kc3-lang/freetype/src/base/ftstroker.c

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• Hash : b08fe2dc
  Author :
  Date : 2002-08-27T20:20:29
  

  * massive re-formatting changes to many, many source files. I don't want to list them all here. The operations performed were all logical transformations of the sources: - trying to convert all enums and constants to CAPITALIZED_STYLE, with #define definitions like #define my_old_constants MY_NEW_CONSTANT - big, big update of the documentation comments * include/freetype/freetype.h, src/base/ftobjs.c, src/smooth/ftsmooth.c, include/freetype/ftimage.h: adding support for LCD-optimized rendering though the new constants/enums: FT_RENDER_MODE_LCD, FT_RENDER_MODE_LCD_V FT_PIXEL_MODE_LCD, FT_PIXEL_MODE_LCD_V this is still work in progress, don't expect everything to work correctly though most of the features have been implemented. * adding new FT_LOAD_XXX flags, used to specify both hinting and rendering targets: FT_LOAD_TARGET_NORMAL :: anti-aliased hinting & rendering FT_LOAD_TARGET_MONO :: monochrome bitmaps FT_LOAD_TARGET_LCD :: horizontal RGB/BGR decimated hinting & rendering FT_LOAD_TARGET_LCD_V :: vertical RGB/BGR decimated hinting & rendering note that FT_LOAD_TARGET_NORMAL is 0, which means that the default behaviour of the font engine is _unchanged_.

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• src/base/ftstroker.c

• #include <ft2build.h>
  #include FT_STROKER_H
  #include FT_TRIGONOMETRY_H
  #include FT_INTERNAL_MEMORY_H
  #include FT_INTERNAL_DEBUG_H
  
   /***************************************************************************/
   /***************************************************************************/
   /*****                                                                 *****/
   /*****                       BEZIER COMPUTATIONS                       *****/
   /*****                                                                 *****/
   /***************************************************************************/
   /***************************************************************************/
  
  #define FT_SMALL_CONIC_THRESHOLD   (FT_ANGLE_PI/6)
  #define FT_SMALL_CUBIC_THRESHOLD   (FT_ANGLE_PI/6)
  #define FT_EPSILON  2
  
  #define FT_IS_SMALL(x)  ((x) > -FT_EPSILON && (x) < FT_EPSILON)
  
    static FT_Pos
    ft_pos_abs( FT_Pos  x )
    {
      return  x >= 0 ? x : -x ;
    }
  
    static void
    ft_conic_split( FT_Vector*  base )
    {
      FT_Pos  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 FT_Bool
    ft_conic_is_small_enough( FT_Vector*  base,
                              FT_Angle   *angle_in,
                              FT_Angle   *angle_out )
    {
      FT_Vector  d1, d2;
      FT_Angle   theta;
      FT_Int     close1, close2;
  
      d1.x = base[1].x - base[2].x;
      d1.y = base[1].y - base[2].y;
      d2.x = base[0].x - base[1].x;
      d2.y = base[0].y - base[1].y;
  
      close1 = FT_IS_SMALL(d1.x) && FT_IS_SMALL(d1.y);
      close2 = FT_IS_SMALL(d2.x) && FT_IS_SMALL(d2.y);
  
      if (close1)
      {
        if (close2)
          *angle_in = *angle_out = 0;
        else
          *angle_in = *angle_out = FT_Atan2( d2.x, d2.y );
      }
      else if (close2)
      {
        *angle_in = *angle_out = FT_Atan2( d1.x, d1.y );
      }
      else
      {
        *angle_in  = FT_Atan2( d1.x, d1.y );
        *angle_out = FT_Atan2( d2.x, d2.y );
      }
  
      theta = ft_pos_abs( FT_Angle_Diff( *angle_in, *angle_out ) );
  
      return FT_BOOL( theta < FT_SMALL_CONIC_THRESHOLD );
    }
  
  
    static void
    ft_cubic_split( FT_Vector*  base )
    {
      FT_Pos  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 FT_Bool
    ft_cubic_is_small_enough( FT_Vector*  base,
                              FT_Angle   *angle_in,
                              FT_Angle   *angle_mid,
                              FT_Angle   *angle_out )
    {
      FT_Vector  d1, d2, d3;
      FT_Angle   theta1, theta2;
      FT_Int     close1, close2, close3;
  
      d1.x = base[2].x - base[3].x;
      d1.y = base[2].y - base[3].y;
      d2.x = base[1].x - base[2].x;
      d2.y = base[1].y - base[2].y;
      d3.x = base[0].x - base[1].x;
      d3.y = base[0].y - base[1].y;
  
      close1 = FT_IS_SMALL(d1.x) && FT_IS_SMALL(d1.y);
      close2 = FT_IS_SMALL(d2.x) && FT_IS_SMALL(d2.y);
      close3 = FT_IS_SMALL(d3.x) && FT_IS_SMALL(d3.y);
  
      if (close1 || close3)
      {
        if (close2)
        {
          /* basically a point */
          *angle_in = *angle_out = *angle_mid = 0;
        }
        else if (close1)
        {
          *angle_in  = *angle_mid = FT_Atan2( d2.x, d2.y );
          *angle_out = FT_Atan2( d3.x, d3.y );
        }
        else  /* close2 */
        {
          *angle_in  = FT_Atan2( d1.x, d1.y );
          *angle_mid = *angle_out = FT_Atan2( d2.x, d2.y );
        }
      }
      else if (close2)
      {
        *angle_in  = *angle_mid = FT_Atan2( d1.x, d1.y );
        *angle_out = FT_Atan2( d3.x, d3.y );
      }
      else
      {
        *angle_in  = FT_Atan2( d1.x, d1.y );
        *angle_mid = FT_Atan2( d2.x, d2.y );
        *angle_out = FT_Atan2( d3.x, d3.y );
      }
      theta1 = ft_pos_abs( FT_Angle_Diff( *angle_in,  *angle_mid ) );
      theta2 = ft_pos_abs( FT_Angle_Diff( *angle_mid, *angle_out ) );
  
      return FT_BOOL( theta1 < FT_SMALL_CUBIC_THRESHOLD &&
                      theta2 < FT_SMALL_CUBIC_THRESHOLD );
    }
  
  
  
   /***************************************************************************/
   /***************************************************************************/
   /*****                                                                 *****/
   /*****                       STROKE BORDERS                            *****/
   /*****                                                                 *****/
   /***************************************************************************/
   /***************************************************************************/
  
    typedef enum
    {
      FT_STROKE_TAG_ON    = 1,   /* on-curve point  */
      FT_STROKE_TAG_CUBIC = 2,   /* cubic off-point */
      FT_STROKE_TAG_BEGIN = 4,   /* sub-path start  */
      FT_STROKE_TAG_END   = 8    /* sub-path end    */
  
    } FT_StrokeTags;
  
  
    typedef struct FT_StrokeBorderRec_
    {
      FT_UInt     num_points;
      FT_UInt     max_points;
      FT_Vector*  points;
      FT_Byte*    tags;
      FT_Bool     movable;
      FT_Int      start;    /* index of current sub-path start point */
      FT_Memory   memory;
  
    } FT_StrokeBorderRec, *FT_StrokeBorder;
  
  
    static FT_Error
    ft_stroke_border_grow( FT_StrokeBorder  border,
                           FT_UInt          new_points )
    {
      FT_UInt   old_max = border->max_points;
      FT_UInt   new_max = border->num_points + new_points;
      FT_Error  error   = 0;
  
      if ( new_max > old_max )
      {
        FT_UInt    cur_max = old_max;
        FT_Memory  memory  = border->memory;
  
        while ( cur_max < new_max )
          cur_max += (cur_max >> 1) + 16;
  
        if ( FT_RENEW_ARRAY( border->points, old_max, cur_max ) ||
             FT_RENEW_ARRAY( border->tags,   old_max, cur_max ) )
          goto Exit;
  
        border->max_points = cur_max;
      }
    Exit:
      return error;
    }
  
    static void
    ft_stroke_border_close( FT_StrokeBorder  border )
    {
      FT_ASSERT( border->start >= 0 );
  
      border->tags[ border->start        ] |= FT_STROKE_TAG_BEGIN;
      border->tags[ border->num_points-1 ] |= FT_STROKE_TAG_END;
  
      border->start   = -1;
      border->movable = 0;
    }
  
  
    static FT_Error
    ft_stroke_border_lineto( FT_StrokeBorder  border,
                             FT_Vector*       to,
                             FT_Bool          movable )
    {
      FT_Error  error = 0;
  
      FT_ASSERT( border->start >= 0 );
  
      if ( border->movable )
      {
        /* move last point */
        border->points[ border->num_points-1 ] = *to;
      }
      else
      {
        /* add one point */
        error = ft_stroke_border_grow( border, 1 );
        if (!error)
        {
          FT_Vector*  vec = border->points + border->num_points;
          FT_Byte*    tag = border->tags   + border->num_points;
  
          vec[0] = *to;
          tag[0] = FT_STROKE_TAG_ON;
  
          border->num_points += 1;
        }
      }
      border->movable = movable;
      return error;
    }
  
  
    static FT_Error
    ft_stroke_border_conicto( FT_StrokeBorder  border,
                              FT_Vector*       control,
                              FT_Vector*       to )
    {
      FT_Error  error;
  
      FT_ASSERT( border->start >= 0 );
  
      error = ft_stroke_border_grow( border, 2 );
      if (!error)
      {
        FT_Vector*  vec = border->points + border->num_points;
        FT_Byte*    tag = border->tags   + border->num_points;
  
        vec[0] = *control;
        vec[1] = *to;
  
        tag[0] = 0;
        tag[1] = FT_STROKE_TAG_ON;
  
        border->num_points += 2;
      }
      border->movable = 0;
      return error;
    }
  
  
    static FT_Error
    ft_stroke_border_cubicto( FT_StrokeBorder  border,
                              FT_Vector*       control1,
                              FT_Vector*       control2,
                              FT_Vector*       to )
    {
      FT_Error  error;
  
      FT_ASSERT( border->start >= 0 );
  
      error = ft_stroke_border_grow( border, 3 );
      if (!error)
      {
        FT_Vector*  vec = border->points + border->num_points;
        FT_Byte*    tag = border->tags   + border->num_points;
  
        vec[0] = *control1;
        vec[1] = *control2;
        vec[2] = *to;
  
        tag[0] = FT_STROKE_TAG_CUBIC;
        tag[1] = FT_STROKE_TAG_CUBIC;
        tag[2] = FT_STROKE_TAG_ON;
  
        border->num_points += 3;
      }
      border->movable = 0;
      return error;
    }
  
  
  #define  FT_ARC_CUBIC_ANGLE  (FT_ANGLE_PI/2)
  
  
    static FT_Error
    ft_stroke_border_arcto( FT_StrokeBorder  border,
                            FT_Vector*       center,
                            FT_Fixed         radius,
                            FT_Angle         angle_start,
                            FT_Angle         angle_diff )
    {
      FT_Angle   total, angle, step, rotate, next, theta;
      FT_Vector  a, b, a2, b2;
      FT_Fixed   length;
      FT_Error   error = 0;
  
      /* compute start point */
      FT_Vector_From_Polar( &a, radius, angle_start );
      a.x += center->x;
      a.y += center->y;
  
      total  = angle_diff;
      angle  = angle_start;
      rotate = ( angle_diff >= 0 ) ? FT_ANGLE_PI2 : -FT_ANGLE_PI2;
  
      while (total != 0)
      {
        step = total;
        if ( step > FT_ARC_CUBIC_ANGLE )
          step   = FT_ARC_CUBIC_ANGLE;
  
        else if ( step < -FT_ARC_CUBIC_ANGLE )
          step = -FT_ARC_CUBIC_ANGLE;
  
        next  = angle + step;
        theta = step;
        if ( theta < 0 )
          theta = -theta;
  
        theta >>= 1;
  
        /* compute end point */
        FT_Vector_From_Polar( &b, radius, next );
        b.x += center->x;
        b.y += center->y;
  
        /* compute first and second control points */
        length = FT_MulDiv( radius, FT_Sin(theta)*4,
                            (0x10000L + FT_Cos(theta))*3 );
  
        FT_Vector_From_Polar( &a2, length, angle + rotate );
        a2.x += a.x;
        a2.y += a.y;
  
        FT_Vector_From_Polar( &b2, length, next - rotate );
        b2.x += b.x;
        b2.y += b.y;
  
        /* add cubic arc */
        error = ft_stroke_border_cubicto( border, &a2, &b2, &b );
        if (error) break;
  
        /* process the rest of the arc ?? */
        a      = b;
        total -= step;
        angle  = next;
      }
      return error;
    }
  
  
    static FT_Error
    ft_stroke_border_moveto( FT_StrokeBorder  border,
                             FT_Vector*       to )
    {
      /* close current open path if any ? */
      if ( border->start >= 0 )
        ft_stroke_border_close( border );
  
      border->start   = border->num_points;
      border->movable = 0;
  
      return ft_stroke_border_lineto( border, to, 0 );
    }
  
  
   static void
   ft_stroke_border_init( FT_StrokeBorder  border,
                          FT_Memory        memory )
   {
     border->memory = memory;
     border->points = NULL;
     border->tags   = NULL;
  
     border->num_points = 0;
     border->max_points = 0;
     border->start      = -1;
   }
  
  
   static void
   ft_stroke_border_reset( FT_StrokeBorder  border )
   {
     border->num_points = 0;
     border->start      = -1;
   }
  
  
   static void
   ft_stroke_border_done( FT_StrokeBorder  border )
   {
     FT_Memory  memory = border->memory;
  
     FT_FREE( border->points );
     FT_FREE( border->tags );
  
     border->num_points = 0;
     border->max_points = 0;
     border->start      = -1;
   }
  
  
   static FT_Error
   ft_stroke_border_get_counts( FT_StrokeBorder  border,
                                FT_UInt         *anum_points,
                                FT_UInt         *anum_contours )
   {
     FT_Error  error        = 0;
     FT_UInt   num_points   = 0;
     FT_UInt   num_contours = 0;
  
     FT_UInt     count      = border->num_points;
     FT_Vector*  point      = border->points;
     FT_Byte*    tags       = border->tags;
     FT_Int      in_contour = 0;
  
     for ( ; count > 0; count--, point++, tags++ )
     {
       if ( tags[0] & FT_STROKE_TAG_BEGIN )
       {
         if ( in_contour != 0 )
           goto Fail;
  
         in_contour = 1;
       }
       else if ( in_contour == 0 )
         goto Fail;
  
       if ( tags[0] & FT_STROKE_TAG_END )
       {
         if ( in_contour == 0 )
           goto Fail;
  
         in_contour = 0;
         num_contours++;
       }
     }
     if ( in_contour != 0 )
       goto Fail;
  
   Exit:
     *anum_points   = num_points;
     *anum_contours = num_contours;
     return error;
  
   Fail:
     num_points   = 0;
     num_contours = 0;
     goto Exit;
   }
  
  
   static void
   ft_stroke_border_export( FT_StrokeBorder  border,
                            FT_Outline*      outline )
   {
     /* copy point locations */
     FT_MEM_COPY( outline->points + outline->n_points,
                  border->points,
                  border->num_points * sizeof(FT_Vector) );
  
     /* copy tags */
     {
       FT_UInt   count = border->num_points;
       FT_Byte*  read  = border->tags;
       FT_Byte*  write = (FT_Byte*) outline->tags + outline->n_points;
  
       for ( ; count > 0; count--, read++, write++ )
       {
         if ( *read & FT_STROKE_TAG_ON )
           *write = FT_CURVE_TAG_ON;
         else if ( *read & FT_STROKE_TAG_CUBIC )
           *write = FT_CURVE_TAG_CUBIC;
         else
           *write = FT_CURVE_TAG_CONIC;
       }
     }
  
     /* copy contours */
     {
       FT_UInt    count = border->num_points;
       FT_Byte*   tags  = border->tags;
       FT_Short*  write = outline->contours + outline->n_contours;
       FT_Short   index = (FT_Short) outline->n_points;
  
       for ( ; count > 0; count--, tags++, write++, index++ )
       {
         if ( *tags & FT_STROKE_TAG_END )
         {
           *write++ = index;
           outline->n_contours++;
         }
       }
     }
  
     outline->n_points  = (short)( outline->n_points + border->num_points );
  
     FT_ASSERT( FT_Outline_Check( outline ) == 0 );
   }
  
  
   /***************************************************************************/
   /***************************************************************************/
   /*****                                                                 *****/
   /*****                           STROKER                               *****/
   /*****                                                                 *****/
   /***************************************************************************/
   /***************************************************************************/
  
  #define  FT_SIDE_TO_ROTATE(s)   (FT_ANGLE_PI2 - (s)*FT_ANGLE_PI)
  
    typedef struct FT_StrokerRec_
    {
      FT_Angle             angle_in;
      FT_Angle             angle_out;
      FT_Vector            center;
      FT_Bool              first_point;
      FT_Bool              subpath_open;
      FT_Angle             subpath_angle;
      FT_Vector            subpath_start;
  
      FT_Stroker_LineCap   line_cap;
      FT_Stroker_LineJoin  line_join;
      FT_Fixed             miter_limit;
      FT_Fixed             radius;
  
      FT_Bool              valid;
      FT_StrokeBorderRec   borders[2];
      FT_Memory            memory;
  
    } FT_StrokerRec;
  
  
    FT_EXPORT_DEF( FT_Error )
    FT_Stroker_New( FT_Memory    memory,
                    FT_Stroker  *astroker )
    {
      FT_Error    error;
      FT_Stroker  stroker;
  
      if ( !FT_NEW( stroker ) )
      {
        stroker->memory = memory;
  
        ft_stroke_border_init( &stroker->borders[0], memory );
        ft_stroke_border_init( &stroker->borders[1], memory );
      }
      *astroker = stroker;
      return error;
    }
  
  
    FT_EXPORT_DEF( void )
    FT_Stroker_Set( FT_Stroker           stroker,
                    FT_Fixed             radius,
                    FT_Stroker_LineCap   line_cap,
                    FT_Stroker_LineJoin  line_join,
                    FT_Fixed             miter_limit )
    {
      stroker->radius      = radius;
      stroker->line_cap    = line_cap;
      stroker->line_join   = line_join;
      stroker->miter_limit = miter_limit;
  
      stroker->valid = 0;
  
      ft_stroke_border_reset( &stroker->borders[0] );
      ft_stroke_border_reset( &stroker->borders[1] );
    }
  
  
    FT_EXPORT_DEF( void )
    FT_Stroker_Done( FT_Stroker  stroker )
    {
      if ( stroker )
      {
        FT_Memory  memory = stroker->memory;
  
        ft_stroke_border_done( &stroker->borders[0] );
        ft_stroke_border_done( &stroker->borders[1] );
  
        stroker->memory = NULL;
        FT_FREE( stroker );
      }
    }
  
  
  
   /* creates a circular arc at a corner or cap */
    static FT_Error
    ft_stroker_arcto( FT_Stroker  stroker,
                      FT_Int      side )
    {
      FT_Angle          total, rotate;
      FT_Fixed          radius = stroker->radius;
      FT_Error          error  = 0;
      FT_StrokeBorder   border = stroker->borders + side;
  
      rotate = FT_SIDE_TO_ROTATE(side);
  
      total = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
      if (total == FT_ANGLE_PI)
        total = -rotate*2;
  
      error = ft_stroke_border_arcto( border,
                                      &stroker->center,
                                      radius,
                                      stroker->angle_in + rotate,
                                      total );
      border->movable = 0;
      return error;
    }
  
  
    /* adds a cap at the end of an opened path */
    static FT_Error
    ft_stroker_cap( FT_Stroker  stroker,
                    FT_Angle    angle,
                    FT_Int      side )
    {
      FT_Error  error  = 0;
  
      if ( stroker->line_cap == FT_STROKER_LINECAP_ROUND )
      {
        /* add a round cap */
        stroker->angle_in  = angle;
        stroker->angle_out = angle + FT_ANGLE_PI;
        error = ft_stroker_arcto( stroker, side );
      }
      else if ( stroker->line_cap == FT_STROKER_LINECAP_SQUARE )
      {
        /* add a square cap */
        FT_Vector         delta, delta2;
        FT_Angle          rotate = FT_SIDE_TO_ROTATE(side);
        FT_Fixed          radius = stroker->radius;
        FT_StrokeBorder   border = stroker->borders + side;
  
        FT_Vector_From_Polar( &delta2, radius, angle+rotate );
        FT_Vector_From_Polar( &delta,  radius, angle );
  
        delta.x += stroker->center.x + delta2.x;
        delta.y += stroker->center.y + delta2.y;
  
        error = ft_stroke_border_lineto( border, &delta, 0 );
        if (error) goto Exit;
  
        FT_Vector_From_Polar( &delta2, radius, angle-rotate );
        FT_Vector_From_Polar( &delta,  radius, angle );
  
        delta.x += delta2.x + stroker->center.x;
        delta.y += delta2.y + stroker->center.y;
  
        error = ft_stroke_border_lineto( border, &delta, 0 );
      }
    Exit:
      return error;
    }
  
  
  
   /* process an inside corner, i.e. compute intersection */
    static FT_Error
    ft_stroker_inside( FT_Stroker  stroker,
                       FT_Int      side)
    {
      FT_StrokeBorder  border = stroker->borders + side;
      FT_Angle         phi, theta, rotate;
      FT_Fixed         length, thcos, sigma;
      FT_Vector        delta;
      FT_Error         error = 0;
  
  
      rotate = FT_SIDE_TO_ROTATE(side);
  
      /* compute median angle */
      theta = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
      if ( theta == FT_ANGLE_PI )
        theta = rotate;
      else
        theta = theta/2;
  
      phi = stroker->angle_in + theta;
  
      thcos  = FT_Cos( theta );
      sigma  = FT_MulFix( stroker->miter_limit, thcos );
  
      if ( sigma < 0x10000L )
      {
        FT_Vector_From_Polar( &delta, stroker->radius, stroker->angle_out + rotate );
        delta.x += stroker->center.x;
        delta.y += stroker->center.y;
        border->movable = 0;
      }
      else
      {
        length = FT_DivFix( stroker->radius, thcos );
  
        FT_Vector_From_Polar( &delta, length, phi + rotate );
        delta.x += stroker->center.x;
        delta.y += stroker->center.y;
      }
  
      error = ft_stroke_border_lineto( border, &delta, 0 );
  
      return error;
    }
  
  
   /* process an outside corner, i.e. compute bevel/miter/round */
    static FT_Error
    ft_stroker_outside( FT_Stroker  stroker,
                        FT_Int      side )
    {
      FT_StrokeBorder  border = stroker->borders + side;
      FT_Error         error;
      FT_Angle         rotate;
  
      if ( stroker->line_join == FT_STROKER_LINEJOIN_ROUND )
      {
        error = ft_stroker_arcto( stroker, side );
      }
      else
      {
        /* this is a mitered or beveled corner */
        FT_Fixed   sigma, radius = stroker->radius;
        FT_Angle   theta, phi;
        FT_Fixed   thcos;
        FT_Bool    miter;
  
        rotate = FT_SIDE_TO_ROTATE(side);
        miter  = FT_BOOL( stroker->line_join == FT_STROKER_LINEJOIN_MITER );
  
        theta  = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
        if (theta == FT_ANGLE_PI)
          theta = rotate;
        else
          theta = theta/2;
  
        thcos  = FT_Cos( theta );
        sigma  = FT_MulFix( stroker->miter_limit, thcos );
  
        if ( sigma >= 0x10000L )
          miter = 0;
  
        phi = stroker->angle_in + theta + rotate;
  
        if (miter)  /* this is a miter (broken angle) */
        {
          FT_Vector  middle, delta;
          FT_Fixed  length;
  
          /* compute middle point */
          FT_Vector_From_Polar( &middle, FT_MulFix( radius, stroker->miter_limit ),
                                phi );
          middle.x += stroker->center.x;
          middle.y += stroker->center.y;
  
          /* compute first angle point */
          length = FT_MulFix( radius, FT_DivFix( 0x10000L - sigma,
                                      ft_pos_abs( FT_Sin( theta ) ) ) );
  
          FT_Vector_From_Polar( &delta, length, phi + rotate );
          delta.x += middle.x;
          delta.y += middle.y;
  
          error = ft_stroke_border_lineto( border, &delta, 0 );
          if (error) goto Exit;
  
          /* compute second angle point */
          FT_Vector_From_Polar( &delta, length, phi - rotate );
          delta.x += middle.x;
          delta.y += middle.y;
  
          error = ft_stroke_border_lineto( border, &delta, 0 );
          if (error) goto Exit;
  
          /* finally, add a movable end point */
          FT_Vector_From_Polar( &delta, radius, stroker->angle_out + rotate );
          delta.x += stroker->center.x;
          delta.y += stroker->center.y;
  
          error = ft_stroke_border_lineto( border, &delta, 1 );
        }
        else /* this is a bevel (intersection) */
        {
          FT_Fixed  length;
          FT_Vector  delta;
  
          length = FT_DivFix( stroker->radius, thcos );
  
          FT_Vector_From_Polar( &delta, length, phi );
          delta.x += stroker->center.x;
          delta.y += stroker->center.y;
  
          error = ft_stroke_border_lineto( border, &delta, 0 );
          if (error) goto Exit;
  
          /* now add end point */
          FT_Vector_From_Polar( &delta, stroker->radius, stroker->angle_out + rotate );
          delta.x += stroker->center.x;
          delta.y += stroker->center.y;
  
          error = ft_stroke_border_lineto( border, &delta, 1 );
        }
      }
    Exit:
      return error;
    }
  
  
    static FT_Error
    ft_stroker_process_corner( FT_Stroker  stroker )
    {
      FT_Error  error = 0;
      FT_Angle  turn;
      FT_Int    inside_side;
  
      turn = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
  
      /* no specific corner processing is required if the turn is 0 */
      if (turn == 0)
        goto Exit;
  
      /* when we turn to the right, the inside side is 0 */
      inside_side = 0;
  
      /* otherwise, the inside side is 1 */
      if (turn < 0)
        inside_side = 1;
  
      /* process the inside side */
      error = ft_stroker_inside( stroker, inside_side );
      if (error) goto Exit;
  
      /* process the outside side */
      error = ft_stroker_outside( stroker, 1-inside_side );
  
    Exit:
      return error;
    }
  
  
   /* add two points to the left and right borders corresponding to the */
   /* start of the subpath..                                            */
    static FT_Error
    ft_stroker_subpath_start( FT_Stroker  stroker,
                              FT_Angle    start_angle )
    {
      FT_Vector        delta;
      FT_Vector        point;
      FT_Error         error;
      FT_StrokeBorder  border;
  
      FT_Vector_From_Polar( &delta, stroker->radius, start_angle + FT_ANGLE_PI2 );
  
      point.x = stroker->center.x + delta.x;
      point.y = stroker->center.y + delta.y;
  
      border = stroker->borders;
      error = ft_stroke_border_moveto( border, &point );
      if (error) goto Exit;
  
      point.x = stroker->center.x - delta.x;
      point.y = stroker->center.y - delta.y;
  
      border++;
      error = ft_stroke_border_moveto( border, &point );
  
      /* save angle for last cap */
      stroker->subpath_angle = start_angle;
      stroker->first_point   = 0;
  
    Exit:
      return error;
    }
  
  
    FT_EXPORT_DEF( FT_Error )
    FT_Stroker_LineTo( FT_Stroker  stroker,
                       FT_Vector*  to )
    {
      FT_Error         error = 0;
      FT_StrokeBorder  border;
      FT_Vector        delta;
      FT_Angle         angle;
      FT_Int           side;
  
      delta.x = to->x - stroker->center.x;
      delta.y = to->y - stroker->center.y;
  
      angle = FT_Atan2( delta.x, delta.y );
      FT_Vector_From_Polar( &delta, stroker->radius, angle + FT_ANGLE_PI2 );
  
      /* process corner if necessary */
      if ( stroker->first_point )
      {
        /* this is the first segment of a subpath. We need to      */
        /* add a point to each border at their respective starting */
        /* point locations..                                       */
        error = ft_stroker_subpath_start( stroker, angle );
        if (error) goto Exit;
      }
      else
      {
        /* process the current corner */
        stroker->angle_out = angle;
        error = ft_stroker_process_corner( stroker );
        if (error) goto Exit;
      }
  
      /* now add a line segment to both the "inside" and "outside" paths */
  
      for ( border = stroker->borders, side = 1; side >= 0; side--, border++ )
      {
        FT_Vector  point;
  
        point.x = to->x + delta.x;
        point.y = to->y + delta.y;
  
        error = ft_stroke_border_lineto( border, &point, 1 );
        if (error) goto Exit;
  
        delta.x = -delta.x;
        delta.y = -delta.y;
      }
  
      stroker->angle_in  = angle;
      stroker->center    = *to;
  
    Exit:
      return error;
    }
  
  
  
    FT_EXPORT_DEF( FT_Error )
    FT_Stroker_ConicTo( FT_Stroker  stroker,
                        FT_Vector*  control,
                        FT_Vector*  to )
    {
      FT_Error    error = 0;
      FT_Vector   bez_stack[34];
      FT_Vector*  arc;
      FT_Vector*  limit = bez_stack + 30;
      FT_Angle    start_angle;
      FT_Bool     first_arc = 1;
  
      arc    = bez_stack;
      arc[0] = *to;
      arc[1] = *control;
      arc[2] = stroker->center;
  
      while ( arc >= bez_stack )
      {
        FT_Angle  angle_in, angle_out;
  
        angle_in = angle_out = 0;  /* remove compiler warnings */
  
        if ( arc < limit &&
             !ft_conic_is_small_enough( arc, &angle_in, &angle_out ) )
        {
          ft_conic_split( arc );
          arc += 2;
          continue;
        }
  
        if ( first_arc )
        {
          first_arc = 0;
  
          start_angle = angle_in;
  
          /* process corner if necessary */
          if ( stroker->first_point )
            error = ft_stroker_subpath_start( stroker, start_angle );
          else
          {
            stroker->angle_out = start_angle;
            error = ft_stroker_process_corner( stroker );
          }
        }
  
        /* the arc's angle is small enough, we can add it directly to each */
        /* border..                                                        */
        {
          FT_Vector  ctrl, end;
          FT_Angle   theta, phi, rotate;
          FT_Fixed  length;
          FT_Int     side;
  
          theta  = FT_Angle_Diff( angle_in, angle_out )/2;
          phi    = angle_in + theta;
          length = FT_DivFix( stroker->radius, FT_Cos(theta) );
  
          for ( side = 0; side <= 1; side++ )
          {
            rotate = FT_SIDE_TO_ROTATE(side);
  
            /* compute control point */
            FT_Vector_From_Polar( &ctrl, length, phi + rotate );
            ctrl.x += arc[1].x;
            ctrl.y += arc[1].y;
  
            /* compute end point */
            FT_Vector_From_Polar( &end, stroker->radius, angle_out + rotate );
            end.x += arc[0].x;
            end.y += arc[0].y;
  
            error = ft_stroke_border_conicto( stroker->borders + side, &ctrl, &end );
            if (error) goto Exit;
          }
        }
  
        arc -= 2;
  
        if (arc < bez_stack)
          stroker->angle_in = angle_out;
      }
  
      stroker->center = *to;
  
    Exit:
      return error;
    }
  
  
  
    FT_EXPORT_DEF( FT_Error )
    FT_Stroker_CubicTo( FT_Stroker  stroker,
                        FT_Vector*      control1,
                        FT_Vector*      control2,
                        FT_Vector*      to )
    {
      FT_Error    error = 0;
      FT_Vector   bez_stack[37];
      FT_Vector*  arc;
      FT_Vector*  limit = bez_stack + 32;
      FT_Angle    start_angle;
      FT_Bool     first_arc = 1;
  
      arc    = bez_stack;
      arc[0] = *to;
      arc[1] = *control2;
      arc[2] = *control1;
      arc[3] = stroker->center;
  
      while ( arc >= bez_stack )
      {
        FT_Angle  angle_in, angle_mid, angle_out;
  
        /* remove compiler warnings */
        angle_in = angle_out = angle_mid = 0;
  
        if ( arc < limit &&
             !ft_cubic_is_small_enough( arc, &angle_in, &angle_mid, &angle_out ) )
        {
          ft_cubic_split( arc );
          arc += 3;
          continue;
        }
  
        if ( first_arc )
        {
          first_arc = 0;
  
          /* process corner if necessary */
          start_angle = angle_in;
  
          if ( stroker->first_point )
            error = ft_stroker_subpath_start( stroker, start_angle );
          else
              {
                stroker->angle_out = start_angle;
                error = ft_stroker_process_corner( stroker );
              }
          if (error) goto Exit;
        }
  
        /* the arc's angle is small enough, we can add it directly to each */
        /* border..                                                        */
        {
          FT_Vector  ctrl1, ctrl2, end;
          FT_Angle   theta1, phi1, theta2, phi2, rotate;
          FT_Fixed   length1, length2;
          FT_Int     side;
  
          theta1  = ft_pos_abs( angle_mid - angle_in )/2;
          theta2  = ft_pos_abs( angle_out - angle_mid )/2;
          phi1    = (angle_mid+angle_in)/2;
          phi2    = (angle_mid+angle_out)/2;
          length1 = FT_DivFix( stroker->radius, FT_Cos(theta1) );
          length2 = FT_DivFix( stroker->radius, FT_Cos(theta2) );
  
          for ( side = 0; side <= 1; side++ )
          {
            rotate = FT_SIDE_TO_ROTATE(side);
  
            /* compute control points */
            FT_Vector_From_Polar( &ctrl1, length1, phi1 + rotate );
            ctrl1.x += arc[2].x;
            ctrl1.y += arc[2].y;
  
            FT_Vector_From_Polar( &ctrl2, length2, phi2 + rotate );
            ctrl2.x += arc[1].x;
            ctrl2.y += arc[1].y;
  
            /* compute end point */
            FT_Vector_From_Polar( &end, stroker->radius, angle_out + rotate );
            end.x += arc[0].x;
            end.y += arc[0].y;
  
            error = ft_stroke_border_cubicto( stroker->borders + side, &ctrl1, &ctrl2, &end );
            if (error) goto Exit;
          }
        }
  
        arc -= 3;
        if (arc < bez_stack)
          stroker->angle_in = angle_out;
      }
  
      stroker->center = *to;
  
    Exit:
      return error;
    }
  
  
    FT_EXPORT_DEF( FT_Error )
    FT_Stroker_BeginSubPath( FT_Stroker  stroker,
                             FT_Vector*  to,
                             FT_Bool     open )
    {
      /* we cannot process the first point, because there is not enough     */
      /* information regarding its corner/cap. The latter will be processed */
      /* in the "end_subpath" routine                                       */
      /*                                                                    */
      stroker->first_point   = 1;
      stroker->center        = *to;
      stroker->subpath_open  = open;
  
      /* record the subpath start point index for each border */
      stroker->subpath_start = *to;
      return 0;
    }
  
  
    static
    FT_Error  ft_stroker_add_reverse_left( FT_Stroker  stroker,
                                           FT_Bool     open )
    {
      FT_StrokeBorder  right  = stroker->borders + 0;
      FT_StrokeBorder  left   = stroker->borders + 1;
      FT_Int           new_points;
      FT_Error         error  = 0;
  
      FT_ASSERT( left->start >= 0 );
  
      new_points = left->num_points - left->start;
      if ( new_points > 0 )
      {
        error = ft_stroke_border_grow( right, (FT_UInt)new_points );
        if (error) goto Exit;
        {
          FT_Vector*    dst_point = right->points + right->num_points;
          FT_Byte*      dst_tag   = right->tags   + right->num_points;
          FT_Vector*    src_point = left->points  + left->num_points - 1;
          FT_Byte*      src_tag   = left->tags    + left->num_points - 1;
  
          while ( src_point >= left->points + left->start )
          {
            *dst_point = *src_point;
            *dst_tag   = *src_tag;
  
            if (open)
              dst_tag[0] &= ~(FT_STROKE_TAG_BEGIN | FT_STROKE_TAG_END);
            else
            {
              /* switch begin/end tags if necessary.. */
              if (dst_tag[0] & (FT_STROKE_TAG_BEGIN | FT_STROKE_TAG_END))
                dst_tag[0] ^= (FT_STROKE_TAG_BEGIN | FT_STROKE_TAG_END);
            }
  
            src_point--;
            src_tag--;
            dst_point++;
            dst_tag++;
          }
        }
        left->num_points   = left->start;
        right->num_points += new_points;
  
        right->movable = 0;
        left->movable  = 0;
      }
    Exit:
      return error;
    }
  
  
   /* there's a lot of magic in this function !! */
    FT_EXPORT_DEF( FT_Error )
    FT_Stroker_EndSubPath( FT_Stroker  stroker )
    {
      FT_Error  error  = 0;
  
      if ( stroker->subpath_open )
      {
        FT_StrokeBorder  right = stroker->borders;
  
        /* all right, this is an opened path, we need to add a cap between     */
        /* right & left, add the reverse of left, then add a final cap between */
        /* left & right..                                                      */
        error = ft_stroker_cap( stroker, stroker->angle_in, 0 );
        if (error) goto Exit;
  
        /* add reversed points from "left" to "right" */
        error = ft_stroker_add_reverse_left( stroker, 1 );
        if (error) goto Exit;
  
        /* now add the final cap */
        stroker->center = stroker->subpath_start;
        error = ft_stroker_cap( stroker, stroker->subpath_angle+FT_ANGLE_PI, 0 );
        if (error) goto Exit;
  
        /* now, end the right subpath accordingly. the left one is */
        /* rewind and doesn't need further processing..            */
        ft_stroke_border_close( right );
      }
      else
      {
        FT_Angle           turn;
        FT_Int             inside_side;
  
        /* process the corner ... */
        stroker->angle_out = stroker->subpath_angle;
        turn               = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
  
        /* no specific corner processing is required if the turn is 0 */
        if (turn != 0)
        {
          /* when we turn to the right, the inside side is 0 */
          inside_side = 0;
  
          /* otherwise, the inside side is 1 */
          if (turn < 0)
            inside_side = 1;
  
          /* IMPORTANT: WE DO NOT PROCESS THE INSIDE BORDER HERE !! */
          /* process the inside side */
          /* error = ft_stroker_inside( stroker, inside_side );
               if (error) goto Exit; */
  
          /* process the outside side */
          error = ft_stroker_outside( stroker, 1-inside_side );
          if (error) goto Exit;
        }
  
        /* we will first end our two subpaths */
        ft_stroke_border_close( stroker->borders + 0 );
        ft_stroke_border_close( stroker->borders + 1 );
  
        /* now, add the reversed left subpath to "right" */
        error = ft_stroker_add_reverse_left( stroker, 0 );
        if (error) goto Exit;
      }
  
    Exit:
      return error;
    }
  
  
    FT_EXPORT_DEF( FT_Error )
    FT_Stroker_GetCounts( FT_Stroker  stroker,
                          FT_UInt    *anum_points,
                          FT_UInt    *anum_contours )
    {
      FT_UInt   count1, count2, num_points   = 0;
      FT_UInt   count3, count4, num_contours = 0;
      FT_Error  error;
  
      error = ft_stroke_border_get_counts( stroker->borders+0, &count1, &count2 );
      if (error) goto Exit;
  
      error = ft_stroke_border_get_counts( stroker->borders+1, &count3, &count4 );
      if (error) goto Exit;
  
      num_points   = count1 + count3;
      num_contours = count2 + count4;
  
      stroker->valid = 1;
  
    Exit:
      *anum_points   = num_points;
      *anum_contours = num_contours;
      return error;
    }
  
  
    FT_EXPORT_DEF( void )
    FT_Stroker_Export( FT_Stroker   stroker,
                       FT_Outline*  outline )
    {
      if ( stroker->valid )
      {
        ft_stroke_border_export( stroker->borders+0, outline );
        ft_stroke_border_export( stroker->borders+1, outline );
      }
    }
  

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