        temp[1] = FT_DivFix( temp[1], temp_scale );
        temp[2] = FT_DivFix( temp[2], temp_scale );
        temp[4] = FT_DivFix( temp[4], temp_scale );
        temp[5] = FT_DivFix( temp[5], temp_scale );
        temp[3] = 0x10000L;
      }

      matrix->xx = temp[0];
      matrix->yx = temp[1];
      matrix->xy = temp[2];
      matrix->yy = temp[3];

      /* note that the font offsets are expressed in integer font units */
      offset->x  = temp[4] >> 16;
      offset->y  = temp[5] >> 16;
    }

tt_size_reset( TT_Size  size )
{
    TT_Face           face;
    FT_Error          error = FT_Err_Ok;
    FT_Size_Metrics*  metrics;


    size->ttmetrics.valid = FALSE;

    face = (TT_Face)size->root.face;

    metrics = &size->metrics;

    /* copy the result from base layer */
    *metrics = size->root.metrics;

    if ( metrics->x_ppem < 1 || metrics->y_ppem < 1 )
        return FT_THROW( Invalid_PPem );

    /* This bit flag, if set, indicates that the ppems must be       */
    /* rounded to integers.  Nearly all TrueType fonts have this bit */
    /* set, as hinting won't work really well otherwise.             */
    /*                                                               */
    if ( face->header.Flags & 8 )
    {
        metrics->x_scale = FT_DivFix( metrics->x_ppem << 6,
                                      face->root.units_per_EM );
        metrics->y_scale = FT_DivFix( metrics->y_ppem << 6,
                                      face->root.units_per_EM );

        metrics->ascender =
            FT_PIX_ROUND( FT_MulFix( face->root.ascender, metrics->y_scale ) );
        metrics->descender =
            FT_PIX_ROUND( FT_MulFix( face->root.descender, metrics->y_scale ) );
        metrics->height =
            FT_PIX_ROUND( FT_MulFix( face->root.height, metrics->y_scale ) );
        metrics->max_advance =
            FT_PIX_ROUND( FT_MulFix( face->root.max_advance_width,
                                     metrics->x_scale ) );
    }

    /* compute new transformation */
    if ( metrics->x_ppem >= metrics->y_ppem )
    {
        size->ttmetrics.scale   = metrics->x_scale;
        size->ttmetrics.ppem    = metrics->x_ppem;
        size->ttmetrics.x_ratio = 0x10000L;
        size->ttmetrics.y_ratio = FT_DivFix( metrics->y_ppem,
                                             metrics->x_ppem );
    }
    else
    {
        size->ttmetrics.scale   = metrics->y_scale;
        size->ttmetrics.ppem    = metrics->y_ppem;
        size->ttmetrics.x_ratio = FT_DivFix( metrics->x_ppem,
                                             metrics->y_ppem );
        size->ttmetrics.y_ratio = 0x10000L;
    }

#ifdef TT_USE_BYTECODE_INTERPRETER
    size->cvt_ready = -1;
#endif /* TT_USE_BYTECODE_INTERPRETER */

    if ( !error )
        size->ttmetrics.valid = TRUE;

    return error;
}

  static FT_Error
  af_cjk_hints_compute_edges( AF_GlyphHints  hints,
                              AF_Dimension   dim )
  {
    AF_AxisHints  axis   = &hints->axis[dim];
    FT_Error      error  = AF_Err_Ok;
    FT_Memory     memory = hints->memory;
    AF_LatinAxis  laxis  = &((AF_LatinMetrics)hints->metrics)->axis[dim];

    AF_Segment    segments      = axis->segments;
    AF_Segment    segment_limit = segments + axis->num_segments;
    AF_Segment    seg;

    FT_Fixed      scale;
    FT_Pos        edge_distance_threshold;


    axis->num_edges = 0;

    scale = ( dim == AF_DIMENSION_HORZ ) ? hints->x_scale
                                         : hints->y_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 is then processed in the second step to compute the    */
    /* edge's properties.                                                */
    /*                                                                   */
    /* Note that the edges table is sorted along the segment/edge        */
    /* position.                                                         */
    /*                                                                   */
    /*********************************************************************/

    edge_distance_threshold = FT_MulFix( laxis->edge_distance_threshold,
                                         scale );
    if ( edge_distance_threshold > 64 / 4 )
      edge_distance_threshold = FT_DivFix( 64 / 4, scale );
    else
      edge_distance_threshold = laxis->edge_distance_threshold;

    for ( seg = segments; seg < segment_limit; seg++ )
    {
      AF_Edge  found = 0;
      FT_Pos   best  = 0xFFFFU;
      FT_Int   ee;


      /* 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;


        if ( edge->dir != seg->dir )
          continue;

        dist = seg->pos - edge->fpos;
        if ( dist < 0 )
          dist = -dist;

        if ( dist < edge_distance_threshold && dist < best )
        {
          AF_Segment  link = seg->link;


          /* check whether all linked segments of the candidate edge */
          /* can make a single edge.                                 */
          if ( link )
          {
            AF_Segment  seg1 = edge->first;
            AF_Segment  link1;
            FT_Pos      dist2 = 0;


            do
            {
              link1 = seg1->link;
              if ( link1 )
              {
                dist2 = AF_SEGMENT_DIST( link, link1 );
                if ( dist2 >= edge_distance_threshold )
                  break;
              }

            } while ( ( seg1 = seg1->edge_next ) != edge->first );

            if ( dist2 >= edge_distance_threshold )
              continue;
          }

          best  = dist;
          found = edge;
        }
      }
//.........这里部分代码省略.........

  static void
  af_cjk_hints_link_segments( AF_GlyphHints  hints,
                              AF_Dimension   dim )
  {
    AF_AxisHints  axis          = &hints->axis[dim];
    AF_Segment    segments      = axis->segments;
    AF_Segment    segment_limit = segments + axis->num_segments;
    AF_Direction  major_dir     = axis->major_dir;
    AF_Segment    seg1, seg2;
    FT_Pos        len_threshold;
    FT_Pos        dist_threshold;


    len_threshold = AF_LATIN_CONSTANT( hints->metrics, 8 );

    dist_threshold = ( dim == AF_DIMENSION_HORZ ) ? hints->x_scale
                                                  : hints->y_scale;
    dist_threshold = FT_DivFix( 64 * 3, dist_threshold );

    /* now compare each segment to the others */
    for ( seg1 = segments; seg1 < segment_limit; seg1++ )
    {
      /* the fake segments are for metrics hinting only */
      if ( seg1->first == seg1->last )
        continue;

      if ( seg1->dir != major_dir )
        continue;

      for ( seg2 = segments; seg2 < segment_limit; seg2++ )
        if ( seg2 != seg1 && seg1->dir + seg2->dir == 0 )
        {
          FT_Pos  dist = seg2->pos - seg1->pos;


          if ( dist < 0 )
            continue;

          {
            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;

            len = max - min;
            if ( len >= len_threshold )
            {
              if ( dist * 8 < seg1->score * 9                        &&
                   ( dist * 8 < seg1->score * 7 || seg1->len < len ) )
              {
                seg1->score = dist;
                seg1->len   = len;
                seg1->link  = seg2;
              }

              if ( dist * 8 < seg2->score * 9                        &&
                   ( dist * 8 < seg2->score * 7 || seg2->len < len ) )
              {
                seg2->score = dist;
                seg2->len   = len;
                seg2->link  = seg1;
              }
            }
          }
        }
    }

    /*
     *  now compute the `serif' segments
     *
     *  In Hanzi, some strokes are wider on one or both of the ends.
     *  We either identify the stems on the ends as serifs or remove
     *  the linkage, depending on the length of the stems.
     *
     */

    {
      AF_Segment  link1, link2;


      for ( seg1 = segments; seg1 < segment_limit; seg1++ )
      {
        link1 = seg1->link;
        if ( !link1 || link1->link != seg1 || link1->pos <= seg1->pos )
          continue;

        if ( seg1->score >= dist_threshold )
          continue;

        for ( seg2 = segments; seg2 < segment_limit; seg2++ )
        {
          if ( seg2->pos > seg1->pos || seg1 == seg2 )
            continue;

//.........这里部分代码省略.........

  static FT_Error
  af_loader_embolden_glyph_in_slot( AF_Loader        loader,
                                    FT_Face          face,
                                    AF_StyleMetrics  style_metrics )
  {
    FT_Error  error = FT_Err_Ok;

    FT_GlyphSlot           slot    = face->glyph;
    AF_FaceGlobals         globals = loader->globals;
    AF_WritingSystemClass  writing_system_class;

    FT_Size_Metrics*  size_metrics = &face->size->internal->autohint_metrics;

    FT_Pos  stdVW = 0;
    FT_Pos  stdHW = 0;

    FT_Bool  size_changed = size_metrics->x_ppem !=
                              globals->stem_darkening_for_ppem;

    FT_Fixed  em_size  = af_intToFixed( face->units_per_EM );
    FT_Fixed  em_ratio = FT_DivFix( af_intToFixed( 1000 ), em_size );

    FT_Matrix  scale_down_matrix = { 0x10000L, 0, 0, 0x10000L };


    /* Skip stem darkening for broken fonts. */
    if ( !face->units_per_EM )
    {
      error = FT_ERR( Corrupted_Font_Header );
      goto Exit;
    }

    /*
     * We depend on the writing system (script analyzers) to supply
     * standard widths for the script of the glyph we are looking at.  If
     * it can't deliver, stem darkening is disabled.
     */
    writing_system_class =
      af_writing_system_classes[style_metrics->style_class->writing_system];

    if ( writing_system_class->style_metrics_getstdw )
      writing_system_class->style_metrics_getstdw( style_metrics,
                                                   &stdHW,
                                                   &stdVW );
    else
    {
      error = FT_ERR( Unimplemented_Feature );
      goto Exit;
    }

    if ( size_changed                                               ||
         ( stdVW > 0 && stdVW != globals->standard_vertical_width ) )
    {
      FT_Fixed  darken_by_font_units_x, darken_x;


      darken_by_font_units_x =
        af_intToFixed( af_loader_compute_darkening( loader,
                                                    face,
                                                    stdVW ) );
      darken_x = FT_DivFix( FT_MulFix( darken_by_font_units_x,
                                       size_metrics->x_scale ),
                            em_ratio );

      globals->standard_vertical_width = stdVW;
      globals->stem_darkening_for_ppem = size_metrics->x_ppem;
      globals->darken_x                = af_fixedToInt( darken_x );
    }

    if ( size_changed                                                 ||
         ( stdHW > 0 && stdHW != globals->standard_horizontal_width ) )
    {
      FT_Fixed  darken_by_font_units_y, darken_y;


      darken_by_font_units_y =
        af_intToFixed( af_loader_compute_darkening( loader,
                                                    face,
                                                    stdHW ) );
      darken_y = FT_DivFix( FT_MulFix( darken_by_font_units_y,
                                       size_metrics->y_scale ),
                            em_ratio );

      globals->standard_horizontal_width = stdHW;
      globals->stem_darkening_for_ppem   = size_metrics->x_ppem;
      globals->darken_y                  = af_fixedToInt( darken_y );

      /*
       * Scale outlines down on the Y-axis to keep them inside their blue
       * zones.  The stronger the emboldening, the stronger the downscaling
       * (plus heuristical padding to prevent outlines still falling out
       * their zones due to rounding).
       *
       * Reason: `FT_Outline_Embolden' works by shifting the rightmost
       * points of stems farther to the right, and topmost points farther
       * up.  This positions points on the Y-axis outside their
       * pre-computed blue zones and leads to distortion when applying the
       * hints in the code further below.  Code outside this emboldening
       * block doesn't know we are presenting it with modified outlines the
       * analyzer didn't see!
//.........这里部分代码省略.........

  static FT_Error
  af_loader_load_g( AF_Loader  loader,
                    AF_Scaler  scaler,
                    FT_UInt    glyph_index,
                    FT_Int32   load_flags )
  {
    AF_Module  module = loader->globals->module;

    FT_Error          error;
    FT_Face           face     = loader->face;
    AF_StyleMetrics   metrics  = loader->metrics;
    AF_GlyphHints     hints    = loader->hints;
    FT_GlyphSlot      slot     = face->glyph;
    FT_Slot_Internal  internal = slot->internal;
    FT_GlyphLoader    gloader  = internal->loader;
    FT_Int32          flags;


    flags = load_flags | FT_LOAD_LINEAR_DESIGN;
    error = FT_Load_Glyph( face, glyph_index, flags );
    if ( error )
      goto Exit;

    /*
     * Apply stem darkening (emboldening) here before hints are applied to
     * the outline.  Glyphs are scaled down proportionally to the
     * emboldening so that curve points don't fall outside their precomputed
     * blue zones.
     *
     * Any emboldening done by the font driver (e.g., the CFF driver)
     * doesn't reach here because the autohinter loads the unprocessed
     * glyphs in font units for analysis (functions `af_*_metrics_init_*')
     * and then above to prepare it for the rasterizers by itself,
     * independently of the font driver.  So emboldening must be done here,
     * within the autohinter.
     *
     * All glyphs to be autohinted pass through here one by one.  The
     * standard widths can therefore change from one glyph to the next,
     * depending on what script a glyph is assigned to (each script has its
     * own set of standard widths and other metrics).  The darkening amount
     * must therefore be recomputed for each size and
     * `standard_{vertical,horizontal}_width' change.
     */
    if ( !module->no_stem_darkening )
    {
      AF_FaceGlobals         globals = loader->globals;
      AF_WritingSystemClass  writing_system_class;

      FT_Pos  stdVW = 0;
      FT_Pos  stdHW = 0;

      FT_Bool  size_changed = face->size->metrics.x_ppem
                                != globals->stem_darkening_for_ppem;

      FT_Fixed  em_size  = af_intToFixed( face->units_per_EM );
      FT_Fixed  em_ratio = FT_DivFix( af_intToFixed( 1000 ), em_size );

      FT_Matrix  scale_down_matrix = { 0x10000L, 0, 0, 0x10000L };


      /* Skip stem darkening for broken fonts. */
      if ( !face->units_per_EM )
        goto After_Emboldening;

      /*
       * We depend on the writing system (script analyzers) to supply
       * standard widths for the script of the glyph we are looking at.  If
       * it can't deliver, stem darkening is effectively disabled.
       */
      writing_system_class =
        AF_WRITING_SYSTEM_CLASSES_GET[metrics->style_class->writing_system];

      if ( writing_system_class->style_metrics_getstdw )
        writing_system_class->style_metrics_getstdw( metrics,
                                                     &stdHW,
                                                     &stdVW );
      else
        goto After_Emboldening;


      if ( size_changed                                               ||
           ( stdVW > 0 && stdVW != globals->standard_vertical_width ) )
      {
        FT_Fixed  darken_by_font_units_x, darken_x;


        darken_by_font_units_x =
          af_intToFixed( af_loader_compute_darkening( loader,
                                                      face,
                                                      stdVW ) );
        darken_x = FT_DivFix( FT_MulFix( darken_by_font_units_x,
                                         face->size->metrics.x_scale ),
                              em_ratio );

        globals->standard_vertical_width = stdVW;
        globals->stem_darkening_for_ppem = face->size->metrics.x_ppem;
        globals->darken_x                = af_fixedToInt( darken_x );
      }

      if ( size_changed                                                 ||
//.........这里部分代码省略.........

static void GK_Outline_Embolden(FT_Outline* outline,FT_Pos strength,int* x_left,int* x_right,int* y_bottom,int* y_top)
{
    FT_Vector*  points;
    FT_Vector   v_prev, v_first, v_next, v_cur;
    FT_Angle    rotate, angle_in, angle_out;
    FT_Int      c, n, first = 0;
    FT_Int      orientation;
    FT_Int      min_x = 35565, max_x = -35565, min_y = 35565, max_y = -35565;
    FT_Int      new_min_x = 35565, new_max_x = -35565, new_min_y = 35565, new_max_y = -35565;

    if (!outline) return;

    strength /= 2;
    if ( strength == 0 ) return;

    orientation = FT_Outline_Get_Orientation(outline);
    if (orientation == FT_ORIENTATION_NONE) return;

#ifdef GLYPH_LOG
    if (glyph_log) { fprintf(glyph_log,"            Emboldening the outline by %ld:\n",strength); }
#endif

    if (orientation == FT_ORIENTATION_TRUETYPE) rotate = -FT_ANGLE_PI2;
    else rotate = FT_ANGLE_PI2;

    points = outline->points;

    for ( c = 0; c < outline->n_contours; c++ )
    {
        int last = outline->contours[c];

        v_first = points[first];
        v_prev  = points[last];
        v_cur   = v_first;

        for ( n = first; n <= last; n++ )
        {
            FT_Vector  in, out;
            FT_Angle   angle_diff;
            FT_Pos     d;
            FT_Fixed   scale;

            if ( n < last ) v_next = points[n + 1];
            else v_next = v_first;

            /* compute the in and out vectors */
            in.x = v_cur.x - v_prev.x;
            in.y = v_cur.y - v_prev.y;

            out.x = v_next.x - v_cur.x;
            out.y = v_next.y - v_cur.y;

            angle_in   = FT_Atan2( in.x, in.y );
            angle_out  = FT_Atan2( out.x, out.y );
            angle_diff = FT_Angle_Diff( angle_in, angle_out );
            scale      = FT_Cos( angle_diff / 2 );

            if ( scale < 0x4000L && scale > -0x4000L ) in.x = in.y = 0;
            else
            {
                d = FT_DivFix( strength, scale );
                FT_Vector_From_Polar( &in, d, angle_in + angle_diff / 2 - rotate );
            }

            outline->points[n].x = v_cur.x + strength + in.x;
            outline->points[n].y = v_cur.y + strength + in.y;

            if (v_cur.x < min_x) min_x = v_cur.x;
            if (v_cur.x > max_x) max_x = v_cur.x;
            if (v_cur.y < min_y) min_y = v_cur.y;
            if (v_cur.y > max_y) max_y = v_cur.y;

            if (outline->points[n].x < new_min_x) new_min_x = outline->points[n].x;
            if (outline->points[n].x > new_max_x) new_max_x = outline->points[n].x;
            if (outline->points[n].y < new_min_y) new_min_y = outline->points[n].y;
            if (outline->points[n].y > new_max_y) new_max_y = outline->points[n].y;

            v_prev = v_cur;
            v_cur  = v_next;
        }

        first = last + 1;
    }

    *x_left = min_x - new_min_x;
    *x_right = new_max_x - max_x;
    *y_top = new_max_y - max_y;
    *y_bottom = min_y - new_min_y;

#ifdef GLYPH_LOG
    if (glyph_log)
    {
        fprintf(glyph_log,"                (%d..%d x %d..%d) -> (%d..%d x %d..%d)\n",
                           min_x,max_x,min_y,max_y,new_min_x,new_max_x,new_min_y,new_max_y);
    }
#endif
}

//.........这里部分代码省略.........

    /* examine (at most) a pixel wide range around the natural width */
    warper->wmin = warper->x2min - warper->x1max;
    warper->wmax = warper->x2max - warper->x1min;

#if 1
    /* some heuristics to reduce the number of widths to be examined */
    {
      int  margin = 16;


      if ( warper->w0 <= 128 )
      {
         margin = 8;
         if ( warper->w0 <= 96 )
           margin = 4;
      }

      if ( warper->wmin < warper->w0 - margin )
        warper->wmin = warper->w0 - margin;

      if ( warper->wmax > warper->w0 + margin )
        warper->wmax = warper->w0 + margin;
    }

    if ( warper->wmin < warper->w0 * 3 / 4 )
      warper->wmin = warper->w0 * 3 / 4;

    if ( warper->wmax > warper->w0 * 5 / 4 )
      warper->wmax = warper->w0 * 5 / 4;
#else
    /* no scaling, just translation */
    warper->wmin = warper->wmax = warper->w0;
#endif

    for ( w = warper->wmin; w <= warper->wmax; w++ )
    {
      FT_Fixed  new_scale;
      FT_Pos    new_delta;
      FT_Pos    xx1, xx2;


      /* compute min and max positions for given width,       */
      /* assuring that they stay within the coordinate ranges */
      xx1 = warper->x1;