freetype2/src/base/ftoutln.c

/***************************************************************************/
/*                                                                         */
/*  ftoutln.c                                                              */
/*                                                                         */
/*    FreeType outline management (body).                                  */
/*                                                                         */
/*  Copyright 1996-2000 by                                                 */
/*  David Turner, Robert Wilhelm, and Werner Lemberg.                      */
/*                                                                         */
/*  This file is part of the FreeType project, and may only be used,       */
/*  modified, and distributed under the terms of the FreeType project      */
/*  license, LICENSE.TXT.  By continuing to use, modify, or distribute     */
/*  this file you indicate that you have read the license and              */
/*  understand and accept it fully.                                        */
/*                                                                         */
/***************************************************************************/


  /*************************************************************************/
  /*                                                                       */
  /* All functions are declared in freetype.h.                             */
  /*                                                                       */
  /*************************************************************************/


#include <freetype/freetype.h>
#include <freetype/config/ftconfig.h>
#include <freetype/internal/ftobjs.h>


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


  static
  const FT_Outline  null_outline = { 0, 0, 0, 0, 0, 0 };


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_Outline_Decompose                                               */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Walks over an outline's structure to decompose it into individual  */
  /*    segments and Bezier arcs.  This function is also able to emit      */
  /*    `move to' and `close to' operations to indicate the start and end  */
  /*    of new contours in the outline.                                    */
  /*                                                                       */
  /* <Input>                                                               */
  /*    outline   :: A pointer to the source target.                       */
  /*                                                                       */
  /*    interface :: A table of `emitters', i.e,. function pointers called */
  /*                 during decomposition to indicate path operations.     */
  /*                                                                       */
  /*    user      :: A typeless pointer which is passed to each emitter    */
  /*                 during the decomposition.  It can be used to store    */
  /*                 the state during the decomposition.                   */
  /*                                                                       */
  /* <Return>                                                              */
  /*    FreeType error code.  0 means sucess.                              */
  /*                                                                       */
  FT_EXPORT_FUNC( FT_Error )  FT_Outline_Decompose(
                                FT_Outline*        outline,
                                FT_Outline_Funcs*  interface,
                                void*              user )
  {
#undef SCALED
#define SCALED( x )  ( ( (x) << shift ) - delta )

    FT_Vector   v_last;
    FT_Vector   v_control;
    FT_Vector   v_start;

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

    FT_Error    error;

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

    FT_Int   shift;
    FT_Pos   delta;


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

    shift = interface->shift;
    delta = interface->delta;
    first = 0;

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


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

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

      v_start.x = SCALED( v_start.x ); v_start.y = SCALED( v_start.y );
      v_last.x  = SCALED( v_last.x );  v_last.y  = SCALED( v_last.y );

      v_control = v_start;

      point = outline->points + first;
      tags  = outline->tags  + first;
      tag   = FT_CURVE_TAG( tags[0] );

      /* A contour cannot start with a cubic control point! */
      if ( tag == FT_Curve_Tag_Cubic )
        goto Invalid_Outline;

      /* check first point to determine origin */
      if ( tag == FT_Curve_Tag_Conic )
      {
        /* first point is conic control.  Yes, this happens. */
        if ( FT_CURVE_TAG( outline->tags[last] ) == FT_Curve_Tag_On )
        {
          /* start at last point if it is on the curve */
          v_start = v_last;
          limit--;
        }
        else
        {
          /* if both first and last points are conic,         */
          /* start at their middle and record its position    */
          /* for closure                                      */
          v_start.x = ( v_start.x + v_last.x ) / 2;
          v_start.y = ( v_start.y + v_last.y ) / 2;

          v_last = v_start;
        }
        point--;
        tags--;
      }

      error = interface->move_to( &v_start, user );
      if ( error )
        goto Exit;

      while ( point < limit )
      {
        point++;
        tags++;

        tag = FT_CURVE_TAG( tags[0] );
        switch ( tag )
        {
        case FT_Curve_Tag_On:  /* emit a single line_to */
          {
            FT_Vector  vec;


            vec.x = SCALED( point->x );
            vec.y = SCALED( point->y );

            error = interface->line_to( &vec, user );
            if ( error )
              goto Exit;
            continue;
          }

        case FT_Curve_Tag_Conic:  /* consume conic arcs */
          {
            v_control.x = SCALED( point->x );
            v_control.y = SCALED( point->y );

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


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

              vec.x = SCALED( point->x );
              vec.y = SCALED( point->y );

              if ( tag == FT_Curve_Tag_On )
              {
                error = interface->conic_to( &v_control, &vec, user );
                if ( error )
                  goto Exit;
                continue;
              }

              if ( tag != FT_Curve_Tag_Conic )
                goto Invalid_Outline;

              v_middle.x = ( v_control.x + vec.x ) / 2;
              v_middle.y = ( v_control.y + vec.y ) / 2;

              error = interface->conic_to( &v_control, &v_middle, user );
              if ( error )
                goto Exit;

              v_control = vec;
              goto Do_Conic;
            }

            error = interface->conic_to( &v_control, &v_start, user );
            goto Close;
          }

        default:  /* FT_Curve_Tag_Cubic */
          {
            FT_Vector  vec1, vec2;


            if ( point + 1 > limit                             ||
                 FT_CURVE_TAG( tags[1] ) != FT_Curve_Tag_Cubic )
              goto Invalid_Outline;

            point += 2;
            tags  += 2;

            vec1.x = SCALED( point[-2].x ); vec1.y = SCALED( point[-2].y );
            vec2.x = SCALED( point[-1].x ); vec2.y = SCALED( point[-1].y );

            if ( point <= limit )
            {
              FT_Vector  vec;


              vec.x = SCALED( point->x );
              vec.y = SCALED( point->y );

              error = interface->cubic_to( &vec1, &vec2, &vec, user );
              if ( error )
                goto Exit;
              continue;
            }

            error = interface->cubic_to( &vec1, &vec2, &v_start, user );
            goto Close;
          }
        }
      }

      /* close the contour with a line segment */
      error = interface->line_to( &v_start, user );

   Close:
      if ( error )
        goto Exit;

      first = last + 1;
    }

    return 0;

  Exit:
    return error;

  Invalid_Outline:
    return FT_Err_Invalid_Outline;
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_Outline_New                                                     */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Creates a new outline of a given size.                             */
  /*                                                                       */
  /* <Input>                                                               */
  /*    library     :: A handle to the library object from where the       */
  /*                   outline is allocated.  Note however that the new    */
  /*                   outline will NOT necessarily be FREED, when         */
  /*                   destroying the library, by FT_Done_FreeType().      */
  /*                                                                       */
  /*    numPoints   :: The maximal number of points within the outline.    */
  /*                                                                       */
  /*    numContours :: The maximal number of contours within the outline.  */
  /*                                                                       */
  /* <Output>                                                              */
  /*    outline     :: A handle to the new outline.  NULL in case of       */
  /*                   error.                                              */
  /*                                                                       */
  /* <Return>                                                              */
  /*    FreeType error code.  0 means success.                             */
  /*                                                                       */
  /* <MT-Note>                                                             */
  /*    No.                                                                */
  /*                                                                       */
  /* <Note>                                                                */
  /*    The reason why this function takes a `library' parameter is simply */
  /*    to use the library's memory allocator.                             */
  /*                                                                       */
  BASE_FUNC( FT_Error )  FT_Outline_New( FT_Library   library,
                                         FT_UInt      numPoints,
                                         FT_Int       numContours,
                                         FT_Outline*  outline )
  {
    FT_Error   error;
    FT_Memory  memory;


    if ( !outline )
      return FT_Err_Invalid_Argument;

    *outline = null_outline;
    memory   = library->memory;

    if ( ALLOC_ARRAY( outline->points,   numPoints * 2L, FT_Pos    ) ||
         ALLOC_ARRAY( outline->tags,     numPoints,      FT_Byte   ) ||
         ALLOC_ARRAY( outline->contours, numContours,    FT_UShort ) )
      goto Fail;

    outline->n_points    = (FT_UShort)numPoints;
    outline->n_contours  = (FT_Short)numContours;
    outline->flags      |= ft_outline_owner;

    return FT_Err_Ok;

  Fail:
    outline->flags |= ft_outline_owner;
    FT_Outline_Done( library, outline );

    return error;
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_Outline_Done                                                    */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Destroys an outline created with FT_Outline_New().                 */
  /*                                                                       */
  /* <Input>                                                               */
  /*    library :: A handle of the library object used to allocate the     */
  /*               outline.                                                */
  /*                                                                       */
  /*    outline :: A pointer to the outline object to be discarded.        */
  /*                                                                       */
  /* <Return>                                                              */
  /*    FreeType error code.  0 means success.                             */
  /*                                                                       */
  /* <MT-Note>                                                             */
  /*    No.                                                                */
  /*                                                                       */
  /* <Note>                                                                */
  /*    If the outline's `owner' field is not set, only the outline        */
  /*    descriptor will be released.                                       */
  /*                                                                       */
  /*    The reason why this function takes an `outline' parameter is       */
  /*    simply to use FT_Free().                                           */
  /*                                                                       */
  BASE_FUNC( FT_Error )  FT_Outline_Done( FT_Library   library,
                                          FT_Outline*  outline )
  {
    FT_Memory  memory = library->memory;


    if ( outline )
    {
      if ( outline->flags & ft_outline_owner )
      {
        FREE( outline->points   );
        FREE( outline->tags    );
        FREE( outline->contours );
      }
      *outline = null_outline;

      return FT_Err_Ok;
    }
    else
      return FT_Err_Invalid_Argument;
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_Outline_Get_CBox                                                */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Returns an outline's `control box'.  The control box encloses all  */
  /*    the outline's points, including Bezier control points.  Though it  */
  /*    coincides with the exact bounding box for most glyphs, it can be   */
  /*    slightly larger in some situations (like when rotating an outline  */
  /*    which contains Bezier outside arcs).                               */
  /*                                                                       */
  /*    Computing the control box is very fast, while getting the bounding */
  /*    box can take much more time as it needs to walk over all segments  */
  /*    and arcs in the outline.  To get the latter, you can use the       */
  /*    `ftbbox' component which is dedicated to this single task.         */
  /*                                                                       */
  /* <Input>                                                               */
  /*    outline :: A pointer to the source outline descriptor.             */
  /*                                                                       */
  /* <Output>                                                              */
  /*    cbox    :: The outline's control box.                              */
  /*                                                                       */
  /* <MT-Note>                                                             */
  /*    Yes.                                                               */
  /*                                                                       */
  BASE_FUNC( void )  FT_Outline_Get_CBox( FT_Outline*  outline,
                                          FT_BBox*     cbox )
  {
    FT_Pos  xMin, yMin, xMax, yMax;


    if ( outline && cbox )
    {
      if ( outline->n_points == 0 )
      {
        xMin = 0;
        yMin = 0;
        xMax = 0;
        yMax = 0;
      }
      else
      {
        FT_Vector*  vec   = outline->points;
        FT_Vector*  limit = vec + outline->n_points;


        xMin = xMax = vec->x;
        yMin = yMax = vec->y;
        vec++;

        for ( ; vec < limit; vec++ )
        {
          FT_Pos  x, y;


          x = vec->x;
          if ( x < xMin ) xMin = x;
          if ( x > xMax ) xMax = x;

          y = vec->y;
          if ( y < yMin ) yMin = y;
          if ( y > yMax ) yMax = y;
        }
      }
      cbox->xMin = xMin;
      cbox->xMax = xMax;
      cbox->yMin = yMin;
      cbox->yMax = yMax;
    }
  }



  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_Outline_Translate                                               */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Applies a simple translation to the points of an outline.          */
  /*                                                                       */
  /* <Input>                                                               */
  /*    outline :: A pointer to the target outline descriptor.             */
  /*                                                                       */
  /*    xOffset :: The horizontal offset.                                  */
  /*                                                                       */
  /*    yOffset :: The vertical offset.                                    */
  /*                                                                       */
  /* <MT-Note>                                                             */
  /*    Yes.                                                               */
  /*                                                                       */
  BASE_FUNC( void )  FT_Outline_Translate( FT_Outline*  outline,
                                           FT_Pos       xOffset,
                                           FT_Pos       yOffset )
  {
    FT_UShort   n;
    FT_Vector*  vec = outline->points;


    for ( n = 0; n < outline->n_points; n++ )
    {
      vec->x += xOffset;
      vec->y += yOffset;
      vec++;
    }
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_Outline_Reverse                                                 */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Reverses the drawing direction of an outline.  This is used to     */
  /*    ensure consistent fill conventions for mirrored glyphs.            */
  /*                                                                       */
  /* <Input>                                                               */
  /*    outline :: A pointer to the target outline descriptor.             */
  /*                                                                       */
  /* <Note>                                                                */
  /*    This functions toggles the bit flag `ft_outline_reverse_fill' in   */
  /*    the outline's `flags' field.                                       */
  /*                                                                       */
  BASE_FUNC( void )  FT_Outline_Reverse( FT_Outline*  outline )
  {
    FT_UShort  n;
    FT_Int     first, last;


    first = 0;

    for ( n = 0; n < outline->n_contours; n++ )
    {
      last  = outline->contours[n];

      /* reverse point table */
      {
        FT_Vector*  p = outline->points + first;
        FT_Vector*  q = outline->points + last;
        FT_Vector   swap;


        while ( p < q )
        {
          swap = *p;
          *p   = *q;
          *q   = swap;
          p++;
          q--;
        }
      }

      /* reverse tags table */
      {
        char*  p = outline->tags + first;
        char*  q = outline->tags + last;
        char   swap;

        while ( p < q )
        {
          swap = *p;
          *p   = *q;
          *q   = swap;
          p++;
          q--;
        }
      }

      first = last + 1;
    }

    outline->flags ^= ft_outline_reverse_fill;
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_Outline_Render                                                  */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Renders an outline within a bitmap using the current scan-convert. */
  /*    This functions uses a FT_Raster_Params as argument, allowing       */
  /*    advanced features like direct composition/translucency, etc.       */
  /*                                                                       */
  /* <Input>                                                               */
  /*    library :: A handle to a FreeType library object.                  */
  /*                                                                       */
  /*    outline :: A pointer to the source outline descriptor.             */
  /*                                                                       */
  /*    params  :: A pointer to a FT_Raster_Params used to describe        */
  /*               the rendering operation.                                */
  /*                                                                       */
  /* <Return>                                                              */
  /*    FreeType error code.  0 means success.                             */
  /*                                                                       */
  /* <MT-Note>                                                             */
  /*    YES.  Rendering is synchronized, so that concurrent calls to the   */
  /*    scan-line converter will be serialized.                            */
  /*                                                                       */
  /* <Note>                                                                */
  /*    You should know what you're doing and the role of FT_Raster_Params */
  /*    to use this function.                                              */
  /*                                                                       */
  /*    The field `params.source' will be set to `outline' before the scan */
  /*    converter is called, which means that the value you give to it is  */
  /*    actually ignored.                                                  */
  /*                                                                       */
  FT_EXPORT_FUNC( FT_Error )  FT_Outline_Render( FT_Library         library,
                                                 FT_Outline*        outline,
                                                 FT_Raster_Params*  params )
  {
    FT_Error           error;
    FT_Renderer        renderer;

    if ( !library )
    {
      error = FT_Err_Invalid_Library_Handle;
      goto Exit;
    }

    if ( !outline || !params )
    {
      error = FT_Err_Invalid_Argument;
      goto Exit;
    }

    /* retrieve the current outline renderer */
    renderer = library->cur_renderer;
    if (!renderer)
    {
      /* XXXX: should use another error code */
      error = FT_Err_Invalid_Argument;
      goto Exit;
    }

    params->source = (void*)outline;
    
    error = renderer->raster_render( renderer->raster, params );

  Exit:
    return error;
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_Outline_Get_Bitmap                                              */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Renders an outline within a bitmap.  The outline's image is simply */
  /*    OR-ed to the target bitmap.                                        */
  /*                                                                       */
  /* <Input>                                                               */
  /*    library :: A handle to a FreeType library object.                  */
  /*                                                                       */
  /*    outline :: A pointer to the source outline descriptor.             */
  /*                                                                       */
  /*    map     :: A pointer to the target bitmap descriptor.              */
  /*                                                                       */
  /* <Return>                                                              */
  /*    FreeType error code.  0 means success.                             */
  /*                                                                       */
  /* <MT-Note>                                                             */
  /*    YES.  Rendering is synchronized, so that concurrent calls to the   */
  /*    scan-line converter will be serialized.                            */
  /*                                                                       */
  /* <Note>                                                                */
  /*    This function does NOT CREATE the bitmap, it only renders an       */
  /*    outline image within the one you pass to it!                       */
  /*                                                                       */
  /*    It will use the raster correponding to the default glyph format.   */
  /*                                                                       */
  FT_EXPORT_FUNC( FT_Error )  FT_Outline_Get_Bitmap( FT_Library   library,
                                                     FT_Outline*  outline,
                                                     FT_Bitmap*   bitmap )
  {
    FT_Raster_Params  params;

    if (!bitmap)
      return FT_Err_Invalid_Argument;

    /* other checks are delayed to FT_Outline_Render */

    params.target = bitmap;
    params.flags  = 0;

    if ( bitmap->pixel_mode == ft_pixel_mode_grays )
      params.flags |= ft_raster_flag_aa;

    return FT_Outline_Render( library, outline, &params );
  }




  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_Vector_Transform                                                */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Transforms a single vector through a 2x2 matrix.                   */
  /*                                                                       */
  /* <InOut>                                                               */
  /*    vector :: The target vector to transform.                          */
  /*                                                                       */
  /* <Input>                                                               */
  /*    matrix :: A pointer to the source 2x2 matrix.                      */
  /*                                                                       */
  /* <MT-Note>                                                             */
  /*    Yes.                                                               */
  /*                                                                       */
  /* <Note>                                                                */
  /*    The result is undefined if either `vector' or `matrix' is invalid. */
  /*                                                                       */
  FT_EXPORT_FUNC( void )  FT_Vector_Transform( FT_Vector*  vector,
                                               FT_Matrix*  matrix )
  {
    FT_Pos xz, yz;

    xz = FT_MulFix( vector->x, matrix->xx ) +
         FT_MulFix( vector->y, matrix->xy );

    yz = FT_MulFix( vector->x, matrix->yx ) +
         FT_MulFix( vector->y, matrix->yy );

    vector->x = xz;
    vector->y = yz;
  }




  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_Outline_Transform                                               */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Applies a simple 2x2 matrix to all of an outline's points.  Useful */
  /*    for applying rotations, slanting, flipping, etc.                   */
  /*                                                                       */
  /* <Input>                                                               */
  /*    outline :: A pointer to the target outline descriptor.             */
  /*                                                                       */
  /*    matrix  :: A pointer to the transformation matrix.                 */
  /*                                                                       */
  /* <MT-Note>                                                             */
  /*    Yes.                                                               */
  /*                                                                       */
  /* <Note>                                                                */
  /*    You can use FT_Outline_Translate() if you need to translate the    */
  /*    outline's points.                                                  */
  /*                                                                       */
  BASE_FUNC( void )  FT_Outline_Transform( FT_Outline*  outline,
                                           FT_Matrix*   matrix )
  {
    FT_Vector*  vec = outline->points;
    FT_Vector*  limit = vec + outline->n_points;
    
    for ( ; vec < limit; vec++ )
      FT_Vector_Transform( vec, matrix );
  }


  /*************************************************************************/
  /*************************************************************************/
  /*************************************************************************/
  /****                                                                 ****/
  /****    The following functions are not used by the font drivers     ****/
  /****    but they are provided as a convenience for client            ****/
  /****    applications.                                                ****/
  /****                                                                 ****/
  /****    Note that they will not be compiled if the configuration     ****/
  /****    macro FT_CONFIG_OPTION_NO_CONVENIENCE_FUNCS is defined.      ****/
  /****                                                                 ****/
  /*************************************************************************/
  /*************************************************************************/
  /*************************************************************************/


#ifndef FT_CONFIG_OPTION_NO_CONVENIENCE_FUNCS


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_Outline_Copy                                                    */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Copies an outline into another one.  Both objects must have the    */
  /*    same sizes (number of points & number of contours) when this       */
  /*    function is called.                                                */
  /*                                                                       */
  /* <Input>                                                               */
  /*    source :: A handle to the source outline.                          */
  /*                                                                       */
  /* <Output>                                                              */
  /*    target :: A handle to the target outline.                          */
  /*                                                                       */
  /* <Return>                                                              */
  /*    FreeType error code.  0 means success.                             */
  /*                                                                       */
  BASE_FUNC( FT_Error )  FT_Outline_Copy( FT_Outline*  source,
                                          FT_Outline*  target )
  {
    FT_Int  is_owner;


    if ( !source            || !target            ||
         source->n_points   != target->n_points   ||
         source->n_contours != target->n_contours )
      return FT_Err_Invalid_Argument;

    MEM_Copy( target->points, source->points,
              source->n_points * 2 * sizeof ( FT_Pos ) );

    MEM_Copy( target->tags, source->tags,
              source->n_points * sizeof ( FT_Byte ) );

    MEM_Copy( target->contours, source->contours,
              source->n_contours * sizeof ( FT_Short ) );

    /* copy all flags, except the `ft_outline_owner' one */
    is_owner      = target->flags & ft_outline_owner;
    target->flags = source->flags;

    target->flags &= ~ft_outline_owner;
    target->flags |= is_owner;

    return FT_Err_Ok;
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_Matrix_Multiply                                                 */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Performs the matrix operation `b = a*b'.                           */
  /*                                                                       */
  /* <Input>                                                               */
  /*    a :: A pointer to matrix `a'.                                      */
  /*                                                                       */
  /* <InOut>                                                               */
  /*    b :: A pointer to matrix `b'.                                      */
  /*                                                                       */
  /* <MT-Note>                                                             */
  /*    Yes.                                                               */
  /*                                                                       */
  BASE_FUNC( void )  FT_Matrix_Multiply( FT_Matrix*  a,
                                         FT_Matrix*  b )
  {
    FT_Fixed  xx, xy, yx, yy;


    xx = FT_MulFix( a->xx, b->xx ) + FT_MulFix( a->xy, b->yx );
    xy = FT_MulFix( a->xx, b->xy ) + FT_MulFix( a->xy, b->yy );
    yx = FT_MulFix( a->yx, b->xx ) + FT_MulFix( a->yy, b->yx );
    yy = FT_MulFix( a->yx, b->xy ) + FT_MulFix( a->yy, b->yy );

    b->xx = xx;  b->xy = xy;
    b->yx = yx;  b->yy = yy;
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_Matrix_Invert                                                   */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Inverts a 2x2 matrix.  Returns an error if it can't be inverted.   */
  /*                                                                       */
  /* <InOut>                                                               */
  /*    matrix :: A pointer to the target matrix.  Remains untouched in    */
  /*              case of error.                                           */
  /*                                                                       */
  /* <Return>                                                              */
  /*    FreeType error code.  0 means success.                             */
  /*                                                                       */
  /* <MT-Note>                                                             */
  /*    Yes.                                                               */
  /*                                                                       */
  BASE_FUNC( FT_Error )  FT_Matrix_Invert( FT_Matrix*  matrix )
  {
    FT_Pos  delta, xx, yy;


    /* compute discriminant */
    delta = FT_MulFix( matrix->xx, matrix->yy ) -
            FT_MulFix( matrix->xy, matrix->yx );

    if ( !delta )
      return FT_Err_Invalid_Argument;  /* matrix can't be inverted */

    matrix->xy = - FT_DivFix( matrix->xy, delta );
    matrix->yx = - FT_DivFix( matrix->yx, delta );

    xx = matrix->xx;
    yy = matrix->yy;

    matrix->xx = FT_DivFix( yy, delta );
    matrix->yy = FT_DivFix( xx, delta );

    return FT_Err_Ok;
  }

#endif /* FT_CONFIG_OPTION_NO_CONVENIENCE_FUNCS */


/* END */