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kc3-lang/freetype/src/smooth/ftgrays.c

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  • Author : Werner Lemberg
    Date : 2001-06-28 17:49:10
    Hash : 415235df
    Message : finishing function header formatting updating copyrights

  • src/smooth/ftgrays.c
  • /***************************************************************************/
    /*                                                                         */
    /*  ftgrays.c                                                              */
    /*                                                                         */
    /*    A new `perfect' anti-aliasing renderer (body).                       */
    /*                                                                         */
    /*  Copyright 2000-2001 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.                                        */
    /*                                                                         */
    /***************************************************************************/
    
      /*************************************************************************/
      /*                                                                       */
      /*  This file can be compiled without the rest of the FreeType engine,   */
      /*  by defining the _STANDALONE_ macro when compiling it.  You also need */
      /*  to put the files `ftgrays.h' and `ftimage.h' into the current        */
      /*  compilation directory.  Typically, you could do something like       */
      /*                                                                       */
      /*  - copy `src/base/ftgrays.c' to your current directory                */
      /*                                                                       */
      /*  - copy `include/freetype/ftimage.h' and                              */
      /*    `include/freetype/ftgrays.h' to the same directory                 */
      /*                                                                       */
      /*  - compile `ftgrays' with the _STANDALONE_ macro defined, as in       */
      /*                                                                       */
      /*      cc -c -D_STANDALONE_ ftgrays.c                                   */
      /*                                                                       */
      /*  The renderer can be initialized with a call to                       */
      /*  `ft_grays_raster.grays_raster_new'; an anti-aliased bitmap can be    */
      /*  generated with a call to `ft_grays_raster.grays_raster_render'.      */
      /*                                                                       */
      /*  See the comments and documentation in the file `ftimage.h' for       */
      /*  more details on how the raster works.                                */
      /*                                                                       */
      /*************************************************************************/
    
      /*************************************************************************/
      /*                                                                       */
      /*  This is a new anti-aliasing scan-converter for FreeType 2.  The      */
      /*  algorithm used here is _very_ different from the one in the standard */
      /*  `ftraster' module.  Actually, `ftgrays' computes the _exact_         */
      /*  coverage of the outline on each pixel cell.                          */
      /*                                                                       */
      /*  It is based on ideas that I initially found in Raph Levien's         */
      /*  excellent LibArt graphics library (see http://www.levien.com/libart  */
      /*  for more information, though the web pages do not tell anything      */
      /*  about the renderer; you'll have to dive into the source code to      */
      /*  understand how it works).                                            */
      /*                                                                       */
      /*  Note, however, that this is a _very_ different implementation        */
      /*  compared to Raph's.  Coverage information is stored in a very        */
      /*  different way, and I don't use sorted vector paths.  Also, it        */
      /*  doesn't use floating point values.                                   */
      /*                                                                       */
      /*  This renderer has the following advantages:                          */
      /*                                                                       */
      /*  - It doesn't need an intermediate bitmap.  Instead, one can supply   */
      /*    a callback function that will be called by the renderer to draw    */
      /*    gray spans on any target surface.  You can thus do direct          */
      /*    composition on any kind of bitmap, provided that you give the      */
      /*    renderer the right callback.                                       */
      /*                                                                       */
      /*  - A perfect anti-aliaser, i.e., it computes the _exact_ coverage on  */
      /*    each pixel cell                                                    */
      /*                                                                       */
      /*  - It performs a single pass on the outline (the `standard' FT2       */
      /*    renderer makes two passes).                                        */
      /*                                                                       */
      /*  - It can easily be modified to render to _any_ number of gray levels */
      /*    cheaply.                                                           */
      /*                                                                       */
      /*  - For small (< 20) pixel sizes, it is faster than the standard       */
      /*    renderer.                                                          */
      /*                                                                       */
      /*************************************************************************/
    
    
    #include <string.h>             /* for memcpy() */
    
    
      /*************************************************************************/
      /*                                                                       */
      /* 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_aaraster
    
    
    #ifdef _STANDALONE_
    
    
    #define ErrRaster_Invalid_Mode     -2
    #define ErrRaster_Invalid_Outline  -1
    
    #include "ftimage.h"
    #include "ftgrays.h"
    
      /* This macro is used to indicate that a function parameter is unused. */
      /* Its purpose is simply to reduce compiler warnings.  Note also that  */
      /* simply defining it as `(void)x' doesn't avoid warnings with certain */
      /* ANSI compilers (e.g. LCC).                                          */
    #define FT_UNUSED( x )  (x) = (x)
    
      /* Disable the tracing mechanism for simplicity -- developers can      */
      /* activate it easily by redefining these two macros.                  */
    #ifndef FT_ERROR
    #define FT_ERROR( x )  do ; while ( 0 )     /* nothing */
    #endif
    
    #ifndef FT_TRACE
    #define FT_TRACE( x )  do ; while ( 0 )     /* nothing */
    #endif
    
    
    #else /* _STANDALONE_ */
    
    
    #include <ft2build.h>
    #include "ftgrays.h"
    #include FT_INTERNAL_OBJECTS_H
    #include FT_INTERNAL_DEBUG_H
    #include FT_OUTLINE_H
    
    #include "ftsmerrs.h"
    
    #define ErrRaster_Invalid_Mode     Smooth_Err_Cannot_Render_Glyph
    #define ErrRaster_Invalid_Outline  Smooth_Err_Invalid_Outline
    
    
    #endif /* _STANDALONE_ */
    
    
      /* define this to dump debugging information */
    #define xxxDEBUG_GRAYS
    
      /* as usual, for the speed hungry :-) */
    
    #ifndef FT_STATIC_RASTER
    
    
    #define RAS_ARG   PRaster  raster
    #define RAS_ARG_  PRaster  raster,
    
    #define RAS_VAR   raster
    #define RAS_VAR_  raster,
    
    #define ras       (*raster)
    
    
    #else /* FT_STATIC_RASTER */
    
    
    #define RAS_ARG   /* empty */
    #define RAS_ARG_  /* empty */
    #define RAS_VAR   /* empty */
    #define RAS_VAR_  /* empty */
    
      static TRaster  ras;
    
    
    #endif /* FT_STATIC_RASTER */
    
    
      /* must be at least 6 bits! */
    #define PIXEL_BITS  8
    
    #define ONE_PIXEL       ( 1L << PIXEL_BITS )
    #define PIXEL_MASK      ( -1L << PIXEL_BITS )
    #define TRUNC( x )      ( (x) >> PIXEL_BITS )
    #define SUBPIXELS( x )  ( (x) << PIXEL_BITS )
    #define FLOOR( x )      ( (x) & -ONE_PIXEL )
    #define CEILING( x )    ( ( (x) + ONE_PIXEL - 1 ) & -ONE_PIXEL )
    #define ROUND( x )      ( ( (x) + ONE_PIXEL / 2 ) & -ONE_PIXEL )
    
    #if PIXEL_BITS >= 6
    #define UPSCALE( x )    ( (x) << ( PIXEL_BITS - 6 ) )
    #define DOWNSCALE( x )  ( (x) >> ( PIXEL_BITS - 6 ) )
    #else
    #define UPSCALE( x )    ( (x) >> ( 6 - PIXEL_BITS ) )
    #define DOWNSCALE( x )  ( (x) << ( 6 - PIXEL_BITS ) )
    #endif
    
      /* Define this if you want to use a more compact storage scheme.  This   */
      /* increases the number of cells available in the render pool but slows  */
      /* down the rendering a bit.  It is useful if you have a really tiny     */
      /* render pool.                                                          */
    #define xxxGRAYS_COMPACT
    
    
      /*************************************************************************/
      /*                                                                       */
      /*   TYPE DEFINITIONS                                                    */
      /*                                                                       */
      typedef int   TScan;   /* integer scanline/pixel coordinate */
      typedef long  TPos;    /* sub-pixel coordinate              */
    
      /* maximal number of gray spans in a call to the span callback */
    #define FT_MAX_GRAY_SPANS  32
    
    
    #ifdef GRAYS_COMPACT
    
      typedef struct  TCell_
      {
        short  x     : 14;
        short  y     : 14;
        int    cover : PIXEL_BITS + 2;
        int    area  : PIXEL_BITS * 2 + 2;
    
      } TCell, *PCell;
    
    #else /* GRAYS_COMPACT */
    
      typedef struct  TCell_
      {
        TScan  x;
        TScan  y;
        int    cover;
        int    area;
    
      } TCell, *PCell;
    
    #endif /* GRAYS_COMPACT */
    
    
      typedef struct  TRaster_
      {
        PCell  cells;
        int    max_cells;
        int    num_cells;
    
        TScan  min_ex, max_ex;
        TScan  min_ey, max_ey;
    
        int    area;
        int    cover;
        int    invalid;
    
        TScan  ex, ey;
        TScan  cx, cy;
        TPos   x,  y;
    
        TScan  last_ey;
    
        FT_Vector   bez_stack[32 * 3 + 1];
        int         lev_stack[32];
    
        FT_Outline  outline;
        FT_Bitmap   target;
        FT_BBox     clip_box;
    
        FT_Span     gray_spans[FT_MAX_GRAY_SPANS];
        int         num_gray_spans;
    
        FT_Raster_Span_Func  render_span;
        void*                render_span_data;
        int                  span_y;
    
        int    band_size;
        int    band_shoot;
        int    conic_level;
        int    cubic_level;
    
        void*  memory;
    
      } TRaster, *PRaster;
    
    
      /*************************************************************************/
      /*                                                                       */
      /* Initialize the cells table.                                           */
      /*                                                                       */
      static void
      init_cells( RAS_ARG_ void*  buffer,
                           long   byte_size )
      {
        ras.cells     = (PCell)buffer;
        ras.max_cells = byte_size / sizeof ( TCell );
        ras.num_cells = 0;
        ras.area      = 0;
        ras.cover     = 0;
        ras.invalid   = 1;
      }
    
    
      /*************************************************************************/
      /*                                                                       */
      /* Compute the outline bounding box.                                     */
      /*                                                                       */
      static void
      compute_cbox( RAS_ARG_ FT_Outline*  outline )
      {
        FT_Vector*  vec   = outline->points;
        FT_Vector*  limit = vec + outline->n_points;
    
    
        if ( outline->n_points <= 0 )
        {
          ras.min_ex = ras.max_ex = 0;
          ras.min_ey = ras.max_ey = 0;
          return;
        }
    
        ras.min_ex = ras.max_ex = vec->x;
        ras.min_ey = ras.max_ey = vec->y;
    
        vec++;
    
        for ( ; vec < limit; vec++ )
        {
          TPos  x = vec->x;
          TPos  y = vec->y;
    
    
          if ( x < ras.min_ex ) ras.min_ex = x;
          if ( x > ras.max_ex ) ras.max_ex = x;
          if ( y < ras.min_ey ) ras.min_ey = y;
          if ( y > ras.max_ey ) ras.max_ey = y;
        }
    
        /* truncate the bounding box to integer pixels */
        ras.min_ex = ras.min_ex >> 6;
        ras.min_ey = ras.min_ey >> 6;
        ras.max_ex = ( ras.max_ex + 63 ) >> 6;
        ras.max_ey = ( ras.max_ey + 63 ) >> 6;
      }
    
    
      /*************************************************************************/
      /*                                                                       */
      /* Record the current cell in the table.                                 */
      /*                                                                       */
      static int
      record_cell( RAS_ARG )
      {
        PCell  cell;
    
    
        if ( !ras.invalid && ( ras.area | ras.cover ) )
        {
          if ( ras.num_cells >= ras.max_cells )
            return 1;
    
          cell        = ras.cells + ras.num_cells++;
          cell->x     = ras.ex - ras.min_ex;
          cell->y     = ras.ey - ras.min_ey;
          cell->area  = ras.area;
          cell->cover = ras.cover;
        }
    
        return 0;
      }
    
    
      /*************************************************************************/
      /*                                                                       */
      /* Set the current cell to a new position.                               */
      /*                                                                       */
      static int
      set_cell( RAS_ARG_ TScan  ex,
                         TScan  ey )
      {
        int  invalid, record, clean;
    
    
        /* Move the cell pointer to a new position.  We set the `invalid'      */
        /* flag to indicate that the cell isn't part of those we're interested */
        /* in during the render phase.  This means that:                       */
        /*                                                                     */
        /* . the new vertical position must be within min_ey..max_ey-1.        */
        /* . the new horizontal position must be strictly less than max_ex     */
        /*                                                                     */
        /* Note that if a cell is to the left of the clipping region, it is    */
        /* actually set to the (min_ex-1) horizontal position.                 */
    
        record  = 0;
        clean   = 1;
    
        invalid = ( ey < ras.min_ey || ey >= ras.max_ey || ex >= ras.max_ex );
        if ( !invalid )
        {
          /* All cells that are on the left of the clipping region go to the */
          /* min_ex - 1 horizontal position.                                 */
          if ( ex < ras.min_ex )
            ex = ras.min_ex - 1;
    
          /* if our position is new, then record the previous cell */
          if ( ex != ras.ex || ey != ras.ey )
            record = 1;
          else
            clean = ras.invalid;  /* do not clean if we didn't move from */
                                  /* a valid cell                        */
        }
    
        /* record the previous cell if needed (i.e., if we changed the cell */
        /* position, of changed the `invalid' flag)                         */
        if ( ( ras.invalid != invalid || record ) && record_cell( RAS_VAR ) )
          return 1;
    
        if ( clean )
        {
          ras.area  = 0;
          ras.cover = 0;
        }
    
        ras.invalid = invalid;
        ras.ex      = ex;
        ras.ey      = ey;
        return 0;
      }
    
    
      /*************************************************************************/
      /*                                                                       */
      /* Start a new contour at a given cell.                                  */
      /*                                                                       */
      static void
      start_cell( RAS_ARG_  TScan  ex,
                            TScan  ey )
      {
        if ( ex < ras.min_ex )
          ex = ras.min_ex - 1;
    
        ras.area    = 0;
        ras.cover   = 0;
        ras.ex      = ex;
        ras.ey      = ey;
        ras.last_ey = SUBPIXELS( ey );
        ras.invalid = 0;
    
        (void)set_cell( RAS_VAR_ ex, ey );
      }
    
    
      /*************************************************************************/
      /*                                                                       */
      /* Render a scanline as one or more cells.                               */
      /*                                                                       */
      static int
      render_scanline( RAS_ARG_  TScan  ey,
                                 TPos   x1,
                                 TScan  y1,
                                 TPos   x2,
                                 TScan  y2 )
      {
        TScan  ex1, ex2, fx1, fx2, delta;
        long   p, first, dx;
        int    incr, lift, mod, rem;
    
    
        dx = x2 - x1;
    
        ex1 = TRUNC( x1 ); /* if (ex1 >= ras.max_ex) ex1 = ras.max_ex-1; */
        ex2 = TRUNC( x2 ); /* if (ex2 >= ras.max_ex) ex2 = ras.max_ex-1; */
        fx1 = x1 - SUBPIXELS( ex1 );
        fx2 = x2 - SUBPIXELS( ex2 );
    
        /* trivial case.  Happens often */
        if ( y1 == y2 )
          return set_cell( RAS_VAR_ ex2, ey );
    
        /* everything is located in a single cell.  That is easy! */
        /*                                                        */
        if ( ex1 == ex2 )
        {
          delta      = y2 - y1;
          ras.area  += ( fx1 + fx2 ) * delta;
          ras.cover += delta;
          return 0;
        }
    
        /* ok, we'll have to render a run of adjacent cells on the same */
        /* scanline...                                                  */
        /*                                                              */
        p     = ( ONE_PIXEL - fx1 ) * ( y2 - y1 );
        first = ONE_PIXEL;
        incr  = 1;
    
        if ( dx < 0 )
        {
          p     = fx1 * ( y2 - y1 );
          first = 0;
          incr  = -1;
          dx    = -dx;
        }
    
        delta = p / dx;
        mod   = p % dx;
        if ( mod < 0 )
        {
          delta--;
          mod += dx;
        }
    
        ras.area  += ( fx1 + first ) * delta;
        ras.cover += delta;
    
        ex1 += incr;
        if ( set_cell( RAS_VAR_ ex1, ey ) )
          goto Error;
        y1  += delta;
    
        if ( ex1 != ex2 )
        {
          p     = ONE_PIXEL * ( y2 - y1 );
          lift  = p / dx;
          rem   = p % dx;
          if ( rem < 0 )
          {
            lift--;
            rem += dx;
          }
    
          mod -= dx;
    
          while ( ex1 != ex2 )
          {
            delta = lift;
            mod  += rem;
            if ( mod >= 0 )
            {
              mod -= dx;
              delta++;
            }
    
            ras.area  += ONE_PIXEL * delta;
            ras.cover += delta;
            y1        += delta;
            ex1       += incr;
            if ( set_cell( RAS_VAR_ ex1, ey ) )
              goto Error;
          }
        }
    
        delta      = y2 - y1;
        ras.area  += ( fx2 + ONE_PIXEL - first ) * delta;
        ras.cover += delta;
    
        return 0;
    
      Error:
        return 1;
      }
    
    
      /*************************************************************************/
      /*                                                                       */
      /* Render a given line as a series of scanlines.                         */
      /*                                                                       */
      static int
      render_line( RAS_ARG_ TPos  to_x,
                            TPos  to_y )
      {
        TScan  ey1, ey2, fy1, fy2;
        TPos   dx, dy, x, x2;
        int    p, rem, mod, lift, delta, first, incr;
    
    
        ey1 = TRUNC( ras.last_ey );
        ey2 = TRUNC( to_y ); /* if (ey2 >= ras.max_ey) ey2 = ras.max_ey-1; */
        fy1 = ras.y - ras.last_ey;
        fy2 = to_y - SUBPIXELS( ey2 );
    
        dx = to_x - ras.x;
        dy = to_y - ras.y;
    
        /* XXX: we should do something about the trivial case where dx == 0, */
        /*      as it happens very often!                                    */
    
        /* perform vertical clipping */
        {
          TScan  min, max;
    
    
          min = ey1;
          max = ey2;
          if ( ey1 > ey2 )
          {
            min = ey2;
            max = ey1;
          }
          if ( min >= ras.max_ey || max < ras.min_ey )
            goto End;
        }
    
        /* everything is on a single scanline */
        if ( ey1 == ey2 )
        {
          if ( render_scanline( RAS_VAR_ ey1, ras.x, fy1, to_x, fy2 ) )
            goto Error;
          goto End;
        }
    
        /* ok, we have to render several scanlines */
        p     = ( ONE_PIXEL - fy1 ) * dx;
        first = ONE_PIXEL;
        incr  = 1;
    
        if ( dy < 0 )
        {
          p     = fy1 * dx;
          first = 0;
          incr  = -1;
          dy    = -dy;
        }
    
        delta = p / dy;
        mod   = p % dy;
        if ( mod < 0 )
        {
          delta--;
          mod += dy;
        }
    
        x = ras.x + delta;
        if ( render_scanline( RAS_VAR_ ey1, ras.x, fy1, x, first ) )
          goto Error;
    
        ey1 += incr;
        if ( set_cell( RAS_VAR_ TRUNC( x ), ey1 ) )
          goto Error;
    
        if ( ey1 != ey2 )
        {
          p     = ONE_PIXEL * dx;
          lift  = p / dy;
          rem   = p % dy;
          if ( rem < 0 )
          {
            lift--;
            rem += dy;
          }
          mod -= dy;
    
          while ( ey1 != ey2 )
          {
            delta = lift;
            mod  += rem;
            if ( mod >= 0 )
            {
              mod -= dy;
              delta++;
            }
    
            x2 = x + delta;
            if ( render_scanline( RAS_VAR_ ey1,
                                  x, ONE_PIXEL - first, x2, first ) )
              goto Error;
            x = x2;
            ey1 += incr;
            if ( set_cell( RAS_VAR_ TRUNC( x ), ey1 ) )
              goto Error;
          }
        }
    
        if ( render_scanline( RAS_VAR_ ey1,
                              x, ONE_PIXEL - first, to_x, fy2 ) )
          goto Error;
    
      End:
        ras.x       = to_x;
        ras.y       = to_y;
        ras.last_ey = SUBPIXELS( ey2 );
    
        return 0;
    
      Error:
        return 1;
      }
    
    
      static void
      split_conic( FT_Vector*  base )
      {
        TPos  a, b;
    
    
        base[4].x = base[2].x;
        b = base[1].x;
        a = base[3].x = ( base[2].x + b ) / 2;
        b = base[1].x = ( base[0].x + b ) / 2;
        base[2].x = ( a + b ) / 2;
    
        base[4].y = base[2].y;
        b = base[1].y;
        a = base[3].y = ( base[2].y + b ) / 2;
        b = base[1].y = ( base[0].y + b ) / 2;
        base[2].y = ( a + b ) / 2;
      }
    
    
      static int
      render_conic( RAS_ARG_ FT_Vector*  control,
                             FT_Vector*  to )
      {
        TPos        dx, dy;
        int         top, level;
        int*        levels;
        FT_Vector*  arc;
    
    
        dx = DOWNSCALE( ras.x ) + to->x - ( control->x << 1 );
        if ( dx < 0 )
          dx = -dx;
        dy = DOWNSCALE( ras.y ) + to->y - ( control->y << 1 );
        if ( dy < 0 )
          dy = -dy;
        if ( dx < dy )
          dx = dy;
    
        level = 1;
        dx = dx / ras.conic_level;
        while ( dx > 0 )
        {
          dx >>= 2;
          level++;
        }
    
        /* a shortcut to speed things up */
        if ( level <= 1 )
        {
          /* we compute the mid-point directly in order to avoid */
          /* calling split_conic()                               */
          TPos   to_x, to_y, mid_x, mid_y;
    
    
          to_x  = UPSCALE( to->x );
          to_y  = UPSCALE( to->y );
          mid_x = ( ras.x + to_x + 2 * UPSCALE( control->x ) ) / 4;
          mid_y = ( ras.y + to_y + 2 * UPSCALE( control->y ) ) / 4;
    
          return render_line( RAS_VAR_ mid_x, mid_y ) ||
                 render_line( RAS_VAR_ to_x, to_y );
        }
    
        arc       = ras.bez_stack;
        levels    = ras.lev_stack;
        top       = 0;
        levels[0] = level;
    
        arc[0].x = UPSCALE( to->x );
        arc[0].y = UPSCALE( to->y );
        arc[1].x = UPSCALE( control->x );
        arc[1].y = UPSCALE( control->y );
        arc[2].x = ras.x;
        arc[2].y = ras.y;
    
        while ( top >= 0 )
        {
          level = levels[top];
          if ( level > 1 )
          {
            /* check that the arc crosses the current band */
            TPos  min, max, y;
    
    
            min = max = arc[0].y;
    
            y = arc[1].y;
            if ( y < min ) min = y;
            if ( y > max ) max = y;
    
            y = arc[2].y;
            if ( y < min ) min = y;
            if ( y > max ) max = y;
    
            if ( TRUNC( min ) >= ras.max_ey || TRUNC( max ) < 0 )
              goto Draw;
    
            split_conic( arc );
            arc += 2;
            top++;
            levels[top] = levels[top - 1] = level - 1;
            continue;
          }
    
        Draw:
          {
            TPos  to_x, to_y, mid_x, mid_y;
    
    
            to_x  = arc[0].x;
            to_y  = arc[0].y;
            mid_x = ( ras.x + to_x + 2 * arc[1].x ) / 4;
            mid_y = ( ras.y + to_y + 2 * arc[1].y ) / 4;
    
            if ( render_line( RAS_VAR_ mid_x, mid_y ) ||
                 render_line( RAS_VAR_ to_x, to_y )   )
              return 1;
    
            top--;
            arc -= 2;
          }
        }
        return 0;
      }
    
    
      static void
      split_cubic( FT_Vector*  base )
      {
        TPos  a, b, c, d;
    
    
        base[6].x = base[3].x;
        c = base[1].x;
        d = base[2].x;
        base[1].x = a = ( base[0].x + c ) / 2;
        base[5].x = b = ( base[3].x + d ) / 2;
        c = ( c + d ) / 2;
        base[2].x = a = ( a + c ) / 2;
        base[4].x = b = ( b + c ) / 2;
        base[3].x = ( a + b ) / 2;
    
        base[6].y = base[3].y;
        c = base[1].y;
        d = base[2].y;
        base[1].y = a = ( base[0].y + c ) / 2;
        base[5].y = b = ( base[3].y + d ) / 2;
        c = ( c + d ) / 2;
        base[2].y = a = ( a + c ) / 2;
        base[4].y = b = ( b + c ) / 2;
        base[3].y = ( a + b ) / 2;
      }
    
    
      static int
      render_cubic( RAS_ARG_ FT_Vector*  control1,
                             FT_Vector*  control2,
                             FT_Vector*  to )
      {
        TPos        dx, dy, da, db;
        int         top, level;
        int*        levels;
        FT_Vector*  arc;
    
    
        dx = DOWNSCALE( ras.x ) + to->x - ( control1->x << 1 );
        if ( dx < 0 )
          dx = -dx;
        dy = DOWNSCALE( ras.y ) + to->y - ( control1->y << 1 );
        if ( dy < 0 )
          dy = -dy;
        if ( dx < dy )
          dx = dy;
        da = dx;
    
        dx = DOWNSCALE( ras.x ) + to->x - 3 * ( control1->x + control2->x );
        if ( dx < 0 )
          dx = -dx;
        dy = DOWNSCALE( ras.y ) + to->y - 3 * ( control1->x + control2->y );
        if ( dy < 0 )
          dy = -dy;
        if ( dx < dy )
          dx = dy;
        db = dx;
    
        level = 1;
        da    = da / ras.cubic_level;
        db    = db / ras.conic_level;
        while ( da > 0 || db > 0 )
        {
          da >>= 2;
          db >>= 3;
          level++;
        }
    
        if ( level <= 1 )
        {
          TPos   to_x, to_y, mid_x, mid_y;
    
    
          to_x  = UPSCALE( to->x );
          to_y  = UPSCALE( to->y );
          mid_x = ( ras.x + to_x +
                    3 * UPSCALE( control1->x + control2->x ) ) / 8;
          mid_y = ( ras.y + to_y +
                    3 * UPSCALE( control1->y + control2->y ) ) / 8;
    
          return render_line( RAS_VAR_ mid_x, mid_y ) ||
                 render_line( RAS_VAR_ to_x, to_y );
        }
    
        arc      = ras.bez_stack;
        arc[0].x = UPSCALE( to->x );
        arc[0].y = UPSCALE( to->y );
        arc[1].x = UPSCALE( control2->x );
        arc[1].y = UPSCALE( control2->y );
        arc[2].x = UPSCALE( control1->x );
        arc[2].y = UPSCALE( control1->y );
        arc[3].x = ras.x;
        arc[3].y = ras.y;
    
        levels    = ras.lev_stack;
        top       = 0;
        levels[0] = level;
    
        while ( top >= 0 )
        {
          level = levels[top];
          if ( level > 1 )
          {
            /* check that the arc crosses the current band */
            TPos  min, max, y;
    
    
            min = max = arc[0].y;
            y = arc[1].y;
            if ( y < min ) min = y;
            if ( y > max ) max = y;
            y = arc[2].y;
            if ( y < min ) min = y;
            if ( y > max ) max = y;
            y = arc[3].y;
            if ( y < min ) min = y;
            if ( y > max ) max = y;
            if ( TRUNC( min ) >= ras.max_ey || TRUNC( max ) < 0 )
              goto Draw;
            split_cubic( arc );
            arc += 3;
            top ++;
            levels[top] = levels[top - 1] = level - 1;
            continue;
          }
    
        Draw:
          {
            TPos  to_x, to_y, mid_x, mid_y;
    
    
            to_x  = arc[0].x;
            to_y  = arc[0].y;
            mid_x = ( ras.x + to_x + 3 * ( arc[1].x + arc[2].x ) ) / 8;
            mid_y = ( ras.y + to_y + 3 * ( arc[1].y + arc[2].y ) ) / 8;
    
            if ( render_line( RAS_VAR_ mid_x, mid_y ) ||
                 render_line( RAS_VAR_ to_x, to_y )   )
              return 1;
            top --;
            arc -= 3;
          }
        }
        return 0;
      }
    
    
      /* a macro comparing two cell pointers.  Returns true if a <= b. */
    #if 1
    
    #define PACK( a )          ( ( (long)(a)->y << 16 ) + (a)->x )
    #define LESS_THAN( a, b )  ( PACK( a ) < PACK( b ) )
    
    #else /* 1 */
    
    #define LESS_THAN( a, b )  ( (a)->y < (b)->y || \
                                 ( (a)->y == (b)->y && (a)->x < (b)->x ) )
    
    #endif /* 1 */
    
    #define SWAP_CELLS( a, b, temp )  do             \
                                      {              \
                                        temp = *(a); \
                                        *(a) = *(b); \
                                        *(b) = temp; \
                                      } while ( 0 )
    #define DEBUG_SORT
    #define QUICK_SORT
    
    #ifdef SHELL_SORT
    
      /* a simple shell sort algorithm that works directly on our */
      /* cells table                                              */
      static void
      shell_sort ( PCell  cells,
                   int    count )
      {
        PCell  i, j, limit = cells + count;
        TCell  temp;
        int    gap;
    
    
        /* compute initial gap */
        for ( gap = 0; ++gap < count; gap *= 3 )
          ;
    
        while ( gap /= 3 )
        {
          for ( i = cells + gap; i < limit; i++ )
          {
            for ( j = i - gap; ; j -= gap )
            {
              PCell  k = j + gap;
    
    
              if ( LESS_THAN( j, k ) )
                break;
    
              SWAP_CELLS( j, k, temp );
    
              if ( j < cells + gap )
                break;
            }
          }
        }
      }
    
    #endif /* SHELL_SORT */
    
    
    #ifdef QUICK_SORT
    
      /* This is a non-recursive quicksort that directly process our cells     */
      /* array.  It should be faster than calling the stdlib qsort(), and we   */
      /* can even tailor our insertion threshold...                            */
    
    #define QSORT_THRESHOLD  9  /* below this size, a sub-array will be sorted */
                                /* through a normal insertion sort             */
    
      static void
      quick_sort( PCell  cells,
                  int    count )
      {
        PCell   stack[40];  /* should be enough ;-) */
        PCell*  top;        /* top of stack */
        PCell   base, limit;
        TCell   temp;
    
    
        limit = cells + count;
        base  = cells;
        top   = stack;
    
        for (;;)
        {
          int    len = (int)( limit - base );
          PCell  i, j, pivot;
    
    
          if ( len > QSORT_THRESHOLD )
          {
            /* we use base + len/2 as the pivot */
            pivot = base + len / 2;
            SWAP_CELLS( base, pivot, temp );
    
            i = base + 1;
            j = limit - 1;
    
            /* now ensure that *i <= *base <= *j */
            if ( LESS_THAN( j, i ) )
              SWAP_CELLS( i, j, temp );
    
            if ( LESS_THAN( base, i ) )
              SWAP_CELLS( base, i, temp );
    
            if ( LESS_THAN( j, base ) )
              SWAP_CELLS( base, j, temp );
    
            for (;;)
            {
              do i++; while ( LESS_THAN( i, base ) );
              do j--; while ( LESS_THAN( base, j ) );
    
              if ( i > j )
                break;
    
              SWAP_CELLS( i, j, temp );
            }
    
            SWAP_CELLS( base, j, temp );
    
            /* now, push the largest sub-array */
            if ( j - base > limit - i )
            {
              top[0] = base;
              top[1] = j;
              base   = i;
            }
            else
            {
              top[0] = i;
              top[1] = limit;
              limit  = j;
            }
            top += 2;
          }
          else
          {
            /* the sub-array is small, perform insertion sort */
            j = base;
            i = j + 1;
    
            for ( ; i < limit; j = i, i++ )
            {
              for ( ; LESS_THAN( j + 1, j ); j-- )
              {
                SWAP_CELLS( j + 1, j, temp );
                if ( j == base )
                  break;
              }
            }
            if ( top > stack )
            {
              top  -= 2;
              base  = top[0];
              limit = top[1];
            }
            else
              break;
          }
        }
      }
    
    #endif /* QUICK_SORT */
    
    
    #ifdef DEBUG_GRAYS
    #ifdef DEBUG_SORT
    
      static int
      check_sort( PCell  cells,
                  int    count )
      {
        PCell  p, q;
    
    
        for ( p = cells + count - 2; p >= cells; p-- )
        {
          q = p + 1;
          if ( !LESS_THAN( p, q ) )
            return 0;
        }
        return 1;
      }
    
    #endif /* DEBUG_SORT */
    #endif /* DEBUG_GRAYS */
    
    
      static int
      Move_To( FT_Vector*  to,
               FT_Raster   raster )
      {
        TPos  x, y;
    
    
        /* record current cell, if any */
        record_cell( (PRaster)raster );
    
        /* start to a new position */
        x = UPSCALE( to->x );
        y = UPSCALE( to->y );
        start_cell( (PRaster)raster, TRUNC( x ), TRUNC( y ) );
        ((PRaster)raster)->x = x;
        ((PRaster)raster)->y = y;
        return 0;
      }
    
    
      static int
      Line_To( FT_Vector*  to,
               FT_Raster   raster )
      {
        return render_line( (PRaster)raster,
                            UPSCALE( to->x ), UPSCALE( to->y ) );
      }
    
    
      static int
      Conic_To( FT_Vector*  control,
                FT_Vector*  to,
                FT_Raster   raster )
      {
        return render_conic( (PRaster)raster, control, to );
      }
    
    
      static int
      Cubic_To( FT_Vector*  control1,
                FT_Vector*  control2,
                FT_Vector*  to,
                FT_Raster   raster )
      {
        return render_cubic( (PRaster)raster, control1, control2, to );
      }
    
    
      static void
      grays_render_span( int       y,
                         int       count,
                         FT_Span*  spans,
                         PRaster   raster )
      {
        unsigned char*  p;
        FT_Bitmap*      map = &raster->target;
    
    
        /* first of all, compute the scanline offset */
        p = (unsigned char*)map->buffer - y * map->pitch;
        if ( map->pitch >= 0 )
          p += ( map->rows - 1 ) * map->pitch;
    
        for ( ; count > 0; count--, spans++ )
        {
          if ( spans->coverage )
    #if 1
            memset( p + spans->x, (unsigned char)spans->coverage, spans->len );
    #else /* 1 */
          {
            q     = p + spans->x;
            limit = q + spans->len;
            for ( ; q < limit; q++ )
              q[0] = (unsigned char)spans->coverage;
          }
    #endif /* 1 */
        }
      }
    
    
    #ifdef DEBUG_GRAYS
    
    #include <stdio.h>
    
      static void
      dump_cells( RAS_ARG )
      {
        PCell  cell, limit;
        int    y = -1;
    
    
        cell  = ras.cells;
        limit = cell + ras.num_cells;
    
        for ( ; cell < limit; cell++ )
        {
          if ( cell->y != y )
          {
            fprintf( stderr, "\n%2d: ", cell->y );
            y = cell->y;
          }
          fprintf( stderr, "[%d %d %d]",
                   cell->x, cell->area, cell->cover );
        }
        fprintf(stderr, "\n" );
      }
    
    #endif /* DEBUG_GRAYS */
    
    
      static void
      grays_hline( RAS_ARG_ TScan  x,
                            TScan  y,
                            TPos   area,
                            int    acount )
      {
        FT_Span*   span;
        int        count;
        int        coverage;
    
    
        /* compute the coverage line's coverage, depending on the    */
        /* outline fill rule                                         */
        /*                                                           */
        /* the coverage percentage is area/(PIXEL_BITS*PIXEL_BITS*2) */
        /*                                                           */
        coverage = area >> ( PIXEL_BITS * 2 + 1 - 8);  /* use range 0..256 */
    
        if ( ras.outline.flags & ft_outline_even_odd_fill )
        {
          if ( coverage < 0 )
            coverage = -coverage;
    
          while ( coverage >= 512 )
            coverage -= 512;
    
          if ( coverage > 256 )
            coverage = 512 - coverage;
          else if ( coverage == 256 )
            coverage = 255;
        }
        else
        {
          /* normal non-zero winding rule */
          if ( coverage < 0 )
            coverage = -coverage;
    
          if ( coverage >= 256 )
            coverage = 255;
        }
    
        y += ras.min_ey;
        x += ras.min_ex;
    
        if ( coverage )
        {
          /* see if we can add this span to the current list */
          count = ras.num_gray_spans;
          span  = ras.gray_spans + count - 1;
          if ( count > 0                          &&
               ras.span_y == y                    &&
               (int)span->x + span->len == (int)x &&
               span->coverage == coverage )
          {
            span->len = (unsigned short)( span->len + acount );
            return;
          }
    
          if ( ras.span_y != y || count >= FT_MAX_GRAY_SPANS )
          {
            if ( ras.render_span && count > 0 )
              ras.render_span( ras.span_y, count, ras.gray_spans,
                               ras.render_span_data );
            /* ras.render_span( span->y, ras.gray_spans, count ); */
    
    #ifdef DEBUG_GRAYS
    
            if ( ras.span_y >= 0 )
            {
              int  n;
    
    
              fprintf( stderr, "y=%3d ", ras.span_y );
              span = ras.gray_spans;
              for ( n = 0; n < count; n++, span++ )
                fprintf( stderr, "[%d..%d]:%02x ",
                         span->x, span->x + span->len - 1, span->coverage );
              fprintf( stderr, "\n" );
            }
    
    #endif /* DEBUG_GRAYS */
    
            ras.num_gray_spans = 0;
            ras.span_y         = y;
    
            count = 0;
            span  = ras.gray_spans;
          }
          else
            span++;
    
          /* add a gray span to the current list */
          span->x        = (short)x;
          span->len      = (unsigned short)acount;
          span->coverage = (unsigned char)coverage;
          ras.num_gray_spans++;
        }
      }
    
    
      static void
      grays_sweep( RAS_ARG_ FT_Bitmap*  target )
      {
        TScan  x, y, cover, area;
        PCell  start, cur, limit;
    
        FT_UNUSED( target );
    
        if ( ras.num_cells == 0 )
          return;
    
        cur   = ras.cells;
        limit = cur + ras.num_cells;
    
        cover              = 0;
        ras.span_y         = -1;
        ras.num_gray_spans = 0;
    
        for (;;)
        {
          start  = cur;
          y      = start->y;
          x      = start->x;
    
          area   = start->area;
          cover += start->cover;
    
          /* accumulate all start cells */
          for (;;)
          {
            ++cur;
            if ( cur >= limit || cur->y != start->y || cur->x != start->x )
              break;
    
            area  += cur->area;
            cover += cur->cover;
          }
    
          /* if the start cell has a non-null area, we must draw an */
          /* individual gray pixel there                            */
          if ( area && x >= 0 )
          {
            grays_hline( RAS_VAR_ x, y, cover * ( ONE_PIXEL * 2 ) - area, 1 );
            x++;
          }
    
          if ( x < 0 )
            x = 0;
    
          if ( cur < limit && start->y == cur->y )
          {
            /* draw a gray span between the start cell and the current one */
            if ( cur->x > x )
              grays_hline( RAS_VAR_ x, y,
                           cover * ( ONE_PIXEL * 2 ), cur->x - x );
          }
          else
          {
            /* draw a gray span until the end of the clipping region */
            if ( cover && x < ras.max_ex - ras.min_ex )
              grays_hline( RAS_VAR_ x, y,
                           cover * ( ONE_PIXEL * 2 ),
                           ras.max_ex - x - ras.min_ex );
            cover = 0;
          }
    
          if ( cur >= limit )
            break;
        }
    
        if ( ras.render_span && ras.num_gray_spans > 0 )
          ras.render_span( ras.span_y, ras.num_gray_spans,
                           ras.gray_spans, ras.render_span_data );
    
    #ifdef DEBUG_GRAYS
    
        {
          int       n;
          FT_Span*  span;
    
    
          fprintf( stderr, "y=%3d ", ras.span_y );
          span = ras.gray_spans;
          for ( n = 0; n < ras.num_gray_spans; n++, span++ )
            fprintf( stderr, "[%d..%d]:%02x ",
                     span->x, span->x + span->len - 1, span->coverage );
          fprintf( stderr, "\n" );
        }
    
    #endif /* DEBUG_GRAYS */
    
      }
    
    
    #ifdef _STANDALONE_
    
      /*************************************************************************/
      /*                                                                       */
      /*  The following function should only compile in stand_alone mode,      */
      /*  i.e., when building this component without the rest of FreeType.     */
      /*                                                                       */
      /*************************************************************************/
    
      /*************************************************************************/
      /*                                                                       */
      /* <Function>                                                            */
      /*    FT_Outline_Decompose                                               */
      /*                                                                       */
      /* <Description>                                                         */
      /*    Walks over an outline's structure to decompose it into individual  */
      /*    segments and Bezier arcs.  This function is also able to emit      */
      /*    `move to' and `close to' operations to indicate the start and end  */
      /*    of new contours in the outline.                                    */
      /*                                                                       */
      /* <Input>                                                               */
      /*    outline   :: A pointer to the source target.                       */
      /*                                                                       */
      /*    interface :: A table of `emitters', i.e,. function pointers called */
      /*                 during decomposition to indicate path operations.     */
      /*                                                                       */
      /*    user      :: A typeless pointer which is passed to each emitter    */
      /*                 during the decomposition.  It can be used to store    */
      /*                 the state during the decomposition.                   */
      /*                                                                       */
      /* <Return>                                                              */
      /*    Error code.  0 means sucess.                                       */
      /*                                                                       */
      static int
      FT_Outline_Decompose( FT_Outline*              outline,
                            const FT_Outline_Funcs*  interface,
                            void*                    user )
      {
    #undef SCALED
    #define SCALED( x )  ( ( (x) << shift ) - delta )
    
        FT_Vector   v_last;
        FT_Vector   v_control;
        FT_Vector   v_start;
    
        FT_Vector*  point;
        FT_Vector*  limit;
        char*       tags;
    
        int     n;         /* index of contour in outline     */
        int     first;     /* index of first point in contour */
        int     error;
        char    tag;       /* current point's state           */
    
        int     shift = interface->shift;
        FT_Pos  delta = interface->delta;
    
    
        first = 0;
    
        for ( n = 0; n < outline->n_contours; n++ )
        {
          int  last;  /* index of last point in contour */
    
    
          last  = outline->contours[n];
          limit = outline->points + last;
    
          v_start = outline->points[first];
          v_last  = outline->points[last];
    
          v_start.x = SCALED( v_start.x ); v_start.y = SCALED( v_start.y );
          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--;
          }
    
          error = 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 );
    
                error = 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 )
                  {
                    error = 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;
    
                  error = interface->conic_to( &v_control, &v_middle, user );
                  if ( error )
                    goto Exit;
    
                  v_control = vec;
                  goto Do_Conic;
                }
    
                error = 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 );
    
                  error = interface->cubic_to( &vec1, &vec2, &vec, user );
                  if ( error )
                    goto Exit;
                  continue;
                }
    
                error = interface->cubic_to( &vec1, &vec2, &v_start, user );
                goto Close;
              }
            }
          }
    
          /* close the contour with a line segment */
          error = interface->line_to( &v_start, user );
    
       Close:
          if ( error )
            goto Exit;
    
          first = last + 1;
        }
    
        return 0;
    
      Exit:
        return error;
    
      Invalid_Outline:
        return ErrRaster_Invalid_Outline;
      }
    
    #endif /* _STANDALONE_ */
    
    
      typedef struct  TBand_
      {
        FT_Pos  min, max;
    
      } TBand;
    
    
      static int
      grays_convert_glyph( RAS_ARG_ FT_Outline*  outline )
      {
        static
        const FT_Outline_Funcs  interface =
        {
          (FT_Outline_MoveTo_Func) Move_To,
          (FT_Outline_LineTo_Func) Line_To,
          (FT_Outline_ConicTo_Func)Conic_To,
          (FT_Outline_CubicTo_Func)Cubic_To,
          0,
          0
        };
    
        TBand     bands[40], *band;
        int       n, num_bands;
        TPos      min, max, max_y;
        FT_BBox*  clip;
    
    
        /* Set up state in the raster object */
        compute_cbox( RAS_VAR_ outline );
    
        /* clip to target bitmap, exit if nothing to do */
        clip = &ras.clip_box;
    
        if ( ras.max_ex <= clip->xMin || ras.min_ex >= clip->xMax ||
             ras.max_ey <= clip->yMin || ras.min_ey >= clip->yMax )
          return 0;
    
        if ( ras.min_ex < clip->xMin ) ras.min_ex = clip->xMin;
        if ( ras.min_ey < clip->yMin ) ras.min_ey = clip->yMin;
    
        if ( ras.max_ex > clip->xMax ) ras.max_ex = clip->xMax;
        if ( ras.max_ey > clip->yMax ) ras.max_ey = clip->yMax;
    
        /* simple heuristic used to speed-up the bezier decomposition -- see */
        /* the code in render_conic() and render_cubic() for more details    */
        ras.conic_level = 32;
        ras.cubic_level = 16;
    
        {
          int level = 0;
    
    
          if ( ras.max_ex > 24 || ras.max_ey > 24 )
            level++;
          if ( ras.max_ex > 120 || ras.max_ey > 120 )
            level++;
    
          ras.conic_level <<= level;
          ras.cubic_level <<= level;
        }
    
        /* setup vertical bands */
        num_bands = ( ras.max_ey - ras.min_ey ) / ras.band_size;
        if ( num_bands == 0 )  num_bands = 1;
        if ( num_bands >= 39 ) num_bands = 39;
    
        ras.band_shoot = 0;
    
        min   = ras.min_ey;
        max_y = ras.max_ey;
    
        for ( n = 0; n < num_bands; n++, min = max )
        {
          max = min + ras.band_size;
          if ( n == num_bands - 1 || max > max_y )
            max = max_y;
    
          bands[0].min = min;
          bands[0].max = max;
          band         = bands;
    
          while ( band >= bands )
          {
            FT_Pos  bottom, top, middle;
            int     error;
    
    
            ras.num_cells = 0;
            ras.invalid   = 1;
            ras.min_ey    = band->min;
            ras.max_ey    = band->max;
    
            error = FT_Outline_Decompose( outline, &interface, &ras ) ||
                    record_cell( RAS_VAR );
    
            if ( !error )
            {
    #ifdef SHELL_SORT
              shell_sort( ras.cells, ras.num_cells );
    #else
              quick_sort( ras.cells, ras.num_cells );
    #endif
    
    #ifdef DEBUG_GRAYS
              check_sort( ras.cells, ras.num_cells );
              dump_cells( RAS_VAR );
    #endif
    
              grays_sweep( RAS_VAR_  &ras.target );
              band--;
              continue;
            }
    
            /* render pool overflow, we will reduce the render band by half */
            bottom = band->min;
            top    = band->max;
            middle = bottom + ( ( top - bottom ) >> 1 );
    
            /* waoow! This is too complex for a single scanline, something */
            /* must be really rotten here!                                 */
            if ( middle == bottom )
            {
    #ifdef DEBUG_GRAYS
              fprintf( stderr, "Rotten glyph!\n" );
    #endif
              return 1;
            }
    
            if ( bottom-top >= ras.band_size )
              ras.band_shoot++;
    
            band[1].min = bottom;
            band[1].max = middle;
            band[0].min = middle;
            band[0].max = top;
            band++;
          }
        }
    
        if ( ras.band_shoot > 8 && ras.band_size > 16 )
          ras.band_size = ras.band_size / 2;
    
        return 0;
      }
    
    
      extern int
      grays_raster_render( PRaster            raster,
                           FT_Raster_Params*  params )
      {
        FT_Outline*  outline = (FT_Outline*)params->source;
        FT_Bitmap*   target_map = params->target;
    
    
        if ( !raster || !raster->cells || !raster->max_cells )
          return -1;
    
        /* return immediately if the outline is empty */
        if ( outline->n_points == 0 || outline->n_contours <= 0 )
          return 0;
    
        if ( !outline || !outline->contours || !outline->points )
          return ErrRaster_Invalid_Outline;
    
        if ( outline->n_points !=
               outline->contours[outline->n_contours - 1] + 1 )
          return ErrRaster_Invalid_Outline;
    
        /* if direct mode is not set, we must have a target bitmap */
        if ( ( params->flags & ft_raster_flag_direct ) == 0 &&
             ( !target_map || !target_map->buffer )         )
          return -1;
    
        /* this version does not support monochrome rendering */
        if ( !( params->flags & ft_raster_flag_aa ) )
          return ErrRaster_Invalid_Mode;
    
        /* compute clipping box */
        if ( ( params->flags & ft_raster_flag_direct ) == 0 )
        {
          /* compute clip box from target pixmap */
          ras.clip_box.xMin = 0;
          ras.clip_box.yMin = 0;
          ras.clip_box.xMax = target_map->width;
          ras.clip_box.yMax = target_map->rows;
        }
        else if ( params->flags & ft_raster_flag_clip )
        {
          ras.clip_box = params->clip_box;
        }
        else
        {
          ras.clip_box.xMin = -32768L;
          ras.clip_box.yMin = -32768L;
          ras.clip_box.xMax =  32767L;
          ras.clip_box.yMax =  32767L;
        }
    
        ras.outline   = *outline;
        ras.num_cells = 0;
        ras.invalid   = 1;
    
        if ( target_map )
          ras.target = *target_map;
    
        ras.render_span      = (FT_Raster_Span_Func)grays_render_span;
        ras.render_span_data = &ras;
    
        if ( params->flags & ft_raster_flag_direct )
        {
          ras.render_span      = (FT_Raster_Span_Func)params->gray_spans;
          ras.render_span_data = params->user;
        }
    
        return grays_convert_glyph( (PRaster)raster, outline );
      }
    
    
      /**** RASTER OBJECT CREATION: In standalone mode, we simply use *****/
      /****                         a static object.                  *****/
    
    #ifdef _STANDALONE_
    
      static int
      grays_raster_new( void*       memory,
                        FT_Raster*  araster )
      {
        static TRaster  the_raster;
    
        FT_UNUSED( memory );
    
    
        *araster = (FT_Raster)&the_raster;
        memset( &the_raster, 0, sizeof ( the_raster ) );
    
        return 0;
      }
    
    
      static void
      grays_raster_done( FT_Raster  raster )
      {
        /* nothing */
        FT_UNUSED( raster );
      }
    
    #else /* _STANDALONE_ */
    
      static int
      grays_raster_new( FT_Memory   memory,
                        FT_Raster*  araster )
      {
        FT_Error  error;
        PRaster   raster;
    
    
        *araster = 0;
        if ( !ALLOC( raster, sizeof ( TRaster ) ) )
        {
          raster->memory = memory;
          *araster = (FT_Raster)raster;
        }
    
        return error;
      }
    
    
      static void
      grays_raster_done( FT_Raster  raster )
      {
        FT_Memory  memory = (FT_Memory)((PRaster)raster)->memory;
    
    
        FREE( raster );
      }
    
    #endif /* _STANDALONE_ */
    
    
      static void
      grays_raster_reset( FT_Raster    raster,
                          const char*  pool_base,
                          long         pool_size )
      {
        PRaster  rast = (PRaster)raster;
    
    
        if ( raster && pool_base && pool_size >= 4096 )
          init_cells( rast, (char*)pool_base, pool_size );
    
        rast->band_size  = ( pool_size / sizeof ( TCell ) ) / 8;
      }
    
    
      const FT_Raster_Funcs  ft_grays_raster =
      {
        ft_glyph_format_outline,
    
        (FT_Raster_New_Func)     grays_raster_new,
        (FT_Raster_Reset_Func)   grays_raster_reset,
        (FT_Raster_Set_Mode_Func)0,
        (FT_Raster_Render_Func)  grays_raster_render,
        (FT_Raster_Done_Func)    grays_raster_done
      };
    
    
    /* END */