code:
/***************************************************************************/
/*                                                                         */
/*  ftstroke.c                                                             */
/*                                                                         */
/*    FreeType path stroker (body).                                        */
/*                                                                         */
/*  Copyright 2002, 2003, 2004, 2005, 2006, 2008, 2009, 2010 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.                                        */
/*                                                                         */
/***************************************************************************/

#include <ft2build.h>
#include FT_STROKER_H
#include FT_TRIGONOMETRY_H
#include FT_OUTLINE_H
#include FT_INTERNAL_MEMORY_H
#include FT_INTERNAL_DEBUG_H
#include FT_INTERNAL_OBJECTS_H

  /* documentation is in ftstroke.h */

  FT_EXPORT_DEF( FT_StrokerBorder )
  FT_Outline_GetInsideBorder( FT_Outline*  outline )
  {
    FT_Orientation  o = FT_Outline_Get_Orientation( outline );

    return o == FT_ORIENTATION_TRUETYPE ? FT_STROKER_BORDER_RIGHT
                                        : FT_STROKER_BORDER_LEFT ;
  }

  /* documentation is in ftstroke.h */

  FT_EXPORT_DEF( FT_StrokerBorder )
  FT_Outline_GetOutsideBorder( FT_Outline*  outline )
  {
    FT_Orientation  o = FT_Outline_Get_Orientation( outline );

    return o == FT_ORIENTATION_TRUETYPE ? FT_STROKER_BORDER_LEFT
                                        : FT_STROKER_BORDER_RIGHT ;
  }

 /***************************************************************************/
 /***************************************************************************/
 /*****                                                                 *****/
 /*****                       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_StrokeTags_
  {
    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;

#define  FT_STROKE_TAG_BEGIN_END  (FT_STROKE_TAG_BEGIN|FT_STROKE_TAG_END)

  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_Bool     valid;

  } 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   = FT_Err_Ok;

    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_Bool          reverse )
  {
    FT_UInt  start = border->start;
    FT_UInt  count = border->num_points;

    FT_ASSERT( border->start >= 0 );

    /* don't record empty paths! */
    if ( count <= start + 1U )
      border->num_points = start;
    else
    {
      /* copy the last point to the start of this sub-path, since */
      /* it contains the `adjusted' starting coordinates          */
      border->num_points    = --count;
      border->points[start] = border->points[count];

      if ( reverse )
      {
        /* reverse the points */
        {
          FT_Vector*  vec1 = border->points + start + 1;
          FT_Vector*  vec2 = border->points + count - 1;

          for ( ; vec1 < vec2; vec1++, vec2-- )
          {
            FT_Vector  tmp;

            tmp   = *vec1;
            *vec1 = *vec2;
            *vec2 = tmp;
          }
        }

        /* then the tags */
        {
          FT_Byte*  tag1 = border->tags + start + 1;
          FT_Byte*  tag2 = border->tags + count - 1;

          for ( ; tag1 < tag2; tag1++, tag2-- )
          {
            FT_Byte  tmp;

            tmp   = *tag1;
            *tag1 = *tag2;
            *tag2 = tmp;
          }
        }
      }

      border->tags[start    ] |= FT_STROKE_TAG_BEGIN;
      border->tags[count - 1] |= FT_STROKE_TAG_END;
    }

    border->start   = -1;
    border->movable = FALSE;
  }

  static FT_Error
  ft_stroke_border_lineto( FT_StrokeBorder  border,
                           FT_Vector*       to,
                           FT_Bool          movable )
  {
    FT_Error  error = FT_Err_Ok;

    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 = FALSE;
    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 = FALSE;
    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 = FT_Err_Ok;

    /* 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, FALSE );

    border->start   = border->num_points;
    border->movable = FALSE;

    return ft_stroke_border_lineto( border, to, FALSE );
  }

  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;
    border->valid      = FALSE;
  }

  static void
  ft_stroke_border_reset( FT_StrokeBorder  border )
  {
    border->num_points = 0;
    border->start      = -1;
    border->valid      = FALSE;
  }

  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;
    border->valid      = FALSE;
  }

  static FT_Error
  ft_stroke_border_get_counts( FT_StrokeBorder  border,
                               FT_UInt         *anum_points,
                               FT_UInt         *anum_contours )
  {
    FT_Error  error        = FT_Err_Ok;
    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--, num_points++, 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 )
      {
        in_contour = 0;
        num_contours++;
      }
    }

    if ( in_contour != 0 )
      goto Fail;

    border->valid = TRUE;

  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_ARRAY_COPY( outline->points + outline->n_points,
                   border->points,
                   border->num_points );

    /* 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   idx   = (FT_Short)outline->n_points;

      for ( ; count > 0; count--, tags++, idx++ )
      {
        if ( *tags & FT_STROKE_TAG_END )
        {
          *write++ = idx;
          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_Library           library;

  } FT_StrokerRec;

  /* documentation is in ftstroke.h */

  FT_EXPORT_DEF( FT_Error )
  FT_Stroker_New( FT_Library   library,
                  FT_Stroker  *astroker )
  {
    FT_Error    error;
    FT_Memory   memory;
    FT_Stroker  stroker;

    if ( !library )
      return FT_Err_Invalid_Argument;

    memory = library->memory;

    if ( !FT_NEW( stroker ) )
    {
      stroker->library = library;

      ft_stroke_border_init( &stroker->borders[0], memory );
      ft_stroke_border_init( &stroker->borders[1], memory );
    }
    *astroker = stroker;
    return error;
  }

  /* documentation is in ftstroke.h */

  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;

    FT_Stroker_Rewind( stroker );
  }

  /* documentation is in ftstroke.h */

  FT_EXPORT_DEF( void )
  FT_Stroker_Rewind( FT_Stroker  stroker )
  {
    if ( stroker )
    {
      ft_stroke_border_reset( &stroker->borders[0] );
      ft_stroke_border_reset( &stroker->borders[1] );
    }
  }

  /* documentation is in ftstroke.h */

  FT_EXPORT_DEF( void )
  FT_Stroker_Done( FT_Stroker  stroker )
  {
    if ( stroker )
    {
      FT_Memory  memory = stroker->library->memory;

      ft_stroke_border_done( &stroker->borders[0] );
      ft_stroke_border_done( &stroker->borders[1] );

      stroker->library = 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  = FT_Err_Ok;
    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 = FALSE;
    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 = FT_Err_Ok;

    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, FALSE );
      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, FALSE );
    }
    else if ( stroker->line_cap == FT_STROKER_LINECAP_BUTT )
    {
      /* add a butt ending */
      FT_Vector        delta;
      FT_Angle         rotate = FT_SIDE_TO_ROTATE( side );
      FT_Fixed         radius = stroker->radius;
      FT_StrokeBorder  border = stroker->borders + side;

      FT_Vector_From_Polar( &delta, radius, angle + rotate );

      delta.x += stroker->center.x;
      delta.y += stroker->center.y;

      error = ft_stroke_border_lineto( border, &delta, FALSE );
      if ( error )
        goto Exit;

      FT_Vector_From_Polar( &delta, radius, angle - rotate );

      delta.x += stroker->center.x;
      delta.y += stroker->center.y;

      error = ft_stroke_border_lineto( border, &delta, FALSE );
    }

  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 = FT_Err_Ok;

    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 );

    /* TODO: find better criterion to switch off the optimization */
    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 = FALSE;
    }
    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, FALSE );

    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;
        phi   = stroker->angle_in;
      }
      else
      {
        theta = theta / 2;
        phi   = stroker->angle_in + theta + rotate;
      }

      thcos = FT_Cos( theta );
      sigma = FT_MulFix( stroker->miter_limit, thcos );

      /* FT_Sin(x) = 0 for x <= 57 */
      if ( sigma >= 0x10000L || ft_pos_abs( theta ) <= 57 )
        miter = FALSE;

      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, FALSE );
        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, FALSE );
        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, TRUE );
      }

      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, FALSE );
        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, TRUE );
      }
    }

  Exit:
    return error;
  }

  static FT_Error
  ft_stroker_process_corner( FT_Stroker  stroker )
  {
    FT_Error  error = FT_Err_Ok;
    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   = FALSE;

  Exit:
    return error;
  }

  /* documentation is in ftstroke.h */

  FT_EXPORT_DEF( FT_Error )
  FT_Stroker_LineTo( FT_Stroker  stroker,
                     FT_Vector*  to )
  {
    FT_Error         error = FT_Err_Ok;
    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, TRUE );
      if ( error )
        goto Exit;

      delta.x = -delta.x;
      delta.y = -delta.y;
    }

    stroker->angle_in = angle;
    stroker->center   = *to;

  Exit:
    return error;
  }

  /* documentation is in ftstroke.h */

  FT_EXPORT_DEF( FT_Error )
  FT_Stroker_ConicTo( FT_Stroker  stroker,
                      FT_Vector*  control,
                      FT_Vector*  to )
  {
    FT_Error    error = FT_Err_Ok;
    FT_Vector   bez_stack[34];
    FT_Vector*  arc;
    FT_Vector*  limit = bez_stack + 30;
    FT_Angle    start_angle;
    FT_Bool     first_arc = TRUE;

    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 = FALSE;

        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;
  }

  /* documentation is in ftstroke.h */

  FT_EXPORT_DEF( FT_Error )
  FT_Stroker_CubicTo( FT_Stroker  stroker,
                      FT_Vector*  control1,
                      FT_Vector*  control2,
                      FT_Vector*  to )
  {
    FT_Error    error = FT_Err_Ok;
    FT_Vector   bez_stack[37];
    FT_Vector*  arc;
    FT_Vector*  limit = bez_stack + 32;
    FT_Angle    start_angle;
    FT_Bool     first_arc = TRUE;

    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 = FALSE;

        /* 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;
  }

  /* documentation is in ftstroke.h */

  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 `FT_Stroker_EndSubPath' routine.                             */
    /*                                                                     */
    stroker->first_point  = TRUE;
    stroker->center       = *to;
    stroker->subpath_open = open;

    /* record the subpath start point for each border */
    stroker->subpath_start = *to;

    return FT_Err_Ok;
  }

  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 = FT_Err_Ok;

    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_END;
          else
          {
            FT_Byte  ttag = (FT_Byte)( dst_tag[0] & FT_STROKE_TAG_BEGIN_END );

            /* switch begin/end tags if necessary */
            if ( ttag == FT_STROKE_TAG_BEGIN ||
                 ttag == FT_STROKE_TAG_END   )
              dst_tag[0] ^= FT_STROKE_TAG_BEGIN_END;

          }

          src_point--;
          src_tag--;
          dst_point++;
          dst_tag++;
        }
      }

      left->num_points   = left->start;
      right->num_points += new_points;

      right->movable = FALSE;
      left->movable  = FALSE;
    }

  Exit:
    return error;
  }

  /* documentation is in ftstroke.h */

  /* there's a lot of magic in this function! */
  FT_EXPORT_DEF( FT_Error )
  FT_Stroker_EndSubPath( FT_Stroker  stroker )
  {
    FT_Error  error = FT_Err_Ok;

    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, TRUE );
      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, FALSE );
    }
    else
    {
      FT_Angle  turn;
      FT_Int    inside_side;

      /* close the path if needed */
      if ( stroker->center.x != stroker->subpath_start.x ||
           stroker->center.y != stroker->subpath_start.y )
      {
        error = FT_Stroker_LineTo( stroker, &stroker->subpath_start );
        if ( error )
          goto Exit;
      }

      /* 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;

        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;
      }

      /* then end our two subpaths */
      ft_stroke_border_close( stroker->borders + 0, TRUE );
      ft_stroke_border_close( stroker->borders + 1, FALSE );
    }

  Exit:
    return error;
  }

  /* documentation is in ftstroke.h */

  FT_EXPORT_DEF( FT_Error )
  FT_Stroker_GetBorderCounts( FT_Stroker        stroker,
                              FT_StrokerBorder  border,
                              FT_UInt          *anum_points,
                              FT_UInt          *anum_contours )
  {
    FT_UInt   num_points = 0, num_contours = 0;
    FT_Error  error;

    if ( !stroker || border > 1 )
    {
      error = FT_Err_Invalid_Argument;
      goto Exit;
    }

    error = ft_stroke_border_get_counts( stroker->borders + border,
                                         &num_points, &num_contours );
  Exit:
    if ( anum_points )
      *anum_points = num_points;

    if ( anum_contours )
      *anum_contours = num_contours;

    return error;
  }

  /* documentation is in ftstroke.h */

  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;

  Exit:
    *anum_points   = num_points;
    *anum_contours = num_contours;
    return error;
  }

  /* documentation is in ftstroke.h */

  FT_EXPORT_DEF( void )
  FT_Stroker_ExportBorder( FT_Stroker        stroker,
                           FT_StrokerBorder  border,
                           FT_Outline*       outline )
  {
    if ( border == FT_STROKER_BORDER_LEFT  ||
         border == FT_STROKER_BORDER_RIGHT )
    {
      FT_StrokeBorder  sborder = & stroker->borders[border];

      if ( sborder->valid )
        ft_stroke_border_export( sborder, outline );
    }
  }

  /* documentation is in ftstroke.h */

  FT_EXPORT_DEF( void )
  FT_Stroker_Export( FT_Stroker   stroker,
                     FT_Outline*  outline )
  {
    FT_Stroker_ExportBorder( stroker, FT_STROKER_BORDER_LEFT, outline );
    FT_Stroker_ExportBorder( stroker, FT_STROKER_BORDER_RIGHT, outline );
  }

  /* documentation is in ftstroke.h */

  /*
   *  The following is very similar to FT_Outline_Decompose, except
   *  that we do support opened paths, and do not scale the outline.
   */
  FT_EXPORT_DEF( FT_Error )
  FT_Stroker_ParseOutline( FT_Stroker   stroker,
                           FT_Outline*  outline,
                           FT_Bool      opened )
  {
    FT_Vector   v_last;
    FT_Vector   v_control;
    FT_Vector   v_start;

    FT_Vector*  point;
    FT_Vector*  limit;
    char*       tags;

    FT_Error    error;

    FT_Int   n;         /* index of contour in outline     */
    FT_UInt  first;     /* index of first point in contour */
    FT_Int   tag;       /* current point's state           */

    if ( !outline || !stroker )
      return FT_Err_Invalid_Argument;

    FT_Stroker_Rewind( stroker );

    first = 0;

    for ( n = 0; n < outline->n_contours; n++ )
    {
      FT_UInt  last;  /* index of last point in contour */

      last  = outline->contours[n];
      limit = outline->points + last;

      /* skip empty points; we don't stroke these */
      if ( last <= first )
      {
        first = last + 1;
        continue;
      }

      v_start = outline->points[first];
      v_last  = outline->points[last];

      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                    */
          v_start.x = ( v_start.x + v_last.x ) / 2;
          v_start.y = ( v_start.y + v_last.y ) / 2;
        }
        point--;
        tags--;
      }

      error = FT_Stroker_BeginSubPath( stroker, &v_start, opened );
      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 = point->x;
            vec.y = point->y;

            error = FT_Stroker_LineTo( stroker, &vec );
            if ( error )
              goto Exit;
            continue;
          }

        case FT_CURVE_TAG_CONIC:  /* consume conic arcs */
          v_control.x = point->x;
          v_control.y = point->y;

        Do_Conic:
          if ( point < limit )
          {
            FT_Vector  vec;
            FT_Vector  v_middle;

            point++;
            tags++;
            tag = FT_CURVE_TAG( tags[0] );

            vec = point[0];

            if ( tag == FT_CURVE_TAG_ON )
            {
              error = FT_Stroker_ConicTo( stroker, &v_control, &vec );
              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 = FT_Stroker_ConicTo( stroker, &v_control, &v_middle );
            if ( error )
              goto Exit;

            v_control = vec;
            goto Do_Conic;
          }

          error = FT_Stroker_ConicTo( stroker, &v_control, &v_start );
          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 = point[-2];
            vec2 = point[-1];

            if ( point <= limit )
            {
              FT_Vector  vec;

              vec = point[0];

              error = FT_Stroker_CubicTo( stroker, &vec1, &vec2, &vec );
              if ( error )
                goto Exit;
              continue;
            }

            error = FT_Stroker_CubicTo( stroker, &vec1, &vec2, &v_start );
            goto Close;
          }
        }
      }

    Close:
      if ( error )
        goto Exit;

      error = FT_Stroker_EndSubPath( stroker );
      if ( error )
        goto Exit;

      first = last + 1;
    }

    return FT_Err_Ok;

  Exit:
    return error;

  Invalid_Outline:
    return FT_Err_Invalid_Outline;
  }

/* declare an extern to access ft_outline_glyph_class global allocated
   in ftglyph.c, and use the FT_OUTLINE_GLYPH_CLASS_GET macro to access
   it when FT_CONFIG_OPTION_PIC is defined */
#ifndef FT_CONFIG_OPTION_PIC
  extern const FT_Glyph_Class  ft_outline_glyph_class;
#endif
#include "basepic.h"

  /* documentation is in ftstroke.h */

  FT_EXPORT_DEF( FT_Error )
  FT_Glyph_Stroke( FT_Glyph    *pglyph,
                   FT_Stroker   stroker,
                   FT_Bool      destroy )
  {
    FT_Error  error = FT_Err_Invalid_Argument;
    FT_Glyph  glyph = NULL;
    FT_Library library = stroker->library;
    FT_UNUSED(library);

    if ( pglyph == NULL )
      goto Exit;

    glyph = *pglyph;
    if ( glyph == NULL || glyph->clazz != FT_OUTLINE_GLYPH_CLASS_GET )
      goto Exit;

    {
      FT_Glyph  copy;

      error = FT_Glyph_Copy( glyph, &copy );
      if ( error )
        goto Exit;

      glyph = copy;
    }

    {
      FT_OutlineGlyph  oglyph  = (FT_OutlineGlyph) glyph;
      FT_Outline*      outline = &oglyph->outline;
      FT_UInt          num_points, num_contours;

      error = FT_Stroker_ParseOutline( stroker, outline, FALSE );
      if ( error )
        goto Fail;

      (void)FT_Stroker_GetCounts( stroker, &num_points, &num_contours );

      FT_Outline_Done( glyph->library, outline );

      error = FT_Outline_New( glyph->library,
                              num_points, num_contours, outline );
      if ( error )
        goto Fail;

      outline->n_points   = 0;
      outline->n_contours = 0;

      FT_Stroker_Export( stroker, outline );
    }

    if ( destroy )
      FT_Done_Glyph( *pglyph );

    *pglyph = glyph;
    goto Exit;

  Fail:
    FT_Done_Glyph( glyph );
    glyph = NULL;

    if ( !destroy )
      *pglyph = NULL;

  Exit:
    return error;
  }

  /* documentation is in ftstroke.h */

  FT_EXPORT_DEF( FT_Error )
  FT_Glyph_StrokeBorder( FT_Glyph    *pglyph,
                         FT_Stroker   stroker,
                         FT_Bool      inside,
                         FT_Bool      destroy )
  {
    FT_Error  error = FT_Err_Invalid_Argument;
    FT_Glyph  glyph = NULL;
    FT_Library library = stroker->library;
    FT_UNUSED(library);

    if ( pglyph == NULL )
      goto Exit;

    glyph = *pglyph;
    if ( glyph == NULL || glyph->clazz != FT_OUTLINE_GLYPH_CLASS_GET )
      goto Exit;

    {
      FT_Glyph  copy;

      error = FT_Glyph_Copy( glyph, &copy );
      if ( error )
        goto Exit;

      glyph = copy;
    }

    {
      FT_OutlineGlyph   oglyph  = (FT_OutlineGlyph) glyph;
      FT_StrokerBorder  border;
      FT_Outline*       outline = &oglyph->outline;
      FT_UInt           num_points, num_contours;

      border = FT_Outline_GetOutsideBorder( outline );
      if ( inside )
      {
        if ( border == FT_STROKER_BORDER_LEFT )
          border = FT_STROKER_BORDER_RIGHT;
        else
          border = FT_STROKER_BORDER_LEFT;
      }

      error = FT_Stroker_ParseOutline( stroker, outline, FALSE );
      if ( error )
        goto Fail;

      (void)FT_Stroker_GetBorderCounts( stroker, border,
                                        &num_points, &num_contours );

      FT_Outline_Done( glyph->library, outline );

      error = FT_Outline_New( glyph->library,
                              num_points,
                              num_contours,
                              outline );
      if ( error )
        goto Fail;

      outline->n_points   = 0;
      outline->n_contours = 0;

      FT_Stroker_ExportBorder( stroker, border, outline );
    }

    if ( destroy )
      FT_Done_Glyph( *pglyph );

    *pglyph = glyph;
    goto Exit;

  Fail:
    FT_Done_Glyph( glyph );
    glyph = NULL;

    if ( !destroy )
      *pglyph = NULL;

  Exit:
    return error;
  }

/* END */


code:
/***************************************************************************/
/*                                                                         */
/*  ftsynth.c                                                              */
/*                                                                         */
/*    FreeType synthesizing code for emboldening and slanting (body).      */
/*                                                                         */
/*  Copyright 2000-2001, 2002, 2003, 2004, 2005, 2006, 2010 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.                                        */
/*                                                                         */
/***************************************************************************/

#include <ft2build.h>
#include FT_SYNTHESIS_H
#include FT_INTERNAL_DEBUG_H
#include FT_INTERNAL_OBJECTS_H
#include FT_OUTLINE_H
#include FT_BITMAP_H

  /*************************************************************************/
  /*                                                                       */
  /* The macro FT_COMPONENT is used in trace mode.  It is an implicit      */
  /* parameter of the FT_TRACE() and FT_ERROR() macros, used to print/log  */
  /* messages during execution.                                            */
  /*                                                                       */
#undef  FT_COMPONENT
#define FT_COMPONENT  trace_synth

  /*************************************************************************/
  /*************************************************************************/
  /****                                                                 ****/
  /****   EXPERIMENTAL OBLIQUING SUPPORT                                ****/
  /****                                                                 ****/
  /*************************************************************************/
  /*************************************************************************/

  /* documentation is in ftsynth.h */

  FT_EXPORT_DEF( void )
  FT_GlyphSlot_Oblique( FT_GlyphSlot  slot )
  {
    FT_Matrix    transform;
    FT_Outline*  outline = &slot->outline;

    /* only oblique outline glyphs */
    if ( slot->format != FT_GLYPH_FORMAT_OUTLINE )
      return;

    /* we don't touch the advance width */

    /* For italic, simply apply a shear transform, with an angle */
    /* of about 12 degrees.                                      */

    transform.xx = 0x10000L;
    transform.yx = 0x00000L;

    transform.xy = 0x06000L;
    transform.yy = 0x10000L;

    FT_Outline_Transform( outline, &transform );
  }

  /*************************************************************************/
  /*************************************************************************/
  /****                                                                 ****/
  /****   EXPERIMENTAL EMBOLDENING/OUTLINING SUPPORT                    ****/
  /****                                                                 ****/
  /*************************************************************************/
  /*************************************************************************/

  /* documentation is in ftsynth.h */

  FT_EXPORT_DEF( void )
  FT_GlyphSlot_Embolden( FT_GlyphSlot  slot )
  {
    FT_Library  library = slot->library;
    FT_Face     face    = slot->face;
    FT_Error    error;
    FT_Pos      xstr, ystr;

    if ( slot->format != FT_GLYPH_FORMAT_OUTLINE &&
         slot->format != FT_GLYPH_FORMAT_BITMAP  )
      return;

    /* some reasonable strength */
    xstr = FT_MulFix( face->units_per_EM,
                      face->size->metrics.y_scale ) / 24;
    ystr = xstr;

    if ( slot->format == FT_GLYPH_FORMAT_OUTLINE )
    {
      /* ignore error */
      (void)FT_Outline_Embolden( &slot->outline, xstr );

      /* this is more than enough for most glyphs; if you need accurate */
      /* values, you have to call FT_Outline_Get_CBox                   */
      xstr = xstr * 2;
      ystr = xstr;
    }
    else /* slot->format == FT_GLYPH_FORMAT_BITMAP */
    {
      /* round to full pixels */
      xstr &= ~63;
      if ( xstr == 0 )
        xstr = 1 << 6;
      ystr &= ~63;

      /*
       * XXX: overflow check for 16-bit system, for compatibility
       *      with FT_GlyphSlot_Embolden() since freetype-2.1.10.
       *      unfortunately, this function return no informations
       *      about the cause of error.
       */
      if ( ( ystr >> 6 ) > FT_INT_MAX || ( ystr >> 6 ) < FT_INT_MIN )
      {
        FT_TRACE1(( "FT_GlyphSlot_Embolden:" ));
        FT_TRACE1(( "too strong embolding parameter ystr=%d\n", ystr ));
        return;
      }
      error = FT_GlyphSlot_Own_Bitmap( slot );
      if ( error )
        return;

      error = FT_Bitmap_Embolden( library, &slot->bitmap, xstr, ystr );
      if ( error )
        return;
    }

    if ( slot->advance.x )
      slot->advance.x += xstr;

    if ( slot->advance.y )
      slot->advance.y += ystr;

    slot->metrics.width        += xstr;
    slot->metrics.height       += ystr;
    slot->metrics.horiBearingY += ystr;
    slot->metrics.horiAdvance  += xstr;
    slot->metrics.vertBearingX -= xstr / 2;
    slot->metrics.vertBearingY += ystr;
    slot->metrics.vertAdvance  += ystr;

    /* XXX: 16-bit overflow case must be excluded before here */
    if ( slot->format == FT_GLYPH_FORMAT_BITMAP )
      slot->bitmap_top += (FT_Int)( ystr >> 6 );
  }

/* END */

license: mit


code:
/***************************************************************************/
/*                                                                         */
/*  ftsystem.c                                                             */
/*                                                                         */
/*    ANSI-specific FreeType low-level system interface (body).            */
/*                                                                         */
/*  Copyright 1996-2001, 2002, 2006, 2008, 2009, 2010 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 contains the default interface used by FreeType to access   */
  /* low-level, i.e. memory management, i/o access as well as thread       */
  /* synchronisation.  It can be replaced by user-specific routines if     */
  /* necessary.                                                            */
  /*                                                                       */
  /*************************************************************************/

#include <ft2build.h>
#include FT_CONFIG_CONFIG_H
#include FT_INTERNAL_DEBUG_H
#include FT_INTERNAL_STREAM_H
#include FT_SYSTEM_H
#include FT_ERRORS_H
#include FT_TYPES_H

  /*************************************************************************/
  /*                                                                       */
  /*                       MEMORY MANAGEMENT INTERFACE                     */
  /*                                                                       */
  /*************************************************************************/

  /*************************************************************************/
  /*                                                                       */
  /* It is not necessary to do any error checking for the                  */
  /* allocation-related functions.  This will be done by the higher level  */
  /* routines like ft_mem_alloc() or ft_mem_realloc().                     */
  /*                                                                       */
  /*************************************************************************/

  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    ft_alloc                                                           */
  /*                                                                       */
  /* <Description>                                                         */
  /*    The memory allocation function.                                    */
  /*                                                                       */
  /* <Input>                                                               */
  /*    memory :: A pointer to the memory object.                          */
  /*                                                                       */
  /*    size   :: The requested size in bytes.                             */
  /*                                                                       */
  /* <Return>                                                              */
  /*    The address of newly allocated block.                              */
  /*                                                                       */
  FT_CALLBACK_DEF( void* )
  ft_alloc( FT_Memory  memory,
            long       size )
  {
    FT_UNUSED( memory );

    return ft_smalloc( size );
  }

  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    ft_realloc                                                         */
  /*                                                                       */
  /* <Description>                                                         */
  /*    The memory reallocation function.                                  */
  /*                                                                       */
  /* <Input>                                                               */
  /*    memory   :: A pointer to the memory object.                        */
  /*                                                                       */
  /*    cur_size :: The current size of the allocated memory block.        */
  /*                                                                       */
  /*    new_size :: The newly requested size in bytes.                     */
  /*                                                                       */
  /*    block    :: The current address of the block in memory.            */
  /*                                                                       */
  /* <Return>                                                              */
  /*    The address of the reallocated memory block.                       */
  /*                                                                       */
  FT_CALLBACK_DEF( void* )
  ft_realloc( FT_Memory  memory,
              long       cur_size,
              long       new_size,
              void*      block )
  {
    FT_UNUSED( memory );
    FT_UNUSED( cur_size );

    return ft_srealloc( block, new_size );
  }

  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    ft_free                                                            */
  /*                                                                       */
  /* <Description>                                                         */
  /*    The memory release function.                                       */
  /*                                                                       */
  /* <Input>                                                               */
  /*    memory  :: A pointer to the memory object.                         */
  /*                                                                       */
  /*    block   :: The address of block in memory to be freed.             */
  /*                                                                       */
  FT_CALLBACK_DEF( void )
  ft_free( FT_Memory  memory,
           void*      block )
  {
    FT_UNUSED( memory );

    ft_sfree( block );
  }

  /*************************************************************************/
  /*                                                                       */
  /*                     RESOURCE MANAGEMENT INTERFACE                     */
  /*                                                                       */
  /*************************************************************************/

  /*************************************************************************/
  /*                                                                       */
  /* 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_io

  /* We use the macro STREAM_FILE for convenience to extract the       */
  /* system-specific stream handle from a given FreeType stream object */
#define STREAM_FILE( stream )  ( (FT_FILE*)stream->descriptor.pointer )

  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    ft_ansi_stream_close                                               */
  /*                                                                       */
  /* <Description>                                                         */
  /*    The function to close a stream.                                    */
  /*                                                                       */
  /* <Input>                                                               */
  /*    stream :: A pointer to the stream object.                          */
  /*                                                                       */
  FT_CALLBACK_DEF( void )
  ft_ansi_stream_close( FT_Stream  stream )
  {
    ft_fclose( STREAM_FILE( stream ) );

    stream->descriptor.pointer = NULL;
    stream->size               = 0;
    stream->base               = 0;
  }

  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    ft_ansi_stream_io                                                  */
  /*                                                                       */
  /* <Description>                                                         */
  /*    The function to open a stream.                                     */
  /*                                                                       */
  /* <Input>                                                               */
  /*    stream :: A pointer to the stream object.                          */
  /*                                                                       */
  /*    offset :: The position in the data stream to start reading.        */
  /*                                                                       */
  /*    buffer :: The address of buffer to store the read data.            */
  /*                                                                       */
  /*    count  :: The number of bytes to read from the stream.             */
  /*                                                                       */
  /* <Return>                                                              */
  /*    The number of bytes actually read.  If `count' is zero (this is,   */
  /*    the function is used for seeking), a non-zero return value         */
  /*    indicates an error.                                                */
  /*                                                                       */
  FT_CALLBACK_DEF( unsigned long )
  ft_ansi_stream_io( FT_Stream       stream,
                     unsigned long   offset,
                     unsigned char*  buffer,
                     unsigned long   count )
  {
    FT_FILE*  file;

    if ( !count && offset > stream->size )
      return 1;

    file = STREAM_FILE( stream );

    if ( stream->pos != offset )
      ft_fseek( file, offset, SEEK_SET );

    return (unsigned long)ft_fread( buffer, 1, count, file );
  }

  /* documentation is in ftstream.h */

  FT_BASE_DEF( FT_Error )
  FT_Stream_Open( FT_Stream    stream,
                  const char*  filepathname )
  {
    FT_FILE*  file;

    if ( !stream )
      return FT_Err_Invalid_Stream_Handle;

    stream->descriptor.pointer = NULL;
    stream->pathname.pointer   = (char*)filepathname;
    stream->base               = 0;
    stream->pos                = 0;
    stream->read               = NULL;
    stream->close              = NULL;

    file = ft_fopen( filepathname, "rb" );
    if ( !file )
    {
      FT_ERROR(( "FT_Stream_Open:"
                 " could not open `%s'\n", filepathname ));

      return FT_Err_Cannot_Open_Resource;
    }

    ft_fseek( file, 0, SEEK_END );
    stream->size = ft_ftell( file );
    if ( !stream->size )
    {
      FT_ERROR(( "FT_Stream_Open:" ));
      FT_ERROR(( " opened `%s' but zero-sized\n", filepathname ));
      ft_fclose( file );
      return FT_Err_Cannot_Open_Stream;
    }
    ft_fseek( file, 0, SEEK_SET );

    stream->descriptor.pointer = file;
    stream->read  = ft_ansi_stream_io;
    stream->close = ft_ansi_stream_close;

    FT_TRACE1(( "FT_Stream_Open:" ));
    FT_TRACE1(( " opened `%s' (%d bytes) successfully\n",
                filepathname, stream->size ));

    return FT_Err_Ok;
  }

#ifdef FT_DEBUG_MEMORY

  extern FT_Int
  ft_mem_debug_init( FT_Memory  memory );

  extern void
  ft_mem_debug_done( FT_Memory  memory );

#endif

  /* documentation is in ftobjs.h */

  FT_BASE_DEF( FT_Memory )
  FT_New_Memory( void )
  {
    FT_Memory  memory;

    memory = (FT_Memory)ft_smalloc( sizeof ( *memory ) );
    if ( memory )
    {
      memory->user    = 0;
      memory->alloc   = ft_alloc;
      memory->realloc = ft_realloc;
      memory->free    = ft_free;
#ifdef FT_DEBUG_MEMORY
      ft_mem_debug_init( memory );
#endif
    }

    return memory;
  }

  /* documentation is in ftobjs.h */

  FT_BASE_DEF( void )
  FT_Done_Memory( FT_Memory  memory )
  {
#ifdef FT_DEBUG_MEMORY
    ft_mem_debug_done( memory );
#endif
    ft_sfree( memory );
  }

/* END */


code:
/***************************************************************************/
/*                                                                         */
/*  fttrigon.c                                                             */
/*                                                                         */
/*    FreeType trigonometric functions (body).                             */
/*                                                                         */
/*  Copyright 2001, 2002, 2003, 2004, 2005 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.                                        */
/*                                                                         */
/***************************************************************************/

#include <ft2build.h>
#include FT_INTERNAL_OBJECTS_H
#include FT_TRIGONOMETRY_H

  /* the following is 0.2715717684432231 * 2^30 */
#define FT_TRIG_COSCALE  0x11616E8EUL

  /* this table was generated for FT_PI = 180L << 16, i.e. degrees */
#define FT_TRIG_MAX_ITERS  23

  static const FT_Fixed
  ft_trig_arctan_table[24] =
  {
    4157273L, 2949120L, 1740967L, 919879L, 466945L, 234379L, 117304L,
    58666L, 29335L, 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L,
    57L, 29L, 14L, 7L, 4L, 2L, 1L
  };

  /* the Cordic shrink factor, multiplied by 2^32 */
#define FT_TRIG_SCALE    1166391785UL  /* 0x4585BA38UL */

#ifdef FT_CONFIG_HAS_INT64

  /* multiply a given value by the CORDIC shrink factor */
  static FT_Fixed
  ft_trig_downscale( FT_Fixed  val )
  {
    FT_Fixed  s;
    FT_Int64  v;

    s   = val;
    val = ( val >= 0 ) ? val : -val;

    v   = ( val * (FT_Int64)FT_TRIG_SCALE ) + 0x100000000UL;
    val = (FT_Fixed)( v >> 32 );

    return ( s >= 0 ) ? val : -val;
  }

#else /* !FT_CONFIG_HAS_INT64 */

  /* multiply a given value by the CORDIC shrink factor */
  static FT_Fixed
  ft_trig_downscale( FT_Fixed  val )
  {
    FT_Fixed   s;
    FT_UInt32  v1, v2, k1, k2, hi, lo1, lo2, lo3;

    s   = val;
    val = ( val >= 0 ) ? val : -val;

    v1 = (FT_UInt32)val >> 16;
    v2 = (FT_UInt32)(val & 0xFFFFL);

    k1 = (FT_UInt32)FT_TRIG_SCALE >> 16;       /* constant */
    k2 = (FT_UInt32)(FT_TRIG_SCALE & 0xFFFFL);   /* constant */

    hi   = k1 * v1;
    lo1  = k1 * v2 + k2 * v1;       /* can't overflow */

    lo2  = ( k2 * v2 ) >> 16;
    lo3  = ( lo1 >= lo2 ) ? lo1 : lo2;
    lo1 += lo2;

    hi  += lo1 >> 16;
    if ( lo1 < lo3 )
      hi += (FT_UInt32)0x10000UL;

    val  = (FT_Fixed)hi;

    return ( s >= 0 ) ? val : -val;
  }

#endif /* !FT_CONFIG_HAS_INT64 */

  static FT_Int
  ft_trig_prenorm( FT_Vector*  vec )
  {
    FT_Fixed  x, y, z;
    FT_Int    shift;

    x = vec->x;
    y = vec->y;

    z     = ( ( x >= 0 ) ? x : - x ) | ( (y >= 0) ? y : -y );
    shift = 0;

#if 1
    /* determine msb bit index in `shift' */
    if ( z >= ( 1L << 16 ) )
    {
      z     >>= 16;
      shift  += 16;
    }
    if ( z >= ( 1L << 8 ) )
    {
      z     >>= 8;
      shift  += 8;
    }
    if ( z >= ( 1L << 4 ) )
    {
      z     >>= 4;
      shift  += 4;
    }
    if ( z >= ( 1L << 2 ) )
    {
      z     >>= 2;
      shift  += 2;
    }
    if ( z >= ( 1L << 1 ) )
    {
      z    >>= 1;
      shift += 1;
    }

    if ( shift <= 27 )
    {
      shift  = 27 - shift;
      vec->x = x << shift;
      vec->y = y << shift;
    }
    else
    {
      shift -= 27;
      vec->x = x >> shift;
      vec->y = y >> shift;
      shift  = -shift;
    }

#else /* 0 */

    if ( z < ( 1L << 27 ) )
    {
      do
      {
        shift++;
        z <<= 1;
      } while ( z < ( 1L << 27 ) );
      vec->x = x << shift;
      vec->y = y << shift;
    }
    else if ( z > ( 1L << 28 ) )
    {
      do
      {
        shift++;
        z >>= 1;
      } while ( z > ( 1L << 28 ) );

      vec->x = x >> shift;
      vec->y = y >> shift;
      shift  = -shift;
    }

#endif /* 0 */

    return shift;
  }

  static void
  ft_trig_pseudo_rotate( FT_Vector*  vec,
                         FT_Angle    theta )
  {
    FT_Int           i;
    FT_Fixed         x, y, xtemp;
    const FT_Fixed  *arctanptr;

    x = vec->x;
    y = vec->y;

    /* Get angle between -90 and 90 degrees */
    while ( theta <= -FT_ANGLE_PI2 )
    {
      x = -x;
      y = -y;
      theta += FT_ANGLE_PI;
    }

    while ( theta > FT_ANGLE_PI2 )
    {
      x = -x;
      y = -y;
      theta -= FT_ANGLE_PI;
    }

    /* Initial pseudorotation, with left shift */
    arctanptr = ft_trig_arctan_table;

    if ( theta < 0 )
    {
      xtemp  = x + ( y << 1 );
      y      = y - ( x << 1 );
      x      = xtemp;
      theta += *arctanptr++;
    }
    else
    {
      xtemp  = x - ( y << 1 );
      y      = y + ( x << 1 );
      x      = xtemp;
      theta -= *arctanptr++;
    }

    /* Subsequent pseudorotations, with right shifts */
    i = 0;
    do
    {
      if ( theta < 0 )
      {
        xtemp  = x + ( y >> i );
        y      = y - ( x >> i );
        x      = xtemp;
        theta += *arctanptr++;
      }
      else
      {
        xtemp  = x - ( y >> i );
        y      = y + ( x >> i );
        x      = xtemp;
        theta -= *arctanptr++;
      }
    } while ( ++i < FT_TRIG_MAX_ITERS );

    vec->x = x;
    vec->y = y;
  }

  static void
  ft_trig_pseudo_polarize( FT_Vector*  vec )
  {
    FT_Fixed         theta;
    FT_Fixed         yi, i;
    FT_Fixed         x, y;
    const FT_Fixed  *arctanptr;

    x = vec->x;
    y = vec->y;

    /* Get the vector into the right half plane */
    theta = 0;
    if ( x < 0 )
    {
      x = -x;
      y = -y;
      theta = 2 * FT_ANGLE_PI2;
    }

    if ( y > 0 )
      theta = - theta;

    arctanptr = ft_trig_arctan_table;

    if ( y < 0 )
    {
      /* Rotate positive */
      yi     = y + ( x << 1 );
      x      = x - ( y << 1 );
      y      = yi;
      theta -= *arctanptr++;  /* Subtract angle */
    }
    else
    {
      /* Rotate negative */
      yi     = y - ( x << 1 );
      x      = x + ( y << 1 );
      y      = yi;
      theta += *arctanptr++;  /* Add angle */
    }

    i = 0;
    do
    {
      if ( y < 0 )
      {
        /* Rotate positive */
        yi     = y + ( x >> i );
        x      = x - ( y >> i );
        y      = yi;
        theta -= *arctanptr++;
      }
      else
      {
        /* Rotate negative */
        yi     = y - ( x >> i );
        x      = x + ( y >> i );
        y      = yi;
        theta += *arctanptr++;
      }
    } while ( ++i < FT_TRIG_MAX_ITERS );

    /* round theta */
    if ( theta >= 0 )
      theta = FT_PAD_ROUND( theta, 32 );
    else
      theta = -FT_PAD_ROUND( -theta, 32 );

    vec->x = x;
    vec->y = theta;
  }

  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( FT_Fixed )
  FT_Cos( FT_Angle  angle )
  {
    FT_Vector  v;

    v.x = FT_TRIG_COSCALE >> 2;
    v.y = 0;
    ft_trig_pseudo_rotate( &v, angle );

    return v.x / ( 1 << 12 );
  }

  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( FT_Fixed )
  FT_Sin( FT_Angle  angle )
  {
    return FT_Cos( FT_ANGLE_PI2 - angle );
  }

  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( FT_Fixed )
  FT_Tan( FT_Angle  angle )
  {
    FT_Vector  v;

    v.x = FT_TRIG_COSCALE >> 2;
    v.y = 0;
    ft_trig_pseudo_rotate( &v, angle );

    return FT_DivFix( v.y, v.x );
  }

  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( FT_Angle )
  FT_Atan2( FT_Fixed  dx,
            FT_Fixed  dy )
  {
    FT_Vector  v;

    if ( dx == 0 && dy == 0 )
      return 0;

    v.x = dx;
    v.y = dy;
    ft_trig_prenorm( &v );
    ft_trig_pseudo_polarize( &v );

    return v.y;
  }

  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( void )
  FT_Vector_Unit( FT_Vector*  vec,
                  FT_Angle    angle )
  {
    vec->x = FT_TRIG_COSCALE >> 2;
    vec->y = 0;
    ft_trig_pseudo_rotate( vec, angle );
    vec->x >>= 12;
    vec->y >>= 12;
  }

  /* these macros return 0 for positive numbers,
     and -1 for negative ones */
#define FT_SIGN_LONG( x )   ( (x) >> ( FT_SIZEOF_LONG * 8 - 1 ) )
#define FT_SIGN_INT( x )    ( (x) >> ( FT_SIZEOF_INT * 8 - 1 ) )
#define FT_SIGN_INT32( x )  ( (x) >> 31 )
#define FT_SIGN_INT16( x )  ( (x) >> 15 )

  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( void )
  FT_Vector_Rotate( FT_Vector*  vec,
                    FT_Angle    angle )
  {
    FT_Int     shift;
    FT_Vector  v;

    v.x   = vec->x;
    v.y   = vec->y;

    if ( angle && ( v.x != 0 || v.y != 0 ) )
    {
      shift = ft_trig_prenorm( &v );
      ft_trig_pseudo_rotate( &v, angle );
      v.x = ft_trig_downscale( v.x );
      v.y = ft_trig_downscale( v.y );

      if ( shift > 0 )
      {
        FT_Int32  half = (FT_Int32)1L << ( shift - 1 );

        vec->x = ( v.x + half + FT_SIGN_LONG( v.x ) ) >> shift;
        vec->y = ( v.y + half + FT_SIGN_LONG( v.y ) ) >> shift;
      }
      else
      {
        shift  = -shift;
        vec->x = v.x << shift;
        vec->y = v.y << shift;
      }
    }
  }

  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( FT_Fixed )
  FT_Vector_Length( FT_Vector*  vec )
  {
    FT_Int     shift;
    FT_Vector  v;

    v = *vec;

    /* handle trivial cases */
    if ( v.x == 0 )
    {
      return ( v.y >= 0 ) ? v.y : -v.y;
    }
    else if ( v.y == 0 )
    {
      return ( v.x >= 0 ) ? v.x : -v.x;
    }

    /* general case */
    shift = ft_trig_prenorm( &v );
    ft_trig_pseudo_polarize( &v );

    v.x = ft_trig_downscale( v.x );

    if ( shift > 0 )
      return ( v.x + ( 1 << ( shift - 1 ) ) ) >> shift;

    return v.x << -shift;
  }

  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( void )
  FT_Vector_Polarize( FT_Vector*  vec,
                      FT_Fixed   *length,
                      FT_Angle   *angle )
  {
    FT_Int     shift;
    FT_Vector  v;

    v = *vec;

    if ( v.x == 0 && v.y == 0 )
      return;

    shift = ft_trig_prenorm( &v );
    ft_trig_pseudo_polarize( &v );

    v.x = ft_trig_downscale( v.x );

    *length = ( shift >= 0 ) ? ( v.x >> shift ) : ( v.x << -shift );
    *angle  = v.y;
  }

  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( void )
  FT_Vector_From_Polar( FT_Vector*  vec,
                        FT_Fixed    length,
                        FT_Angle    angle )
  {
    vec->x = length;
    vec->y = 0;

    FT_Vector_Rotate( vec, angle );
  }

  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( FT_Angle )
  FT_Angle_Diff( FT_Angle  angle1,
                 FT_Angle  angle2 )
  {
    FT_Angle  delta = angle2 - angle1;

    delta %= FT_ANGLE_2PI;
    if ( delta < 0 )
      delta += FT_ANGLE_2PI;

    if ( delta > FT_ANGLE_PI )
      delta -= FT_ANGLE_2PI;

    return delta;
  }

/* END */


code:
/***************************************************************************/
/*                                                                         */
/*  fttype1.c                                                              */
/*                                                                         */
/*    FreeType utility file for PS names support (body).                   */
/*                                                                         */
/*  Copyright 2002, 2003, 2004 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.                                        */
/*                                                                         */
/***************************************************************************/

#include <ft2build.h>
#include FT_INTERNAL_OBJECTS_H
#include FT_INTERNAL_SERVICE_H
#include FT_SERVICE_POSTSCRIPT_INFO_H

  /* documentation is in t1tables.h */

  FT_EXPORT_DEF( FT_Error )
  FT_Get_PS_Font_Info( FT_Face          face,
                       PS_FontInfoRec*  afont_info )
  {
    FT_Error  error = FT_Err_Invalid_Argument;

    if ( face )
    {
      FT_Service_PsInfo  service = NULL;

      FT_FACE_FIND_SERVICE( face, service, POSTSCRIPT_INFO );

      if ( service && service->ps_get_font_info )
        error = service->ps_get_font_info( face, afont_info );
    }

    return error;
  }

  /* documentation is in t1tables.h */

  FT_EXPORT_DEF( FT_Int )
  FT_Has_PS_Glyph_Names( FT_Face  face )
  {
    FT_Int             result  = 0;
    FT_Service_PsInfo  service = NULL;

    if ( face )
    {
      FT_FACE_FIND_SERVICE( face, service, POSTSCRIPT_INFO );

      if ( service && service->ps_has_glyph_names )
        result = service->ps_has_glyph_names( face );
    }

    return result;
  }

  /* documentation is in t1tables.h */

  FT_EXPORT_DEF( FT_Error )
  FT_Get_PS_Font_Private( FT_Face         face,
                          PS_PrivateRec*  afont_private )
  {
    FT_Error  error = FT_Err_Invalid_Argument;

    if ( face )
    {
      FT_Service_PsInfo  service = NULL;

      FT_FACE_FIND_SERVICE( face, service, POSTSCRIPT_INFO );

      if ( service && service->ps_get_font_private )
        error = service->ps_get_font_private( face, afont_private );
    }

    return error;
  }

/* END */


code:
/***************************************************************************/
/*                                                                         */
/*  ftutil.c                                                               */
/*                                                                         */
/*    FreeType utility file for memory and list management (body).         */
/*                                                                         */
/*  Copyright 2002, 2004, 2005, 2006, 2007 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.                                        */
/*                                                                         */
/***************************************************************************/

#include <ft2build.h>
#include FT_INTERNAL_DEBUG_H
#include FT_INTERNAL_MEMORY_H
#include FT_INTERNAL_OBJECTS_H
#include FT_LIST_H

  /*************************************************************************/
  /*                                                                       */
  /* The macro FT_COMPONENT is used in trace mode.  It is an implicit      */
  /* parameter of the FT_TRACE() and FT_ERROR() macros, used to print/log  */
  /* messages during execution.                                            */
  /*                                                                       */
#undef  FT_COMPONENT
#define FT_COMPONENT  trace_memory

  /*************************************************************************/
  /*************************************************************************/
  /*************************************************************************/
  /*****                                                               *****/
  /*****                                                               *****/
  /*****               M E M O R Y   M A N A G E M E N T               *****/
  /*****                                                               *****/
  /*****                                                               *****/
  /*************************************************************************/
  /*************************************************************************/
  /*************************************************************************/

  FT_BASE_DEF( FT_Pointer )
  ft_mem_alloc( FT_Memory  memory,
                FT_Long    size,
                FT_Error  *p_error )
  {
    FT_Error    error;
    FT_Pointer  block = ft_mem_qalloc( memory, size, &error );

    if ( !error && size > 0 )
      FT_MEM_ZERO( block, size );

    *p_error = error;
    return block;
  }

  FT_BASE_DEF( FT_Pointer )
  ft_mem_qalloc( FT_Memory  memory,
                 FT_Long    size,
                 FT_Error  *p_error )
  {
    FT_Error    error = FT_Err_Ok;
    FT_Pointer  block = NULL;

    if ( size > 0 )
    {
      block = memory->alloc( memory, size );
      if ( block == NULL )
        error = FT_Err_Out_Of_Memory;
    }
    else if ( size < 0 )
    {
      /* may help catch/prevent security issues */
      error = FT_Err_Invalid_Argument;
    }

    *p_error = error;
    return block;
  }

  FT_BASE_DEF( FT_Pointer )
  ft_mem_realloc( FT_Memory  memory,
                  FT_Long    item_size,
                  FT_Long    cur_count,
                  FT_Long    new_count,
                  void*      block,
                  FT_Error  *p_error )
  {
    FT_Error  error = FT_Err_Ok;

    block = ft_mem_qrealloc( memory, item_size,
                             cur_count, new_count, block, &error );
    if ( !error && new_count > cur_count )
      FT_MEM_ZERO( (char*)block + cur_count * item_size,
                   ( new_count - cur_count ) * item_size );

    *p_error = error;
    return block;
  }

  FT_BASE_DEF( FT_Pointer )
  ft_mem_qrealloc( FT_Memory  memory,
                   FT_Long    item_size,
                   FT_Long    cur_count,
                   FT_Long    new_count,
                   void*      block,
                   FT_Error  *p_error )
  {
    FT_Error  error = FT_Err_Ok;

    /* Note that we now accept `item_size == 0' as a valid parameter, in
     * order to cover very weird cases where an ALLOC_MULT macro would be
     * called.
     */
    if ( cur_count < 0 || new_count < 0 || item_size < 0 )
    {
      /* may help catch/prevent nasty security issues */
      error = FT_Err_Invalid_Argument;
    }
    else if ( new_count == 0 || item_size == 0 )
    {
      ft_mem_free( memory, block );
      block = NULL;
    }
    else if ( new_count > FT_INT_MAX/item_size )
    {
      error = FT_Err_Array_Too_Large;
    }
    else if ( cur_count == 0 )
    {
      FT_ASSERT( block == NULL );

      block = ft_mem_alloc( memory, new_count*item_size, &error );
    }
    else
    {
      FT_Pointer  block2;
      FT_Long     cur_size = cur_count*item_size;
      FT_Long     new_size = new_count*item_size;

      block2 = memory->realloc( memory, cur_size, new_size, block );
      if ( block2 == NULL )
        error = FT_Err_Out_Of_Memory;
      else
        block = block2;
    }

    *p_error = error;
    return block;
  }

  FT_BASE_DEF( void )
  ft_mem_free( FT_Memory   memory,
               const void *P )
  {
    if ( P )
      memory->free( memory, (void*)P );
  }

  FT_BASE_DEF( FT_Pointer )
  ft_mem_dup( FT_Memory    memory,
              const void*  address,
              FT_ULong     size,
              FT_Error    *p_error )
  {
    FT_Error    error;
    FT_Pointer  p = ft_mem_qalloc( memory, size, &error );

    if ( !error && address )
      ft_memcpy( p, address, size );

    *p_error = error;
    return p;
  }

  FT_BASE_DEF( FT_Pointer )
  ft_mem_strdup( FT_Memory    memory,
                 const char*  str,
                 FT_Error    *p_error )
  {
    FT_ULong  len = str ? (FT_ULong)ft_strlen( str ) + 1
                        : 0;

    return ft_mem_dup( memory, str, len, p_error );
  }

  FT_BASE_DEF( FT_Int )
  ft_mem_strcpyn( char*        dst,
                  const char*  src,
                  FT_ULong     size )
  {
    while ( size > 1 && *src != 0 )
    {
      *dst++ = *src++;
      size--;
    }

    *dst = 0;  /* always zero-terminate */

    return *src != 0;
  }

  /*************************************************************************/
  /*************************************************************************/
  /*************************************************************************/
  /*****                                                               *****/
  /*****                                                               *****/
  /*****            D O U B L Y   L I N K E D   L I S T S              *****/
  /*****                                                               *****/
  /*****                                                               *****/
  /*************************************************************************/
  /*************************************************************************/
  /*************************************************************************/

#undef  FT_COMPONENT
#define FT_COMPONENT  trace_list

  /* documentation is in ftlist.h */

  FT_EXPORT_DEF( FT_ListNode )
  FT_List_Find( FT_List  list,
                void*    data )
  {
    FT_ListNode  cur;

    cur = list->head;
    while ( cur )
    {
      if ( cur->data == data )
        return cur;

      cur = cur->next;
    }

    return (FT_ListNode)0;
  }

  /* documentation is in ftlist.h */

  FT_EXPORT_DEF( void )
  FT_List_Add( FT_List      list,
               FT_ListNode  node )
  {
    FT_ListNode  before = list->tail;

    node->next = 0;
    node->prev = before;

    if ( before )
      before->next = node;
    else
      list->head = node;

    list->tail = node;
  }

  /* documentation is in ftlist.h */

  FT_EXPORT_DEF( void )
  FT_List_Insert( FT_List      list,
                  FT_ListNode  node )
  {
    FT_ListNode  after = list->head;

    node->next = after;
    node->prev = 0;

    if ( !after )
      list->tail = node;
    else
      after->prev = node;

    list->head = node;
  }

  /* documentation is in ftlist.h */

  FT_EXPORT_DEF( void )
  FT_List_Remove( FT_List      list,
                  FT_ListNode  node )
  {
    FT_ListNode  before, after;

    before = node->prev;
    after  = node->next;

    if ( before )
      before->next = after;
    else
      list->head = after;

    if ( after )
      after->prev = before;
    else
      list->tail = before;
  }

  /* documentation is in ftlist.h */

  FT_EXPORT_DEF( void )
  FT_List_Up( FT_List      list,
              FT_ListNode  node )
  {
    FT_ListNode  before, after;

    before = node->prev;
    after  = node->next;

    /* check whether we are already on top of the list */
    if ( !before )
      return;

    before->next = after;

    if ( after )
      after->prev = before;
    else
      list->tail = before;

    node->prev       = 0;
    node->next       = list->head;
    list->head->prev = node;
    list->head       = node;
  }

  /* documentation is in ftlist.h */

  FT_EXPORT_DEF( FT_Error )
  FT_List_Iterate( FT_List            list,
                   FT_List_Iterator   iterator,
                   void*              user )
  {
    FT_ListNode  cur   = list->head;
    FT_Error     error = FT_Err_Ok;

    while ( cur )
    {
      FT_ListNode  next = cur->next;

      error = iterator( cur, user );
      if ( error )
        break;

      cur = next;
    }

    return error;
  }

  /* documentation is in ftlist.h */

  FT_EXPORT_DEF( void )
  FT_List_Finalize( FT_List             list,
                    FT_List_Destructor  destroy,
                    FT_Memory           memory,
                    void*               user )
  {
    FT_ListNode  cur;

    cur = list->head;
    while ( cur )
    {
      FT_ListNode  next = cur->next;
      void*        data = cur->data;

      if ( destroy )
        destroy( memory, data, user );

      FT_FREE( cur );
      cur = next;
    }

    list->head = 0;
    list->tail = 0;
  }

  FT_BASE_DEF( FT_UInt32 )
  ft_highpow2( FT_UInt32  value )
  {
    FT_UInt32  value2;

    /*
     *  We simply clear the lowest bit in each iteration.  When
     *  we reach 0, we know that the previous value was our result.
     */
    for ( ;; )
    {
      value2 = value & (value - 1);  /* clear lowest bit */
      if ( value2 == 0 )
        break;

      value = value2;
    }
    return value;
  }

#ifdef FT_CONFIG_OPTION_OLD_INTERNALS

  FT_BASE_DEF( FT_Error )
  FT_Alloc( FT_Memory  memory,
            FT_Long    size,
            void*     *P )
  {
    FT_Error  error;

    (void)FT_ALLOC( *P, size );
    return error;
  }

  FT_BASE_DEF( FT_Error )
  FT_QAlloc( FT_Memory  memory,
             FT_Long    size,
             void*     *p )
  {
    FT_Error  error;

    (void)FT_QALLOC( *p, size );
    return error;
  }

  FT_BASE_DEF( FT_Error )
  FT_Realloc( FT_Memory  memory,
              FT_Long    current,
              FT_Long    size,
              void*     *P )
  {
    FT_Error  error;

    (void)FT_REALLOC( *P, current, size );
    return error;
  }

  FT_BASE_DEF( FT_Error )
  FT_QRealloc( FT_Memory  memory,
               FT_Long    current,
               FT_Long    size,
               void*     *p )
  {
    FT_Error  error;

    (void)FT_QREALLOC( *p, current, size );
    return error;
  }

  FT_BASE_DEF( void )
  FT_Free( FT_Memory  memory,
           void*     *P )
  {
    if ( *P )
      FT_MEM_FREE( *P );
  }

#endif /* FT_CONFIG_OPTION_OLD_INTERNALS */

/* END */