text: /***************************************************************************/
  /*                                                                         */
  /*  ftoutln.c                                                              */
  /*                                                                         */
  /*    FreeType outline management (body).                                  */
  /*                                                                         */
  /*  Copyright 1996-2015 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.                                        */
  /*                                                                         */
  /***************************************************************************/
  
  
    /*************************************************************************/
    /*                                                                       */
    /* All functions are declared in freetype.h.                             */
    /*                                                                       */
    /*************************************************************************/
  
  
  #include <ft2build.h>
  #include FT_OUTLINE_H
  #include FT_INTERNAL_OBJECTS_H
  #include FT_INTERNAL_CALC_H
  #include FT_INTERNAL_DEBUG_H
  #include FT_TRIGONOMETRY_H
  
  
    /*************************************************************************/
    /*                                                                       */
    /* The macro FT_COMPONENT is used in trace mode.  It is an implicit      */
    /* parameter of the FT_TRACE() and FT_ERROR() macros, used to print/log  */
    /* messages during execution.                                            */
    /*                                                                       */
  #undef  FT_COMPONENT
  #define FT_COMPONENT  trace_outline
  
  
    static
    const FT_Outline  null_outline = { 0, 0, 0, 0, 0, 0 };
  
  
    /* documentation is in ftoutln.h */
  
    FT_EXPORT_DEF( FT_Error )
    FT_Outline_Decompose( FT_Outline*              outline,
                          const FT_Outline_Funcs*  func_interface,
                          void*                    user )
    {
  #undef  SCALED
  #define SCALED( x )  ( ( (x) < 0 ? -( -(x) << shift )             \
                                   :  (  (x) << shift ) ) - delta )
  
      FT_Vector   v_last;
      FT_Vector   v_control;
      FT_Vector   v_start;
  
      FT_Vector*  point;
      FT_Vector*  limit;
      char*       tags;
  
      FT_Error    error;
  
      FT_Int   n;         /* index of contour in outline     */
      FT_UInt  first;     /* index of first point in contour */
      FT_Int   tag;       /* current point's state           */
  
      FT_Int   shift;
      FT_Pos   delta;
  
  
      if ( !outline )
        return FT_THROW( Invalid_Outline );
  
      if ( !func_interface )
        return FT_THROW( Invalid_Argument );
  
      shift = func_interface->shift;
      delta = func_interface->delta;
      first = 0;
  
      for ( n = 0; n < outline->n_contours; n++ )
      {
        FT_Int  last;  /* index of last point in contour */
  
  
        FT_TRACE5(( "FT_Outline_Decompose: Outline %d\n", n ));
  
        last = outline->contours[n];
        if ( last < 0 )
          goto Invalid_Outline;
        limit = outline->points + last;
  
        v_start   = outline->points[first];
        v_start.x = SCALED( v_start.x );
        v_start.y = SCALED( v_start.y );
  
        v_last   = outline->points[last];
        v_last.x = SCALED( v_last.x );
        v_last.y = SCALED( v_last.y );
  
        v_control = v_start;
  
        point = outline->points + first;
        tags  = outline->tags   + first;
        tag   = FT_CURVE_TAG( tags[0] );
  
        /* A contour cannot start with a cubic control point! */
        if ( tag == FT_CURVE_TAG_CUBIC )
          goto Invalid_Outline;
  
        /* check first point to determine origin */
        if ( tag == FT_CURVE_TAG_CONIC )
        {
          /* first point is conic control.  Yes, this happens. */
          if ( FT_CURVE_TAG( outline->tags[last] ) == FT_CURVE_TAG_ON )
          {
            /* start at last point if it is on the curve */
            v_start = v_last;
            limit--;
          }
          else
          {
            /* if both first and last points are conic,         */
            /* start at their middle and record its position    */
            /* for closure                                      */
            v_start.x = ( v_start.x + v_last.x ) / 2;
            v_start.y = ( v_start.y + v_last.y ) / 2;
  
         /* v_last = v_start; */
          }
          point--;
          tags--;
        }
  
        FT_TRACE5(( "  move to (%.2f, %.2f)\n",
                    v_start.x / 64.0, v_start.y / 64.0 ));
        error = func_interface->move_to( &v_start, user );
        if ( error )
          goto Exit;
  
        while ( point < limit )
        {
          point++;
          tags++;
  
          tag = FT_CURVE_TAG( tags[0] );
          switch ( tag )
          {
          case FT_CURVE_TAG_ON:  /* emit a single line_to */
            {
              FT_Vector  vec;
  
  
              vec.x = SCALED( point->x );
              vec.y = SCALED( point->y );
  
              FT_TRACE5(( "  line to (%.2f, %.2f)\n",
                          vec.x / 64.0, vec.y / 64.0 ));
              error = func_interface->line_to( &vec, user );
              if ( error )
                goto Exit;
              continue;
            }
  
          case FT_CURVE_TAG_CONIC:  /* consume conic arcs */
            v_control.x = SCALED( point->x );
            v_control.y = SCALED( point->y );
  
          Do_Conic:
            if ( point < limit )
            {
              FT_Vector  vec;
              FT_Vector  v_middle;
  
  
              point++;
              tags++;
              tag = FT_CURVE_TAG( tags[0] );
  
              vec.x = SCALED( point->x );
              vec.y = SCALED( point->y );
  
              if ( tag == FT_CURVE_TAG_ON )
              {
                FT_TRACE5(( "  conic to (%.2f, %.2f)"
                            " with control (%.2f, %.2f)\n",
                            vec.x / 64.0, vec.y / 64.0,
                            v_control.x / 64.0, v_control.y / 64.0 ));
                error = func_interface->conic_to( &v_control, &vec, user );
                if ( error )
                  goto Exit;
                continue;
              }
  
              if ( tag != FT_CURVE_TAG_CONIC )
                goto Invalid_Outline;
  
              v_middle.x = ( v_control.x + vec.x ) / 2;
              v_middle.y = ( v_control.y + vec.y ) / 2;
  
              FT_TRACE5(( "  conic to (%.2f, %.2f)"
                          " with control (%.2f, %.2f)\n",
                          v_middle.x / 64.0, v_middle.y / 64.0,
                          v_control.x / 64.0, v_control.y / 64.0 ));
              error = func_interface->conic_to( &v_control, &v_middle, user );
              if ( error )
                goto Exit;
  
              v_control = vec;
              goto Do_Conic;
            }
  
            FT_TRACE5(( "  conic to (%.2f, %.2f)"
                        " with control (%.2f, %.2f)\n",
                        v_start.x / 64.0, v_start.y / 64.0,
                        v_control.x / 64.0, v_control.y / 64.0 ));
            error = func_interface->conic_to( &v_control, &v_start, user );
            goto Close;
  
          default:  /* FT_CURVE_TAG_CUBIC */
            {
              FT_Vector  vec1, vec2;
  
  
              if ( point + 1 > limit                             ||
                   FT_CURVE_TAG( tags[1] ) != FT_CURVE_TAG_CUBIC )
                goto Invalid_Outline;
  
              point += 2;
              tags  += 2;
  
              vec1.x = SCALED( point[-2].x );
              vec1.y = SCALED( point[-2].y );
  
              vec2.x = SCALED( point[-1].x );
              vec2.y = SCALED( point[-1].y );
  
              if ( point <= limit )
              {
                FT_Vector  vec;
  
  
                vec.x = SCALED( point->x );
                vec.y = SCALED( point->y );
  
                FT_TRACE5(( "  cubic to (%.2f, %.2f)"
                            " with controls (%.2f, %.2f) and (%.2f, %.2f)\n",
                            vec.x / 64.0, vec.y / 64.0,
                            vec1.x / 64.0, vec1.y / 64.0,
                            vec2.x / 64.0, vec2.y / 64.0 ));
                error = func_interface->cubic_to( &vec1, &vec2, &vec, user );
                if ( error )
                  goto Exit;
                continue;
              }
  
              FT_TRACE5(( "  cubic to (%.2f, %.2f)"
                          " with controls (%.2f, %.2f) and (%.2f, %.2f)\n",
                          v_start.x / 64.0, v_start.y / 64.0,
                          vec1.x / 64.0, vec1.y / 64.0,
                          vec2.x / 64.0, vec2.y / 64.0 ));
              error = func_interface->cubic_to( &vec1, &vec2, &v_start, user );
              goto Close;
            }
          }
        }
  
        /* close the contour with a line segment */
        FT_TRACE5(( "  line to (%.2f, %.2f)\n",
                    v_start.x / 64.0, v_start.y / 64.0 ));
        error = func_interface->line_to( &v_start, user );
  
      Close:
        if ( error )
          goto Exit;
  
        first = (FT_UInt)last + 1;
      }
  
      FT_TRACE5(( "FT_Outline_Decompose: Done\n", n ));
      return FT_Err_Ok;
  
    Exit:
      FT_TRACE5(( "FT_Outline_Decompose: Error %d\n", error ));
      return error;
  
    Invalid_Outline:
      return FT_THROW( Invalid_Outline );
    }
  
  
    FT_EXPORT_DEF( FT_Error )
    FT_Outline_New_Internal( FT_Memory    memory,
                             FT_UInt      numPoints,
                             FT_Int       numContours,
                             FT_Outline  *anoutline )
    {
      FT_Error  error;
  
  
      if ( !anoutline || !memory )
        return FT_THROW( Invalid_Argument );
  
      *anoutline = null_outline;
  
      if ( numContours < 0                  ||
           (FT_UInt)numContours > numPoints )
        return FT_THROW( Invalid_Argument );
  
      if ( numPoints > FT_OUTLINE_POINTS_MAX )
        return FT_THROW( Array_Too_Large );
  
      if ( FT_NEW_ARRAY( anoutline->points,   numPoints   ) ||
           FT_NEW_ARRAY( anoutline->tags,     numPoints   ) ||
           FT_NEW_ARRAY( anoutline->contours, numContours ) )
        goto Fail;
  
      anoutline->n_points    = (FT_Short)numPoints;
      anoutline->n_contours  = (FT_Short)numContours;
      anoutline->flags      |= FT_OUTLINE_OWNER;
  
      return FT_Err_Ok;
  
    Fail:
      anoutline->flags |= FT_OUTLINE_OWNER;
      FT_Outline_Done_Internal( memory, anoutline );
  
      return error;
    }
  
  
    /* documentation is in ftoutln.h */
  
    FT_EXPORT_DEF( FT_Error )
    FT_Outline_New( FT_Library   library,
                    FT_UInt      numPoints,
                    FT_Int       numContours,
                    FT_Outline  *anoutline )
    {
      if ( !library )
        return FT_THROW( Invalid_Library_Handle );
  
      return FT_Outline_New_Internal( library->memory, numPoints,
                                      numContours, anoutline );
    }
  
  
    /* documentation is in ftoutln.h */
  
    FT_EXPORT_DEF( FT_Error )
    FT_Outline_Check( FT_Outline*  outline )
    {
      if ( outline )
      {
        FT_Int  n_points   = outline->n_points;
        FT_Int  n_contours = outline->n_contours;
        FT_Int  end0, end;
        FT_Int  n;
  
  
        /* empty glyph? */
        if ( n_points == 0 && n_contours == 0 )
          return FT_Err_Ok;
  
        /* check point and contour counts */
        if ( n_points <= 0 || n_contours <= 0 )
          goto Bad;
  
        end0 = end = -1;
        for ( n = 0; n < n_contours; n++ )
        {
          end = outline->contours[n];
  
          /* note that we don't accept empty contours */
          if ( end <= end0 || end >= n_points )
            goto Bad;
  
          end0 = end;
        }
  
        if ( end != n_points - 1 )
          goto Bad;
  
        /* XXX: check the tags array */
        return FT_Err_Ok;
      }
  
    Bad:
      return FT_THROW( Invalid_Argument );
    }
  
  
    /* documentation is in ftoutln.h */
  
    FT_EXPORT_DEF( FT_Error )
    FT_Outline_Copy( const FT_Outline*  source,
                     FT_Outline        *target )
    {
      FT_Int  is_owner;
  
  
      if ( !source || !target )
        return FT_THROW( Invalid_Outline );
  
      if ( source->n_points   != target->n_points   ||
           source->n_contours != target->n_contours )
        return FT_THROW( Invalid_Argument );
  
      if ( source == target )
        return FT_Err_Ok;
  
      FT_ARRAY_COPY( target->points, source->points, source->n_points );
  
      FT_ARRAY_COPY( target->tags, source->tags, source->n_points );
  
      FT_ARRAY_COPY( target->contours, source->contours, source->n_contours );
  
      /* copy all flags, except the `FT_OUTLINE_OWNER' one */
      is_owner      = target->flags & FT_OUTLINE_OWNER;
      target->flags = source->flags;
  
      target->flags &= ~FT_OUTLINE_OWNER;
      target->flags |= is_owner;
  
      return FT_Err_Ok;
    }
  
  
    FT_EXPORT_DEF( FT_Error )
    FT_Outline_Done_Internal( FT_Memory    memory,
                              FT_Outline*  outline )
    {
      if ( !outline )
        return FT_THROW( Invalid_Outline );
  
      if ( !memory )
        return FT_THROW( Invalid_Argument );
  
      if ( outline->flags & FT_OUTLINE_OWNER )
      {
        FT_FREE( outline->points   );
        FT_FREE( outline->tags     );
        FT_FREE( outline->contours );
      }
      *outline = null_outline;
  
      return FT_Err_Ok;
    }
  
  
    /* documentation is in ftoutln.h */
  
    FT_EXPORT_DEF( FT_Error )
    FT_Outline_Done( FT_Library   library,
                     FT_Outline*  outline )
    {
      /* check for valid `outline' in FT_Outline_Done_Internal() */
  
      if ( !library )
        return FT_THROW( Invalid_Library_Handle );
  
      return FT_Outline_Done_Internal( library->memory, outline );
    }
  
  
    /* documentation is in ftoutln.h */
  
    FT_EXPORT_DEF( void )
    FT_Outline_Get_CBox( const FT_Outline*  outline,
                         FT_BBox           *acbox )
    {
      FT_Pos  xMin, yMin, xMax, yMax;
  
  
      if ( outline && acbox )
      {
        if ( outline->n_points == 0 )
        {
          xMin = 0;
          yMin = 0;
          xMax = 0;
          yMax = 0;
        }
        else
        {
          FT_Vector*  vec   = outline->points;
          FT_Vector*  limit = vec + outline->n_points;
  
  
          xMin = xMax = vec->x;
          yMin = yMax = vec->y;
          vec++;
  
          for ( ; vec < limit; vec++ )
          {
            FT_Pos  x, y;
  
  
            x = vec->x;
            if ( x < xMin ) xMin = x;
            if ( x > xMax ) xMax = x;
  
            y = vec->y;
            if ( y < yMin ) yMin = y;
            if ( y > yMax ) yMax = y;
          }
        }
        acbox->xMin = xMin;
        acbox->xMax = xMax;
        acbox->yMin = yMin;
        acbox->yMax = yMax;
      }
    }
  
  
    /* documentation is in ftoutln.h */
  
    FT_EXPORT_DEF( void )
    FT_Outline_Translate( const FT_Outline*  outline,
                          FT_Pos             xOffset,
                          FT_Pos             yOffset )
    {
      FT_UShort   n;
      FT_Vector*  vec;
  
  
      if ( !outline )
        return;
  
      vec = outline->points;
  
      for ( n = 0; n < outline->n_points; n++ )
      {
        vec->x += xOffset;
        vec->y += yOffset;
        vec++;
      }
    }
  
  
    /* documentation is in ftoutln.h */
  
    FT_EXPORT_DEF( void )
    FT_Outline_Reverse( FT_Outline*  outline )
    {
      FT_UShort  n;
      FT_Int     first, last;
  
  
      if ( !outline )
        return;
  
      first = 0;
  
      for ( n = 0; n < outline->n_contours; n++ )
      {
        last  = outline->contours[n];
  
        /* reverse point table */
        {
          FT_Vector*  p = outline->points + first;
          FT_Vector*  q = outline->points + last;
          FT_Vector   swap;
  
  
          while ( p < q )
          {
            swap = *p;
            *p   = *q;
            *q   = swap;
            p++;
            q--;
          }
        }
  
        /* reverse tags table */
        {
          char*  p = outline->tags + first;
          char*  q = outline->tags + last;
  
  
          while ( p < q )
          {
            char  swap;
  
  
            swap = *p;
            *p   = *q;
            *q   = swap;
            p++;
            q--;
          }
        }
  
        first = last + 1;
      }
  
      outline->flags ^= FT_OUTLINE_REVERSE_FILL;
    }
  
  
    /* documentation is in ftoutln.h */
  
    FT_EXPORT_DEF( FT_Error )
    FT_Outline_Render( FT_Library         library,
                       FT_Outline*        outline,
                       FT_Raster_Params*  params )
    {
      FT_Error     error;
      FT_Renderer  renderer;
      FT_ListNode  node;
  
  
      if ( !library )
        return FT_THROW( Invalid_Library_Handle );
  
      if ( !outline )
        return FT_THROW( Invalid_Outline );
  
      if ( !params )
        return FT_THROW( Invalid_Argument );
  
      renderer = library->cur_renderer;
      node     = library->renderers.head;
  
      params->source = (void*)outline;
  
      error = FT_ERR( Cannot_Render_Glyph );
      while ( renderer )
      {
        error = renderer->raster_render( renderer->raster, params );
        if ( !error || FT_ERR_NEQ( error, Cannot_Render_Glyph ) )
          break;
  
        /* FT_Err_Cannot_Render_Glyph is returned if the render mode   */
        /* is unsupported by the current renderer for this glyph image */
        /* format                                                      */
  
        /* now, look for another renderer that supports the same */
        /* format                                                */
        renderer = FT_Lookup_Renderer( library, FT_GLYPH_FORMAT_OUTLINE,
                                       &node );
      }
  
      return error;
    }
  
  
    /* documentation is in ftoutln.h */
  
    FT_EXPORT_DEF( FT_Error )
    FT_Outline_Get_Bitmap( FT_Library        library,
                           FT_Outline*       outline,
                           const FT_Bitmap  *abitmap )
    {
      FT_Raster_Params  params;
  
  
      if ( !abitmap )
        return FT_THROW( Invalid_Argument );
  
      /* other checks are delayed to `FT_Outline_Render' */
  
      params.target = abitmap;
      params.flags  = 0;
  
      if ( abitmap->pixel_mode == FT_PIXEL_MODE_GRAY  ||
           abitmap->pixel_mode == FT_PIXEL_MODE_LCD   ||
           abitmap->pixel_mode == FT_PIXEL_MODE_LCD_V )
        params.flags |= FT_RASTER_FLAG_AA;
  
      return FT_Outline_Render( library, outline, &params );
    }
  
  
    /* documentation is in freetype.h */
  
    FT_EXPORT_DEF( void )
    FT_Vector_Transform( FT_Vector*        vector,
                         const FT_Matrix*  matrix )
    {
      FT_Pos  xz, yz;
  
  
      if ( !vector || !matrix )
        return;
  
      xz = FT_MulFix( vector->x, matrix->xx ) +
           FT_MulFix( vector->y, matrix->xy );
  
      yz = FT_MulFix( vector->x, matrix->yx ) +
           FT_MulFix( vector->y, matrix->yy );
  
      vector->x = xz;
      vector->y = yz;
    }
  
  
    /* documentation is in ftoutln.h */
  
    FT_EXPORT_DEF( void )
    FT_Outline_Transform( const FT_Outline*  outline,
                          const FT_Matrix*   matrix )
    {
      FT_Vector*  vec;
      FT_Vector*  limit;
  
  
      if ( !outline || !matrix )
        return;
  
      vec   = outline->points;
      limit = vec + outline->n_points;
  
      for ( ; vec < limit; vec++ )
        FT_Vector_Transform( vec, matrix );
    }
  
  
  #if 0
  
  #define FT_OUTLINE_GET_CONTOUR( outline, c, first, last )  \
    do                                                       \
    {                                                        \
      (first) = ( c > 0 ) ? (outline)->points +              \
                              (outline)->contours[c - 1] + 1 \
                          : (outline)->points;               \
      (last) = (outline)->points + (outline)->contours[c];   \
    } while ( 0 )
  
  
    /* Is a point in some contour?                     */
    /*                                                 */
    /* We treat every point of the contour as if it    */
    /* it were ON.  That is, we allow false positives, */
    /* but disallow false negatives.  (XXX really?)    */
    static FT_Bool
    ft_contour_has( FT_Outline*  outline,
                    FT_Short     c,
                    FT_Vector*   point )
    {
      FT_Vector*  first;
      FT_Vector*  last;
      FT_Vector*  a;
      FT_Vector*  b;
      FT_UInt     n = 0;
  
  
      FT_OUTLINE_GET_CONTOUR( outline, c, first, last );
  
      for ( a = first; a <= last; a++ )
      {
        FT_Pos  x;
        FT_Int  intersect;
  
  
        b = ( a == last ) ? first : a + 1;
  
        intersect = ( a->y - point->y ) ^ ( b->y - point->y );
  
        /* a and b are on the same side */
        if ( intersect >= 0 )
        {
          if ( intersect == 0 && a->y == point->y )
          {
            if ( ( a->x <= point->x && b->x >= point->x ) ||
                 ( a->x >= point->x && b->x <= point->x ) )
              return 1;
          }
  
          continue;
        }
  
        x = a->x + ( b->x - a->x ) * (point->y - a->y ) / ( b->y - a->y );
  
        if ( x < point->x )
          n++;
        else if ( x == point->x )
          return 1;
      }
  
      return n & 1;
    }
  
  
    static FT_Bool
    ft_contour_enclosed( FT_Outline*  outline,
                         FT_UShort    c )
    {
      FT_Vector*  first;
      FT_Vector*  last;
      FT_Short    i;
  
  
      FT_OUTLINE_GET_CONTOUR( outline, c, first, last );
  
      for ( i = 0; i < outline->n_contours; i++ )
      {
        if ( i != c && ft_contour_has( outline, i, first ) )
        {
          FT_Vector*  pt;
  
  
          for ( pt = first + 1; pt <= last; pt++ )
            if ( !ft_contour_has( outline, i, pt ) )
              return 0;
  
          return 1;
        }
      }
  
      return 0;
    }
  
  
    /* This version differs from the public one in that each */
    /* part (contour not enclosed in another contour) of the */
    /* outline is checked for orientation.  This is          */
    /* necessary for some buggy CJK fonts.                   */
    static FT_Orientation
    ft_outline_get_orientation( FT_Outline*  outline )
    {
      FT_Short        i;
      FT_Vector*      first;
      FT_Vector*      last;
      FT_Orientation  orient = FT_ORIENTATION_NONE;
  
  
      first = outline->points;
      for ( i = 0; i < outline->n_contours; i++, first = last + 1 )
      {
        FT_Vector*  point;
        FT_Vector*  xmin_point;
        FT_Pos      xmin;
  
  
        last = outline->points + outline->contours[i];
  
        /* skip degenerate contours */
        if ( last < first + 2 )
          continue;
  
        if ( ft_contour_enclosed( outline, i ) )
          continue;
  
        xmin       = first->x;
        xmin_point = first;
  
        for ( point = first + 1; point <= last; point++ )
        {
          if ( point->x < xmin )
          {
            xmin       = point->x;
            xmin_point = point;
          }
        }
  
        /* check the orientation of the contour */
        {
          FT_Vector*      prev;
          FT_Vector*      next;
          FT_Orientation  o;
  
  
          prev = ( xmin_point == first ) ? last : xmin_point - 1;
          next = ( xmin_point == last ) ? first : xmin_point + 1;
  
          if ( FT_Atan2( prev->x - xmin_point->x, prev->y - xmin_point->y ) >
               FT_Atan2( next->x - xmin_point->x, next->y - xmin_point->y ) )
            o = FT_ORIENTATION_POSTSCRIPT;
          else
            o = FT_ORIENTATION_TRUETYPE;
  
          if ( orient == FT_ORIENTATION_NONE )
            orient = o;
          else if ( orient != o )
            return FT_ORIENTATION_NONE;
        }
      }
  
      return orient;
    }
  
  #endif /* 0 */
  
  
    /* documentation is in ftoutln.h */
  
    FT_EXPORT_DEF( FT_Error )
    FT_Outline_Embolden( FT_Outline*  outline,
                         FT_Pos       strength )
    {
      return FT_Outline_EmboldenXY( outline, strength, strength );
    }
  
  
    /* documentation is in ftoutln.h */
  
    FT_EXPORT_DEF( FT_Error )
    FT_Outline_EmboldenXY( FT_Outline*  outline,
                           FT_Pos       xstrength,
                           FT_Pos       ystrength )
    {
      FT_Vector*  points;
      FT_Int      c, first, last;
      FT_Int      orientation;
  
  
      if ( !outline )
        return FT_THROW( Invalid_Outline );
  
      xstrength /= 2;
      ystrength /= 2;
      if ( xstrength == 0 && ystrength == 0 )
        return FT_Err_Ok;
  
      orientation = FT_Outline_Get_Orientation( outline );
      if ( orientation == FT_ORIENTATION_NONE )
      {
        if ( outline->n_contours )
          return FT_THROW( Invalid_Argument );
        else
          return FT_Err_Ok;
      }
  
      points = outline->points;
  
      first = 0;
      for ( c = 0; c < outline->n_contours; c++ )
      {
        FT_Vector  in, out, anchor, shift;
        FT_Fixed   l_in, l_out, l_anchor = 0, l, q, d;
        FT_Int     i, j, k;
  
  
        l_in = 0;
        last = outline->contours[c];
  
        /* Counter j cycles though the points; counter i advances only  */
        /* when points are moved; anchor k marks the first moved point. */
        for ( i = last, j = first, k = -1;
              j != i && i != k;
              j = j < last ? j + 1 : first )
        {
          if ( j != k )
          {
            out.x = points[j].x - points[i].x;
            out.y = points[j].y - points[i].y;
            l_out = (FT_Fixed)FT_Vector_NormLen( &out );
  
            if ( l_out == 0 )
              continue;
          }
          else
          {
            out   = anchor;
            l_out = l_anchor;
          }
  
          if ( l_in != 0 )
          {
            if ( k < 0 )
            {
              k        = i;
              anchor   = in;
              l_anchor = l_in;
            }
  
            d = FT_MulFix( in.x, out.x ) + FT_MulFix( in.y, out.y );
  
            /* shift only if turn is less than ~160 degrees */
            if ( d > -0xF000L )
            {
              d = d + 0x10000L;
  
              /* shift components along lateral bisector in proper orientation */
              shift.x = in.y + out.y;
              shift.y = in.x + out.x;
  
              if ( orientation == FT_ORIENTATION_TRUETYPE )
                shift.x = -shift.x;
              else
                shift.y = -shift.y;
  
              /* restrict shift magnitude to better handle collapsing segments */
              q = FT_MulFix( out.x, in.y ) - FT_MulFix( out.y, in.x );
              if ( orientation == FT_ORIENTATION_TRUETYPE )
                q = -q;
  
              l = FT_MIN( l_in, l_out );
  
              /* non-strict inequalities avoid divide-by-zero when q == l == 0 */
              if ( FT_MulFix( xstrength, q ) <= FT_MulFix( l, d ) )
                shift.x = FT_MulDiv( shift.x, xstrength, d );
              else
                shift.x = FT_MulDiv( shift.x, l, q );
  
  
              if ( FT_MulFix( ystrength, q ) <= FT_MulFix( l, d ) )
                shift.y = FT_MulDiv( shift.y, ystrength, d );
              else
                shift.y = FT_MulDiv( shift.y, l, q );
            }
            else
              shift.x = shift.y = 0;
  
            for ( ;
                  i != j;
                  i = i < last ? i + 1 : first )
            {
              points[i].x += xstrength + shift.x;
              points[i].y += ystrength + shift.y;
            }
          }
          else
            i = j;
  
          in   = out;
          l_in = l_out;
        }
  
        first = last + 1;
      }
  
      return FT_Err_Ok;
    }
  
  
    /* documentation is in ftoutln.h */
  
    FT_EXPORT_DEF( FT_Orientation )
    FT_Outline_Get_Orientation( FT_Outline*  outline )
    {
      FT_BBox     cbox;
      FT_Int      xshift, yshift;
      FT_Vector*  points;
      FT_Vector   v_prev, v_cur;
      FT_Int      c, n, first;
      FT_Pos      area = 0;
  
  
      if ( !outline || outline->n_points <= 0 )
        return FT_ORIENTATION_TRUETYPE;
  
      /* We use the nonzero winding rule to find the orientation.       */
      /* Since glyph outlines behave much more `regular' than arbitrary */
      /* cubic or quadratic curves, this test deals with the polygon    */
      /* only that is spanned up by the control points.                 */
  
      FT_Outline_Get_CBox( outline, &cbox );
  
      /* Handle collapsed outlines to avoid undefined FT_MSB. */
      if ( cbox.xMin == cbox.xMax || cbox.yMin == cbox.yMax )
        return FT_ORIENTATION_NONE;
  
      xshift = FT_MSB( (FT_UInt32)( FT_ABS( cbox.xMax ) |
                                    FT_ABS( cbox.xMin ) ) ) - 14;
      xshift = FT_MAX( xshift, 0 );
  
      yshift = FT_MSB( (FT_UInt32)( cbox.yMax - cbox.yMin ) ) - 14;
      yshift = FT_MAX( yshift, 0 );
  
      points = outline->points;
  
      first = 0;
      for ( c = 0; c < outline->n_contours; c++ )
      {
        FT_Int  last = outline->contours[c];
  
  
        v_prev = points[last];
  
        for ( n = first; n <= last; n++ )
        {
          v_cur = points[n];
          area += ( ( v_cur.y - v_prev.y ) >> yshift ) *
                  ( ( v_cur.x + v_prev.x ) >> xshift );
          v_prev = v_cur;
        }
  
        first = last + 1;
      }
  
      if ( area > 0 )
        return FT_ORIENTATION_POSTSCRIPT;
      else if ( area < 0 )
        return FT_ORIENTATION_TRUETYPE;
      else
        return FT_ORIENTATION_NONE;
    }
  
  
  /* END */
  