Commit message: https://github.com/ImageMagick/ImageMagick/issues/3195
CVE: CVE-2021-20246
CWE: CWE-369
Vulnerability description: A flaw was found in ImageMagick in MagickCore/resample.c. An attacker who submits a crafted file that is processed by ImageMagick could trigger undefined behavior in the form of math division by zero. The highest threat from this vulnerability is to system availability.

Project: ImageMagick
File: resample.c

MagickExport MagickBooleanType SetResampleFilterVirtualPixelMethod(
  ResampleFilter *resample_filter,const VirtualPixelMethod method)
{
  assert(resample_filter != (ResampleFilter *) NULL);
  assert(resample_filter->signature == MagickCoreSignature);
  assert(resample_filter->image != (Image *) NULL);
  if (resample_filter->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",
      resample_filter->image->filename);
  resample_filter->virtual_pixel=method;
  if (method != UndefinedVirtualPixelMethod)
    (void) SetCacheViewVirtualPixelMethod(resample_filter->view,method);
  return(MagickTrue);
}

Project: ImageMagick
File: resample.c

MagickExport ResampleFilter *DestroyResampleFilter(
  ResampleFilter *resample_filter)
{
  assert(resample_filter != (ResampleFilter *) NULL);
  assert(resample_filter->signature == MagickCoreSignature);
  assert(resample_filter->image != (Image *) NULL);
  if (resample_filter->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",
      resample_filter->image->filename);
  resample_filter->view=DestroyCacheView(resample_filter->view);
  resample_filter->image=DestroyImage(resample_filter->image);
#if ! FILTER_LUT
  resample_filter->filter_def=DestroyResizeFilter(resample_filter->filter_def);
#endif
  resample_filter->signature=(~MagickCoreSignature);
  resample_filter=(ResampleFilter *) RelinquishMagickMemory(resample_filter);
  return(resample_filter);
}

Project: ImageMagick
File: resample.c

static inline void ClampUpAxes(const double dux,
			       const double dvx,
			       const double duy,
			       const double dvy,
			       double *major_mag,
			       double *minor_mag,
			       double *major_unit_x,
			       double *major_unit_y,
			       double *minor_unit_x,
			       double *minor_unit_y)
{
  /*
   * ClampUpAxes takes an input 2x2 matrix
   *
   * [ a b ] = [ dux duy ]
   * [ c d ] = [ dvx dvy ]
   *
   * and computes from it the major and minor axis vectors [major_x,
   * major_y] and [minor_x,minor_y] of the smallest ellipse containing
   * both the unit disk and the ellipse which is the image of the unit
   * disk by the linear transformation
   *
   * [ dux duy ] [S] = [s]
   * [ dvx dvy ] [T] = [t]
   *
   * (The vector [S,T] is the difference between a position in output
   * space and [X,Y]; the vector [s,t] is the difference between a
   * position in input space and [x,y].)
   */
  /*
   * Output:
   *
   * major_mag is the half-length of the major axis of the "new"
   * ellipse.
   *
   * minor_mag is the half-length of the minor axis of the "new"
   * ellipse.
   *
   * major_unit_x is the x-coordinate of the major axis direction vector
   * of both the "old" and "new" ellipses.
   *
   * major_unit_y is the y-coordinate of the major axis direction vector.
   *
   * minor_unit_x is the x-coordinate of the minor axis direction vector.
   *
   * minor_unit_y is the y-coordinate of the minor axis direction vector.
   *
   * Unit vectors are useful for computing projections, in particular,
   * to compute the distance between a point in output space and the
   * center of a unit disk in output space, using the position of the
   * corresponding point [s,t] in input space. Following the clamping,
   * the square of this distance is
   *
   * ( ( s * major_unit_x + t * major_unit_y ) / major_mag )^2
   * +
   * ( ( s * minor_unit_x + t * minor_unit_y ) / minor_mag )^2
   *
   * If such distances will be computed for many [s,t]'s, it makes
   * sense to actually compute the reciprocal of major_mag and
   * minor_mag and multiply them by the above unit lengths.
   *
   * Now, if you want to modify the input pair of tangent vectors so
   * that it defines the modified ellipse, all you have to do is set
   *
   * newdux = major_mag * major_unit_x
   * newdvx = major_mag * major_unit_y
   * newduy = minor_mag * minor_unit_x = minor_mag * -major_unit_y
   * newdvy = minor_mag * minor_unit_y = minor_mag *  major_unit_x
   *
   * and use these tangent vectors as if they were the original ones.
   * Usually, this is a drastic change in the tangent vectors even if
   * the singular values are not clamped; for example, the minor axis
   * vector always points in a direction which is 90 degrees
   * counterclockwise from the direction of the major axis vector.
   */
  /*
   * Discussion:
   *
   * GOAL: Fix things so that the pullback, in input space, of a disk
   * of radius r in output space is an ellipse which contains, at
   * least, a disc of radius r. (Make this hold for any r>0.)
   *
   * ESSENCE OF THE METHOD: Compute the product of the first two
   * factors of an SVD of the linear transformation defining the
   * ellipse and make sure that both its columns have norm at least 1.
   * Because rotations and reflexions map disks to themselves, it is
   * not necessary to compute the third (rightmost) factor of the SVD.
   *
   * DETAILS: Find the singular values and (unit) left singular
   * vectors of Jinv, clampling up the singular values to 1, and
   * multiply the unit left singular vectors by the new singular
   * values in order to get the minor and major ellipse axis vectors.
   *
   * Image resampling context:
   *
   * The Jacobian matrix of the transformation at the output point
   * under consideration is defined as follows:
   *
   * Consider the transformation (x,y) -> (X,Y) from input locations
   * to output locations. (Anthony Thyssen, elsewhere in resample.c,
   * uses the notation (u,v) -> (x,y).)
   *
   * The Jacobian matrix of the transformation at (x,y) is equal to
   *
   *   J = [ A, B ] = [ dX/dx, dX/dy ]
   *       [ C, D ]   [ dY/dx, dY/dy ]
   *
   * that is, the vector [A,C] is the tangent vector corresponding to
   * input changes in the horizontal direction, and the vector [B,D]
   * is the tangent vector corresponding to input changes in the
   * vertical direction.
   *
   * In the context of resampling, it is natural to use the inverse
   * Jacobian matrix Jinv because resampling is generally performed by
   * pulling pixel locations in the output image back to locations in
   * the input image. Jinv is
   *
   *   Jinv = [ a, b ] = [ dx/dX, dx/dY ]
   *          [ c, d ]   [ dy/dX, dy/dY ]
   *
   * Note: Jinv can be computed from J with the following matrix
   * formula:
   *
   *   Jinv = 1/(A*D-B*C) [  D, -B ]
   *                      [ -C,  A ]
   *
   * What we do is modify Jinv so that it generates an ellipse which
   * is as close as possible to the original but which contains the
   * unit disk. This can be accomplished as follows:
   *
   * Let
   *
   *   Jinv = U Sigma V^T
   *
   * be an SVD decomposition of Jinv. (The SVD is not unique, but the
   * final ellipse does not depend on the particular SVD.)
   *
   * We could clamp up the entries of the diagonal matrix Sigma so
   * that they are at least 1, and then set
   *
   *   Jinv = U newSigma V^T.
   *
   * However, we do not need to compute V for the following reason:
   * V^T is an orthogonal matrix (that is, it represents a combination
   * of rotations and reflexions) so that it maps the unit circle to
   * itself. For this reason, the exact value of V does not affect the
   * final ellipse, and we can choose V to be the identity
   * matrix. This gives
   *
   *   Jinv = U newSigma.
   *
   * In the end, we return the two diagonal entries of newSigma
   * together with the two columns of U.
   */
  /*
   * ClampUpAxes was written by Nicolas Robidoux and Chantal Racette
   * of Laurentian University with insightful suggestions from Anthony
   * Thyssen and funding from the National Science and Engineering
   * Research Council of Canada. It is distinguished from its
   * predecessors by its efficient handling of degenerate cases.
   *
   * The idea of clamping up the EWA ellipse's major and minor axes so
   * that the result contains the reconstruction kernel filter support
   * is taken from Andreas Gustaffson's Masters thesis "Interactive
   * Image Warping", Helsinki University of Technology, Faculty of
   * Information Technology, 59 pages, 1993 (see Section 3.6).
   *
   * The use of the SVD to clamp up the singular values of the
   * Jacobian matrix of the pullback transformation for EWA resampling
   * is taken from the astrophysicist Craig DeForest.  It is
   * implemented in his PDL::Transform code (PDL = Perl Data
   * Language).
   */
  const double a = dux;
  const double b = duy;
  const double c = dvx;
  const double d = dvy;
  /*
   * n is the matrix Jinv * transpose(Jinv). Eigenvalues of n are the
   * squares of the singular values of Jinv.
   */
  const double aa = a*a;
  const double bb = b*b;
  const double cc = c*c;
  const double dd = d*d;
  /*
   * Eigenvectors of n are left singular vectors of Jinv.
   */
  const double n11 = aa+bb;
  const double n12 = a*c+b*d;
  const double n21 = n12;
  const double n22 = cc+dd;
  const double det = a*d-b*c;
  const double twice_det = det+det;
  const double frobenius_squared = n11+n22;
  const double discriminant =
    (frobenius_squared+twice_det)*(frobenius_squared-twice_det);
  /*
   * In exact arithmetic, discriminant can't be negative. In floating
   * point, it can, because of the bad conditioning of SVD
   * decompositions done through the associated normal matrix.
   */
  const double sqrt_discriminant =
    sqrt(discriminant > 0.0 ? discriminant : 0.0);
  /*
   * s1 is the largest singular value of the inverse Jacobian
   * matrix. In other words, its reciprocal is the smallest singular
   * value of the Jacobian matrix itself.
   * If s1 = 0, both singular values are 0, and any orthogonal pair of
   * left and right factors produces a singular decomposition of Jinv.
   */
  /*
   * Initially, we only compute the squares of the singular values.
   */
  const double s1s1 = 0.5*(frobenius_squared+sqrt_discriminant);
  /*
   * s2 the smallest singular value of the inverse Jacobian
   * matrix. Its reciprocal is the largest singular value of the
   * Jacobian matrix itself.
   */
  const double s2s2 = 0.5*(frobenius_squared-sqrt_discriminant);
  const double s1s1minusn11 = s1s1-n11;
  const double s1s1minusn22 = s1s1-n22;
  /*
   * u1, the first column of the U factor of a singular decomposition
   * of Jinv, is a (non-normalized) left singular vector corresponding
   * to s1. It has entries u11 and u21. We compute u1 from the fact
   * that it is an eigenvector of n corresponding to the eigenvalue
   * s1^2.
   */
  const double s1s1minusn11_squared = s1s1minusn11*s1s1minusn11;
  const double s1s1minusn22_squared = s1s1minusn22*s1s1minusn22;
  /*
   * The following selects the largest row of n-s1^2 I as the one
   * which is used to find the eigenvector. If both s1^2-n11 and
   * s1^2-n22 are zero, n-s1^2 I is the zero matrix.  In that case,
   * any vector is an eigenvector; in addition, norm below is equal to
   * zero, and, in exact arithmetic, this is the only case in which
   * norm = 0. So, setting u1 to the simple but arbitrary vector [1,0]
   * if norm = 0 safely takes care of all cases.
   */
  const double temp_u11 =
    ( (s1s1minusn11_squared>=s1s1minusn22_squared) ? n12 : s1s1minusn22 );
  const double temp_u21 =
    ( (s1s1minusn11_squared>=s1s1minusn22_squared) ? s1s1minusn11 : n21 );
  const double norm = sqrt(temp_u11*temp_u11+temp_u21*temp_u21);
  /*
   * Finalize the entries of first left singular vector (associated
   * with the largest singular value).
   */
  const double u11 = ( (norm>0.0) ? temp_u11/norm : 1.0 );
  const double u21 = ( (norm>0.0) ? temp_u21/norm : 0.0 );
  /*
   * Clamp the singular values up to 1.
   */
  *major_mag = ( (s1s1<=1.0) ? 1.0 : sqrt(s1s1) );
  *minor_mag = ( (s2s2<=1.0) ? 1.0 : sqrt(s2s2) );
  /*
   * Return the unit major and minor axis direction vectors.
   */
  *major_unit_x = u11;
  *major_unit_y = u21;
  *minor_unit_x = -u21;
  *minor_unit_y = u11;
}

Project: ImageMagick
File: resample.c

MagickExport ResampleFilter *AcquireResampleFilter(const Image *image,
  ExceptionInfo *exception)
{
  ResampleFilter
    *resample_filter;

  assert(image != (Image *) NULL);
  assert(image->signature == MagickCoreSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  assert(exception != (ExceptionInfo *) NULL);
  assert(exception->signature == MagickCoreSignature);
  resample_filter=(ResampleFilter *) AcquireCriticalMemory(sizeof(
    *resample_filter));
  (void) memset(resample_filter,0,sizeof(*resample_filter));
  resample_filter->exception=exception;
  resample_filter->image=ReferenceImage((Image *) image);
  resample_filter->view=AcquireVirtualCacheView(resample_filter->image,
    exception);
  resample_filter->debug=IsEventLogging();
  resample_filter->image_area=(ssize_t) (image->columns*image->rows);
  resample_filter->average_defined=MagickFalse;
  resample_filter->signature=MagickCoreSignature;
  SetResampleFilter(resample_filter,image->filter);
  (void) SetResampleFilterInterpolateMethod(resample_filter,image->interpolate);
  (void) SetResampleFilterVirtualPixelMethod(resample_filter,
    GetImageVirtualPixelMethod(image));
  return(resample_filter);
}

Project: ImageMagick
File: resample.c

MagickExport MagickBooleanType SetResampleFilterInterpolateMethod(
  ResampleFilter *resample_filter,const PixelInterpolateMethod method)
{
  assert(resample_filter != (ResampleFilter *) NULL);
  assert(resample_filter->signature == MagickCoreSignature);
  assert(resample_filter->image != (Image *) NULL);
  if (resample_filter->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",
      resample_filter->image->filename);
  resample_filter->interpolate=method;
  return(MagickTrue);
}

Project: ImageMagick
File: resample.c

MagickExport void SetResampleFilter(ResampleFilter *resample_filter,
  const FilterType filter)
{
  ResizeFilter
     *resize_filter;

  assert(resample_filter != (ResampleFilter *) NULL);
  assert(resample_filter->signature == MagickCoreSignature);

  resample_filter->do_interpolate = MagickFalse;
  resample_filter->filter = filter;

  /* Default cylindrical filter is a Cubic Keys filter */
  if ( filter == UndefinedFilter )
    resample_filter->filter = RobidouxFilter;

  if ( resample_filter->filter == PointFilter ) {
    resample_filter->do_interpolate = MagickTrue;
    return;  /* EWA turned off - nothing more to do */
  }

  resize_filter = AcquireResizeFilter(resample_filter->image,
    resample_filter->filter,MagickTrue,resample_filter->exception);
  if (resize_filter == (ResizeFilter *) NULL) {
    (void) ThrowMagickException(resample_filter->exception,GetMagickModule(),
         ModuleError, "UnableToSetFilteringValue",
         "Fall back to Interpolated 'Point' filter");
    resample_filter->filter = PointFilter;
    resample_filter->do_interpolate = MagickTrue;
    return;  /* EWA turned off - nothing more to do */
  }

  /* Get the practical working support for the filter,
   * after any API call blur factors have been accoded for.
   */
#if EWA
  resample_filter->support = GetResizeFilterSupport(resize_filter);
#else
  resample_filter->support = 2.0;  /* fixed support size for HQ-EWA */
#endif

#if FILTER_LUT
  /* Fill the LUT with the weights from the selected filter function */
  { int
       Q;
    double
       r_scale;

    /* Scale radius so the filter LUT covers the full support range */
    r_scale = resample_filter->support*sqrt(1.0/(double)WLUT_WIDTH);
    for(Q=0; Q<WLUT_WIDTH; Q++)
      resample_filter->filter_lut[Q] = (double)
           GetResizeFilterWeight(resize_filter,sqrt((double)Q)*r_scale);

    /* finished with the resize filter */
    resize_filter = DestroyResizeFilter(resize_filter);
  }
#else
  /* save the filter and the scaled ellipse bounds needed for filter */
  resample_filter->filter_def = resize_filter;
  resample_filter->F = resample_filter->support*resample_filter->support;
#endif

  /*
    Adjust the scaling of the default unit circle
    This assumes that any real scaling changes will always
    take place AFTER the filter method has been initialized.
  */
  ScaleResampleFilter(resample_filter, 1.0, 0.0, 0.0, 1.0);

#if 0
  /*
    This is old code kept as a reference only. Basically it generates
    a Gaussian bell curve, with sigma = 0.5 if the support is 2.0

    Create Normal Gaussian 2D Filter Weighted Lookup Table.
    A normal EWA guassual lookup would use   exp(Q*ALPHA)
    where  Q = distance squared from 0.0 (center) to 1.0 (edge)
    and    ALPHA = -4.0*ln(2.0)  ==>  -2.77258872223978123767
    The table is of length 1024, and equates to support radius of 2.0
    thus needs to be scaled by  ALPHA*4/1024 and any blur factor squared

    The it comes from reference code provided by Fred Weinhaus.
  */
  r_scale = -2.77258872223978123767/(WLUT_WIDTH*blur*blur);
  for(Q=0; Q<WLUT_WIDTH; Q++)
    resample_filter->filter_lut[Q] = exp((double)Q*r_scale);
  resample_filter->support = WLUT_WIDTH;
#endif

#if FILTER_LUT
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp single
#endif
  {
    if (IsStringTrue(GetImageArtifact(resample_filter->image,
        "resample:verbose")) != MagickFalse)
      {
        int
          Q;
        double
          r_scale;

        /* Debug output of the filter weighting LUT
          Gnuplot the LUT data, the x scale index has been adjusted
            plot [0:2][-.2:1] "lut.dat" with lines
          The filter values should be normalized for comparision
        */
        printf("#\n");
        printf("# Resampling Filter LUT (%d values) for '%s' filter\n",
                   WLUT_WIDTH, CommandOptionToMnemonic(MagickFilterOptions,
                   resample_filter->filter) );
        printf("#\n");
        printf("# Note: values in table are using a squared radius lookup.\n");
        printf("# As such its distribution is not uniform.\n");
        printf("#\n");
        printf("# The X value is the support distance for the Y weight\n");
        printf("# so you can use gnuplot to plot this cylindrical filter\n");
        printf("#    plot [0:2][-.2:1] \"lut.dat\" with lines\n");
        printf("#\n");

        /* Scale radius so the filter LUT covers the full support range */
        r_scale = resample_filter->support*sqrt(1.0/(double)WLUT_WIDTH);
        for(Q=0; Q<WLUT_WIDTH; Q++)
          printf("%8.*g %.*g\n",
              GetMagickPrecision(),sqrt((double)Q)*r_scale,
              GetMagickPrecision(),resample_filter->filter_lut[Q] );
        printf("\n\n"); /* generate a 'break' in gnuplot if multiple outputs */
      }
    /* Output the above once only for each image, and each setting
    (void) DeleteImageArtifact(resample_filter->image,"resample:verbose");
    */
  }
#endif /* FILTER_LUT */
  return;
}

Project: ImageMagick
File: resample.c

MagickExport MagickBooleanType ResamplePixelColor(
  ResampleFilter *resample_filter,const double u0,const double v0,
  PixelInfo *pixel,ExceptionInfo *exception)
{
  MagickBooleanType
    status;

  ssize_t u,v, v1, v2, uw, hit;
  double u1;
  double U,V,Q,DQ,DDQ;
  double divisor_c,divisor_m;
  double weight;
  const Quantum *pixels;
  assert(resample_filter != (ResampleFilter *) NULL);
  assert(resample_filter->signature == MagickCoreSignature);

  status=MagickTrue;
  /* GetPixelInfo(resample_filter->image,pixel); */
  if ( resample_filter->do_interpolate ) {
    status=InterpolatePixelInfo(resample_filter->image,resample_filter->view,
      resample_filter->interpolate,u0,v0,pixel,resample_filter->exception);
    return(status);
  }

#if DEBUG_ELLIPSE
  (void) FormatLocaleFile(stderr, "u0=%lf; v0=%lf;\n", u0, v0);
#endif

  /*
    Does resample area Miss the image Proper?
    If and that area a simple solid color - then simply return that color!
    This saves a lot of calculation when resampling outside the bounds of
    the source image.

    However it probably should be expanded to image bounds plus the filters
    scaled support size.
  */
  hit = 0;
  switch ( resample_filter->virtual_pixel ) {
    case BackgroundVirtualPixelMethod:
    case TransparentVirtualPixelMethod:
    case BlackVirtualPixelMethod:
    case GrayVirtualPixelMethod:
    case WhiteVirtualPixelMethod:
    case MaskVirtualPixelMethod:
      if ( resample_filter->limit_reached
           || u0 + resample_filter->Ulimit < 0.0
           || u0 - resample_filter->Ulimit > (double) resample_filter->image->columns-1.0
           || v0 + resample_filter->Vlimit < 0.0
           || v0 - resample_filter->Vlimit > (double) resample_filter->image->rows-1.0
           )
        hit++;
      break;

    case UndefinedVirtualPixelMethod:
    case EdgeVirtualPixelMethod:
      if (    ( u0 + resample_filter->Ulimit < 0.0 && v0 + resample_filter->Vlimit < 0.0 )
           || ( u0 + resample_filter->Ulimit < 0.0
                && v0 - resample_filter->Vlimit > (double) resample_filter->image->rows-1.0 )
           || ( u0 - resample_filter->Ulimit > (double) resample_filter->image->columns-1.0
                && v0 + resample_filter->Vlimit < 0.0 )
           || ( u0 - resample_filter->Ulimit > (double) resample_filter->image->columns-1.0
                && v0 - resample_filter->Vlimit > (double) resample_filter->image->rows-1.0 )
           )
        hit++;
      break;
    case HorizontalTileVirtualPixelMethod:
      if (    v0 + resample_filter->Vlimit < 0.0
           || v0 - resample_filter->Vlimit > (double) resample_filter->image->rows-1.0
           )
        hit++;  /* outside the horizontally tiled images. */
      break;
    case VerticalTileVirtualPixelMethod:
      if (    u0 + resample_filter->Ulimit < 0.0
           || u0 - resample_filter->Ulimit > (double) resample_filter->image->columns-1.0
           )
        hit++;  /* outside the vertically tiled images. */
      break;
    case DitherVirtualPixelMethod:
      if (    ( u0 + resample_filter->Ulimit < -32.0 && v0 + resample_filter->Vlimit < -32.0 )
           || ( u0 + resample_filter->Ulimit < -32.0
                && v0 - resample_filter->Vlimit > (double) resample_filter->image->rows+31.0 )
           || ( u0 - resample_filter->Ulimit > (double) resample_filter->image->columns+31.0
                && v0 + resample_filter->Vlimit < -32.0 )
           || ( u0 - resample_filter->Ulimit > (double) resample_filter->image->columns+31.0
                && v0 - resample_filter->Vlimit > (double) resample_filter->image->rows+31.0 )
           )
        hit++;
      break;
    case TileVirtualPixelMethod:
    case MirrorVirtualPixelMethod:
    case RandomVirtualPixelMethod:
    case HorizontalTileEdgeVirtualPixelMethod:
    case VerticalTileEdgeVirtualPixelMethod:
    case CheckerTileVirtualPixelMethod:
      /* resampling of area is always needed - no VP limits */
      break;
  }
  if ( hit ) {
    /* The area being resampled is simply a solid color
     * just return a single lookup color.
     *
     * Should this return the users requested interpolated color?
     */
    status=InterpolatePixelInfo(resample_filter->image,resample_filter->view,
      IntegerInterpolatePixel,u0,v0,pixel,resample_filter->exception);
    return(status);
  }

  /*
    When Scaling limits reached, return an 'averaged' result.
  */
  if ( resample_filter->limit_reached ) {
    switch ( resample_filter->virtual_pixel ) {
      /*  This is always handled by the above, so no need.
        case BackgroundVirtualPixelMethod:
        case ConstantVirtualPixelMethod:
        case TransparentVirtualPixelMethod:
        case GrayVirtualPixelMethod,
        case WhiteVirtualPixelMethod
        case MaskVirtualPixelMethod:
      */
      case UndefinedVirtualPixelMethod:
      case EdgeVirtualPixelMethod:
      case DitherVirtualPixelMethod:
      case HorizontalTileEdgeVirtualPixelMethod:
      case VerticalTileEdgeVirtualPixelMethod:
        /* We need an average edge pixel, from the correct edge!
           How should I calculate an average edge color?
           Just returning an averaged neighbourhood,
           works well in general, but falls down for TileEdge methods.
           This needs to be done properly!!!!!!
        */
        status=InterpolatePixelInfo(resample_filter->image,
          resample_filter->view,AverageInterpolatePixel,u0,v0,pixel,
          resample_filter->exception);
        break;
      case HorizontalTileVirtualPixelMethod:
      case VerticalTileVirtualPixelMethod:
        /* just return the background pixel - Is there more direct way? */
        status=InterpolatePixelInfo(resample_filter->image,
          resample_filter->view,IntegerInterpolatePixel,-1.0,-1.0,pixel,
          resample_filter->exception);
        break;
      case TileVirtualPixelMethod:
      case MirrorVirtualPixelMethod:
      case RandomVirtualPixelMethod:
      case CheckerTileVirtualPixelMethod:
      default:
        /* generate a average color of the WHOLE image */
        if ( resample_filter->average_defined == MagickFalse ) {
          Image
            *average_image;

          CacheView
            *average_view;

          GetPixelInfo(resample_filter->image,(PixelInfo *)
            &resample_filter->average_pixel);
          resample_filter->average_defined=MagickTrue;

          /* Try to get an averaged pixel color of whole image */
          average_image=ResizeImage(resample_filter->image,1,1,BoxFilter,
            resample_filter->exception);
          if (average_image == (Image *) NULL)
            {
              *pixel=resample_filter->average_pixel; /* FAILED */
              break;
            }
          average_view=AcquireVirtualCacheView(average_image,exception);
          pixels=GetCacheViewVirtualPixels(average_view,0,0,1,1,
            resample_filter->exception);
          if (pixels == (const Quantum *) NULL) {
            average_view=DestroyCacheView(average_view);
            average_image=DestroyImage(average_image);
            *pixel=resample_filter->average_pixel; /* FAILED */
            break;
          }
          GetPixelInfoPixel(resample_filter->image,pixels,
            &(resample_filter->average_pixel));
          average_view=DestroyCacheView(average_view);
          average_image=DestroyImage(average_image);

          if ( resample_filter->virtual_pixel == CheckerTileVirtualPixelMethod )
            {
              /* CheckerTile is a alpha blend of the image's average pixel
                 color and the current background color */

              /* image's average pixel color */
              weight = QuantumScale*((double)
                resample_filter->average_pixel.alpha);
              resample_filter->average_pixel.red *= weight;
              resample_filter->average_pixel.green *= weight;
              resample_filter->average_pixel.blue *= weight;
              divisor_c = weight;

              /* background color */
              weight = QuantumScale*((double)
                resample_filter->image->background_color.alpha);
              resample_filter->average_pixel.red +=
                      weight*resample_filter->image->background_color.red;
              resample_filter->average_pixel.green +=
                      weight*resample_filter->image->background_color.green;
              resample_filter->average_pixel.blue +=
                      weight*resample_filter->image->background_color.blue;
              resample_filter->average_pixel.alpha +=
                      resample_filter->image->background_color.alpha;
              divisor_c += weight;

              /* alpha blend */
              resample_filter->average_pixel.red /= divisor_c;
              resample_filter->average_pixel.green /= divisor_c;
              resample_filter->average_pixel.blue /= divisor_c;
              resample_filter->average_pixel.alpha /= 2; /* 50% blend */

            }
        }
        *pixel=resample_filter->average_pixel;
        break;
    }
    return(status);
  }

  /*
    Initialize weighted average data collection
  */
  hit = 0;
  divisor_c = 0.0;
  divisor_m = 0.0;
  pixel->red = pixel->green = pixel->blue = 0.0;
  if (pixel->colorspace == CMYKColorspace)
    pixel->black = 0.0;
  if (pixel->alpha_trait != UndefinedPixelTrait)
    pixel->alpha = 0.0;

  /*
    Determine the parellelogram bounding box fitted to the ellipse
    centered at u0,v0.  This area is bounding by the lines...
  */
  v1 = (ssize_t)ceil(v0 - resample_filter->Vlimit);  /* range of scan lines */
  v2 = (ssize_t)floor(v0 + resample_filter->Vlimit);

  /* scan line start and width accross the parallelogram */
  u1 = u0 + (v1-v0)*resample_filter->slope - resample_filter->Uwidth;
  uw = (ssize_t)(2.0*resample_filter->Uwidth)+1;

#if DEBUG_ELLIPSE
  (void) FormatLocaleFile(stderr, "v1=%ld; v2=%ld\n", (long)v1, (long)v2);
  (void) FormatLocaleFile(stderr, "u1=%ld; uw=%ld\n", (long)u1, (long)uw);
#else
# define DEBUG_HIT_MISS 0 /* only valid if DEBUG_ELLIPSE is enabled */
#endif

  /*
    Do weighted resampling of all pixels,  within the scaled ellipse,
    bound by a Parellelogram fitted to the ellipse.
  */
  DDQ = 2*resample_filter->A;
  for( v=v1; v<=v2;  v++ ) {
#if DEBUG_HIT_MISS
    long uu = ceil(u1);   /* actual pixel location (for debug only) */
    (void) FormatLocaleFile(stderr, "# scan line from pixel %ld, %ld\n", (long)uu, (long)v);
#endif
    u = (ssize_t)ceil(u1);        /* first pixel in scanline */
    u1 += resample_filter->slope; /* start of next scan line */


    /* location of this first pixel, relative to u0,v0 */
    U = (double)u-u0;
    V = (double)v-v0;

    /* Q = ellipse quotent ( if Q<F then pixel is inside ellipse) */
    Q = (resample_filter->A*U + resample_filter->B*V)*U + resample_filter->C*V*V;
    DQ = resample_filter->A*(2.0*U+1) + resample_filter->B*V;

    /* get the scanline of pixels for this v */
    pixels=GetCacheViewVirtualPixels(resample_filter->view,u,v,(size_t) uw,
      1,resample_filter->exception);
    if (pixels == (const Quantum *) NULL)
      return(MagickFalse);

    /* count up the weighted pixel colors */
    for( u=0; u<uw; u++ ) {
#if FILTER_LUT
      /* Note that the ellipse has been pre-scaled so F = WLUT_WIDTH */
      if ( Q < (double)WLUT_WIDTH ) {
        weight = resample_filter->filter_lut[(int)Q];
#else
      /* Note that the ellipse has been pre-scaled so F = support^2 */
      if ( Q < (double)resample_filter->F ) {
        weight = GetResizeFilterWeight(resample_filter->filter_def,
             sqrt(Q));    /* a SquareRoot!  Arrggghhhhh... */
#endif

        pixel->alpha  += weight*GetPixelAlpha(resample_filter->image,pixels);
        divisor_m += weight;

        if (pixel->alpha_trait != UndefinedPixelTrait)
          weight *= QuantumScale*((double) GetPixelAlpha(resample_filter->image,pixels));
        pixel->red   += weight*GetPixelRed(resample_filter->image,pixels);
        pixel->green += weight*GetPixelGreen(resample_filter->image,pixels);
        pixel->blue  += weight*GetPixelBlue(resample_filter->image,pixels);
        if (pixel->colorspace == CMYKColorspace)
          pixel->black += weight*GetPixelBlack(resample_filter->image,pixels);
        divisor_c += weight;

        hit++;
#if DEBUG_HIT_MISS
        /* mark the pixel according to hit/miss of the ellipse */
        (void) FormatLocaleFile(stderr, "set arrow from %lf,%lf to %lf,%lf nohead ls 3\n",
                     (long)uu-.1,(double)v-.1,(long)uu+.1,(long)v+.1);
        (void) FormatLocaleFile(stderr, "set arrow from %lf,%lf to %lf,%lf nohead ls 3\n",
                     (long)uu+.1,(double)v-.1,(long)uu-.1,(long)v+.1);
      } else {
        (void) FormatLocaleFile(stderr, "set arrow from %lf,%lf to %lf,%lf nohead ls 1\n",
                     (long)uu-.1,(double)v-.1,(long)uu+.1,(long)v+.1);
        (void) FormatLocaleFile(stderr, "set arrow from %lf,%lf to %lf,%lf nohead ls 1\n",
                     (long)uu+.1,(double)v-.1,(long)uu-.1,(long)v+.1);
      }
      uu++;
#else
      }
#endif
      pixels+=GetPixelChannels(resample_filter->image);
      Q += DQ;
      DQ += DDQ;
    }
  }
#if DEBUG_ELLIPSE
  (void) FormatLocaleFile(stderr, "Hit=%ld;  Total=%ld;\n", (long)hit, (long)uw*(v2-v1) );
#endif

  /*
    Result sanity check -- this should NOT happen
  */
  if ( hit == 0 || divisor_m <= MagickEpsilon || divisor_c <= MagickEpsilon ) {
    /* not enough pixels, or bad weighting in resampling,
       resort to direct interpolation */
#if DEBUG_NO_PIXEL_HIT
    pixel->alpha = pixel->red = pixel->green = pixel->blue = 0;
    pixel->red = QuantumRange; /* show pixels for which EWA fails */
#else
    status=InterpolatePixelInfo(resample_filter->image,
      resample_filter->view,resample_filter->interpolate,u0,v0,pixel,
      resample_filter->exception);
#endif
    return status;
  }

  /*
    Finialize results of resampling
  */
  divisor_m = 1.0/divisor_m;
  if (pixel->alpha_trait != UndefinedPixelTrait)
    pixel->alpha = (double) ClampToQuantum(divisor_m*pixel->alpha);
  divisor_c = 1.0/divisor_c;
  pixel->red   = (double) ClampToQuantum(divisor_c*pixel->red);
  pixel->green = (double) ClampToQuantum(divisor_c*pixel->green);
  pixel->blue  = (double) ClampToQuantum(divisor_c*pixel->blue);
  if (pixel->colorspace == CMYKColorspace)
    pixel->black = (double) ClampToQuantum(divisor_c*pixel->black);
  return(MagickTrue);
}

Project: ImageMagick
File: resample.c

MagickExport void ScaleResampleFilter(ResampleFilter *resample_filter,
  const double dux,const double duy,const double dvx,const double dvy)
{
  double A,B,C,F;

  assert(resample_filter != (ResampleFilter *) NULL);
  assert(resample_filter->signature == MagickCoreSignature);

  resample_filter->limit_reached = MagickFalse;

  /* A 'point' filter forces use of interpolation instead of area sampling */
  if ( resample_filter->filter == PointFilter )
    return; /* EWA turned off - nothing to do */

#if DEBUG_ELLIPSE
  (void) FormatLocaleFile(stderr, "# -----\n" );
  (void) FormatLocaleFile(stderr, "dux=%lf; dvx=%lf;   duy=%lf; dvy=%lf;\n",
       dux, dvx, duy, dvy);
#endif

  /* Find Ellipse Coefficents such that
        A*u^2 + B*u*v + C*v^2 = F
     With u,v relative to point around which we are resampling.
     And the given scaling dx,dy vectors in u,v space
         du/dx,dv/dx   and  du/dy,dv/dy
  */
#if EWA
  /* Direct conversion of derivatives into elliptical coefficients
     However when magnifying images, the scaling vectors will be small
     resulting in a ellipse that is too small to sample properly.
     As such we need to clamp the major/minor axis to a minumum of 1.0
     to prevent it getting too small.
  */
#if EWA_CLAMP
  { double major_mag,
           minor_mag,
           major_x,
           major_y,
           minor_x,
           minor_y;

  ClampUpAxes(dux,dvx,duy,dvy, &major_mag, &minor_mag,
                &major_x, &major_y, &minor_x, &minor_y);
  major_x *= major_mag;  major_y *= major_mag;
  minor_x *= minor_mag;  minor_y *= minor_mag;
#if DEBUG_ELLIPSE
  (void) FormatLocaleFile(stderr, "major_x=%lf; major_y=%lf;  minor_x=%lf; minor_y=%lf;\n",
        major_x, major_y, minor_x, minor_y);
#endif
  A = major_y*major_y+minor_y*minor_y;
  B = -2.0*(major_x*major_y+minor_x*minor_y);
  C = major_x*major_x+minor_x*minor_x;
  F = major_mag*minor_mag;
  F *= F; /* square it */
  }
#else /* raw unclamped EWA */
  A = dvx*dvx+dvy*dvy;
  B = -2.0*(dux*dvx+duy*dvy);
  C = dux*dux+duy*duy;
  F = dux*dvy-duy*dvx;
  F *= F; /* square it */
#endif /* EWA_CLAMP */

#else /* HQ_EWA */
  /*
    This Paul Heckbert's "Higher Quality EWA" formula, from page 60 in his
    thesis, which adds a unit circle to the elliptical area so as to do both
    Reconstruction and Prefiltering of the pixels in the resampling.  It also
    means it is always likely to have at least 4 pixels within the area of the
    ellipse, for weighted averaging.  No scaling will result with F == 4.0 and
    a circle of radius 2.0, and F smaller than this means magnification is
    being used.

    NOTE: This method produces a very blury result at near unity scale while
    producing perfect results for strong minitification and magnifications.

    However filter support is fixed to 2.0 (no good for Windowed Sinc filters)
  */
  A = dvx*dvx+dvy*dvy+1;
  B = -2.0*(dux*dvx+duy*dvy);
  C = dux*dux+duy*duy+1;
  F = A*C - B*B/4;
#endif

#if DEBUG_ELLIPSE
  (void) FormatLocaleFile(stderr, "A=%lf; B=%lf; C=%lf; F=%lf\n", A,B,C,F);

  /* Figure out the various information directly about the ellipse.
     This information currently not needed at this time, but may be
     needed later for better limit determination.

     It is also good to have as a record for future debugging
  */
  { double alpha, beta, gamma, Major, Minor;
    double Eccentricity, Ellipse_Area, Ellipse_Angle;

    alpha = A+C;
    beta  = A-C;
    gamma = sqrt(beta*beta + B*B );

    if ( alpha - gamma <= MagickEpsilon )
      Major=MagickMaximumValue;
    else
      Major=sqrt(2*F/(alpha - gamma));
    Minor = sqrt(2*F/(alpha + gamma));

    (void) FormatLocaleFile(stderr, "# Major=%lf; Minor=%lf\n", Major, Minor );

    /* other information about ellipse include... */
    Eccentricity = Major/Minor;
    Ellipse_Area = MagickPI*Major*Minor;
    Ellipse_Angle = atan2(B, A-C);

    (void) FormatLocaleFile(stderr, "# Angle=%lf   Area=%lf\n",
         (double) RadiansToDegrees(Ellipse_Angle), Ellipse_Area);
  }
#endif

  /* If one or both of the scaling vectors is impossibly large
     (producing a very large raw F value), we may as well not bother
     doing any form of resampling since resampled area is very large.
     In this case some alternative means of pixel sampling, such as
     the average of the whole image is needed to get a reasonable
     result. Calculate only as needed.
  */
  if ( (4*A*C - B*B) > MagickMaximumValue ) {
    resample_filter->limit_reached = MagickTrue;
    return;
  }

  /* Scale ellipse to match the filters support
     (that is, multiply F by the square of the support)
     Simplier to just multiply it by the support twice!
  */
  F *= resample_filter->support;
  F *= resample_filter->support;

  /* Orthogonal bounds of the ellipse */
  resample_filter->Ulimit = sqrt(C*F/(A*C-0.25*B*B));
  resample_filter->Vlimit = sqrt(A*F/(A*C-0.25*B*B));

  /* Horizontally aligned parallelogram fitted to Ellipse */
  resample_filter->Uwidth = sqrt(F/A); /* Half of the parallelogram width */
  resample_filter->slope = -B/(2.0*A); /* Reciprocal slope of the parallelogram */

#if DEBUG_ELLIPSE
  (void) FormatLocaleFile(stderr, "Ulimit=%lf; Vlimit=%lf; UWidth=%lf; Slope=%lf;\n",
           resample_filter->Ulimit, resample_filter->Vlimit,
           resample_filter->Uwidth, resample_filter->slope );
#endif

  /* Check the absolute area of the parallelogram involved.
   * This limit needs more work, as it is too slow for larger images
   * with tiled views of the horizon.
  */
  if ( (resample_filter->Uwidth * resample_filter->Vlimit)
         > (4.0*resample_filter->image_area)) {
    resample_filter->limit_reached = MagickTrue;
    return;
  }

  /* Scale ellipse formula to directly index the Filter Lookup Table */
  { double scale;
#if FILTER_LUT
    /* scale so that F = WLUT_WIDTH; -- hardcoded */
    scale=(double) WLUT_WIDTH*PerceptibleReciprocal(F);
#else
    /* scale so that F = resample_filter->F (support^2) */
    scale=resample_filter->F*PerceptibleReciprocal(F);
#endif
    resample_filter->A = A*scale;
    resample_filter->B = B*scale;
    resample_filter->C = C*scale;
  }
}