]> granicus.if.org Git - imagemagick/blobdiff - MagickCore/shear.c
Fix CLUT interpolation method
[imagemagick] / MagickCore / shear.c
index da0f8b2270e4d231fdc832e51e35d8baad685260..024de5c5437f5f8bcd93b6d6808cde2323b27417 100644 (file)
@@ -17,7 +17,7 @@
 %                                  July 1992                                  %
 %                                                                             %
 %                                                                             %
-%  Copyright 1999-2011 ImageMagick Studio LLC, a non-profit organization      %
+%  Copyright 1999-2012 ImageMagick Studio LLC, a non-profit organization      %
 %  dedicated to making software imaging solutions freely available.           %
 %                                                                             %
 %  You may not use this file except in compliance with the License.  You may  %
 %                                                                             %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %
-%  The RotateImage, XShearImage, and YShearImage methods are based on the
-%  paper "A Fast Algorithm for General Raster Rotatation" by Alan W. Paeth,
-%  Graphics Interface '86 (Vancouver).  RotateImage is adapted from a similar
+%  The XShearImage() and YShearImage() methods are based on the paper "A Fast
+%  Algorithm for General Raster Rotatation" by Alan W. Paeth, Graphics
+%  Interface '86 (Vancouver).  ShearRotateImage() is adapted from a similar
 %  method based on the Paeth paper written by Michael Halle of the Spatial
 %  Imaging Group, MIT Media Lab.
 %
-%
 */
 \f
 /*
 %                                                                             %
 %                                                                             %
 %                                                                             %
-%     A f f i n e T r a n s f o r m I m a g e                                 %
-%                                                                             %
-%                                                                             %
-%                                                                             %
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%  AffineTransformImage() transforms an image as dictated by the affine matrix.
-%  It allocates the memory necessary for the new Image structure and returns
-%  a pointer to the new image.
-%
-%  The format of the AffineTransformImage method is:
-%
-%      Image *AffineTransformImage(const Image *image,
-%        AffineMatrix *affine_matrix,ExceptionInfo *exception)
-%
-%  A description of each parameter follows:
-%
-%    o image: the image.
-%
-%    o affine_matrix: the affine matrix.
-%
-%    o exception: return any errors or warnings in this structure.
-%
-*/
-MagickExport Image *AffineTransformImage(const Image *image,
-  const AffineMatrix *affine_matrix,ExceptionInfo *exception)
-{
-  double
-    distort[6];
-
-  Image
-    *deskew_image;
-
-  /*
-    Affine transform image.
-  */
-  assert(image->signature == MagickSignature);
-  if (image->debug != MagickFalse)
-    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
-  assert(affine_matrix != (AffineMatrix *) NULL);
-  assert(exception != (ExceptionInfo *) NULL);
-  assert(exception->signature == MagickSignature);
-  distort[0]=affine_matrix->sx;
-  distort[1]=affine_matrix->rx;
-  distort[2]=affine_matrix->ry;
-  distort[3]=affine_matrix->sy;
-  distort[4]=affine_matrix->tx;
-  distort[5]=affine_matrix->ty;
-  deskew_image=DistortImage(image,AffineProjectionDistortion,6,distort,
-    MagickTrue,exception);
-  return(deskew_image);
-}
-\f
-/*
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%                                                                             %
-%                                                                             %
-%                                                                             %
 +   C r o p T o F i t I m a g e                                               %
 %                                                                             %
 %                                                                             %
@@ -631,7 +572,7 @@ static void RadonProjection(RadonInfo *source_cells,
     q=swap;
   }
 #if defined(MAGICKCORE_OPENMP_SUPPORT)
-  #pragma omp parallel for schedule(dynamic,4)
+  #pragma omp parallel for schedule(static,4)
 #endif
   for (x=0; x < (ssize_t) p->width; x++)
   {
@@ -711,7 +652,7 @@ static MagickBooleanType RadonTransform(const Image *image,
   status=MagickTrue;
   image_view=AcquireCacheView(image);
 #if defined(MAGICKCORE_OPENMP_SUPPORT)
-  #pragma omp parallel for schedule(dynamic,4) shared(status)
+  #pragma omp parallel for schedule(static,4) shared(status)
 #endif
   for (y=0; y < (ssize_t) image->rows; y++)
   {
@@ -760,7 +701,7 @@ static MagickBooleanType RadonTransform(const Image *image,
   RadonProjection(source_cells,destination_cells,-1,projection);
   (void) ResetRadonCells(source_cells);
 #if defined(MAGICKCORE_OPENMP_SUPPORT)
-  #pragma omp parallel for schedule(dynamic,4) shared(status)
+  #pragma omp parallel for schedule(static,4) shared(status)
 #endif
   for (y=0; y < (ssize_t) image->rows; y++)
   {
@@ -940,7 +881,8 @@ MagickExport Image *DeskewImage(const Image *image,const double threshold,
   clone_image=CloneImage(image,0,0,MagickTrue,exception);
   if (clone_image == (Image *) NULL)
     return((Image *) NULL);
-  (void) SetImageVirtualPixelMethod(clone_image,BackgroundVirtualPixelMethod);
+  (void) SetImageVirtualPixelMethod(clone_image,BackgroundVirtualPixelMethod,
+    exception);
   degrees=RadiansToDegrees(-atan((double) skew/width/8));
   if (image->debug != MagickFalse)
     (void) LogMagickEvent(TransformEvent,GetMagickModule(),
@@ -989,7 +931,7 @@ MagickExport Image *DeskewImage(const Image *image,const double threshold,
 %                                                                             %
 %                                                                             %
 %                                                                             %
-+   I n t e g r a l R o t a t e I m a g e                                     %
+%   I n t e g r a l R o t a t e I m a g e                                     %
 %                                                                             %
 %                                                                             %
 %                                                                             %
@@ -1011,7 +953,7 @@ MagickExport Image *DeskewImage(const Image *image,const double threshold,
 %    o rotations: Specifies the number of 90 degree rotations.
 %
 */
-static Image *IntegralRotateImage(const Image *image,size_t rotations,
+MagickExport Image *IntegralRotateImage(const Image *image,size_t rotations,
   ExceptionInfo *exception)
 {
 #define RotateImageTag  "Rotate/Image"
@@ -1080,9 +1022,8 @@ static Image *IntegralRotateImage(const Image *image,size_t rotations,
         Rotate 90 degrees.
       */
       GetPixelCacheTileSize(image,&tile_width,&tile_height);
-      tile_width=image->columns;
 #if defined(MAGICKCORE_OPENMP_SUPPORT)
-      #pragma omp parallel for schedule(dynamic,4) shared(progress, status) omp_throttle(1)
+      #pragma omp parallel for schedule(static,4) shared(progress,status)
 #endif
       for (tile_y=0; tile_y < (ssize_t) image->rows; tile_y+=(ssize_t) tile_height)
       {
@@ -1147,6 +1088,12 @@ static Image *IntegralRotateImage(const Image *image,size_t rotations,
               register ssize_t
                 i;
 
+              if (GetPixelMask(image,tile_pixels) != 0)
+                {
+                  tile_pixels-=width*GetPixelChannels(image);
+                  q+=GetPixelChannels(rotate_image);
+                  continue;
+                }
               for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
               {
                 PixelChannel
@@ -1156,8 +1103,8 @@ static Image *IntegralRotateImage(const Image *image,size_t rotations,
                   rotate_traits,
                   traits;
 
-                traits=GetPixelChannelMapTraits(image,(PixelChannel) i);
-                channel=GetPixelChannelMapChannel(image,(PixelChannel) i);
+                channel=GetPixelChannelMapChannel(image,i);
+                traits=GetPixelChannelMapTraits(image,channel);
                 rotate_traits=GetPixelChannelMapTraits(rotate_image,channel);
                 if ((traits == UndefinedPixelTrait) ||
                     (rotate_traits == UndefinedPixelTrait))
@@ -1200,7 +1147,7 @@ static Image *IntegralRotateImage(const Image *image,size_t rotations,
         Rotate 180 degrees.
       */
 #if defined(MAGICKCORE_OPENMP_SUPPORT)
-      #pragma omp parallel for schedule(dynamic,4) shared(progress,status) omp_throttle(1)
+      #pragma omp parallel for schedule(static) shared(progress,status)
 #endif
       for (y=0; y < (ssize_t) image->rows; y++)
       {
@@ -1233,6 +1180,11 @@ static Image *IntegralRotateImage(const Image *image,size_t rotations,
             i;
 
           q-=GetPixelChannels(rotate_image);
+          if (GetPixelMask(image,p) != 0)
+            {
+              p+=GetPixelChannels(image);
+              continue;
+            }
           for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
           {
             PixelChannel
@@ -1242,8 +1194,8 @@ static Image *IntegralRotateImage(const Image *image,size_t rotations,
               rotate_traits,
               traits;
 
-            traits=GetPixelChannelMapTraits(image,(PixelChannel) i);
-            channel=GetPixelChannelMapChannel(image,(PixelChannel) i);
+            channel=GetPixelChannelMapChannel(image,i);
+            traits=GetPixelChannelMapTraits(image,channel);
             rotate_traits=GetPixelChannelMapTraits(rotate_image,channel);
             if ((traits == UndefinedPixelTrait) ||
                 (rotate_traits == UndefinedPixelTrait))
@@ -1290,9 +1242,8 @@ static Image *IntegralRotateImage(const Image *image,size_t rotations,
         Rotate 270 degrees.
       */
       GetPixelCacheTileSize(image,&tile_width,&tile_height);
-      tile_width=image->columns;
 #if defined(MAGICKCORE_OPENMP_SUPPORT)
-      #pragma omp parallel for schedule(dynamic,4) shared(progress,status) omp_throttle(1)
+      #pragma omp parallel for schedule(static,4) shared(progress,status)
 #endif
       for (tile_y=0; tile_y < (ssize_t) image->rows; tile_y+=(ssize_t) tile_height)
       {
@@ -1356,6 +1307,12 @@ static Image *IntegralRotateImage(const Image *image,size_t rotations,
               register ssize_t
                 i;
 
+              if (GetPixelMask(image,tile_pixels) != 0)
+                {
+                  tile_pixels+=width*GetPixelChannels(image);
+                  q+=GetPixelChannels(rotate_image);
+                  continue;
+                }
               for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
               {
                 PixelChannel
@@ -1365,8 +1322,8 @@ static Image *IntegralRotateImage(const Image *image,size_t rotations,
                   rotate_traits,
                   traits;
 
-                traits=GetPixelChannelMapTraits(image,(PixelChannel) i);
-                channel=GetPixelChannelMapChannel(image,(PixelChannel) i);
+                channel=GetPixelChannelMapChannel(image,i);
+                traits=GetPixelChannelMapTraits(image,channel);
                 rotate_traits=GetPixelChannelMapTraits(rotate_image,channel);
                 if ((traits == UndefinedPixelTrait) ||
                     (rotate_traits == UndefinedPixelTrait))
@@ -1488,7 +1445,7 @@ static MagickBooleanType XShearImage(Image *image,const MagickRealType degrees,
   progress=0;
   image_view=AcquireCacheView(image);
 #if defined(MAGICKCORE_OPENMP_SUPPORT)
-  #pragma omp parallel for schedule(dynamic,4) shared(progress, status)
+  #pragma omp parallel for schedule(static,4) shared(progress,status)
 #endif
   for (y=0; y < (ssize_t) height; y++)
   {
@@ -1555,25 +1512,25 @@ static MagickBooleanType XShearImage(Image *image,const MagickRealType degrees,
           if ((x_offset+i) < step)
             {
               p+=GetPixelChannels(image);
-              SetPixelInfo(image,p,&pixel);
+              GetPixelInfoPixel(image,p,&pixel);
               q+=GetPixelChannels(image);
               continue;
             }
-          SetPixelInfo(image,p,&source);
+          GetPixelInfoPixel(image,p,&source);
           CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
             &source,(MagickRealType) GetPixelAlpha(image,p),area,&destination);
-          SetPixelPixelInfo(image,&destination,q);
-          SetPixelInfo(image,p,&pixel);
+          SetPixelInfoPixel(image,&destination,q);
+          GetPixelInfoPixel(image,p,&pixel);
           p+=GetPixelChannels(image);
           q+=GetPixelChannels(image);
         }
         CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
           &background,(MagickRealType) background.alpha,area,&destination);
-        SetPixelPixelInfo(image,&destination,q);
+        SetPixelInfoPixel(image,&destination,q);
         q+=GetPixelChannels(image);
         for (i=0; i < (step-1); i++)
         {
-          SetPixelPixelInfo(image,&background,q);
+          SetPixelInfoPixel(image,&background,q);
           q+=GetPixelChannels(image);
         }
         break;
@@ -1591,20 +1548,20 @@ static MagickBooleanType XShearImage(Image *image,const MagickRealType degrees,
           q-=GetPixelChannels(image);
           if ((size_t) (x_offset+width+step-i) >= image->columns)
             continue;
-          SetPixelInfo(image,p,&source);
+          GetPixelInfoPixel(image,p,&source);
           CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
             &source,(MagickRealType) GetPixelAlpha(image,p),area,&destination);
-          SetPixelPixelInfo(image,&destination,q);
-          SetPixelInfo(image,p,&pixel);
+          SetPixelInfoPixel(image,&destination,q);
+          GetPixelInfoPixel(image,p,&pixel);
         }
         CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
           &background,(MagickRealType) background.alpha,area,&destination);
         q-=GetPixelChannels(image);
-        SetPixelPixelInfo(image,&destination,q);
+        SetPixelInfoPixel(image,&destination,q);
         for (i=0; i < (step-1); i++)
         {
           q-=GetPixelChannels(image);
-          SetPixelPixelInfo(image,&background,q);
+          SetPixelInfoPixel(image,&background,q);
         }
         break;
       }
@@ -1703,7 +1660,7 @@ static MagickBooleanType YShearImage(Image *image,const MagickRealType degrees,
   background=image->background_color;
   image_view=AcquireCacheView(image);
 #if defined(MAGICKCORE_OPENMP_SUPPORT)
-  #pragma omp parallel for schedule(dynamic,4) shared(progress, status)
+  #pragma omp parallel for schedule(static,4) shared(progress,status)
 #endif
   for (x=0; x < (ssize_t) width; x++)
   {
@@ -1770,26 +1727,26 @@ static MagickBooleanType YShearImage(Image *image,const MagickRealType degrees,
           if ((y_offset+i) < step)
             {
               p+=GetPixelChannels(image);
-              SetPixelInfo(image,p,&pixel);
+              GetPixelInfoPixel(image,p,&pixel);
               q+=GetPixelChannels(image);
               continue;
             }
-          SetPixelInfo(image,p,&source);
+          GetPixelInfoPixel(image,p,&source);
           CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
             &source,(MagickRealType) GetPixelAlpha(image,p),area,
             &destination);
-          SetPixelPixelInfo(image,&destination,q);
-          SetPixelInfo(image,p,&pixel);
+          SetPixelInfoPixel(image,&destination,q);
+          GetPixelInfoPixel(image,p,&pixel);
           p+=GetPixelChannels(image);
           q+=GetPixelChannels(image);
         }
         CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
           &background,(MagickRealType) background.alpha,area,&destination);
-        SetPixelPixelInfo(image,&destination,q);
+        SetPixelInfoPixel(image,&destination,q);
         q+=GetPixelChannels(image);
         for (i=0; i < (step-1); i++)
         {
-          SetPixelPixelInfo(image,&background,q);
+          SetPixelInfoPixel(image,&background,q);
           q+=GetPixelChannels(image);
         }
         break;
@@ -1807,21 +1764,21 @@ static MagickBooleanType YShearImage(Image *image,const MagickRealType degrees,
           q-=GetPixelChannels(image);
           if ((size_t) (y_offset+height+step-i) >= image->rows)
             continue;
-          SetPixelInfo(image,p,&source);
+          GetPixelInfoPixel(image,p,&source);
           CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
             &source,(MagickRealType) GetPixelAlpha(image,p),area,
             &destination);
-          SetPixelPixelInfo(image,&destination,q);
-          SetPixelInfo(image,p,&pixel);
+          SetPixelInfoPixel(image,&destination,q);
+          GetPixelInfoPixel(image,p,&pixel);
         }
         CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
           &background,(MagickRealType) background.alpha,area,&destination);
         q-=GetPixelChannels(image);
-        SetPixelPixelInfo(image,&destination,q);
+        SetPixelInfoPixel(image,&destination,q);
         for (i=0; i < (step-1); i++)
         {
           q-=GetPixelChannels(image);
-          SetPixelPixelInfo(image,&background,q);
+          SetPixelInfoPixel(image,&background,q);
         }
         break;
       }
@@ -1850,79 +1807,6 @@ static MagickBooleanType YShearImage(Image *image,const MagickRealType degrees,
 %                                                                             %
 %                                                                             %
 %                                                                             %
-%   R o t a t e I m a g e                                                     %
-%                                                                             %
-%                                                                             %
-%                                                                             %
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%  RotateImage() creates a new image that is a rotated copy of an existing
-%  one.  Positive angles rotate counter-clockwise (right-hand rule), while
-%  negative angles rotate clockwise.  Rotated images are usually larger than
-%  the originals and have 'empty' triangular corners.  X axis.  Empty
-%  triangles left over from shearing the image are filled with the background
-%  color defined by member 'background_color' of the image.  RotateImage
-%  allocates the memory necessary for the new Image structure and returns a
-%  pointer to the new image.
-%
-%  The format of the RotateImage method is:
-%
-%      Image *RotateImage(const Image *image,const double degrees,
-%        ExceptionInfo *exception)
-%
-%  A description of each parameter follows.
-%
-%    o image: the image.
-%
-%    o degrees: Specifies the number of degrees to rotate the image.
-%
-%    o exception: return any errors or warnings in this structure.
-%
-*/
-MagickExport Image *RotateImage(const Image *image,const double degrees,
-  ExceptionInfo *exception)
-{
-  Image
-    *rotate_image;
-
-  MagickRealType
-    angle;
-
-  PointInfo
-    shear;
-
-  size_t
-    rotations;
-
-  /*
-    Adjust rotation angle.
-  */
-  assert(image != (Image *) NULL);
-  assert(image->signature == MagickSignature);
-  if (image->debug != MagickFalse)
-    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
-  assert(exception != (ExceptionInfo *) NULL);
-  assert(exception->signature == MagickSignature);
-  angle=degrees;
-  while (angle < -45.0)
-    angle+=360.0;
-  for (rotations=0; angle > 45.0; rotations++)
-    angle-=90.0;
-  rotations%=4;
-  shear.x=(-tan((double) DegreesToRadians(angle)/2.0));
-  shear.y=sin((double) DegreesToRadians(angle));
-  if ((fabs(shear.x) < MagickEpsilon) && (fabs(shear.y) < MagickEpsilon))
-    return(IntegralRotateImage(image,rotations,exception));
-  rotate_image=DistortImage(image,ScaleRotateTranslateDistortion,1,&degrees,
-    MagickTrue,exception);
-  return(rotate_image);
-}
-\f
-/*
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%                                                                             %
-%                                                                             %
-%                                                                             %
 %   S h e a r I m a g e                                                       %
 %                                                                             %
 %                                                                             %
@@ -2057,3 +1941,167 @@ MagickExport Image *ShearImage(const Image *image,const double x_shear,
   shear_image->page.height=0;
   return(shear_image);
 }
+\f
+/*
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%                                                                             %
+%                                                                             %
+%                                                                             %
+%   S h e a r R o t a t e I m a g e                                           %
+%                                                                             %
+%                                                                             %
+%                                                                             %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%  ShearRotateImage() creates a new image that is a rotated copy of an existing
+%  one.  Positive angles rotate counter-clockwise (right-hand rule), while
+%  negative angles rotate clockwise.  Rotated images are usually larger than
+%  the originals and have 'empty' triangular corners.  X axis.  Empty
+%  triangles left over from shearing the image are filled with the background
+%  color defined by member 'background_color' of the image.  ShearRotateImage
+%  allocates the memory necessary for the new Image structure and returns a
+%  pointer to the new image.
+%
+%  ShearRotateImage() is based on the paper "A Fast Algorithm for General
+%  Raster Rotatation" by Alan W. Paeth.  ShearRotateImage is adapted from a
+%  similar method based on the Paeth paper written by Michael Halle of the
+%  Spatial Imaging Group, MIT Media Lab.
+%
+%  The format of the ShearRotateImage method is:
+%
+%      Image *ShearRotateImage(const Image *image,const double degrees,
+%        ExceptionInfo *exception)
+%
+%  A description of each parameter follows.
+%
+%    o image: the image.
+%
+%    o degrees: Specifies the number of degrees to rotate the image.
+%
+%    o exception: return any errors or warnings in this structure.
+%
+*/
+MagickExport Image *ShearRotateImage(const Image *image,const double degrees,
+  ExceptionInfo *exception)
+{
+  Image
+    *integral_image,
+    *rotate_image;
+
+  MagickBooleanType
+    status;
+
+  MagickRealType
+    angle;
+
+  PointInfo
+    shear;
+
+  RectangleInfo
+    border_info;
+
+  size_t
+    height,
+    rotations,
+    width,
+    y_width;
+
+  ssize_t
+    x_offset,
+    y_offset;
+
+  /*
+    Adjust rotation angle.
+  */
+  assert(image != (Image *) NULL);
+  assert(image->signature == MagickSignature);
+  if (image->debug != MagickFalse)
+    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
+  assert(exception != (ExceptionInfo *) NULL);
+  assert(exception->signature == MagickSignature);
+  angle=degrees;
+  while (angle < -45.0)
+    angle+=360.0;
+  for (rotations=0; angle > 45.0; rotations++)
+    angle-=90.0;
+  rotations%=4;
+  /*
+    Calculate shear equations.
+  */
+  integral_image=IntegralRotateImage(image,rotations,exception);
+  if (integral_image == (Image *) NULL)
+    ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
+  shear.x=(-tan((double) DegreesToRadians(angle)/2.0));
+  shear.y=sin((double) DegreesToRadians(angle));
+  if ((shear.x == 0.0) && (shear.y == 0.0))
+    return(integral_image);
+  if (SetImageStorageClass(integral_image,DirectClass,exception) == MagickFalse)
+    {
+      integral_image=DestroyImage(integral_image);
+      return(integral_image);
+    }
+  if (integral_image->matte == MagickFalse)
+    (void) SetImageAlphaChannel(integral_image,OpaqueAlphaChannel,exception);
+  /*
+    Compute image size.
+  */
+  width=image->columns;
+  height=image->rows;
+  if ((rotations == 1) || (rotations == 3))
+    {
+      width=image->rows;
+      height=image->columns;
+    }
+  y_width=width+(ssize_t) floor(fabs(shear.x)*height+0.5);
+  x_offset=(ssize_t) ceil((double) width+((fabs(shear.y)*height)-width)/2.0-
+    0.5);
+  y_offset=(ssize_t) ceil((double) height+((fabs(shear.y)*y_width)-height)/2.0-
+    0.5);
+  /*
+    Surround image with a border.
+  */
+  integral_image->border_color=integral_image->background_color;
+  integral_image->compose=CopyCompositeOp;
+  border_info.width=(size_t) x_offset;
+  border_info.height=(size_t) y_offset;
+  rotate_image=BorderImage(integral_image,&border_info,image->compose,
+    exception);
+  integral_image=DestroyImage(integral_image);
+  if (rotate_image == (Image *) NULL)
+    ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
+  /*
+    Rotate the image.
+  */
+  status=XShearImage(rotate_image,shear.x,width,height,x_offset,(ssize_t)
+    (rotate_image->rows-height)/2,exception);
+  if (status == MagickFalse)
+    {
+      rotate_image=DestroyImage(rotate_image);
+      return((Image *) NULL);
+    }
+  status=YShearImage(rotate_image,shear.y,y_width,height,(ssize_t)
+    (rotate_image->columns-y_width)/2,y_offset,exception);
+  if (status == MagickFalse)
+    {
+      rotate_image=DestroyImage(rotate_image);
+      return((Image *) NULL);
+    }
+  status=XShearImage(rotate_image,shear.x,y_width,rotate_image->rows,(ssize_t)
+    (rotate_image->columns-y_width)/2,0,exception);
+  if (status == MagickFalse)
+    {
+      rotate_image=DestroyImage(rotate_image);
+      return((Image *) NULL);
+    }
+  status=CropToFitImage(&rotate_image,shear.x,shear.y,(MagickRealType) width,
+    (MagickRealType) height,MagickTrue,exception);
+  if (status == MagickFalse)
+    {
+      rotate_image=DestroyImage(rotate_image);
+      return((Image *) NULL);
+    }
+  rotate_image->compose=image->compose;
+  rotate_image->page.width=0;
+  rotate_image->page.height=0;
+  return(rotate_image);
+}