root/magick/shear.c

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DEFINITIONS

This source file includes following definitions.
  1. AffineTransformImage
  2. CropToFitImage
  3. DestroyRadonInfo
  4. ResetRadonCells
  5. AcquireRadonInfo
  6. MagickMin
  7. ReadRadonCell
  8. WriteRadonCell
  9. GetRadonCell
  10. SetRadonCell
  11. RadonProjection
  12. RadonTransform
  13. GetImageBackgroundColor
  14. DeskewImage
  15. IntegralRotateImage
  16. XShearImage
  17. YShearImage
  18. RotateImage
  19. ShearImage

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%                      SSSSS  H   H  EEEEE   AAA    RRRR                      %
%                      SS     H   H  E      A   A   R   R                     %
%                       SSS   HHHHH  EEE    AAAAA   RRRR                      %
%                         SS  H   H  E      A   A   R R                       %
%                      SSSSS  H   H  EEEEE  A   A   R  R                      %
%                                                                             %
%                                                                             %
%    MagickCore Methods to Shear or Rotate an Image by an Arbitrary Angle     %
%                                                                             %
%                               Software Design                               %
%                                 John Cristy                                 %
%                                  July 1992                                  %
%                                                                             %
%                                                                             %
%  Copyright 1999-2011 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  %
%  obtain a copy of the License at                                            %
%                                                                             %
%    http://www.imagemagick.org/script/license.php                            %
%                                                                             %
%  Unless required by applicable law or agreed to in writing, software        %
%  distributed under the License is distributed on an "AS IS" BASIS,          %
%  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.   %
%  See the License for the specific language governing permissions and        %
%  limitations under the License.                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  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
%  method based on the Paeth paper written by Michael Halle of the Spatial
%  Imaging Group, MIT Media Lab.
%
%
*/

/*
  Include declarations.
*/
#include "magick/studio.h"
#include "magick/artifact.h"
#include "magick/attribute.h"
#include "magick/blob-private.h"
#include "magick/cache-private.h"
#include "magick/color-private.h"
#include "magick/colorspace-private.h"
#include "magick/composite.h"
#include "magick/composite-private.h"
#include "magick/decorate.h"
#include "magick/distort.h"
#include "magick/draw.h"
#include "magick/exception.h"
#include "magick/exception-private.h"
#include "magick/gem.h"
#include "magick/geometry.h"
#include "magick/image.h"
#include "magick/image-private.h"
#include "magick/memory_.h"
#include "magick/list.h"
#include "magick/monitor.h"
#include "magick/monitor-private.h"
#include "magick/pixel-private.h"
#include "magick/quantum.h"
#include "magick/resource_.h"
#include "magick/shear.h"
#include "magick/statistic.h"
#include "magick/string_.h"
#include "magick/string-private.h"
#include "magick/thread-private.h"
#include "magick/threshold.h"
#include "magick/transform.h"

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%     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);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
+   C r o p T o F i t I m a g e                                               %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  CropToFitImage() crops the sheared image as determined by the bounding box
%  as defined by width and height and shearing angles.
%
%  The format of the CropToFitImage method is:
%
%      MagickBooleanType CropToFitImage(Image **image,
%        const MagickRealType x_shear,const MagickRealType x_shear,
%        const MagickRealType width,const MagickRealType height,
%        const MagickBooleanType rotate,ExceptionInfo *exception)
%
%  A description of each parameter follows.
%
%    o image: the image.
%
%    o x_shear, y_shear, width, height: Defines a region of the image to crop.
%
%    o exception: return any errors or warnings in this structure.
%
*/
static MagickBooleanType CropToFitImage(Image **image,
  const MagickRealType x_shear,const MagickRealType y_shear,
  const MagickRealType width,const MagickRealType height,
  const MagickBooleanType rotate,ExceptionInfo *exception)
{
  Image
    *crop_image;

  PointInfo
    extent[4],
    min,
    max;

  RectangleInfo
    geometry,
    page;

  register ssize_t
    i;

  /*
    Calculate the rotated image size.
  */
  extent[0].x=(double) (-width/2.0);
  extent[0].y=(double) (-height/2.0);
  extent[1].x=(double) width/2.0;
  extent[1].y=(double) (-height/2.0);
  extent[2].x=(double) (-width/2.0);
  extent[2].y=(double) height/2.0;
  extent[3].x=(double) width/2.0;
  extent[3].y=(double) height/2.0;
  for (i=0; i < 4; i++)
  {
    extent[i].x+=x_shear*extent[i].y;
    extent[i].y+=y_shear*extent[i].x;
    if (rotate != MagickFalse)
      extent[i].x+=x_shear*extent[i].y;
    extent[i].x+=(double) (*image)->columns/2.0;
    extent[i].y+=(double) (*image)->rows/2.0;
  }
  min=extent[0];
  max=extent[0];
  for (i=1; i < 4; i++)
  {
    if (min.x > extent[i].x)
      min.x=extent[i].x;
    if (min.y > extent[i].y)
      min.y=extent[i].y;
    if (max.x < extent[i].x)
      max.x=extent[i].x;
    if (max.y < extent[i].y)
      max.y=extent[i].y;
  }
  geometry.x=(ssize_t) ceil(min.x-0.5);
  geometry.y=(ssize_t) ceil(min.y-0.5);
  geometry.width=(size_t) floor(max.x-min.x+0.5);
  geometry.height=(size_t) floor(max.y-min.y+0.5);
  page=(*image)->page;
  (void) ParseAbsoluteGeometry("0x0+0+0",&(*image)->page);
  crop_image=CropImage(*image,&geometry,exception);
  if (crop_image == (Image *) NULL)
    return(MagickFalse);
  crop_image->page=page;
  *image=DestroyImage(*image);
  *image=crop_image;
  return(MagickTrue);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%     D e s k e w I m a g e                                                   %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  DeskewImage() removes skew from the image.  Skew is an artifact that
%  occurs in scanned images because of the camera being misaligned,
%  imperfections in the scanning or surface, or simply because the paper was
%  not placed completely flat when scanned.
%
%  The format of the DeskewImage method is:
%
%      Image *DeskewImage(const Image *image,const double threshold,
%        ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o threshold: separate background from foreground.
%
%    o exception: return any errors or warnings in this structure.
%
*/

typedef struct _RadonInfo
{
  CacheType
    type;

  size_t
    width,
    height;

  MagickSizeType
    length;

  MagickBooleanType
    mapped;

  char
    path[MaxTextExtent];

  int
    file;

  unsigned short
    *cells;
} RadonInfo;

static RadonInfo *DestroyRadonInfo(RadonInfo *radon_info)
{
  assert(radon_info != (RadonInfo *) NULL);
  switch (radon_info->type)
  {
    case MemoryCache:
    {
      if (radon_info->mapped == MagickFalse)
        radon_info->cells=(unsigned short *) RelinquishMagickMemory(
          radon_info->cells);
      else
        radon_info->cells=(unsigned short *) UnmapBlob(radon_info->cells,
          (size_t) radon_info->length);
      RelinquishMagickResource(MemoryResource,radon_info->length);
      break;
    }
    case MapCache:
    {
      radon_info->cells=(unsigned short *) UnmapBlob(radon_info->cells,(size_t)
        radon_info->length);
      RelinquishMagickResource(MapResource,radon_info->length);
    }
    case DiskCache:
    {
      if (radon_info->file != -1)
        (void) close(radon_info->file);
      (void) RelinquishUniqueFileResource(radon_info->path);
      RelinquishMagickResource(DiskResource,radon_info->length);
      break;
    }
    default:
      break;
  }
  return((RadonInfo *) RelinquishMagickMemory(radon_info));
}

static MagickBooleanType ResetRadonCells(RadonInfo *radon_info)
{
  register ssize_t
    x;

  ssize_t
    count,
    y;

  unsigned short
    value;

  if (radon_info->type != DiskCache)
    {
      (void) ResetMagickMemory(radon_info->cells,0,(size_t) radon_info->length);
      return(MagickTrue);
    }
  value=0;
  (void) lseek(radon_info->file,0,SEEK_SET);
  for (y=0; y < (ssize_t) radon_info->height; y++)
  {
    for (x=0; x < (ssize_t) radon_info->width; x++)
    {
      count=write(radon_info->file,&value,sizeof(*radon_info->cells));
      if (count != (ssize_t) sizeof(*radon_info->cells))
        break;
    }
    if (x < (ssize_t) radon_info->width)
      break;
  }
  return(y < (ssize_t) radon_info->height ? MagickFalse : MagickTrue);
}

static RadonInfo *AcquireRadonInfo(const Image *image,const size_t width,
  const size_t height,ExceptionInfo *exception)
{
  MagickBooleanType
    status;

  RadonInfo
    *radon_info;

  radon_info=(RadonInfo *) AcquireMagickMemory(sizeof(*radon_info));
  if (radon_info == (RadonInfo *) NULL)
    return((RadonInfo *) NULL);
  (void) ResetMagickMemory(radon_info,0,sizeof(*radon_info));
  radon_info->width=width;
  radon_info->height=height;
  radon_info->length=(MagickSizeType) width*height*sizeof(*radon_info->cells);
  radon_info->type=MemoryCache;
  status=AcquireMagickResource(AreaResource,radon_info->length);
  if ((status != MagickFalse) &&
      (radon_info->length == (MagickSizeType) ((size_t) radon_info->length)))
    {
      status=AcquireMagickResource(MemoryResource,radon_info->length);
      if (status != MagickFalse)
        {
          radon_info->mapped=MagickFalse;
          radon_info->cells=(unsigned short *) AcquireMagickMemory((size_t)
            radon_info->length);
          if (radon_info->cells == (unsigned short *) NULL)
            {
              radon_info->mapped=MagickTrue;
              radon_info->cells=(unsigned short *) MapBlob(-1,IOMode,0,(size_t)
                radon_info->length);
            }
          if (radon_info->cells == (unsigned short *) NULL)
            RelinquishMagickResource(MemoryResource,radon_info->length);
        }
    }
  radon_info->file=(-1);
  if (radon_info->cells == (unsigned short *) NULL)
    {
      status=AcquireMagickResource(DiskResource,radon_info->length);
      if (status == MagickFalse)
        {
          (void) ThrowMagickException(exception,GetMagickModule(),CacheError,
            "CacheResourcesExhausted","`%s'",image->filename);
          return(DestroyRadonInfo(radon_info));
        }
      radon_info->type=DiskCache;
      (void) AcquireMagickResource(MemoryResource,radon_info->length);
      radon_info->file=AcquireUniqueFileResource(radon_info->path);
      if (radon_info->file == -1)
        return(DestroyRadonInfo(radon_info));
      status=AcquireMagickResource(MapResource,radon_info->length);
      if (status != MagickFalse)
        {
          status=ResetRadonCells(radon_info);
          if (status != MagickFalse)
            {
              radon_info->cells=(unsigned short *) MapBlob(radon_info->file,
                IOMode,0,(size_t) radon_info->length);
              if (radon_info->cells != (unsigned short *) NULL)
                radon_info->type=MapCache;
              else
                RelinquishMagickResource(MapResource,radon_info->length);
            }
        }
    }
  return(radon_info);
}

static inline size_t MagickMin(const size_t x,const size_t y)
{
  if (x < y)
    return(x);
  return(y);
}

static inline ssize_t ReadRadonCell(const RadonInfo *radon_info,
  const MagickOffsetType offset,const size_t length,unsigned char *buffer)
{
  register ssize_t
    i;

  ssize_t
    count;

#if !defined(MAGICKCORE_HAVE_PPREAD)
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp critical (MagickCore_ReadRadonCell)
#endif
  {
    i=(-1);
    if (lseek(radon_info->file,offset,SEEK_SET) >= 0)
      {
#endif
        count=0;
        for (i=0; i < (ssize_t) length; i+=count)
        {
#if !defined(MAGICKCORE_HAVE_PPREAD)
          count=read(radon_info->file,buffer+i,MagickMin(length-i,(size_t)
            SSIZE_MAX));
#else
          count=pread(radon_info->file,buffer+i,MagickMin(length-i,(size_t)
            SSIZE_MAX),offset+i);
#endif
          if (count > 0)
            continue;
          count=0;
          if (errno != EINTR)
            {
              i=(-1);
              break;
            }
        }
#if !defined(MAGICKCORE_HAVE_PPREAD)
      }
  }
#endif
  return(i);
}

static inline ssize_t WriteRadonCell(const RadonInfo *radon_info,
  const MagickOffsetType offset,const size_t length,const unsigned char *buffer)
{
  register ssize_t
    i;

  ssize_t
    count;

#if !defined(MAGICKCORE_HAVE_PWRITE)
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp critical (MagickCore_WriteRadonCell)
#endif
  {
    if (lseek(radon_info->file,offset,SEEK_SET) >= 0)
      {
#endif
        count=0;
        for (i=0; i < (ssize_t) length; i+=count)
        {
#if !defined(MAGICKCORE_HAVE_PWRITE)
          count=write(radon_info->file,buffer+i,MagickMin(length-i,(size_t)
            SSIZE_MAX));
#else
          count=pwrite(radon_info->file,buffer+i,MagickMin(length-i,(size_t)
            SSIZE_MAX),offset+i);
#endif
          if (count > 0)
            continue;
          count=0;
          if (errno != EINTR)
            {
              i=(-1);
              break;
            }
        }
#if !defined(MAGICKCORE_HAVE_PWRITE)
      }
  }
#endif
  return(i);
}

static inline unsigned short GetRadonCell(const RadonInfo *radon_info,
  const ssize_t x,const ssize_t y)
{
  MagickOffsetType
    i;

  unsigned short
    value;

  i=(MagickOffsetType) radon_info->height*x+y;
  if ((i < 0) ||
      ((MagickSizeType) (i*sizeof(*radon_info->cells)) >= radon_info->length))
    return(0);
  if (radon_info->type != DiskCache)
    return(radon_info->cells[i]);
  value=0;
  (void) ReadRadonCell(radon_info,i*sizeof(*radon_info->cells),
    sizeof(*radon_info->cells),(unsigned char *) &value);
  return(value);
}

static inline MagickBooleanType SetRadonCell(const RadonInfo *radon_info,
  const ssize_t x,const ssize_t y,const unsigned short value)
{
  MagickOffsetType
    i;

  ssize_t
    count;

  i=(MagickOffsetType) radon_info->height*x+y;
  if ((i < 0) ||
      ((MagickSizeType) (i*sizeof(*radon_info->cells)) >= radon_info->length))
    return(MagickFalse);
  if (radon_info->type != DiskCache)
    {
      radon_info->cells[i]=value;
      return(MagickTrue);
    }
  count=WriteRadonCell(radon_info,i*sizeof(*radon_info->cells),
    sizeof(*radon_info->cells),(const unsigned char *) &value);
  if (count != (ssize_t) sizeof(*radon_info->cells))
    return(MagickFalse);
  return(MagickTrue);
}

static void RadonProjection(RadonInfo *source_cells,
  RadonInfo *destination_cells,const ssize_t sign,size_t *projection)
{
  RadonInfo
    *swap;

  register ssize_t
    x;

  register RadonInfo
    *p,
    *q;

  size_t
    step;

  p=source_cells;
  q=destination_cells;
  for (step=1; step < p->width; step*=2)
  {
    for (x=0; x < (ssize_t) p->width; x+=2*(ssize_t) step)
    {
      register ssize_t
        i;

      ssize_t
        y;

      unsigned short
        cell;

      for (i=0; i < (ssize_t) step; i++)
      {
        for (y=0; y < (ssize_t) (p->height-i-1); y++)
        {
          cell=GetRadonCell(p,x+i,y);
          (void) SetRadonCell(q,x+2*i,y,cell+GetRadonCell(p,x+i+(ssize_t)
            step,y+i));
          (void) SetRadonCell(q,x+2*i+1,y,cell+GetRadonCell(p,x+i+(ssize_t)
            step,y+i+1));
        }
        for ( ; y < (ssize_t) (p->height-i); y++)
        {
          cell=GetRadonCell(p,x+i,y);
          (void) SetRadonCell(q,x+2*i,y,cell+GetRadonCell(p,x+i+(ssize_t) step,
            y+i));
          (void) SetRadonCell(q,x+2*i+1,y,cell);
        }
        for ( ; y < (ssize_t) p->height; y++)
        {
          cell=GetRadonCell(p,x+i,y);
          (void) SetRadonCell(q,x+2*i,y,cell);
          (void) SetRadonCell(q,x+2*i+1,y,cell);
        }
      }
    }
    swap=p;
    p=q;
    q=swap;
  }
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp parallel for schedule(dynamic,4)
#endif
  for (x=0; x < (ssize_t) p->width; x++)
  {
    register ssize_t
      y;

    size_t
      sum;

    sum=0;
    for (y=0; y < (ssize_t) (p->height-1); y++)
    {
      ssize_t
        delta;

      delta=GetRadonCell(p,x,y)-(ssize_t) GetRadonCell(p,x,y+1);
      sum+=delta*delta;
    }
    projection[p->width+sign*x-1]=sum;
  }
}

static MagickBooleanType RadonTransform(const Image *image,
  const double threshold,size_t *projection,ExceptionInfo *exception)
{
  CacheView
    *image_view;

  MagickBooleanType
    status;

  RadonInfo
    *destination_cells,
    *source_cells;

  register ssize_t
    i;

  size_t
    count,
    width;

  ssize_t
    y;

  unsigned char
    byte;

  unsigned short
    bits[256];

  for (width=1; width < ((image->columns+7)/8); width<<=1) ;
  source_cells=AcquireRadonInfo(image,width,image->rows,exception);
  destination_cells=AcquireRadonInfo(image,width,image->rows,exception);
  if ((source_cells == (RadonInfo *) NULL) ||
      (destination_cells == (RadonInfo *) NULL))
    {
      if (destination_cells != (RadonInfo *) NULL)
        destination_cells=DestroyRadonInfo(destination_cells);
      if (source_cells != (RadonInfo *) NULL)
        source_cells=DestroyRadonInfo(source_cells);
      return(MagickFalse);
    }
  if (ResetRadonCells(source_cells) == MagickFalse)
    {
      destination_cells=DestroyRadonInfo(destination_cells);
      source_cells=DestroyRadonInfo(source_cells);
      return(MagickFalse);
    }
  for (i=0; i < 256; i++)
  {
    byte=(unsigned char) i;
    for (count=0; byte != 0; byte>>=1)
      count+=byte & 0x01;
    bits[i]=(unsigned short) count;
  }
  status=MagickTrue;
  image_view=AcquireCacheView(image);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp parallel for schedule(dynamic,4) shared(status)
#endif
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    register const PixelPacket
      *restrict p;

    register ssize_t
      i,
      x;

    size_t
      bit,
      byte;

    if (status == MagickFalse)
      continue;
    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
    if (p == (const PixelPacket *) NULL)
      {
        status=MagickFalse;
        continue;
      }
    bit=0;
    byte=0;
    i=(ssize_t) (image->columns+7)/8;
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      byte<<=1;
      if (((MagickRealType) p->red < threshold) ||
          ((MagickRealType) p->green < threshold) ||
          ((MagickRealType) p->blue < threshold))
        byte|=0x01;
      bit++;
      if (bit == 8)
        {
          (void) SetRadonCell(source_cells,--i,y,bits[byte]);
          bit=0;
          byte=0;
        }
      p++;
    }
    if (bit != 0)
      {
        byte<<=(8-bit);
        (void) SetRadonCell(source_cells,--i,y,bits[byte]);
      }
  }
  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)
#endif
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    register const PixelPacket
      *restrict p;

    register ssize_t
      i,
      x;

    size_t
      bit,
      byte;

    if (status == MagickFalse)
      continue;
    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
    if (p == (const PixelPacket *) NULL)
      {
        status=MagickFalse;
        continue;
      }
    bit=0;
    byte=0;
    i=0;
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      byte<<=1;
      if (((MagickRealType) p->red < threshold) ||
          ((MagickRealType) p->green < threshold) ||
          ((MagickRealType) p->blue < threshold))
        byte|=0x01;
      bit++;
      if (bit == 8)
        {
          (void) SetRadonCell(source_cells,i++,y,bits[byte]);
          bit=0;
          byte=0;
        }
      p++;
    }
    if (bit != 0)
      {
        byte<<=(8-bit);
        (void) SetRadonCell(source_cells,i++,y,bits[byte]);
      }
  }
  RadonProjection(source_cells,destination_cells,1,projection);
  image_view=DestroyCacheView(image_view);
  destination_cells=DestroyRadonInfo(destination_cells);
  source_cells=DestroyRadonInfo(source_cells);
  return(MagickTrue);
}

static void GetImageBackgroundColor(Image *image,const ssize_t offset,
  ExceptionInfo *exception)
{
  CacheView
    *image_view;

  MagickPixelPacket
    background;

  MagickRealType
    count;

  ssize_t
    y;

  /*
    Compute average background color.
  */
  if (offset <= 0)
    return;
  GetMagickPixelPacket(image,&background);
  count=0.0;
  image_view=AcquireCacheView(image);
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    register const PixelPacket
      *restrict p;

    register ssize_t
      x;

    if ((y >= offset) && (y < ((ssize_t) image->rows-offset)))
      continue;
    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
    if (p == (const PixelPacket *) NULL)
      continue;
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      if ((x >= offset) && (x < ((ssize_t) image->columns-offset)))
        continue;
      background.red+=QuantumScale*GetRedPixelComponent(p);
      background.green+=QuantumScale*GetGreenPixelComponent(p);
      background.blue+=QuantumScale*GetBluePixelComponent(p);
      background.opacity+=QuantumScale*GetOpacityPixelComponent(p);
      count++;
      p++;
    }
  }
  image_view=DestroyCacheView(image_view);
  image->background_color.red=ClampToQuantum((MagickRealType) QuantumRange*
    background.red/count);
  image->background_color.green=ClampToQuantum((MagickRealType) QuantumRange*
    background.green/count);
  image->background_color.blue=ClampToQuantum((MagickRealType) QuantumRange*
    background.blue/count);
  image->background_color.opacity=ClampToQuantum((MagickRealType) QuantumRange*
    background.opacity/count);
}

MagickExport Image *DeskewImage(const Image *image,const double threshold,
  ExceptionInfo *exception)
{
  AffineMatrix
    affine_matrix;

  const char
    *artifact;

  double
    degrees;

  Image
    *clone_image,
    *crop_image,
    *deskew_image,
    *median_image;

  MagickBooleanType
    status;

  RectangleInfo
    geometry;

  register ssize_t
    i;

  size_t
    max_projection,
    *projection,
    width;

  ssize_t
    skew;

  /*
    Compute deskew angle.
  */
  for (width=1; width < ((image->columns+7)/8); width<<=1) ;
  projection=(size_t *) AcquireQuantumMemory((size_t) (2*width-1),
    sizeof(*projection));
  if (projection == (size_t *) NULL)
    ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
  status=RadonTransform(image,threshold,projection,exception);
  if (status == MagickFalse)
    {
      projection=(size_t *) RelinquishMagickMemory(projection);
      ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
    }
  max_projection=0;
  skew=0;
  for (i=0; i < (ssize_t) (2*width-1); i++)
  {
    if (projection[i] > max_projection)
      {
        skew=i-(ssize_t) width+1;
        max_projection=projection[i];
      }
  }
  projection=(size_t *) RelinquishMagickMemory(projection);
  /*
    Deskew image.
  */
  clone_image=CloneImage(image,0,0,MagickTrue,exception);
  if (clone_image == (Image *) NULL)
    return((Image *) NULL);
  (void) SetImageVirtualPixelMethod(clone_image,BackgroundVirtualPixelMethod);
  degrees=RadiansToDegrees(-atan((double) skew/width/8));
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TransformEvent,GetMagickModule(),
      "  Deskew angle: %g",degrees);
  affine_matrix.sx=cos(DegreesToRadians(fmod((double) degrees,360.0)));
  affine_matrix.rx=sin(DegreesToRadians(fmod((double) degrees,360.0)));
  affine_matrix.ry=(-sin(DegreesToRadians(fmod((double) degrees,360.0))));
  affine_matrix.sy=cos(DegreesToRadians(fmod((double) degrees,360.0)));
  affine_matrix.tx=0.0;
  affine_matrix.ty=0.0;
  artifact=GetImageArtifact(image,"deskew:auto-crop");
  if (artifact == (const char *) NULL)
    {
      deskew_image=AffineTransformImage(clone_image,&affine_matrix,exception);
      clone_image=DestroyImage(clone_image);
      return(deskew_image);
    }
  /*
    Auto-crop image.
  */
  GetImageBackgroundColor(clone_image,(ssize_t) StringToLong(artifact),
    exception);
  deskew_image=AffineTransformImage(clone_image,&affine_matrix,exception);
  clone_image=DestroyImage(clone_image);
  if (deskew_image == (Image *) NULL)
    return((Image *) NULL);
  median_image=StatisticImage(deskew_image,MedianStatistic,3,3,exception);
  if (median_image == (Image *) NULL)
    {
      deskew_image=DestroyImage(deskew_image);
      return((Image *) NULL);
    }
  geometry=GetImageBoundingBox(median_image,exception);
  median_image=DestroyImage(median_image);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TransformEvent,GetMagickModule(),"  Deskew geometry: "
      "%.20gx%.20g%+.20g%+.20g",(double) geometry.width,(double)
      geometry.height,(double) geometry.x,(double) geometry.y);
  crop_image=CropImage(deskew_image,&geometry,exception);
  deskew_image=DestroyImage(deskew_image);
  return(crop_image);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
+   I n t e g r a l R o t a t e I m a g e                                     %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  IntegralRotateImage() rotates the image an integral of 90 degrees.  It
%  allocates the memory necessary for the new Image structure and returns a
%  pointer to the rotated image.
%
%  The format of the IntegralRotateImage method is:
%
%      Image *IntegralRotateImage(const Image *image,size_t rotations,
%        ExceptionInfo *exception)
%
%  A description of each parameter follows.
%
%    o image: the image.
%
%    o rotations: Specifies the number of 90 degree rotations.
%
*/
static Image *IntegralRotateImage(const Image *image,size_t rotations,
  ExceptionInfo *exception)
{
#define RotateImageTag  "Rotate/Image"

  CacheView
    *image_view,
    *rotate_view;

  Image
    *rotate_image;

  MagickBooleanType
    status;

  MagickOffsetType
    progress;

  RectangleInfo
    page;

  ssize_t
    y;

  /*
    Initialize rotated image attributes.
  */
  assert(image != (Image *) NULL);
  page=image->page;
  rotations%=4;
  if (rotations == 0)
    return(CloneImage(image,0,0,MagickTrue,exception));
  if ((rotations == 1) || (rotations == 3))
    rotate_image=CloneImage(image,image->rows,image->columns,MagickTrue,
      exception);
  else
    rotate_image=CloneImage(image,image->columns,image->rows,MagickTrue,
      exception);
  if (rotate_image == (Image *) NULL)
    return((Image *) NULL);
  /*
    Integral rotate the image.
  */
  status=MagickTrue;
  progress=0;
  image_view=AcquireCacheView(image);
  rotate_view=AcquireCacheView(rotate_image);
  switch (rotations)
  {
    case 0:
    {
      /*
        Rotate 0 degrees.
      */
      break;
    }
    case 1:
    {
      size_t
        tile_height,
        tile_width;

      ssize_t
        tile_y;

      /*
        Rotate 90 degrees.
      */
      GetPixelCacheTileSize(image,&tile_width,&tile_height);
#if defined(MAGICKCORE_OPENMP_SUPPORT) 
  #pragma omp parallel for schedule(static,1) shared(progress, status) omp_throttle(1)
#endif
      for (tile_y=0; tile_y < (ssize_t) image->rows; tile_y+=(ssize_t) tile_height)
      {
        register ssize_t
          tile_x;

        if (status == MagickFalse)
          continue;
        for (tile_x=0; tile_x < (ssize_t) image->columns; tile_x+=(ssize_t) tile_width)
        {
          MagickBooleanType
            sync;

          register const IndexPacket
            *restrict indexes;

          register const PixelPacket
            *restrict p;

          register IndexPacket
            *restrict rotate_indexes;

          register ssize_t
            y;

          register PixelPacket
            *restrict q;

          size_t
            height,
            width;

          width=tile_width;
          if ((tile_x+(ssize_t) tile_width) > (ssize_t) image->columns)
            width=(size_t) (tile_width-(tile_x+tile_width-
              image->columns));
          height=tile_height;
          if ((tile_y+(ssize_t) tile_height) > (ssize_t) image->rows)
            height=(size_t) (tile_height-(tile_y+tile_height-
              image->rows));
          p=GetCacheViewVirtualPixels(image_view,tile_x,tile_y,width,height,
            exception);
          if (p == (const PixelPacket *) NULL)
            {
              status=MagickFalse;
              break;
            }
          indexes=GetCacheViewVirtualIndexQueue(image_view);
          for (y=0; y < (ssize_t) width; y++)
          {
            register const PixelPacket
              *restrict tile_pixels;

            register ssize_t
              x;

            q=QueueCacheViewAuthenticPixels(rotate_view,(ssize_t)
              (rotate_image->columns-(tile_y+height)),y+tile_x,height,
              1,exception);
            if (q == (PixelPacket *) NULL)
              {
                status=MagickFalse;
                break;
              }
            tile_pixels=p+(height-1)*width+y;
            for (x=0; x < (ssize_t) height; x++)
            {
              *q++=(*tile_pixels);
              tile_pixels-=width;
            }
            rotate_indexes=GetCacheViewAuthenticIndexQueue(rotate_view);
            if ((indexes != (IndexPacket *) NULL) &&
                (rotate_indexes != (IndexPacket *) NULL))
              {
                register const IndexPacket
                  *restrict tile_indexes;

                tile_indexes=indexes+(height-1)*width+y;
                for (x=0; x < (ssize_t) height; x++)
                {
                  *rotate_indexes++=(*tile_indexes);
                  tile_indexes-=width;
                }
              }
            sync=SyncCacheViewAuthenticPixels(rotate_view,exception);
            if (sync == MagickFalse)
              status=MagickFalse;
          }
        }
        if (image->progress_monitor != (MagickProgressMonitor) NULL)
          {
            MagickBooleanType
              proceed;

            proceed=SetImageProgress(image,RotateImageTag,progress+=tile_height,
              image->rows);
            if (proceed == MagickFalse)
              status=MagickFalse;
          }
      }
      (void) SetImageProgress(image,RotateImageTag,(MagickOffsetType)
        image->rows-1,image->rows);
      Swap(page.width,page.height);
      Swap(page.x,page.y);
      if (page.width != 0)
        page.x=(ssize_t) (page.width-rotate_image->columns-page.x);
      break;
    }
    case 2:
    {
      /*
        Rotate 180 degrees.
      */
#if defined(MAGICKCORE_OPENMP_SUPPORT) 
  #pragma omp parallel for schedule(static,8) shared(progress,status) omp_throttle(1)
#endif
      for (y=0; y < (ssize_t) image->rows; y++)
      {
        MagickBooleanType
          sync;

        register const IndexPacket
          *restrict indexes;

        register const PixelPacket
          *restrict p;

        register IndexPacket
          *restrict rotate_indexes;

        register ssize_t
          x;

        register PixelPacket
          *restrict q;

        if (status == MagickFalse)
          continue;
        p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,
          exception);
        q=QueueCacheViewAuthenticPixels(rotate_view,0,(ssize_t) (image->rows-
          y-1),image->columns,1,exception);
        if ((p == (const PixelPacket *) NULL) || (q == (PixelPacket *) NULL))
          {
            status=MagickFalse;
            continue;
          }
        indexes=GetCacheViewVirtualIndexQueue(image_view);
        rotate_indexes=GetCacheViewAuthenticIndexQueue(rotate_view);
        q+=image->columns;
        for (x=0; x < (ssize_t) image->columns; x++)
          *--q=(*p++);
        if ((indexes != (IndexPacket *) NULL) &&
            (rotate_indexes != (IndexPacket *) NULL))
          for (x=0; x < (ssize_t) image->columns; x++)
            rotate_indexes[image->columns-x-1]=indexes[x];
        sync=SyncCacheViewAuthenticPixels(rotate_view,exception);
        if (sync == MagickFalse)
          status=MagickFalse;
        if (image->progress_monitor != (MagickProgressMonitor) NULL)
          {
            MagickBooleanType
              proceed;

            proceed=SetImageProgress(image,RotateImageTag,progress++,
              image->rows);
            if (proceed == MagickFalse)
              status=MagickFalse;
          }
      }
      if (page.width != 0)
        page.x=(ssize_t) (page.width-rotate_image->columns-page.x);
      if (page.height != 0)
        page.y=(ssize_t) (page.height-rotate_image->rows-page.y);
      break;
    }
    case 3:
    {
      size_t
        tile_height,
        tile_width;

      ssize_t
        tile_y;

      /*
        Rotate 270 degrees.
      */
      GetPixelCacheTileSize(image,&tile_width,&tile_height);
#if defined(MAGICKCORE_OPENMP_SUPPORT) 
  #pragma omp parallel for schedule(static,1) shared(progress,status) omp_throttle(1)
#endif
      for (tile_y=0; tile_y < (ssize_t) image->rows; tile_y+=(ssize_t) tile_height)
      {
        register ssize_t
          tile_x;

        if (status == MagickFalse)
          continue;
        for (tile_x=0; tile_x < (ssize_t) image->columns; tile_x+=(ssize_t) tile_width)
        {
          MagickBooleanType
            sync;

          register const IndexPacket
            *restrict indexes;

          register const PixelPacket
            *restrict p;

          register IndexPacket
            *restrict rotate_indexes;

          register ssize_t
            y;

          register PixelPacket
            *restrict q;

          size_t
            height,
            width;

          width=tile_width;
          if ((tile_x+(ssize_t) tile_width) > (ssize_t) image->columns)
            width=(size_t) (tile_width-(tile_x+tile_width-
              image->columns));
          height=tile_height;
          if ((tile_y+(ssize_t) tile_height) > (ssize_t) image->rows)
            height=(size_t) (tile_height-(tile_y+tile_height-
              image->rows));
          p=GetCacheViewVirtualPixels(image_view,tile_x,tile_y,width,
            height,exception);
          if (p == (const PixelPacket *) NULL)
            {
              status=MagickFalse;
              break;
            }
          indexes=GetCacheViewVirtualIndexQueue(image_view);
          for (y=0; y < (ssize_t) width; y++)
          {
            register const PixelPacket
              *restrict tile_pixels;

            register ssize_t
              x;

            q=QueueCacheViewAuthenticPixels(rotate_view,tile_y,(ssize_t)
              (y+rotate_image->rows-(tile_x+width)),height,1,exception);
            if (q == (PixelPacket *) NULL)
              {
                status=MagickFalse;
                break;
              }
            tile_pixels=p+(width-1)-y;
            for (x=0; x < (ssize_t) height; x++)
            {
              *q++=(*tile_pixels);
              tile_pixels+=width;
            }
            rotate_indexes=GetCacheViewAuthenticIndexQueue(rotate_view);
            if ((indexes != (IndexPacket *) NULL) &&
                (rotate_indexes != (IndexPacket *) NULL))
              {
                register const IndexPacket
                  *restrict tile_indexes;

                tile_indexes=indexes+(width-1)-y;
                for (x=0; x < (ssize_t) height; x++)
                {
                  *rotate_indexes++=(*tile_indexes);
                  tile_indexes+=width;
                }
              }
            sync=SyncCacheViewAuthenticPixels(rotate_view,exception);
            if (sync == MagickFalse)
              status=MagickFalse;
          }
        }
        if (image->progress_monitor != (MagickProgressMonitor) NULL)
          {
            MagickBooleanType
              proceed;

            proceed=SetImageProgress(image,RotateImageTag,progress+=tile_height,
              image->rows);
            if (proceed == MagickFalse)
              status=MagickFalse;
          }
      }
      (void) SetImageProgress(image,RotateImageTag,(MagickOffsetType)
        image->rows-1,image->rows);
      Swap(page.width,page.height);
      Swap(page.x,page.y);
      if (page.height != 0)
        page.y=(ssize_t) (page.height-rotate_image->rows-page.y);
      break;
    }
  }
  rotate_view=DestroyCacheView(rotate_view);
  image_view=DestroyCacheView(image_view);
  rotate_image->type=image->type;
  rotate_image->page=page;
  if (status == MagickFalse)
    rotate_image=DestroyImage(rotate_image);
  return(rotate_image);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
+   X S h e a r I m a g e                                                     %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  XShearImage() shears the image in the X direction with a shear angle of
%  'degrees'.  Positive angles shear counter-clockwise (right-hand rule), and
%  negative angles shear clockwise.  Angles are measured relative to a vertical
%  Y-axis.  X shears will widen an image creating 'empty' triangles on the left
%  and right sides of the source image.
%
%  The format of the XShearImage method is:
%
%      MagickBooleanType XShearImage(Image *image,const MagickRealType degrees,
%        const size_t width,const size_t height,
%        const ssize_t x_offset,const ssize_t y_offset,ExceptionInfo *exception)
%
%  A description of each parameter follows.
%
%    o image: the image.
%
%    o degrees: A MagickRealType representing the shearing angle along the X
%      axis.
%
%    o width, height, x_offset, y_offset: Defines a region of the image
%      to shear.
%
%    o exception: return any errors or warnings in this structure.
%
*/
static MagickBooleanType XShearImage(Image *image,const MagickRealType degrees,
  const size_t width,const size_t height,const ssize_t x_offset,
  const ssize_t y_offset,ExceptionInfo *exception)
{
#define XShearImageTag  "XShear/Image"

  typedef enum
  {
    LEFT,
    RIGHT
  } ShearDirection;

  CacheView
    *image_view;

  MagickBooleanType
    status;

  MagickOffsetType
    progress;

  MagickPixelPacket
    background;

  ssize_t
    y;

  assert(image != (Image *) NULL);
  assert(image->signature == MagickSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  GetMagickPixelPacket(image,&background);
  SetMagickPixelPacket(image,&image->background_color,(IndexPacket *) NULL,
    &background);
  if (image->colorspace == CMYKColorspace)
    ConvertRGBToCMYK(&background);
  /*
    X shear image.
  */
  status=MagickTrue;
  progress=0;
  image_view=AcquireCacheView(image);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp parallel for schedule(dynamic,4) shared(progress, status)
#endif
  for (y=0; y < (ssize_t) height; y++)
  {
    MagickPixelPacket
      pixel,
      source,
      destination;

    MagickRealType
      area,
      displacement;

    register IndexPacket
      *restrict indexes,
      *restrict shear_indexes;

    register PixelPacket
      *restrict p,
      *restrict q;

    register ssize_t
      i;

    ShearDirection
      direction;

    ssize_t
      step;

    if (status == MagickFalse)
      continue;
    p=GetCacheViewAuthenticPixels(image_view,0,y_offset+y,image->columns,1,
      exception);
    if (p == (PixelPacket *) NULL)
      {
        status=MagickFalse;
        continue;
      }
    indexes=GetCacheViewAuthenticIndexQueue(image_view);
    p+=x_offset;
    indexes+=x_offset;
    displacement=degrees*(MagickRealType) (y-height/2.0);
    if (displacement == 0.0)
      continue;
    if (displacement > 0.0)
      direction=RIGHT;
    else
      {
        displacement*=(-1.0);
        direction=LEFT;
      }
    step=(ssize_t) floor((double) displacement);
    area=(MagickRealType) (displacement-step);
    step++;
    pixel=background;
    GetMagickPixelPacket(image,&source);
    GetMagickPixelPacket(image,&destination);
    switch (direction)
    {
      case LEFT:
      {
        /*
          Transfer pixels left-to-right.
        */
        if (step > x_offset)
          break;
        q=p-step;
        shear_indexes=indexes-step;
        for (i=0; i < (ssize_t) width; i++)
        {
          if ((x_offset+i) < step)
            {
              SetMagickPixelPacket(image,++p,++indexes,&pixel);
              q++;
              shear_indexes++;
              continue;
            }
          SetMagickPixelPacket(image,p,indexes,&source);
          MagickPixelCompositeAreaBlend(&pixel,(MagickRealType) pixel.opacity,
            &source,(MagickRealType) p->opacity,area,&destination);
          SetPixelPacket(image,&destination,q++,shear_indexes++);
          SetMagickPixelPacket(image,p++,indexes++,&pixel);
        }
        MagickPixelCompositeAreaBlend(&pixel,(MagickRealType) pixel.opacity,
          &background,(MagickRealType) background.opacity,area,&destination);
        SetPixelPacket(image,&destination,q++,shear_indexes++);
        for (i=0; i < (step-1); i++)
          SetPixelPacket(image,&background,q++,shear_indexes++);
        break;
      }
      case RIGHT:
      {
        /*
          Transfer pixels right-to-left.
        */
        p+=width;
        indexes+=width;
        q=p+step;
        shear_indexes=indexes+step;
        for (i=0; i < (ssize_t) width; i++)
        {
          p--;
          indexes--;
          q--;
          shear_indexes--;
          if ((size_t) (x_offset+width+step-i) >= image->columns)
            continue;
          SetMagickPixelPacket(image,p,indexes,&source);
          MagickPixelCompositeAreaBlend(&pixel,(MagickRealType) pixel.opacity,
            &source,(MagickRealType) p->opacity,area,&destination);
          SetPixelPacket(image,&destination,q,shear_indexes);
          SetMagickPixelPacket(image,p,indexes,&pixel);
        }
        MagickPixelCompositeAreaBlend(&pixel,(MagickRealType) pixel.opacity,
          &background,(MagickRealType) background.opacity,area,&destination);
        SetPixelPacket(image,&destination,--q,--shear_indexes);
        for (i=0; i < (step-1); i++)
          SetPixelPacket(image,&background,--q,--shear_indexes);
        break;
      }
    }
    if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
      status=MagickFalse;
    if (image->progress_monitor != (MagickProgressMonitor) NULL)
      {
        MagickBooleanType
          proceed;

#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp critical (MagickCore_XShearImage)
#endif
        proceed=SetImageProgress(image,XShearImageTag,progress++,height);
        if (proceed == MagickFalse)
          status=MagickFalse;
      }
  }
  image_view=DestroyCacheView(image_view);
  return(status);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
+   Y S h e a r I m a g e                                                     %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  YShearImage shears the image in the Y direction with a shear angle of
%  'degrees'.  Positive angles shear counter-clockwise (right-hand rule), and
%  negative angles shear clockwise.  Angles are measured relative to a
%  horizontal X-axis.  Y shears will increase the height of an image creating
%  'empty' triangles on the top and bottom of the source image.
%
%  The format of the YShearImage method is:
%
%      MagickBooleanType YShearImage(Image *image,const MagickRealType degrees,
%        const size_t width,const size_t height,
%        const ssize_t x_offset,const ssize_t y_offset,ExceptionInfo *exception)
%
%  A description of each parameter follows.
%
%    o image: the image.
%
%    o degrees: A MagickRealType representing the shearing angle along the Y
%      axis.
%
%    o width, height, x_offset, y_offset: Defines a region of the image
%      to shear.
%
%    o exception: return any errors or warnings in this structure.
%
*/
static MagickBooleanType YShearImage(Image *image,const MagickRealType degrees,
  const size_t width,const size_t height,const ssize_t x_offset,
  const ssize_t y_offset,ExceptionInfo *exception)
{
#define YShearImageTag  "YShear/Image"

  typedef enum
  {
    UP,
    DOWN
  } ShearDirection;

  CacheView
    *image_view;

  MagickBooleanType
    status;

  MagickOffsetType
    progress;

  MagickPixelPacket
    background;

  ssize_t
    x;

  assert(image != (Image *) NULL);
  assert(image->signature == MagickSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  GetMagickPixelPacket(image,&background);
  SetMagickPixelPacket(image,&image->background_color,(IndexPacket *) NULL,
    &background);
  if (image->colorspace == CMYKColorspace)
    ConvertRGBToCMYK(&background);
  /*
    Y Shear image.
  */
  status=MagickTrue;
  progress=0;
  image_view=AcquireCacheView(image);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp parallel for schedule(dynamic,4) shared(progress, status)
#endif
  for (x=0; x < (ssize_t) width; x++)
  {
    ssize_t
      step;

    MagickPixelPacket
      pixel,
      source,
      destination;

    MagickRealType
      area,
      displacement;

    register IndexPacket
      *restrict indexes,
      *restrict shear_indexes;

    register ssize_t
      i;

    register PixelPacket
      *restrict p,
      *restrict q;

    ShearDirection
      direction;

    if (status == MagickFalse)
      continue;
    p=GetCacheViewAuthenticPixels(image_view,x_offset+x,0,1,image->rows,
      exception);
    if (p == (PixelPacket *) NULL)
      {
        status=MagickFalse;
        continue;
      }
    indexes=GetCacheViewAuthenticIndexQueue(image_view);
    p+=y_offset;
    indexes+=y_offset;
    displacement=degrees*(MagickRealType) (x-width/2.0);
    if (displacement == 0.0)
      continue;
    if (displacement > 0.0)
      direction=DOWN;
    else
      {
        displacement*=(-1.0);
        direction=UP;
      }
    step=(ssize_t) floor((double) displacement);
    area=(MagickRealType) (displacement-step);
    step++;
    pixel=background;
    GetMagickPixelPacket(image,&source);
    GetMagickPixelPacket(image,&destination);
    switch (direction)
    {
      case UP:
      {
        /*
          Transfer pixels top-to-bottom.
        */
        if (step > y_offset)
          break;
        q=p-step;
        shear_indexes=indexes-step;
        for (i=0; i < (ssize_t) height; i++)
        {
          if ((y_offset+i) < step)
            {
              SetMagickPixelPacket(image,++p,++indexes,&pixel);
              q++;
              shear_indexes++;
              continue;
            }
          SetMagickPixelPacket(image,p,indexes,&source);
          MagickPixelCompositeAreaBlend(&pixel,(MagickRealType) pixel.opacity,
            &source,(MagickRealType) p->opacity,area,&destination);
          SetPixelPacket(image,&destination,q++,shear_indexes++);
          SetMagickPixelPacket(image,p++,indexes++,&pixel);
        }
        MagickPixelCompositeAreaBlend(&pixel,(MagickRealType) pixel.opacity,
          &background,(MagickRealType) background.opacity,area,&destination);
        SetPixelPacket(image,&destination,q++,shear_indexes++);
        for (i=0; i < (step-1); i++)
          SetPixelPacket(image,&background,q++,shear_indexes++);
        break;
      }
      case DOWN:
      {
        /*
          Transfer pixels bottom-to-top.
        */
        p+=height;
        indexes+=height;
        q=p+step;
        shear_indexes=indexes+step;
        for (i=0; i < (ssize_t) height; i++)
        {
          p--;
          indexes--;
          q--;
          shear_indexes--;
          if ((size_t) (y_offset+height+step-i) >= image->rows)
            continue;
          SetMagickPixelPacket(image,p,indexes,&source);
          MagickPixelCompositeAreaBlend(&pixel,(MagickRealType) pixel.opacity,
            &source,(MagickRealType) p->opacity,area,&destination);
          SetPixelPacket(image,&destination,q,shear_indexes);
          SetMagickPixelPacket(image,p,indexes,&pixel);
        }
        MagickPixelCompositeAreaBlend(&pixel,(MagickRealType) pixel.opacity,
          &background,(MagickRealType) background.opacity,area,&destination);
        SetPixelPacket(image,&destination,--q,--shear_indexes);
        for (i=0; i < (step-1); i++)
          SetPixelPacket(image,&background,--q,--shear_indexes);
        break;
      }
    }
    if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
      status=MagickFalse;
    if (image->progress_monitor != (MagickProgressMonitor) NULL)
      {
        MagickBooleanType
          proceed;

#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp critical (MagickCore_YShearImage)
#endif
        proceed=SetImageProgress(image,YShearImageTag,progress++,image->rows);
        if (proceed == MagickFalse)
          status=MagickFalse;
      }
  }
  image_view=DestroyCacheView(image_view);
  return(status);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%   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.
%
%  RotateImage() is based on the paper "A Fast Algorithm for General
%  Raster Rotatation" by Alan W. Paeth.  RotateImage 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 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
    *integral_image,
    *rotate_image;

  ssize_t
    x_offset,
    y_offset;

  MagickBooleanType
    status;

  MagickRealType
    angle;

  PointInfo
    shear;

  RectangleInfo
    border_info;

  size_t
    height,
    rotations,
    width,
    y_width;

  /*
    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) == MagickFalse)
    {
      InheritException(exception,&integral_image->exception);
      integral_image=DestroyImage(integral_image);
      return(integral_image);
    }
  if (integral_image->matte == MagickFalse)
    (void) SetImageAlphaChannel(integral_image,OpaqueAlphaChannel);
  /*
    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,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);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%   S h e a r I m a g e                                                       %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  ShearImage() creates a new image that is a shear_image copy of an existing
%  one.  Shearing slides one edge of an image along the X or Y axis, creating
%  a parallelogram.  An X direction shear slides an edge along the X axis,
%  while a Y direction shear slides an edge along the Y axis.  The amount of
%  the shear is controlled by a shear angle.  For X direction shears, x_shear
%  is measured relative to the Y axis, and similarly, for Y direction shears
%  y_shear is measured relative to the X axis.  Empty triangles left over from
%  shearing the image are filled with the background color defined by member
%  'background_color' of the image..  ShearImage() allocates the memory
%  necessary for the new Image structure and returns a pointer to the new image.
%
%  ShearImage() is based on the paper "A Fast Algorithm for General Raster
%  Rotatation" by Alan W. Paeth.
%
%  The format of the ShearImage method is:
%
%      Image *ShearImage(const Image *image,const double x_shear,
%        const double y_shear,ExceptionInfo *exception)
%
%  A description of each parameter follows.
%
%    o image: the image.
%
%    o x_shear, y_shear: Specifies the number of degrees to shear the image.
%
%    o exception: return any errors or warnings in this structure.
%
*/
MagickExport Image *ShearImage(const Image *image,const double x_shear,
  const double y_shear,ExceptionInfo *exception)
{
  Image
    *integral_image,
    *shear_image;

  ssize_t
    x_offset,
    y_offset;

  MagickBooleanType
    status;

  PointInfo
    shear;

  RectangleInfo
    border_info;

  size_t
    y_width;

  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);
  if ((x_shear != 0.0) && (fmod(x_shear,90.0) == 0.0))
    ThrowImageException(ImageError,"AngleIsDiscontinuous");
  if ((y_shear != 0.0) && (fmod(y_shear,90.0) == 0.0))
    ThrowImageException(ImageError,"AngleIsDiscontinuous");
  /*
    Initialize shear angle.
  */
  integral_image=CloneImage(image,0,0,MagickTrue,exception);
  if (integral_image == (Image *) NULL)
    ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
  shear.x=(-tan(DegreesToRadians(fmod(x_shear,360.0))));
  shear.y=tan(DegreesToRadians(fmod(y_shear,360.0)));
  if ((shear.x == 0.0) && (shear.y == 0.0))
    return(integral_image);
  if (SetImageStorageClass(integral_image,DirectClass) == MagickFalse)
    {
      InheritException(exception,&integral_image->exception);
      integral_image=DestroyImage(integral_image);
      return(integral_image);
    }
  if (integral_image->matte == MagickFalse)
    (void) SetImageAlphaChannel(integral_image,OpaqueAlphaChannel);
  /*
    Compute image size.
  */
  y_width=image->columns+(ssize_t) floor(fabs(shear.x)*image->rows+0.5);
  x_offset=(ssize_t) ceil((double) image->columns+((fabs(shear.x)*image->rows)-
    image->columns)/2.0-0.5);
  y_offset=(ssize_t) ceil((double) image->rows+((fabs(shear.y)*y_width)-
    image->rows)/2.0-0.5);
  /*
    Surround image with 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;
  shear_image=BorderImage(integral_image,&border_info,exception);
  integral_image=DestroyImage(integral_image);
  if (shear_image == (Image *) NULL)
    ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
  /*
    Shear the image.
  */
  if (shear_image->matte == MagickFalse)
    (void) SetImageAlphaChannel(shear_image,OpaqueAlphaChannel);
  status=XShearImage(shear_image,shear.x,image->columns,image->rows,x_offset,
    (ssize_t) (shear_image->rows-image->rows)/2,exception);
  if (status == MagickFalse)
    {
      shear_image=DestroyImage(shear_image);
      return((Image *) NULL);
    }
  status=YShearImage(shear_image,shear.y,y_width,image->rows,(ssize_t)
    (shear_image->columns-y_width)/2,y_offset,exception);
  if (status == MagickFalse)
    {
      shear_image=DestroyImage(shear_image);
      return((Image *) NULL);
    }
  status=CropToFitImage(&shear_image,shear.x,shear.y,(MagickRealType)
    image->columns,(MagickRealType) image->rows,MagickFalse,exception);
  if (status == MagickFalse)
    {
      shear_image=DestroyImage(shear_image);
      return((Image *) NULL);
    }
  shear_image->compose=image->compose;
  shear_image->page.width=0;
  shear_image->page.height=0;
  return(shear_image);
}

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