ftstroke.c

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/***************************************************************************/
/*                                                                         */
/*  ftstroke.c                                                             */
/*                                                                         */
/*    FreeType path stroker (body).                                        */
/*                                                                         */
/*  Copyright 2002, 2003, 2004, 2005, 2006 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_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   = 0;


    if ( new_max > old_max )
    {
      FT_UInt    cur_max = old_max;
      FT_Memory  memory  = border->memory;


      while ( cur_max < new_max )
        cur_max += ( cur_max >> 1 ) + 16;

      if ( FT_RENEW_ARRAY( border->points, old_max, cur_max ) ||
           FT_RENEW_ARRAY( border->tags,   old_max, cur_max ) )
        goto Exit;

      border->max_points = cur_max;
    }
  Exit:
    return error;
  }


  static void
  ft_stroke_border_close( FT_StrokeBorder  border,
                          FT_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 = 0;
  }


  static FT_Error
  ft_stroke_border_lineto( FT_StrokeBorder  border,
                           FT_Vector*       to,
                           FT_Bool          movable )
  {
    FT_Error  error = 0;


    FT_ASSERT( border->start >= 0 );

    if ( border->movable )
    {
      /* move last point */
      border->points[border->num_points - 1] = *to;
    }
    else
    {
      /* add one point */
      error = ft_stroke_border_grow( border, 1 );
      if ( !error )
      {
        FT_Vector*  vec = border->points + border->num_points;
        FT_Byte*    tag = border->tags   + border->num_points;


        vec[0] = *to;
        tag[0] = FT_STROKE_TAG_ON;

        border->num_points += 1;
      }
    }
    border->movable = movable;
    return error;
  }


  static FT_Error
  ft_stroke_border_conicto( FT_StrokeBorder  border,
                            FT_Vector*       control,
                            FT_Vector*       to )
  {
    FT_Error  error;


    FT_ASSERT( border->start >= 0 );

    error = ft_stroke_border_grow( border, 2 );
    if ( !error )
    {
      FT_Vector*  vec = border->points + border->num_points;
      FT_Byte*    tag = border->tags   + border->num_points;

      vec[0] = *control;
      vec[1] = *to;

      tag[0] = 0;
      tag[1] = FT_STROKE_TAG_ON;

      border->num_points += 2;
    }
    border->movable = 0;
    return error;
  }


  static FT_Error
  ft_stroke_border_cubicto( FT_StrokeBorder  border,
                            FT_Vector*       control1,
                            FT_Vector*       control2,
                            FT_Vector*       to )
  {
    FT_Error  error;


    FT_ASSERT( border->start >= 0 );

    error = ft_stroke_border_grow( border, 3 );
    if ( !error )
    {
      FT_Vector*  vec = border->points + border->num_points;
      FT_Byte*    tag = border->tags   + border->num_points;


      vec[0] = *control1;
      vec[1] = *control2;
      vec[2] = *to;

      tag[0] = FT_STROKE_TAG_CUBIC;
      tag[1] = FT_STROKE_TAG_CUBIC;
      tag[2] = FT_STROKE_TAG_ON;

      border->num_points += 3;
    }
    border->movable = 0;
    return error;
  }


#define FT_ARC_CUBIC_ANGLE  ( FT_ANGLE_PI / 2 )


  static FT_Error
  ft_stroke_border_arcto( FT_StrokeBorder  border,
                          FT_Vector*       center,
                          FT_Fixed         radius,
                          FT_Angle         angle_start,
                          FT_Angle         angle_diff )
  {
    FT_Angle   total, angle, step, rotate, next, theta;
    FT_Vector  a, b, a2, b2;
    FT_Fixed   length;
    FT_Error   error = 0;


    /* compute start point */
    FT_Vector_From_Polar( &a, radius, angle_start );
    a.x += center->x;
    a.y += center->y;

    total  = angle_diff;
    angle  = angle_start;
    rotate = ( angle_diff >= 0 ) ? FT_ANGLE_PI2 : -FT_ANGLE_PI2;

    while ( total != 0 )
    {
      step = total;
      if ( step > FT_ARC_CUBIC_ANGLE )
        step = FT_ARC_CUBIC_ANGLE;

      else if ( step < -FT_ARC_CUBIC_ANGLE )
        step = -FT_ARC_CUBIC_ANGLE;

      next  = angle + step;
      theta = step;
      if ( theta < 0 )
        theta = -theta;

      theta >>= 1;

      /* compute end point */
      FT_Vector_From_Polar( &b, radius, next );
      b.x += center->x;
      b.y += center->y;

      /* compute first and second control points */
      length = FT_MulDiv( radius, FT_Sin( theta ) * 4,
                          ( 0x10000L + FT_Cos( theta ) ) * 3 );

      FT_Vector_From_Polar( &a2, length, angle + rotate );
      a2.x += a.x;
      a2.y += a.y;