shithub: purgatorio

ref: a8083462e62459b2ae8a243dc4ba88416eba03b1

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/***************************************************************************/
/*                                                                         */
/*  ahglyph.c                                                              */
/*                                                                         */
/*    Routines used to load and analyze a given glyph before hinting       */
/*    (body).                                                              */
/*                                                                         */
/*  Copyright 2000-2001, 2002 Catharon Productions Inc.                    */
/*  Author: David Turner                                                   */
/*                                                                         */
/*  This file is part of the Catharon Typography Project and shall only    */
/*  be used, modified, and distributed under the terms of the Catharon     */
/*  Open Source License that should come with this file under the name     */
/*  `CatharonLicense.txt'.  By continuing to use, modify, or distribute    */
/*  this file you indicate that you have read the license and              */
/*  understand and accept it fully.                                        */
/*                                                                         */
/*  Note that this license is compatible with the FreeType license.        */
/*                                                                         */
/***************************************************************************/


#include <ft2build.h>
#include "ahglyph.h"
#include "ahangles.h"
#include "ahglobal.h"
#include "aherrors.h"


#ifdef AH_DEBUG

#include <stdio.h>

  void
  ah_dump_edges( AH_Outline  outline )
  {
    AH_Edge     edges;
    AH_Edge     edge_limit;
    AH_Segment  segments;
    FT_Int      dimension;


    edges      = outline->horz_edges;
    edge_limit = edges + outline->num_hedges;
    segments   = outline->horz_segments;

    for ( dimension = 1; dimension >= 0; dimension-- )
    {
      AH_Edge   edge;


      printf ( "Table of %s edges:\n",
               !dimension ? "vertical" : "horizontal" );
      printf ( "  [ index |  pos |  dir  | link |"
               " serif | blue | opos  |  pos  ]\n" );

      for ( edge = edges; edge < edge_limit; edge++ )
      {
        printf ( "  [ %5d | %4d | %5s | %4d | %5d |  %c  | %5.2f | %5.2f ]\n",
                 edge - edges,
                 (int)edge->fpos,
                 edge->dir == AH_DIR_UP
                   ? "up"
                   : ( edge->dir == AH_DIR_DOWN
                         ? "down"
                         : ( edge->dir == AH_DIR_LEFT
                               ? "left"
                               : ( edge->dir == AH_DIR_RIGHT
                                     ? "right"
                                     : "none" ) ) ),
                 edge->link ? ( edge->link - edges ) : -1,
                 edge->serif ? ( edge->serif - edges ) : -1,
                 edge->blue_edge ? 'y' : 'n',
                 edge->opos / 64.0,
                 edge->pos / 64.0 );
      }

      edges      = outline->vert_edges;
      edge_limit = edges + outline->num_vedges;
      segments   = outline->vert_segments;
    }
  }


  /* A function used to dump the array of linked segments */
  void
  ah_dump_segments( AH_Outline  outline )
  {
    AH_Segment  segments;
    AH_Segment  segment_limit;
    AH_Point    points;
    FT_Int      dimension;


    points        = outline->points;
    segments      = outline->horz_segments;
    segment_limit = segments + outline->num_hsegments;

    for ( dimension = 1; dimension >= 0; dimension-- )
    {
      AH_Segment  seg;


      printf ( "Table of %s segments:\n",
               !dimension ? "vertical" : "horizontal" );
      printf ( "  [ index |  pos |  dir  | link | serif |"
               " numl | first | start ]\n" );

      for ( seg = segments; seg < segment_limit; seg++ )
      {
        printf ( "  [ %5d | %4d | %5s | %4d | %5d | %4d | %5d | %5d ]\n",
                 seg - segments,
                 (int)seg->pos,
                 seg->dir == AH_DIR_UP
                   ? "up"
                   : ( seg->dir == AH_DIR_DOWN
                         ? "down"
                         : ( seg->dir == AH_DIR_LEFT
                               ? "left"
                               : ( seg->dir == AH_DIR_RIGHT
                                     ? "right"
                                     : "none" ) ) ),
                 seg->link ? (seg->link-segments) : -1,
                 seg->serif ? (seg->serif-segments) : -1,
                 (int)seg->num_linked,
                 seg->first - points,
                 seg->last - points );
      }

      segments      = outline->vert_segments;
      segment_limit = segments + outline->num_vsegments;
    }
  }

#endif /* AH_DEBUG */


  /* compute the direction value of a given vector.. */
  static AH_Direction
  ah_compute_direction( FT_Pos  dx,
                        FT_Pos  dy )
  {
    AH_Direction  dir;
    FT_Pos        ax = ABS( dx );
    FT_Pos        ay = ABS( dy );


    dir = AH_DIR_NONE;

    /* test for vertical direction */
    if ( ax * 12 < ay )
    {
      dir = dy > 0 ? AH_DIR_UP : AH_DIR_DOWN;
    }
    /* test for horizontal direction */
    else if ( ay * 12 < ax )
    {
      dir = dx > 0 ? AH_DIR_RIGHT : AH_DIR_LEFT;
    }

    return dir;
  }


  /* this function is used by ah_get_orientation (see below) to test */
  /* the fill direction of a given bbox extrema                      */
  static FT_Int
  ah_test_extrema( FT_Outline*  outline,
                   FT_Int       n )
  {
    FT_Vector  *prev, *cur, *next;
    FT_Pos      product;
    FT_Int      first, last, c;
    FT_Int      retval;


    /* we need to compute the `previous' and `next' point */
    /* for these extrema                                  */
    cur  = outline->points + n;
    prev = cur - 1;
    next = cur + 1;

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

      if ( n == first )
        prev = outline->points + last;

      if ( n == last )
        next = outline->points + first;

      first = last + 1;
    }

    product = FT_MulDiv( cur->x  - prev->x,  /* in.x  */
                         next->y - cur->y,   /* out.y */
                         0x40 )
              -
              FT_MulDiv( cur->y  - prev->y,  /* in.y  */
                         next->x - cur->x,   /* out.x */
                         0x40 );

    retval = 0;
    if ( product )
      retval = product > 0 ? 2 : 1;

    return retval;
  }


  /* Compute the orientation of path filling.  It differs between TrueType */
  /* and Type1 formats.  We could use the `FT_OUTLINE_REVERSE_FILL' flag,  */
  /* but it is better to re-compute it directly (it seems that this flag   */
  /* isn't correctly set for some weird composite glyphs currently).       */
  /*                                                                       */
  /* We do this by computing bounding box points, and computing their      */
  /* curvature.                                                            */
  /*                                                                       */
  /* The function returns either 1 or -1.                                  */
  /*                                                                       */
  static FT_Int
  ah_get_orientation( FT_Outline*  outline )
  {
    FT_BBox  box;
    FT_Int   indices_xMin, indices_yMin, indices_xMax, indices_yMax;
    FT_Int   n, last;


    indices_xMin = -1;
    indices_yMin = -1;
    indices_xMax = -1;
    indices_yMax = -1;

    box.xMin = box.yMin =  32767L;
    box.xMax = box.yMax = -32768L;

    /* is it empty? */
    if ( outline->n_contours < 1 )
      return 1;

    last = outline->contours[outline->n_contours - 1];

    for ( n = 0; n <= last; n++ )
    {
      FT_Pos  x, y;


      x = outline->points[n].x;
      if ( x < box.xMin )
      {
        box.xMin     = x;
        indices_xMin = n;
      }
      if ( x > box.xMax )
      {
        box.xMax     = x;
        indices_xMax = n;
      }

      y = outline->points[n].y;
      if ( y < box.yMin )
      {
        box.yMin     = y;
        indices_yMin = n;
      }
      if ( y > box.yMax )
      {
        box.yMax     = y;
        indices_yMax = n;
      }
    }

    /* test orientation of the xmin */
    n = ah_test_extrema( outline, indices_xMin );
    if ( n )
      goto Exit;

    n = ah_test_extrema( outline, indices_yMin );
    if ( n )
      goto Exit;

    n = ah_test_extrema( outline, indices_xMax );
    if ( n )
      goto Exit;

    n = ah_test_extrema( outline, indices_yMax );
    if ( !n )
      n = 1;

  Exit:
    return n;
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    ah_outline_new                                                     */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Creates a new and empty AH_OutlineRec object.                      */
  /*                                                                       */
  FT_LOCAL_DEF( FT_Error )
  ah_outline_new( FT_Memory    memory,
                  AH_Outline*  aoutline )
  {
    FT_Error     error;
    AH_Outline   outline;


    if ( !FT_NEW( outline ) )
    {
      outline->memory = memory;
      *aoutline = outline;
    }

    return error;
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    ah_outline_done                                                    */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Destroys a given AH_OutlineRec object.                             */
  /*                                                                       */
  FT_LOCAL_DEF( void )
  ah_outline_done( AH_Outline  outline )
  {
    FT_Memory memory = outline->memory;


    FT_FREE( outline->horz_edges );
    FT_FREE( outline->horz_segments );
    FT_FREE( outline->contours );
    FT_FREE( outline->points );

    FT_FREE( outline );
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    ah_outline_save                                                    */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Saves the contents of a given AH_OutlineRec object into a face's   */
  /*    glyph slot.                                                        */
  /*                                                                       */
  FT_LOCAL_DEF( void )
  ah_outline_save( AH_Outline  outline,
                   AH_Loader   gloader )
  {
    AH_Point    point       = outline->points;
    AH_Point    point_limit = point + outline->num_points;
    FT_Vector*  vec         = gloader->current.outline.points;
    char*       tag         = gloader->current.outline.tags;


    /* we assume that the glyph loader has already been checked for storage */
    for ( ; point < point_limit; point++, vec++, tag++ )
    {
      vec->x = point->x;
      vec->y = point->y;

      if ( point->flags & AH_FLAG_CONIC )
        tag[0] = FT_CURVE_TAG_CONIC;
      else if ( point->flags & AH_FLAG_CUBIC )
        tag[0] = FT_CURVE_TAG_CUBIC;
      else
        tag[0] = FT_CURVE_TAG_ON;
    }
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    ah_outline_load                                                    */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Loads an unscaled outline from a glyph slot into an AH_OutlineRec  */
  /*    object.                                                            */
  /*                                                                       */
  FT_LOCAL_DEF( FT_Error )
  ah_outline_load( AH_Outline  outline,
                   FT_Face     face )
  {
    FT_Memory    memory       = outline->memory;
    FT_Error     error        = AH_Err_Ok;
    FT_Outline*  source       = &face->glyph->outline;
    FT_Int       num_points   = source->n_points;
    FT_Int       num_contours = source->n_contours;
    AH_Point     points;


    /* check arguments */
    if ( !face                                          ||
         !face->size                                    ||
         face->glyph->format != FT_GLYPH_FORMAT_OUTLINE )
      return AH_Err_Invalid_Argument;

    /* first of all, reallocate the contours array if necessary */
    if ( num_contours > outline->max_contours )
    {
      FT_Int  new_contours = ( num_contours + 3 ) & -4;


      if ( FT_RENEW_ARRAY( outline->contours,
                           outline->max_contours,
                           new_contours ) )
        goto Exit;

      outline->max_contours = new_contours;
    }

    /* then, reallocate the points, segments & edges arrays if needed -- */
    /* note that we reserved two additional point positions, used to     */
    /* hint metrics appropriately                                        */
    /*                                                                   */
    if ( num_points + 2 > outline->max_points )
    {
      FT_Int  news = ( num_points + 2 + 7 ) & -8;
      FT_Int  max  = outline->max_points;


      if ( FT_RENEW_ARRAY( outline->points,        max,     news     ) ||
           FT_RENEW_ARRAY( outline->horz_edges,    max * 2, news * 2 ) ||
           FT_RENEW_ARRAY( outline->horz_segments, max * 2, news * 2 ) )
        goto Exit;

      /* readjust some pointers */
      outline->vert_edges    = outline->horz_edges    + news;
      outline->vert_segments = outline->horz_segments + news;
      outline->max_points    = news;
    }

    outline->num_points   = num_points;
    outline->num_contours = num_contours;

    outline->num_hedges    = 0;
    outline->num_vedges    = 0;
    outline->num_hsegments = 0;
    outline->num_vsegments = 0;

    /* We can't rely on the value of `FT_Outline.flags' to know the fill  */
    /* direction used for a glyph, given that some fonts are broken (e.g. */
    /* the Arphic ones). We thus recompute it each time we need to.       */
    /*                                                                    */
    outline->vert_major_dir = AH_DIR_UP;
    outline->horz_major_dir = AH_DIR_LEFT;

    if ( ah_get_orientation( source ) > 1 )
    {
      outline->vert_major_dir = AH_DIR_DOWN;
      outline->horz_major_dir = AH_DIR_RIGHT;
    }

    outline->x_scale = face->size->metrics.x_scale;
    outline->y_scale = face->size->metrics.y_scale;

    points = outline->points;
    if ( outline->num_points == 0 )
      goto Exit;

    {
      /* do one thing at a time -- it is easier to understand, and */
      /* the code is clearer                                       */
      AH_Point  point;
      AH_Point  point_limit = points + outline->num_points;


      /* compute coordinates */
      {
        FT_Vector*  vec     = source->points;
        FT_Fixed    x_scale = outline->x_scale;
        FT_Fixed    y_scale = outline->y_scale;


        for ( point = points; point < point_limit; vec++, point++ )
        {
          point->fx = vec->x;
          point->fy = vec->y;
          point->ox = point->x = FT_MulFix( vec->x, x_scale );
          point->oy = point->y = FT_MulFix( vec->y, y_scale );

          point->flags = 0;
        }
      }

      /* compute Bezier flags */
      {
        char*  tag = source->tags;


        for ( point = points; point < point_limit; point++, tag++ )
        {
          switch ( FT_CURVE_TAG( *tag ) )
          {
          case FT_CURVE_TAG_CONIC:
            point->flags = AH_FLAG_CONIC; break;
          case FT_CURVE_TAG_CUBIC:
            point->flags = AH_FLAG_CUBIC; break;
          default:
            ;
          }
        }
      }

      /* compute `next' and `prev' */
      {
        FT_Int    contour_index;
        AH_Point  prev;
        AH_Point  first;
        AH_Point  end;


        contour_index = 0;

        first = points;
        end   = points + source->contours[0];
        prev  = end;

        for ( point = points; point < point_limit; point++ )
        {
          point->prev = prev;
          if ( point < end )
          {
            point->next = point + 1;
            prev        = point;
          }
          else
          {
            point->next = first;
            contour_index++;
            if ( point + 1 < point_limit )
            {
              end   = points + source->contours[contour_index];
              first = point + 1;
              prev  = end;
            }
          }
        }
      }

      /* set-up the contours array */
      {
        AH_Point*  contour       = outline->contours;
        AH_Point*  contour_limit = contour + outline->num_contours;
        short*     end           = source->contours;
        short      idx           = 0;


        for ( ; contour < contour_limit; contour++, end++ )
        {
          contour[0] = points + idx;
          idx        = (short)( end[0] + 1 );
        }
      }

      /* compute directions of in & out vectors */
      {
        for ( point = points; point < point_limit; point++ )
        {
          AH_Point   prev;
          AH_Point   next;
          FT_Vector  ivec, ovec;


          prev   = point->prev;
          ivec.x = point->fx - prev->fx;
          ivec.y = point->fy - prev->fy;

          point->in_dir = ah_compute_direction( ivec.x, ivec.y );

          next   = point->next;
          ovec.x = next->fx - point->fx;
          ovec.y = next->fy - point->fy;

          point->out_dir = ah_compute_direction( ovec.x, ovec.y );

#ifndef AH_OPTION_NO_WEAK_INTERPOLATION
          if ( point->flags & (AH_FLAG_CONIC | AH_FLAG_CUBIC) )
          {
          Is_Weak_Point:
            point->flags |= AH_FLAG_WEAK_INTERPOLATION;
          }
          else if ( point->out_dir == point->in_dir )
          {
            AH_Angle  angle_in, angle_out, delta;


            if ( point->out_dir != AH_DIR_NONE )
              goto Is_Weak_Point;

            angle_in  = ah_angle( &ivec );
            angle_out = ah_angle( &ovec );
            delta     = angle_in - angle_out;

            if ( delta > AH_PI )
              delta = AH_2PI - delta;

            if ( delta < 0 )
              delta = -delta;

            if ( delta < 2 )
              goto Is_Weak_Point;
          }
          else if ( point->in_dir == -point->out_dir )
            goto Is_Weak_Point;
#endif
        }
      }
    }

  Exit:
    return error;
  }


  FT_LOCAL_DEF( void )
  ah_setup_uv( AH_Outline  outline,
               AH_UV       source )
  {
    AH_Point  point       = outline->points;
    AH_Point  point_limit = point + outline->num_points;


    for ( ; point < point_limit; point++ )
    {
      FT_Pos  u, v;


      switch ( source )
      {
      case AH_UV_FXY:
        u = point->fx;
        v = point->fy;
        break;
      case AH_UV_FYX:
        u = point->fy;
        v = point->fx;
        break;
      case AH_UV_OXY:
        u = point->ox;
        v = point->oy;
        break;
      case AH_UV_OYX:
        u = point->oy;
        v = point->ox;
        break;
      case AH_UV_YX:
        u = point->y;
        v = point->x;
        break;
      case AH_UV_OX:
        u = point->x;
        v = point->ox;
        break;
      case AH_UV_OY:
        u = point->y;
        v = point->oy;
        break;
      default:
        u = point->x;
        v = point->y;
        break;
      }
      point->u = u;
      point->v = v;
    }
  }


  /* compute all inflex points in a given glyph */
  static void
  ah_outline_compute_inflections( AH_Outline  outline )
  {
    AH_Point*  contour       =  outline->contours;
    AH_Point*  contour_limit =  contour + outline->num_contours;


    /* load original coordinates in (u,v) */
    ah_setup_uv( outline, AH_UV_FXY );

    /* do each contour separately */
    for ( ; contour < contour_limit; contour++ )
    {
      FT_Vector  vec;
      AH_Point   point   = contour[0];
      AH_Point   first   = point;
      AH_Point   start   = point;
      AH_Point   end     = point;
      AH_Point   before;
      AH_Point   after;
      AH_Angle   angle_in, angle_seg, angle_out;
      AH_Angle   diff_in, diff_out;
      FT_Int     finished = 0;


      /* compute first segment in contour */
      first = point;

      start = end = first;
      do
      {
        end = end->next;
        if ( end == first )
          goto Skip;

      } while ( end->u == first->u && end->v == first->v );

      vec.x = end->u - start->u;
      vec.y = end->v - start->v;
      angle_seg = ah_angle( &vec );

      /* extend the segment start whenever possible */
      before = start;
      do
      {
        do
        {
          start  = before;
          before = before->prev;
          if ( before == first )
            goto Skip;

        } while ( before->u == start->u && before->v == start->v );

        vec.x    = start->u - before->u;
        vec.y    = start->v - before->v;
        angle_in = ah_angle( &vec );

      } while ( angle_in == angle_seg );

      first   = start;
      diff_in = ah_angle_diff( angle_in, angle_seg );

      /* now, process all segments in the contour */
      do
      {
        /* first, extend current segment's end whenever possible */
        after = end;
        do
        {
          do
          {
            end   = after;
            after = after->next;
            if ( after == first )
              finished = 1;

          } while ( end->u == after->u && end->v == after->v );

          vec.x     = after->u - end->u;
          vec.y     = after->v - end->v;
          angle_out = ah_angle( &vec );

        } while ( angle_out == angle_seg );

        diff_out = ah_angle_diff( angle_seg, angle_out );

        if ( ( diff_in ^ diff_out ) < 0 )
        {
          /* diff_in and diff_out have different signs, we have */
          /* inflection points here...                          */

          do
          {
            start->flags |= AH_FLAG_INFLECTION;
            start = start->next;

          } while ( start != end );

          start->flags |= AH_FLAG_INFLECTION;
        }

        start     = end;
        end       = after;
        angle_seg = angle_out;
        diff_in   = diff_out;

      } while ( !finished );

    Skip:
      ;
    }
  }


  FT_LOCAL_DEF( void )
  ah_outline_compute_segments( AH_Outline  outline )
  {
    int           dimension;
    AH_Segment    segments;
    FT_Int*       p_num_segments;
    AH_Direction  segment_dir;
    AH_Direction  major_dir;


    segments       = outline->horz_segments;
    p_num_segments = &outline->num_hsegments;
    major_dir      = AH_DIR_RIGHT;      /* This value must be positive! */
    segment_dir    = major_dir;

    /* set up (u,v) in each point */
    ah_setup_uv( outline, AH_UV_FYX );

    for ( dimension = 1; dimension >= 0; dimension-- )
    {
      AH_Point*   contour       =  outline->contours;
      AH_Point*   contour_limit =  contour + outline->num_contours;
      AH_Segment  segment       =  segments;
      FT_Int      num_segments  =  0;

#ifdef AH_HINT_METRICS
      AH_Point    min_point     =  0;
      AH_Point    max_point     =  0;
      FT_Pos      min_coord     =  32000;
      FT_Pos      max_coord     = -32000;
#endif


      /* do each contour separately */
      for ( ; contour < contour_limit; contour++ )
      {
        AH_Point  point   = contour[0];
        AH_Point  last    = point->prev;
        int       on_edge = 0;
        FT_Pos    min_pos = +32000;  /* minimum segment pos != min_coord */
        FT_Pos    max_pos = -32000;  /* maximum segment pos != max_coord */
        FT_Bool   passed;


#ifdef AH_HINT_METRICS
        if ( point->u < min_coord )
        {
          min_coord = point->u;
          min_point = point;
        }
        if ( point->u > max_coord )
        {
          max_coord = point->u;
          max_point = point;
        }
#endif

        if ( point == last )  /* skip singletons -- just in case? */
          continue;

        if ( ABS( last->out_dir )  == major_dir &&
             ABS( point->out_dir ) == major_dir )
        {
          /* we are already on an edge, try to locate its start */
          last = point;

          for (;;)
          {
            point = point->prev;
            if ( 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 )
          {
            u = point->u;
            if ( u < min_pos )
              min_pos = u;
            if ( u > max_pos )
              max_pos = u;

            if ( point->out_dir != segment_dir || point == last )
            {
              /* we are just leaving an edge; record a new segment! */
              segment->last = point;
              segment->pos  = ( min_pos + max_pos ) >> 1;

              /* a segment is round if either its first or last point */
              /* is a control point                                   */
              if ( ( segment->first->flags | point->flags ) &
                     AH_FLAG_CONTROL                        )
                segment->flags |= AH_EDGE_ROUND;

              /* compute segment size */
              min_pos = max_pos = point->v;

              v = segment->first->v;
              if ( v < min_pos )
                min_pos = v;
              if ( v > max_pos )
                max_pos = v;

              segment->min_coord = min_pos;
              segment->max_coord = max_pos;

              on_edge = 0;
              num_segments++;
              segment++;
              /* fallthrough */
            }
          }

          /* now exit if we are at the start/end point */
          if ( point == last )
          {
            if ( passed )
              break;
            passed = 1;
          }

          if ( !on_edge && ABS( point->out_dir ) == major_dir )
          {
            /* this is the start of a new segment! */
            segment_dir = point->out_dir;

            /* clear all segment fields */
            FT_ZERO( segment );

            segment->dir      = segment_dir;
            segment->flags    = AH_EDGE_NORMAL;
            min_pos = max_pos = point->u;
            segment->first    = point;
            segment->last     = point;
            segment->contour  = contour;
            on_edge           = 1;

#ifdef AH_HINT_METRICS
            if ( point == max_point )
              max_point = 0;

            if ( point == min_point )
              min_point = 0;
#endif
          }

          point = point->next;
        }

      } /* contours */

#ifdef AH_HINT_METRICS
      /* we need to ensure that there are edges on the left-most and  */
      /* right-most points of the glyph in order to hint the metrics; */
      /* we do this by inserting fake segments when needed            */
      if ( dimension == 0 )
      {
        AH_Point  point       =  outline->points;
        AH_Point  point_limit =  point + outline->num_points;

        FT_Pos    min_pos     =  32000;
        FT_Pos    max_pos     = -32000;


        min_point = 0;
        max_point = 0;

        /* compute minimum and maximum points */
        for ( ; point < point_limit; point++ )
        {
          FT_Pos  x = point->fx;


          if ( x < min_pos )
          {
            min_pos   = x;
            min_point = point;
          }
          if ( x > max_pos )
          {
            max_pos   = x;
            max_point = point;
          }
        }

        /* insert minimum segment */
        if ( min_point )
        {
          /* clear all segment fields */
          FT_ZERO( segment );

          segment->dir   = segment_dir;
          segment->flags = AH_EDGE_NORMAL;
          segment->first = min_point;
          segment->last  = min_point;
          segment->pos   = min_pos;

          num_segments++;
          segment++;
        }

        /* insert maximum segment */
        if ( max_point )
        {
          /* clear all segment fields */
          FT_ZERO( segment );

          segment->dir   = segment_dir;
          segment->flags = AH_EDGE_NORMAL;
          segment->first = max_point;
          segment->last  = max_point;
          segment->pos   = max_pos;

          num_segments++;
          segment++;
        }
      }
#endif /* AH_HINT_METRICS */

      *p_num_segments = num_segments;

      segments       = outline->vert_segments;
      major_dir      = AH_DIR_UP;
      p_num_segments = &outline->num_vsegments;
      ah_setup_uv( outline, AH_UV_FXY );
    }
  }


  FT_LOCAL_DEF( void )
  ah_outline_link_segments( AH_Outline  outline )
  {
    AH_Segment  segments;
    AH_Segment  segment_limit;
    int         dimension;


    ah_setup_uv( outline, AH_UV_FYX );

    segments      = outline->horz_segments;
    segment_limit = segments + outline->num_hsegments;

    for ( dimension = 1; dimension >= 0; dimension-- )
    {
      AH_Segment  seg1;
      AH_Segment  seg2;


      /* now compare each segment to the others */
      for ( seg1 = segments; seg1 < segment_limit; seg1++ )
      {
        FT_Pos      best_score;
        AH_Segment  best_segment;


        /* the fake segments are introduced to hint the metrics -- */
        /* we must never link them to anything                     */
        if ( seg1->first == seg1->last )
          continue;

        best_segment = seg1->link;
        if ( best_segment )
          best_score = seg1->score;
        else
          best_score = 32000;

        for ( seg2 = segments; seg2 < segment_limit; seg2++ )
          if ( seg1 != seg2 && seg1->dir + seg2->dir == 0 )
          {
            FT_Pos   pos1 = seg1->pos;
            FT_Pos   pos2 = seg2->pos;
            FT_Bool  is_dir;
            FT_Bool  is_pos;


            /* check that the segments are correctly oriented and */
            /* positioned to form a black distance                */

            is_dir = (FT_Bool)( seg1->dir == outline->horz_major_dir ||
                                seg1->dir == outline->vert_major_dir );
            is_pos = (FT_Bool)( pos1 > pos2 );

            if ( pos1 == pos2 || !(is_dir ^ is_pos) )
              continue;

            {
              FT_Pos  min = seg1->min_coord;
              FT_Pos  max = seg1->max_coord;
              FT_Pos  len, dist, score;


              if ( min < seg2->min_coord )
                min = seg2->min_coord;

              if ( max > seg2->max_coord )
                max = seg2->max_coord;

              len = max - min;
              if ( len >= 8 )
              {
                dist = seg2->pos - seg1->pos;
                if ( dist < 0 )
                  dist = -dist;

                score = dist + 3000 / len;

                if ( score < best_score )
                {
                  best_score   = score;
                  best_segment = seg2;
                }
              }
            }
          }

        if ( best_segment )
        {
          seg1->link  = best_segment;
          seg1->score = best_score;

          best_segment->num_linked++;
        }

      } /* edges 1 */

      /* now, compute the `serif' segments */
      for ( seg1 = segments; seg1 < segment_limit; seg1++ )
      {
        seg2 = seg1->link;

        if ( seg2 && seg2->link != seg1 )
        {
          seg1->link  = 0;
          seg1->serif = seg2->link;
        }
      }

      ah_setup_uv( outline, AH_UV_FXY );

      segments      = outline->vert_segments;
      segment_limit = segments + outline->num_vsegments;
    }
  }


  static void
  ah_outline_compute_edges( AH_Outline  outline )
  {
    AH_Edge       edges;
    AH_Segment    segments;
    AH_Segment    segment_limit;
    AH_Direction  up_dir;
    FT_Int*       p_num_edges;
    FT_Int        dimension;
    FT_Fixed      scale;
    FT_Pos        edge_distance_threshold;


    edges         = outline->horz_edges;
    segments      = outline->horz_segments;
    segment_limit = segments + outline->num_hsegments;
    p_num_edges   = &outline->num_hedges;
    up_dir        = AH_DIR_RIGHT;
    scale         = outline->y_scale;

    for ( dimension = 1; dimension >= 0; dimension-- )
    {
      AH_Edge     edge;
      AH_Edge     edge_limit;  /* really == edge + num_edges */
      AH_Segment  seg;


      /*********************************************************************/
      /*                                                                   */
      /* We will 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 will be 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( outline->edge_distance_threshold,
                                           scale );
      if ( edge_distance_threshold > 64 / 4 )
        edge_distance_threshold = 64 / 4;

      edge_limit = edges;
      for ( seg = segments; seg < segment_limit; seg++ )
      {
        AH_Edge  found = 0;


        /* look for an edge corresponding to the segment */
        for ( edge = edges; edge < edge_limit; edge++ )
        {
          FT_Pos  dist;


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

          dist = FT_MulFix( dist, scale );
          if ( dist < edge_distance_threshold )
          {
            found = edge;
            break;
          }
        }

        if ( !found )
        {
          /* insert a new edge in the list and */
          /* sort according to the position    */
          while ( edge > edges && edge[-1].fpos > seg->pos )
          {
            edge[0] = edge[-1];
            edge--;
          }
          edge_limit++;

          /* clear all edge fields */
          FT_MEM_ZERO( edge, sizeof ( *edge ) );

          /* add the segment to the new edge's list */
          edge->first    = seg;
          edge->last     = seg;
          edge->fpos     = seg->pos;
          edge->opos     = edge->pos = FT_MulFix( seg->pos, scale );
          seg->edge_next = seg;
        }
        else
        {
          /* if an edge was found, simply add the segment to the edge's */
          /* list                                                       */
          seg->edge_next        = edge->first;
          edge->last->edge_next = seg;
          edge->last            = seg;
        }
      }

      *p_num_edges = (FT_Int)( edge_limit - edges );


      /*********************************************************************/
      /*                                                                   */
      /* Good, we will now compute each edge's properties according to     */
      /* segments found on its position.  Basically, these are:            */
      /*                                                                   */
      /*  - edge's main direction                                          */
      /*  - stem edge, serif edge or both (which defaults to stem then)    */
      /*  - rounded edge, straigth 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                       */
      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? */
        FT_Pos  ups         = 0;  /* number of upwards segments         */
        FT_Pos  downs       = 0;  /* number of downwards segments       */


        seg = edge->first;

        do
        {
          FT_Bool  is_serif;


          /* check for roundness of segment */
          if ( seg->flags & AH_EDGE_ROUND )
            is_round++;
          else
            is_straight++;

          /* check for segment direction */
          if ( seg->dir == up_dir )
            ups   += seg->max_coord-seg->min_coord;
          else
            downs += seg->max_coord-seg->min_coord;

          /* check for links -- if seg->serif is set, then seg->link must */
          /* be ignored                                                   */
          is_serif = (FT_Bool)( seg->serif && seg->serif->edge != edge );

          if ( seg->link || is_serif )
          {
            AH_Edge     edge2;
            AH_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;
            else
              edge->link  = edge2;
          }

          seg = seg->edge_next;

        } while ( seg != edge->first );

        /* set the round/straight flags */
        edge->flags = AH_EDGE_NORMAL;

        if ( is_round > 0 && is_round >= is_straight )
          edge->flags |= AH_EDGE_ROUND;

        /* set the edge's main direction */
        edge->dir = AH_DIR_NONE;

        if ( ups > downs )
          edge->dir = up_dir;

        else if ( ups < downs )
          edge->dir = - up_dir;

        else if ( ups == downs )
          edge->dir = 0;  /* both up and down !! */

        /* gets 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 = 0;
      }

      edges         = outline->vert_edges;
      segments      = outline->vert_segments;
      segment_limit = segments + outline->num_vsegments;
      p_num_edges   = &outline->num_vedges;
      up_dir        = AH_DIR_UP;
      scale         = outline->x_scale;
    }
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    ah_outline_detect_features                                         */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Performs feature detection on a given AH_OutlineRec object.        */
  /*                                                                       */
  FT_LOCAL_DEF( void )
  ah_outline_detect_features( AH_Outline  outline )
  {
    ah_outline_compute_segments   ( outline );
    ah_outline_link_segments      ( outline );
    ah_outline_compute_edges      ( outline );
    ah_outline_compute_inflections( outline );
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    ah_outline_compute_blue_edges                                      */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Computes the `blue edges' in a given outline (i.e. those that must */
  /*    be snapped to a blue zone edge (top or bottom).                    */
  /*                                                                       */
  FT_LOCAL_DEF( void )
  ah_outline_compute_blue_edges( AH_Outline       outline,
                                 AH_Face_Globals  face_globals )
  {
    AH_Edge     edge       = outline->horz_edges;
    AH_Edge     edge_limit = edge + outline->num_hedges;
    AH_Globals  globals    = &face_globals->design;
    FT_Fixed    y_scale    = outline->y_scale;

    FT_Bool     blue_active[AH_BLUE_MAX];


    /* compute which blue zones are active, i.e. have their scaled */
    /* size < 3/4 pixels                                           */
    {
      AH_Blue  blue;
      FT_Bool  check = 0;


      for ( blue = AH_BLUE_CAPITAL_TOP; blue < AH_BLUE_MAX; blue++ )
      {
        FT_Pos  ref, shoot, dist;


        ref   = globals->blue_refs[blue];
        shoot = globals->blue_shoots[blue];
        dist  = ref-shoot;
        if ( dist < 0 )
          dist = -dist;

        blue_active[blue] = 0;

        if ( FT_MulFix( dist, y_scale ) < 48 )
        {
          blue_active[blue] = 1;
          check = 1;
        }
      }

      /* return immediately if no blue zone is active */
      if ( !check )
        return;
    }

    /* compute for each horizontal edge, which blue zone is closer */
    for ( ; edge < edge_limit; edge++ )
    {
      AH_Blue  blue;
      FT_Pos*  best_blue = 0;
      FT_Pos   best_dist;  /* initial threshold */


      /* compute the initial threshold as a fraction of the EM size */
      best_dist = FT_MulFix( face_globals->face->units_per_EM / 40, y_scale );
      if ( best_dist > 64 / 4 )
        best_dist = 64 / 4;

      for ( blue = AH_BLUE_CAPITAL_TOP; blue < AH_BLUE_MAX; blue++ )
      {
        /* if it is a top zone, check for right edges -- if it is a bottom */
        /* zone, check for left edges                                      */
        /*                                                                 */
        /* of course, that's for TrueType XXX                              */
        FT_Bool  is_top_blue  =
                   FT_BOOL( AH_IS_TOP_BLUE( blue ) );
        FT_Bool  is_major_dir =
                   FT_BOOL( edge->dir == outline->horz_major_dir );

        if ( !blue_active[blue] )
          continue;

        /* if it is a top zone, the edge must be against the major    */
        /* direction; if it is a bottom zone, it must be in the major */
        /* direction                                                  */
        if ( is_top_blue ^ is_major_dir )
        {
          FT_Pos   dist;
          FT_Pos*  blue_pos = globals->blue_refs + blue;


          /* first of all, compare it to the reference position */
          dist = edge->fpos - *blue_pos;
          if ( dist < 0 )
            dist = -dist;

          dist = FT_MulFix( dist, y_scale );
          if ( dist < best_dist )
          {
            best_dist = dist;
            best_blue = blue_pos;
          }

          /* now, compare it to the overshoot position if the edge is     */
          /* rounded, and if the edge is over the reference position of a */
          /* top zone, or under the reference position of a bottom zone   */
          if ( edge->flags & AH_EDGE_ROUND && dist != 0 )
          {
            FT_Bool  is_under_ref = FT_BOOL( edge->fpos < *blue_pos );


            if ( is_top_blue ^ is_under_ref )
            {
              blue_pos = globals->blue_shoots + blue;
              dist = edge->fpos - *blue_pos;
              if ( dist < 0 )
                dist = -dist;

              dist = FT_MulFix( dist, y_scale );
              if ( dist < best_dist )
              {
                best_dist = dist;
                best_blue = blue_pos;
              }
            }
          }
        }
      }

      if ( best_blue )
        edge->blue_edge = best_blue;
    }
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    ah_outline_scale_blue_edges                                        */
  /*                                                                       */
  /* <Description>                                                         */
  /*    This functions must be called before hinting in order to re-adjust */
  /*    the contents of the detected edges (basically change the `blue     */
  /*    edge' pointer from `design units' to `scaled ones').               */
  /*                                                                       */
  FT_LOCAL_DEF( void )
  ah_outline_scale_blue_edges( AH_Outline       outline,
                               AH_Face_Globals  globals )
  {
    AH_Edge  edge       = outline->horz_edges;
    AH_Edge  edge_limit = edge + outline->num_hedges;
    FT_Pos   delta;


    delta = globals->scaled.blue_refs - globals->design.blue_refs;

    for ( ; edge < edge_limit; edge++ )
    {
      if ( edge->blue_edge )
        edge->blue_edge += delta;
    }
  }


/* END */