granicus.if.org Git - imagemagick/blob - MagickCore/shear.c

   1 /*
   2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   3 %                                                                             %
   4 %                                                                             %
   5 %                                                                             %
   6 %                      SSSSS  H   H  EEEEE   AAA    RRRR                      %
   7 %                      SS     H   H  E      A   A   R   R                     %
   8 %                       SSS   HHHHH  EEE    AAAAA   RRRR                      %
   9 %                         SS  H   H  E      A   A   R R                       %
  10 %                      SSSSS  H   H  EEEEE  A   A   R  R                      %
  11 %                                                                             %
  12 %                                                                             %
  13 %    MagickCore Methods to Shear or Rotate an Image by an Arbitrary Angle     %
  14 %                                                                             %
  15 %                               Software Design                               %
  16 %                                 John Cristy                                 %
  17 %                                  July 1992                                  %
  18 %                                                                             %
  19 %                                                                             %
  20 %  Copyright 1999-2013 ImageMagick Studio LLC, a non-profit organization      %
  21 %  dedicated to making software imaging solutions freely available.           %
  22 %                                                                             %
  23 %  You may not use this file except in compliance with the License.  You may  %
  24 %  obtain a copy of the License at                                            %
  25 %                                                                             %
  26 %    http://www.imagemagick.org/script/license.php                            %
  27 %                                                                             %
  28 %  Unless required by applicable law or agreed to in writing, software        %
  29 %  distributed under the License is distributed on an "AS IS" BASIS,          %
  30 %  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.   %
  31 %  See the License for the specific language governing permissions and        %
  32 %  limitations under the License.                                             %
  33 %                                                                             %
  34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  35 %
  36 %  The XShearImage() and YShearImage() methods are based on the paper "A Fast
  37 %  Algorithm for General Raster Rotatation" by Alan W. Paeth, Graphics
  38 %  Interface '86 (Vancouver).  ShearRotateImage() is adapted from a similar
  39 %  method based on the Paeth paper written by Michael Halle of the Spatial
  40 %  Imaging Group, MIT Media Lab.
  41 %
  42 */
  43 \f
  44 /*
  45   Include declarations.
  46 */
  47 #include "MagickCore/studio.h"
  48 #include "MagickCore/artifact.h"
  49 #include "MagickCore/attribute.h"
  50 #include "MagickCore/blob-private.h"
  51 #include "MagickCore/cache-private.h"
  52 #include "MagickCore/color-private.h"
  53 #include "MagickCore/colorspace-private.h"
  54 #include "MagickCore/composite.h"
  55 #include "MagickCore/composite-private.h"
  56 #include "MagickCore/decorate.h"
  57 #include "MagickCore/distort.h"
  58 #include "MagickCore/draw.h"
  59 #include "MagickCore/exception.h"
  60 #include "MagickCore/exception-private.h"
  61 #include "MagickCore/gem.h"
  62 #include "MagickCore/geometry.h"
  63 #include "MagickCore/image.h"
  64 #include "MagickCore/image-private.h"
  65 #include "MagickCore/memory_.h"
  66 #include "MagickCore/list.h"
  67 #include "MagickCore/monitor.h"
  68 #include "MagickCore/monitor-private.h"
  69 #include "MagickCore/nt-base-private.h"
  70 #include "MagickCore/pixel-accessor.h"
  71 #include "MagickCore/quantum.h"
  72 #include "MagickCore/resource_.h"
  73 #include "MagickCore/shear.h"
  74 #include "MagickCore/statistic.h"
  75 #include "MagickCore/string_.h"
  76 #include "MagickCore/string-private.h"
  77 #include "MagickCore/thread-private.h"
  78 #include "MagickCore/threshold.h"
  79 #include "MagickCore/transform.h"
  80 \f
  81 /*
  82 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  83 %                                                                             %
  84 %                                                                             %
  85 %                                                                             %
  86 +   C r o p T o F i t I m a g e                                               %
  87 %                                                                             %
  88 %                                                                             %
  89 %                                                                             %
  90 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  91 %
  92 %  CropToFitImage() crops the sheared image as determined by the bounding box
  93 %  as defined by width and height and shearing angles.
  94 %
  95 %  The format of the CropToFitImage method is:
  96 %
  97 %      MagickBooleanType CropToFitImage(Image **image,
  98 %        const double x_shear,const double x_shear,
  99 %        const double width,const double height,
 100 %        const MagickBooleanType rotate,ExceptionInfo *exception)
 101 %
 102 %  A description of each parameter follows.
 103 %
 104 %    o image: the image.
 105 %
 106 %    o x_shear, y_shear, width, height: Defines a region of the image to crop.
 107 %
 108 %    o exception: return any errors or warnings in this structure.
 109 %
 110 */
 111 static MagickBooleanType CropToFitImage(Image **image,
 112   const double x_shear,const double y_shear,
 113   const double width,const double height,
 114   const MagickBooleanType rotate,ExceptionInfo *exception)
 115 {
 116   Image
 117     *crop_image;
 118
 119   PointInfo
 120     extent[4],
 121     min,
 122     max;
 123
 124   RectangleInfo
 125     geometry,
 126     page;
 127
 128   register ssize_t
 129     i;
 130
 131   /*
 132     Calculate the rotated image size.
 133   */
 134   extent[0].x=(double) (-width/2.0);
 135   extent[0].y=(double) (-height/2.0);
 136   extent[1].x=(double) width/2.0;
 137   extent[1].y=(double) (-height/2.0);
 138   extent[2].x=(double) (-width/2.0);
 139   extent[2].y=(double) height/2.0;
 140   extent[3].x=(double) width/2.0;
 141   extent[3].y=(double) height/2.0;
 142   for (i=0; i < 4; i++)
 143   {
 144     extent[i].x+=x_shear*extent[i].y;
 145     extent[i].y+=y_shear*extent[i].x;
 146     if (rotate != MagickFalse)
 147       extent[i].x+=x_shear*extent[i].y;
 148     extent[i].x+=(double) (*image)->columns/2.0;
 149     extent[i].y+=(double) (*image)->rows/2.0;
 150   }
 151   min=extent[0];
 152   max=extent[0];
 153   for (i=1; i < 4; i++)
 154   {
 155     if (min.x > extent[i].x)
 156       min.x=extent[i].x;
 157     if (min.y > extent[i].y)
 158       min.y=extent[i].y;
 159     if (max.x < extent[i].x)
 160       max.x=extent[i].x;
 161     if (max.y < extent[i].y)
 162       max.y=extent[i].y;
 163   }
 164   geometry.x=(ssize_t) ceil(min.x-0.5);
 165   geometry.y=(ssize_t) ceil(min.y-0.5);
 166   geometry.width=(size_t) floor(max.x-min.x+0.5);
 167   geometry.height=(size_t) floor(max.y-min.y+0.5);
 168   page=(*image)->page;
 169   (void) ParseAbsoluteGeometry("0x0+0+0",&(*image)->page);
 170   crop_image=CropImage(*image,&geometry,exception);
 171   if (crop_image == (Image *) NULL)
 172     return(MagickFalse);
 173   crop_image->page=page;
 174   *image=DestroyImage(*image);
 175   *image=crop_image;
 176   return(MagickTrue);
 177 }
 178 \f
 179 /*
 180 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 181 %                                                                             %
 182 %                                                                             %
 183 %                                                                             %
 184 %     D e s k e w I m a g e                                                   %
 185 %                                                                             %
 186 %                                                                             %
 187 %                                                                             %
 188 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 189 %
 190 %  DeskewImage() removes skew from the image.  Skew is an artifact that
 191 %  occurs in scanned images because of the camera being misaligned,
 192 %  imperfections in the scanning or surface, or simply because the paper was
 193 %  not placed completely flat when scanned.
 194 %
 195 %  The result will be auto-croped if the artifact "deskew:auto-crop" is
 196 %  defined, while the amount the image is to be deskewed, in degrees is also
 197 %  saved as the artifact "deskew:angle".
 198 %
 199 %  If the artifact "deskew:auto-crop" is given the image will be automatically
 200 %  cropped of the excess background.  The value is the border width of all
 201 %  pixels around the edge that will be used to determine an average border
 202 %  color for the automatic trim.
 203 %
 204 %  The format of the DeskewImage method is:
 205 %
 206 %      Image *DeskewImage(const Image *image,const double threshold,
 207 %        ExceptionInfo *exception)
 208 %
 209 %  A description of each parameter follows:
 210 %
 211 %    o image: the image.
 212 %
 213 %    o threshold: separate background from foreground.
 214 %
 215 %    o exception: return any errors or warnings in this structure.
 216 %
 217 */
 218
 219 typedef struct _RadonInfo
 220 {
 221   CacheType
 222     type;
 223
 224   size_t
 225     width,
 226     height;
 227
 228   MagickSizeType
 229     length;
 230
 231   MagickBooleanType
 232     mapped;
 233
 234   char
 235     path[MaxTextExtent];
 236
 237   int
 238     file;
 239
 240   unsigned short
 241     *cells;
 242 } RadonInfo;
 243
 244 static RadonInfo *DestroyRadonInfo(RadonInfo *radon_info)
 245 {
 246   assert(radon_info != (RadonInfo *) NULL);
 247   switch (radon_info->type)
 248   {
 249     case MemoryCache:
 250     {
 251       if (radon_info->mapped == MagickFalse)
 252         radon_info->cells=(unsigned short *) RelinquishMagickMemory(
 253           radon_info->cells);
 254       else
 255         radon_info->cells=(unsigned short *) UnmapBlob(radon_info->cells,
 256           (size_t) radon_info->length);
 257       RelinquishMagickResource(MemoryResource,radon_info->length);
 258       break;
 259     }
 260     case MapCache:
 261     {
 262       radon_info->cells=(unsigned short *) UnmapBlob(radon_info->cells,(size_t)
 263         radon_info->length);
 264       RelinquishMagickResource(MapResource,radon_info->length);
 265     }
 266     case DiskCache:
 267     {
 268       if (radon_info->file != -1)
 269         (void) close(radon_info->file);
 270       (void) RelinquishUniqueFileResource(radon_info->path);
 271       RelinquishMagickResource(DiskResource,radon_info->length);
 272       break;
 273     }
 274     default:
 275       break;
 276   }
 277   return((RadonInfo *) RelinquishMagickMemory(radon_info));
 278 }
 279
 280 static MagickBooleanType ResetRadonCells(RadonInfo *radon_info)
 281 {
 282   register ssize_t
 283     x;
 284
 285   ssize_t
 286     count,
 287     y;
 288
 289   unsigned short
 290     value;
 291
 292   if (radon_info->type != DiskCache)
 293     {
 294       (void) ResetMagickMemory(radon_info->cells,0,(size_t) radon_info->length);
 295       return(MagickTrue);
 296     }
 297   value=0;
 298   (void) lseek(radon_info->file,0,SEEK_SET);
 299   for (y=0; y < (ssize_t) radon_info->height; y++)
 300   {
 301     for (x=0; x < (ssize_t) radon_info->width; x++)
 302     {
 303       count=write(radon_info->file,&value,sizeof(*radon_info->cells));
 304       if (count != (ssize_t) sizeof(*radon_info->cells))
 305         break;
 306     }
 307     if (x < (ssize_t) radon_info->width)
 308       break;
 309   }
 310   return(y < (ssize_t) radon_info->height ? MagickFalse : MagickTrue);
 311 }
 312
 313 static RadonInfo *AcquireRadonInfo(const Image *image,const size_t width,
 314   const size_t height,ExceptionInfo *exception)
 315 {
 316   MagickBooleanType
 317     status;
 318
 319   RadonInfo
 320     *radon_info;
 321
 322   radon_info=(RadonInfo *) AcquireMagickMemory(sizeof(*radon_info));
 323   if (radon_info == (RadonInfo *) NULL)
 324     return((RadonInfo *) NULL);
 325   (void) ResetMagickMemory(radon_info,0,sizeof(*radon_info));
 326   radon_info->width=width;
 327   radon_info->height=height;
 328   radon_info->length=(MagickSizeType) width*height*sizeof(*radon_info->cells);
 329   radon_info->type=MemoryCache;
 330   status=AcquireMagickResource(AreaResource,radon_info->length);
 331   if ((status != MagickFalse) &&
 332       (radon_info->length == (MagickSizeType) ((size_t) radon_info->length)))
 333     {
 334       status=AcquireMagickResource(MemoryResource,radon_info->length);
 335       if (status != MagickFalse)
 336         {
 337           radon_info->mapped=MagickFalse;
 338           radon_info->cells=(unsigned short *) AcquireMagickMemory((size_t)
 339             radon_info->length);
 340           if (radon_info->cells == (unsigned short *) NULL)
 341             {
 342               radon_info->mapped=MagickTrue;
 343               radon_info->cells=(unsigned short *) MapBlob(-1,IOMode,0,(size_t)
 344                 radon_info->length);
 345             }
 346           if (radon_info->cells == (unsigned short *) NULL)
 347             RelinquishMagickResource(MemoryResource,radon_info->length);
 348         }
 349     }
 350   radon_info->file=(-1);
 351   if (radon_info->cells == (unsigned short *) NULL)
 352     {
 353       status=AcquireMagickResource(DiskResource,radon_info->length);
 354       if (status == MagickFalse)
 355         {
 356           (void) ThrowMagickException(exception,GetMagickModule(),CacheError,
 357             "CacheResourcesExhausted","`%s'",image->filename);
 358           return(DestroyRadonInfo(radon_info));
 359         }
 360       radon_info->type=DiskCache;
 361       (void) AcquireMagickResource(MemoryResource,radon_info->length);
 362       radon_info->file=AcquireUniqueFileResource(radon_info->path);
 363       if (radon_info->file == -1)
 364         return(DestroyRadonInfo(radon_info));
 365       status=AcquireMagickResource(MapResource,radon_info->length);
 366       if (status != MagickFalse)
 367         {
 368           status=ResetRadonCells(radon_info);
 369           if (status != MagickFalse)
 370             {
 371               radon_info->cells=(unsigned short *) MapBlob(radon_info->file,
 372                 IOMode,0,(size_t) radon_info->length);
 373               if (radon_info->cells != (unsigned short *) NULL)
 374                 radon_info->type=MapCache;
 375               else
 376                 RelinquishMagickResource(MapResource,radon_info->length);
 377             }
 378         }
 379     }
 380   return(radon_info);
 381 }
 382
 383 static inline size_t MagickMin(const size_t x,const size_t y)
 384 {
 385   if (x < y)
 386     return(x);
 387   return(y);
 388 }
 389
 390 static inline ssize_t ReadRadonCell(const RadonInfo *radon_info,
 391   const MagickOffsetType offset,const size_t length,unsigned char *buffer)
 392 {
 393   register ssize_t
 394     i;
 395
 396   ssize_t
 397     count;
 398
 399 #if !defined(MAGICKCORE_HAVE_PPREAD)
 400 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 401   #pragma omp critical (MagickCore_ReadRadonCell)
 402 #endif
 403   {
 404     i=(-1);
 405     if (lseek(radon_info->file,offset,SEEK_SET) >= 0)
 406       {
 407 #endif
 408         count=0;
 409         for (i=0; i < (ssize_t) length; i+=count)
 410         {
 411 #if !defined(MAGICKCORE_HAVE_PPREAD)
 412           count=read(radon_info->file,buffer+i,MagickMin(length-i,(size_t)
 413             SSIZE_MAX));
 414 #else
 415           count=pread(radon_info->file,buffer+i,MagickMin(length-i,(size_t)
 416             SSIZE_MAX),offset+i);
 417 #endif
 418           if (count > 0)
 419             continue;
 420           count=0;
 421           if (errno != EINTR)
 422             {
 423               i=(-1);
 424               break;
 425             }
 426         }
 427 #if !defined(MAGICKCORE_HAVE_PPREAD)
 428       }
 429   }
 430 #endif
 431   return(i);
 432 }
 433
 434 static inline ssize_t WriteRadonCell(const RadonInfo *radon_info,
 435   const MagickOffsetType offset,const size_t length,const unsigned char *buffer)
 436 {
 437   register ssize_t
 438     i;
 439
 440   ssize_t
 441     count;
 442
 443 #if !defined(MAGICKCORE_HAVE_PWRITE)
 444 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 445   #pragma omp critical (MagickCore_WriteRadonCell)
 446 #endif
 447   {
 448     if (lseek(radon_info->file,offset,SEEK_SET) >= 0)
 449       {
 450 #endif
 451         count=0;
 452         for (i=0; i < (ssize_t) length; i+=count)
 453         {
 454 #if !defined(MAGICKCORE_HAVE_PWRITE)
 455           count=write(radon_info->file,buffer+i,MagickMin(length-i,(size_t)
 456             SSIZE_MAX));
 457 #else
 458           count=pwrite(radon_info->file,buffer+i,MagickMin(length-i,(size_t)
 459             SSIZE_MAX),offset+i);
 460 #endif
 461           if (count > 0)
 462             continue;
 463           count=0;
 464           if (errno != EINTR)
 465             {
 466               i=(-1);
 467               break;
 468             }
 469         }
 470 #if !defined(MAGICKCORE_HAVE_PWRITE)
 471       }
 472   }
 473 #endif
 474   return(i);
 475 }
 476
 477 static inline unsigned short GetRadonCell(const RadonInfo *radon_info,
 478   const ssize_t x,const ssize_t y)
 479 {
 480   MagickOffsetType
 481     i;
 482
 483   unsigned short
 484     value;
 485
 486   i=(MagickOffsetType) radon_info->height*x+y;
 487   if ((i < 0) ||
 488       ((MagickSizeType) (i*sizeof(*radon_info->cells)) >= radon_info->length))
 489     return(0);
 490   if (radon_info->type != DiskCache)
 491     return(radon_info->cells[i]);
 492   value=0;
 493   (void) ReadRadonCell(radon_info,i*sizeof(*radon_info->cells),
 494     sizeof(*radon_info->cells),(unsigned char *) &value);
 495   return(value);
 496 }
 497
 498 static inline MagickBooleanType SetRadonCell(const RadonInfo *radon_info,
 499   const ssize_t x,const ssize_t y,const unsigned short value)
 500 {
 501   MagickOffsetType
 502     i;
 503
 504   ssize_t
 505     count;
 506
 507   i=(MagickOffsetType) radon_info->height*x+y;
 508   if ((i < 0) ||
 509       ((MagickSizeType) (i*sizeof(*radon_info->cells)) >= radon_info->length))
 510     return(MagickFalse);
 511   if (radon_info->type != DiskCache)
 512     {
 513       radon_info->cells[i]=value;
 514       return(MagickTrue);
 515     }
 516   count=WriteRadonCell(radon_info,i*sizeof(*radon_info->cells),
 517     sizeof(*radon_info->cells),(const unsigned char *) &value);
 518   if (count != (ssize_t) sizeof(*radon_info->cells))
 519     return(MagickFalse);
 520   return(MagickTrue);
 521 }
 522
 523 static void RadonProjection(const Image *image,RadonInfo *source_cells,
 524   RadonInfo *destination_cells,const ssize_t sign,size_t *projection)
 525 {
 526   RadonInfo
 527     *swap;
 528
 529   register ssize_t
 530     x;
 531
 532   register RadonInfo
 533     *p,
 534     *q;
 535
 536   size_t
 537     step;
 538
 539   p=source_cells;
 540   q=destination_cells;
 541   for (step=1; step < p->width; step*=2)
 542   {
 543     for (x=0; x < (ssize_t) p->width; x+=2*(ssize_t) step)
 544     {
 545       register ssize_t
 546         i;
 547
 548       ssize_t
 549         y;
 550
 551       unsigned short
 552         cell;
 553
 554       for (i=0; i < (ssize_t) step; i++)
 555       {
 556         for (y=0; y < (ssize_t) (p->height-i-1); y++)
 557         {
 558           cell=GetRadonCell(p,x+i,y);
 559           (void) SetRadonCell(q,x+2*i,y,cell+GetRadonCell(p,x+i+(ssize_t)
 560             step,y+i));
 561           (void) SetRadonCell(q,x+2*i+1,y,cell+GetRadonCell(p,x+i+(ssize_t)
 562             step,y+i+1));
 563         }
 564         for ( ; y < (ssize_t) (p->height-i); y++)
 565         {
 566           cell=GetRadonCell(p,x+i,y);
 567           (void) SetRadonCell(q,x+2*i,y,cell+GetRadonCell(p,x+i+(ssize_t) step,
 568             y+i));
 569           (void) SetRadonCell(q,x+2*i+1,y,cell);
 570         }
 571         for ( ; y < (ssize_t) p->height; y++)
 572         {
 573           cell=GetRadonCell(p,x+i,y);
 574           (void) SetRadonCell(q,x+2*i,y,cell);
 575           (void) SetRadonCell(q,x+2*i+1,y,cell);
 576         }
 577       }
 578     }
 579     swap=p;
 580     p=q;
 581     q=swap;
 582   }
 583 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 584   #pragma omp parallel for schedule(static,4) \
 585     magick_threads(image,image,1,1)
 586 #endif
 587   for (x=0; x < (ssize_t) p->width; x++)
 588   {
 589     register ssize_t
 590       y;
 591
 592     size_t
 593       sum;
 594
 595     sum=0;
 596     for (y=0; y < (ssize_t) (p->height-1); y++)
 597     {
 598       ssize_t
 599         delta;
 600
 601       delta=GetRadonCell(p,x,y)-(ssize_t) GetRadonCell(p,x,y+1);
 602       sum+=delta*delta;
 603     }
 604     projection[p->width+sign*x-1]=sum;
 605   }
 606 }
 607
 608 static MagickBooleanType RadonTransform(const Image *image,
 609   const double threshold,size_t *projection,ExceptionInfo *exception)
 610 {
 611   CacheView
 612     *image_view;
 613
 614   MagickBooleanType
 615     status;
 616
 617   RadonInfo
 618     *destination_cells,
 619     *source_cells;
 620
 621   register ssize_t
 622     i;
 623
 624   size_t
 625     count,
 626     width;
 627
 628   ssize_t
 629     y;
 630
 631   unsigned char
 632     byte;
 633
 634   unsigned short
 635     bits[256];
 636
 637   for (width=1; width < ((image->columns+7)/8); width<<=1) ;
 638   source_cells=AcquireRadonInfo(image,width,image->rows,exception);
 639   destination_cells=AcquireRadonInfo(image,width,image->rows,exception);
 640   if ((source_cells == (RadonInfo *) NULL) ||
 641       (destination_cells == (RadonInfo *) NULL))
 642     {
 643       if (destination_cells != (RadonInfo *) NULL)
 644         destination_cells=DestroyRadonInfo(destination_cells);
 645       if (source_cells != (RadonInfo *) NULL)
 646         source_cells=DestroyRadonInfo(source_cells);
 647       return(MagickFalse);
 648     }
 649   if (ResetRadonCells(source_cells) == MagickFalse)
 650     {
 651       destination_cells=DestroyRadonInfo(destination_cells);
 652       source_cells=DestroyRadonInfo(source_cells);
 653       return(MagickFalse);
 654     }
 655   for (i=0; i < 256; i++)
 656   {
 657     byte=(unsigned char) i;
 658     for (count=0; byte != 0; byte>>=1)
 659       count+=byte & 0x01;
 660     bits[i]=(unsigned short) count;
 661   }
 662   status=MagickTrue;
 663   image_view=AcquireVirtualCacheView(image,exception);
 664 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 665   #pragma omp parallel for schedule(static,4) shared(status) \
 666     magick_threads(image,image,image->rows,1)
 667 #endif
 668   for (y=0; y < (ssize_t) image->rows; y++)
 669   {
 670     register const Quantum
 671       *restrict p;
 672
 673     register ssize_t
 674       i,
 675       x;
 676
 677     size_t
 678       bit,
 679       byte;
 680
 681     if (status == MagickFalse)
 682       continue;
 683     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 684     if (p == (const Quantum *) NULL)
 685       {
 686         status=MagickFalse;
 687         continue;
 688       }
 689     bit=0;
 690     byte=0;
 691     i=(ssize_t) (image->columns+7)/8;
 692     for (x=0; x < (ssize_t) image->columns; x++)
 693     {
 694       byte<<=1;
 695       if (GetPixelIntensity(image,p) < threshold)
 696         byte|=0x01;
 697       bit++;
 698       if (bit == 8)
 699         {
 700           (void) SetRadonCell(source_cells,--i,y,bits[byte]);
 701           bit=0;
 702           byte=0;
 703         }
 704       p+=GetPixelChannels(image);
 705     }
 706     if (bit != 0)
 707       {
 708         byte<<=(8-bit);
 709         (void) SetRadonCell(source_cells,--i,y,bits[byte]);
 710       }
 711   }
 712   RadonProjection(image,source_cells,destination_cells,-1,projection);
 713   (void) ResetRadonCells(source_cells);
 714 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 715   #pragma omp parallel for schedule(static,4) shared(status) \
 716     magick_threads(image,image,1,1)
 717 #endif
 718   for (y=0; y < (ssize_t) image->rows; y++)
 719   {
 720     register const Quantum
 721       *restrict p;
 722
 723     register ssize_t
 724       i,
 725       x;
 726
 727     size_t
 728       bit,
 729       byte;
 730
 731     if (status == MagickFalse)
 732       continue;
 733     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 734     if (p == (const Quantum *) NULL)
 735       {
 736         status=MagickFalse;
 737         continue;
 738       }
 739     bit=0;
 740     byte=0;
 741     i=0;
 742     for (x=0; x < (ssize_t) image->columns; x++)
 743     {
 744       byte<<=1;
 745       if (GetPixelIntensity(image,p) < threshold)
 746         byte|=0x01;
 747       bit++;
 748       if (bit == 8)
 749         {
 750           (void) SetRadonCell(source_cells,i++,y,bits[byte]);
 751           bit=0;
 752           byte=0;
 753         }
 754       p+=GetPixelChannels(image);
 755     }
 756     if (bit != 0)
 757       {
 758         byte<<=(8-bit);
 759         (void) SetRadonCell(source_cells,i++,y,bits[byte]);
 760       }
 761   }
 762   RadonProjection(image,source_cells,destination_cells,1,projection);
 763   image_view=DestroyCacheView(image_view);
 764   destination_cells=DestroyRadonInfo(destination_cells);
 765   source_cells=DestroyRadonInfo(source_cells);
 766   return(MagickTrue);
 767 }
 768
 769 static void GetImageBackgroundColor(Image *image,const ssize_t offset,
 770   ExceptionInfo *exception)
 771 {
 772   CacheView
 773     *image_view;
 774
 775   PixelInfo
 776     background;
 777
 778   double
 779     count;
 780
 781   ssize_t
 782     y;
 783
 784   /*
 785     Compute average background color.
 786   */
 787   if (offset <= 0)
 788     return;
 789   GetPixelInfo(image,&background);
 790   count=0.0;
 791   image_view=AcquireVirtualCacheView(image,exception);
 792   for (y=0; y < (ssize_t) image->rows; y++)
 793   {
 794     register const Quantum
 795       *restrict p;
 796
 797     register ssize_t
 798       x;
 799
 800     if ((y >= offset) && (y < ((ssize_t) image->rows-offset)))
 801       continue;
 802     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 803     if (p == (const Quantum *) NULL)
 804       continue;
 805     for (x=0; x < (ssize_t) image->columns; x++)
 806     {
 807       if ((x >= offset) && (x < ((ssize_t) image->columns-offset)))
 808         continue;
 809       background.red+=QuantumScale*GetPixelRed(image,p);
 810       background.green+=QuantumScale*GetPixelGreen(image,p);
 811       background.blue+=QuantumScale*GetPixelBlue(image,p);
 812       if ((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0)
 813         background.alpha+=QuantumScale*GetPixelAlpha(image,p);
 814       count++;
 815       p+=GetPixelChannels(image);
 816     }
 817   }
 818   image_view=DestroyCacheView(image_view);
 819   image->background_color.red=(double) ClampToQuantum(QuantumRange*
 820     background.red/count);
 821   image->background_color.green=(double) ClampToQuantum(QuantumRange*
 822     background.green/count);
 823   image->background_color.blue=(double) ClampToQuantum(QuantumRange*
 824     background.blue/count);
 825   if ((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0)
 826     image->background_color.alpha=(double) ClampToQuantum(QuantumRange*
 827       background.alpha/count);
 828 }
 829
 830 MagickExport Image *DeskewImage(const Image *image,const double threshold,
 831   ExceptionInfo *exception)
 832 {
 833   AffineMatrix
 834     affine_matrix;
 835
 836   const char
 837     *artifact;
 838
 839   double
 840     degrees;
 841
 842   Image
 843     *clone_image,
 844     *crop_image,
 845     *deskew_image,
 846     *median_image;
 847
 848   MagickBooleanType
 849     status;
 850
 851   RectangleInfo
 852     geometry;
 853
 854   register ssize_t
 855     i;
 856
 857   size_t
 858     max_projection,
 859     *projection,
 860     width;
 861
 862   ssize_t
 863     skew;
 864
 865   /*
 866     Compute deskew angle.
 867   */
 868   for (width=1; width < ((image->columns+7)/8); width<<=1) ;
 869   projection=(size_t *) AcquireQuantumMemory((size_t) (2*width-1),
 870     sizeof(*projection));
 871   if (projection == (size_t *) NULL)
 872     ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
 873   status=RadonTransform(image,threshold,projection,exception);
 874   if (status == MagickFalse)
 875     {
 876       projection=(size_t *) RelinquishMagickMemory(projection);
 877       ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
 878     }
 879   max_projection=0;
 880   skew=0;
 881   for (i=0; i < (ssize_t) (2*width-1); i++)
 882   {
 883     if (projection[i] > max_projection)
 884       {
 885         skew=i-(ssize_t) width+1;
 886         max_projection=projection[i];
 887       }
 888   }
 889   projection=(size_t *) RelinquishMagickMemory(projection);
 890   degrees=RadiansToDegrees(-atan((double) skew/width/8));
 891   if (image->debug != MagickFalse)
 892     (void) LogMagickEvent(TransformEvent,GetMagickModule(),
 893       "  Deskew angle: %g",degrees);
 894   /*
 895     Deskew image.
 896   */
 897   clone_image=CloneImage(image,0,0,MagickTrue,exception);
 898   if (clone_image == (Image *) NULL)
 899     return((Image *) NULL);
 900   {
 901     char
 902       angle[MaxTextExtent];
 903
 904     (void) FormatLocaleString(angle,MaxTextExtent,"%.20g",degrees);
 905     (void) SetImageArtifact(clone_image,"deskew:angle",angle);
 906   }
 907   (void) SetImageVirtualPixelMethod(clone_image,BackgroundVirtualPixelMethod,
 908     exception);
 909   affine_matrix.sx=cos(DegreesToRadians(fmod((double) degrees,360.0)));
 910   affine_matrix.rx=sin(DegreesToRadians(fmod((double) degrees,360.0)));
 911   affine_matrix.ry=(-sin(DegreesToRadians(fmod((double) degrees,360.0))));
 912   affine_matrix.sy=cos(DegreesToRadians(fmod((double) degrees,360.0)));
 913   affine_matrix.tx=0.0;
 914   affine_matrix.ty=0.0;
 915   artifact=GetImageArtifact(image,"deskew:auto-crop");
 916   if (artifact == (const char *) NULL)
 917     {
 918       deskew_image=AffineTransformImage(clone_image,&affine_matrix,exception);
 919       clone_image=DestroyImage(clone_image);
 920       return(deskew_image);
 921     }
 922   /*
 923     Auto-crop image.
 924   */
 925   GetImageBackgroundColor(clone_image,(ssize_t) StringToLong(artifact),
 926     exception);
 927   deskew_image=AffineTransformImage(clone_image,&affine_matrix,exception);
 928   clone_image=DestroyImage(clone_image);
 929   if (deskew_image == (Image *) NULL)
 930     return((Image *) NULL);
 931   median_image=StatisticImage(deskew_image,MedianStatistic,3,3,exception);
 932   if (median_image == (Image *) NULL)
 933     {
 934       deskew_image=DestroyImage(deskew_image);
 935       return((Image *) NULL);
 936     }
 937   geometry=GetImageBoundingBox(median_image,exception);
 938   median_image=DestroyImage(median_image);
 939   if (image->debug != MagickFalse)
 940     (void) LogMagickEvent(TransformEvent,GetMagickModule(),"  Deskew geometry: "
 941       "%.20gx%.20g%+.20g%+.20g",(double) geometry.width,(double)
 942       geometry.height,(double) geometry.x,(double) geometry.y);
 943   crop_image=CropImage(deskew_image,&geometry,exception);
 944   deskew_image=DestroyImage(deskew_image);
 945   return(crop_image);
 946 }
 947 \f
 948 /*
 949 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 950 %                                                                             %
 951 %                                                                             %
 952 %                                                                             %
 953 %   I n t e g r a l R o t a t e I m a g e                                     %
 954 %                                                                             %
 955 %                                                                             %
 956 %                                                                             %
 957 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 958 %
 959 %  IntegralRotateImage() rotates the image an integral of 90 degrees.  It
 960 %  allocates the memory necessary for the new Image structure and returns a
 961 %  pointer to the rotated image.
 962 %
 963 %  The format of the IntegralRotateImage method is:
 964 %
 965 %      Image *IntegralRotateImage(const Image *image,size_t rotations,
 966 %        ExceptionInfo *exception)
 967 %
 968 %  A description of each parameter follows.
 969 %
 970 %    o image: the image.
 971 %
 972 %    o rotations: Specifies the number of 90 degree rotations.
 973 %
 974 */
 975 MagickExport Image *IntegralRotateImage(const Image *image,size_t rotations,
 976   ExceptionInfo *exception)
 977 {
 978 #define RotateImageTag  "Rotate/Image"
 979
 980   CacheView
 981     *image_view,
 982     *rotate_view;
 983
 984   Image
 985     *rotate_image;
 986
 987   MagickBooleanType
 988     status;
 989
 990   MagickOffsetType
 991     progress;
 992
 993   RectangleInfo
 994     page;
 995
 996   ssize_t
 997     y;
 998
 999   /*
1000     Initialize rotated image attributes.
1001   */
1002   assert(image != (Image *) NULL);
1003   page=image->page;
1004   rotations%=4;
1005   if (rotations == 0)
1006     return(CloneImage(image,0,0,MagickTrue,exception));
1007   if ((rotations == 1) || (rotations == 3))
1008     rotate_image=CloneImage(image,image->rows,image->columns,MagickTrue,
1009       exception);
1010   else
1011     rotate_image=CloneImage(image,image->columns,image->rows,MagickTrue,
1012       exception);
1013   if (rotate_image == (Image *) NULL)
1014     return((Image *) NULL);
1015   /*
1016     Integral rotate the image.
1017   */
1018   status=MagickTrue;
1019   progress=0;
1020   image_view=AcquireVirtualCacheView(image,exception);
1021   rotate_view=AcquireAuthenticCacheView(rotate_image,exception);
1022   switch (rotations)
1023   {
1024     case 0:
1025     {
1026       /*
1027         Rotate 0 degrees.
1028       */
1029       break;
1030     }
1031     case 1:
1032     {
1033       size_t
1034         tile_height,
1035         tile_width;
1036
1037       ssize_t
1038         tile_y;
1039
1040       /*
1041         Rotate 90 degrees.
1042       */
1043       GetPixelCacheTileSize(image,&tile_width,&tile_height);
1044       tile_width=image->columns;
1045 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1046       #pragma omp parallel for schedule(static,4) shared(status) \
1047         magick_threads(image,image,1,1)
1048 #endif
1049       for (tile_y=0; tile_y < (ssize_t) image->rows; tile_y+=(ssize_t) tile_height)
1050       {
1051         register ssize_t
1052           tile_x;
1053
1054         if (status == MagickFalse)
1055           continue;
1056         tile_x=0;
1057         for ( ; tile_x < (ssize_t) image->columns; tile_x+=(ssize_t) tile_width)
1058         {
1059           MagickBooleanType
1060             sync;
1061
1062           register const Quantum
1063             *restrict p;
1064
1065           register Quantum
1066             *restrict q;
1067
1068           register ssize_t
1069             y;
1070
1071           size_t
1072             height,
1073             width;
1074
1075           width=tile_width;
1076           if ((tile_x+(ssize_t) tile_width) > (ssize_t) image->columns)
1077             width=(size_t) (tile_width-(tile_x+tile_width-image->columns));
1078           height=tile_height;
1079           if ((tile_y+(ssize_t) tile_height) > (ssize_t) image->rows)
1080             height=(size_t) (tile_height-(tile_y+tile_height-image->rows));
1081           p=GetCacheViewVirtualPixels(image_view,tile_x,tile_y,width,height,
1082             exception);
1083           if (p == (const Quantum *) NULL)
1084             {
1085               status=MagickFalse;
1086               break;
1087             }
1088           for (y=0; y < (ssize_t) width; y++)
1089           {
1090             register const Quantum
1091               *restrict tile_pixels;
1092
1093             register ssize_t
1094               x;
1095
1096             if (status == MagickFalse)
1097               continue;
1098             q=QueueCacheViewAuthenticPixels(rotate_view,(ssize_t)
1099               (rotate_image->columns-(tile_y+height)),y+tile_x,height,1,
1100               exception);
1101             if (q == (Quantum *) NULL)
1102               {
1103                 status=MagickFalse;
1104                 continue;
1105               }
1106             tile_pixels=p+((height-1)*width+y)*GetPixelChannels(image);
1107             for (x=0; x < (ssize_t) height; x++)
1108             {
1109               register ssize_t
1110                 i;
1111
1112               if (GetPixelReadMask(image,tile_pixels) == 0)
1113                 {
1114                   tile_pixels-=width*GetPixelChannels(image);
1115                   q+=GetPixelChannels(rotate_image);
1116                   continue;
1117                 }
1118               for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1119               {
1120                 PixelChannel channel=GetPixelChannelChannel(image,i);
1121                 PixelTrait traits=GetPixelChannelTraits(image,channel);
1122                 PixelTrait rotate_traits=GetPixelChannelTraits(rotate_image,
1123                   channel);
1124                 if ((traits == UndefinedPixelTrait) ||
1125                     (rotate_traits == UndefinedPixelTrait))
1126                   continue;
1127                 SetPixelChannel(rotate_image,channel,tile_pixels[i],q);
1128               }
1129               tile_pixels-=width*GetPixelChannels(image);
1130               q+=GetPixelChannels(rotate_image);
1131             }
1132             sync=SyncCacheViewAuthenticPixels(rotate_view,exception);
1133             if (sync == MagickFalse)
1134               status=MagickFalse;
1135           }
1136         }
1137         if (image->progress_monitor != (MagickProgressMonitor) NULL)
1138           {
1139             MagickBooleanType
1140               proceed;
1141
1142 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1143             #pragma omp critical (MagickCore_IntegralRotateImage)
1144 #endif
1145             proceed=SetImageProgress(image,RotateImageTag,progress+=tile_height,
1146               image->rows);
1147             if (proceed == MagickFalse)
1148               status=MagickFalse;
1149           }
1150       }
1151       (void) SetImageProgress(image,RotateImageTag,(MagickOffsetType)
1152         image->rows-1,image->rows);
1153       Swap(page.width,page.height);
1154       Swap(page.x,page.y);
1155       if (page.width != 0)
1156         page.x=(ssize_t) (page.width-rotate_image->columns-page.x);
1157       break;
1158     }
1159     case 2:
1160     {
1161       /*
1162         Rotate 180 degrees.
1163       */
1164 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1165       #pragma omp parallel for schedule(static,4) shared(status) \
1166         magick_threads(image,image,1,1)
1167 #endif
1168       for (y=0; y < (ssize_t) image->rows; y++)
1169       {
1170         MagickBooleanType
1171           sync;
1172
1173         register const Quantum
1174           *restrict p;
1175
1176         register Quantum
1177           *restrict q;
1178
1179         register ssize_t
1180           x;
1181
1182         if (status == MagickFalse)
1183           continue;
1184         p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
1185         q=QueueCacheViewAuthenticPixels(rotate_view,0,(ssize_t) (image->rows-y-
1186           1),image->columns,1,exception);
1187         if ((p == (const Quantum *) NULL) || (q == (Quantum *) NULL))
1188           {
1189             status=MagickFalse;
1190             continue;
1191           }
1192         q+=GetPixelChannels(rotate_image)*image->columns;
1193         for (x=0; x < (ssize_t) image->columns; x++)
1194         {
1195           register ssize_t
1196             i;
1197
1198           q-=GetPixelChannels(rotate_image);
1199           if (GetPixelReadMask(image,p) == 0)
1200             {
1201               p+=GetPixelChannels(image);
1202               continue;
1203             }
1204           for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1205           {
1206             PixelChannel channel=GetPixelChannelChannel(image,i);
1207             PixelTrait traits=GetPixelChannelTraits(image,channel);
1208             PixelTrait rotate_traits=GetPixelChannelTraits(rotate_image,
1209               channel);
1210             if ((traits == UndefinedPixelTrait) ||
1211                 (rotate_traits == UndefinedPixelTrait))
1212               continue;
1213             SetPixelChannel(rotate_image,channel,p[i],q);
1214           }
1215           p+=GetPixelChannels(image);
1216         }
1217         sync=SyncCacheViewAuthenticPixels(rotate_view,exception);
1218         if (sync == MagickFalse)
1219           status=MagickFalse;
1220         if (image->progress_monitor != (MagickProgressMonitor) NULL)
1221           {
1222             MagickBooleanType
1223               proceed;
1224
1225 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1226             #pragma omp critical (MagickCore_IntegralRotateImage)
1227 #endif
1228             proceed=SetImageProgress(image,RotateImageTag,progress++,
1229               image->rows);
1230             if (proceed == MagickFalse)
1231               status=MagickFalse;
1232           }
1233       }
1234       (void) SetImageProgress(image,RotateImageTag,(MagickOffsetType)
1235         image->rows-1,image->rows);
1236       Swap(page.width,page.height);
1237       Swap(page.x,page.y);
1238       if (page.width != 0)
1239         page.x=(ssize_t) (page.width-rotate_image->columns-page.x);
1240       break;
1241     }
1242     case 3:
1243     {
1244       size_t
1245         tile_height,
1246         tile_width;
1247
1248       ssize_t
1249         tile_y;
1250
1251       /*
1252         Rotate 270 degrees.
1253       */
1254       GetPixelCacheTileSize(image,&tile_width,&tile_height);
1255       tile_width=image->columns;
1256 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1257       #pragma omp parallel for schedule(static,4) shared(status) \
1258         magick_threads(image,image,1,1)
1259 #endif
1260       for (tile_y=0; tile_y < (ssize_t) image->rows; tile_y+=(ssize_t) tile_height)
1261       {
1262         register ssize_t
1263           tile_x;
1264
1265         if (status == MagickFalse)
1266           continue;
1267         tile_x=0;
1268         for ( ; tile_x < (ssize_t) image->columns; tile_x+=(ssize_t) tile_width)
1269         {
1270           MagickBooleanType
1271             sync;
1272
1273           register const Quantum
1274             *restrict p;
1275
1276           register Quantum
1277             *restrict q;
1278
1279           register ssize_t
1280             y;
1281
1282           size_t
1283             height,
1284             width;
1285
1286           width=tile_width;
1287           if ((tile_x+(ssize_t) tile_width) > (ssize_t) image->columns)
1288             width=(size_t) (tile_width-(tile_x+tile_width-image->columns));
1289           height=tile_height;
1290           if ((tile_y+(ssize_t) tile_height) > (ssize_t) image->rows)
1291             height=(size_t) (tile_height-(tile_y+tile_height-image->rows));
1292           p=GetCacheViewVirtualPixels(image_view,tile_x,tile_y,width,height,
1293             exception);
1294           if (p == (const Quantum *) NULL)
1295             {
1296               status=MagickFalse;
1297               break;
1298             }
1299           for (y=0; y < (ssize_t) width; y++)
1300           {
1301             register const Quantum
1302               *restrict tile_pixels;
1303
1304             register ssize_t
1305               x;
1306
1307             if (status == MagickFalse)
1308               continue;
1309             q=QueueCacheViewAuthenticPixels(rotate_view,tile_y,(ssize_t) (y+
1310               rotate_image->rows-(tile_x+width)),height,1,exception);
1311             if (q == (Quantum *) NULL)
1312               {
1313                 status=MagickFalse;
1314                 continue;
1315               }
1316             tile_pixels=p+((width-1)-y)*GetPixelChannels(image);
1317             for (x=0; x < (ssize_t) height; x++)
1318             {
1319               register ssize_t
1320                 i;
1321
1322               if (GetPixelReadMask(image,tile_pixels) == 0)
1323                 {
1324                   tile_pixels+=width*GetPixelChannels(image);
1325                   q+=GetPixelChannels(rotate_image);
1326                   continue;
1327                 }
1328               for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1329               {
1330                 PixelChannel channel=GetPixelChannelChannel(image,i);
1331                 PixelTrait traits=GetPixelChannelTraits(image,channel);
1332                 PixelTrait rotate_traits=GetPixelChannelTraits(rotate_image,
1333                   channel);
1334                 if ((traits == UndefinedPixelTrait) ||
1335                     (rotate_traits == UndefinedPixelTrait))
1336                   continue;
1337                 SetPixelChannel(rotate_image,channel,tile_pixels[i],q);
1338               }
1339               tile_pixels+=width*GetPixelChannels(image);
1340               q+=GetPixelChannels(rotate_image);
1341             }
1342 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1343             #pragma omp critical (MagickCore_IntegralRotateImage)
1344 #endif
1345             sync=SyncCacheViewAuthenticPixels(rotate_view,exception);
1346             if (sync == MagickFalse)
1347               status=MagickFalse;
1348           }
1349         }
1350         if (image->progress_monitor != (MagickProgressMonitor) NULL)
1351           {
1352             MagickBooleanType
1353               proceed;
1354
1355             proceed=SetImageProgress(image,RotateImageTag,progress+=tile_height,
1356               image->rows);
1357             if (proceed == MagickFalse)
1358               status=MagickFalse;
1359           }
1360       }
1361       (void) SetImageProgress(image,RotateImageTag,(MagickOffsetType)
1362         image->rows-1,image->rows);
1363       Swap(page.width,page.height);
1364       Swap(page.x,page.y);
1365       if (page.width != 0)
1366         page.x=(ssize_t) (page.width-rotate_image->columns-page.x);
1367       break;
1368     }
1369   }
1370   rotate_view=DestroyCacheView(rotate_view);
1371   image_view=DestroyCacheView(image_view);
1372   rotate_image->type=image->type;
1373   rotate_image->page=page;
1374   if (status == MagickFalse)
1375     rotate_image=DestroyImage(rotate_image);
1376   return(rotate_image);
1377 }
1378 \f
1379 /*
1380 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1381 %                                                                             %
1382 %                                                                             %
1383 %                                                                             %
1384 +   X S h e a r I m a g e                                                     %
1385 %                                                                             %
1386 %                                                                             %
1387 %                                                                             %
1388 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1389 %
1390 %  XShearImage() shears the image in the X direction with a shear angle of
1391 %  'degrees'.  Positive angles shear counter-clockwise (right-hand rule), and
1392 %  negative angles shear clockwise.  Angles are measured relative to a vertical
1393 %  Y-axis.  X shears will widen an image creating 'empty' triangles on the left
1394 %  and right sides of the source image.
1395 %
1396 %  The format of the XShearImage method is:
1397 %
1398 %      MagickBooleanType XShearImage(Image *image,const double degrees,
1399 %        const size_t width,const size_t height,
1400 %        const ssize_t x_offset,const ssize_t y_offset,ExceptionInfo *exception)
1401 %
1402 %  A description of each parameter follows.
1403 %
1404 %    o image: the image.
1405 %
1406 %    o degrees: A double representing the shearing angle along the X
1407 %      axis.
1408 %
1409 %    o width, height, x_offset, y_offset: Defines a region of the image
1410 %      to shear.
1411 %
1412 %    o exception: return any errors or warnings in this structure.
1413 %
1414 */
1415 static MagickBooleanType XShearImage(Image *image,const double degrees,
1416   const size_t width,const size_t height,const ssize_t x_offset,
1417   const ssize_t y_offset,ExceptionInfo *exception)
1418 {
1419 #define XShearImageTag  "XShear/Image"
1420
1421   typedef enum
1422   {
1423     LEFT,
1424     RIGHT
1425   } ShearDirection;
1426
1427   CacheView
1428     *image_view;
1429
1430   MagickBooleanType
1431     status;
1432
1433   MagickOffsetType
1434     progress;
1435
1436   PixelInfo
1437     background;
1438
1439   ssize_t
1440     y;
1441
1442   /*
1443     X shear image.
1444   */
1445   assert(image != (Image *) NULL);
1446   assert(image->signature == MagickSignature);
1447   if (image->debug != MagickFalse)
1448     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1449   status=MagickTrue;
1450   background=image->background_color;
1451   progress=0;
1452   image_view=AcquireAuthenticCacheView(image,exception);
1453 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1454   #pragma omp parallel for schedule(static,4) shared(progress,status) \
1455     magick_threads(image,image,height,1)
1456 #endif
1457   for (y=0; y < (ssize_t) height; y++)
1458   {
1459     PixelInfo
1460       pixel,
1461       source,
1462       destination;
1463
1464     double
1465       area,
1466       displacement;
1467
1468     register Quantum
1469       *restrict p,
1470       *restrict q;
1471
1472     register ssize_t
1473       i;
1474
1475     ShearDirection
1476       direction;
1477
1478     ssize_t
1479       step;
1480
1481     if (status == MagickFalse)
1482       continue;
1483     p=GetCacheViewAuthenticPixels(image_view,0,y_offset+y,image->columns,1,
1484       exception);
1485     if (p == (Quantum *) NULL)
1486       {
1487         status=MagickFalse;
1488         continue;
1489       }
1490     p+=x_offset*GetPixelChannels(image);
1491     displacement=degrees*(double) (y-height/2.0);
1492     if (displacement == 0.0)
1493       continue;
1494     if (displacement > 0.0)
1495       direction=RIGHT;
1496     else
1497       {
1498         displacement*=(-1.0);
1499         direction=LEFT;
1500       }
1501     step=(ssize_t) floor((double) displacement);
1502     area=(double) (displacement-step);
1503     step++;
1504     pixel=background;
1505     GetPixelInfo(image,&source);
1506     GetPixelInfo(image,&destination);
1507     switch (direction)
1508     {
1509       case LEFT:
1510       {
1511         /*
1512           Transfer pixels left-to-right.
1513         */
1514         if (step > x_offset)
1515           break;
1516         q=p-step*GetPixelChannels(image);
1517         for (i=0; i < (ssize_t) width; i++)
1518         {
1519           if ((x_offset+i) < step)
1520             {
1521               p+=GetPixelChannels(image);
1522               GetPixelInfoPixel(image,p,&pixel);
1523               q+=GetPixelChannels(image);
1524               continue;
1525             }
1526           GetPixelInfoPixel(image,p,&source);
1527           CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1528             &source,(double) GetPixelAlpha(image,p),area,&destination);
1529           SetPixelInfoPixel(image,&destination,q);
1530           GetPixelInfoPixel(image,p,&pixel);
1531           p+=GetPixelChannels(image);
1532           q+=GetPixelChannels(image);
1533         }
1534         CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1535           &background,(double) background.alpha,area,&destination);
1536         SetPixelInfoPixel(image,&destination,q);
1537         q+=GetPixelChannels(image);
1538         for (i=0; i < (step-1); i++)
1539         {
1540           SetPixelInfoPixel(image,&background,q);
1541           q+=GetPixelChannels(image);
1542         }
1543         break;
1544       }
1545       case RIGHT:
1546       {
1547         /*
1548           Transfer pixels right-to-left.
1549         */
1550         p+=width*GetPixelChannels(image);
1551         q=p+step*GetPixelChannels(image);
1552         for (i=0; i < (ssize_t) width; i++)
1553         {
1554           p-=GetPixelChannels(image);
1555           q-=GetPixelChannels(image);
1556           if ((size_t) (x_offset+width+step-i) >= image->columns)
1557             continue;
1558           GetPixelInfoPixel(image,p,&source);
1559           CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1560             &source,(double) GetPixelAlpha(image,p),area,&destination);
1561           SetPixelInfoPixel(image,&destination,q);
1562           GetPixelInfoPixel(image,p,&pixel);
1563         }
1564         CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1565           &background,(double) background.alpha,area,&destination);
1566         q-=GetPixelChannels(image);
1567         SetPixelInfoPixel(image,&destination,q);
1568         for (i=0; i < (step-1); i++)
1569         {
1570           q-=GetPixelChannels(image);
1571           SetPixelInfoPixel(image,&background,q);
1572         }
1573         break;
1574       }
1575     }
1576     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
1577       status=MagickFalse;
1578     if (image->progress_monitor != (MagickProgressMonitor) NULL)
1579       {
1580         MagickBooleanType
1581           proceed;
1582
1583 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1584         #pragma omp critical (MagickCore_XShearImage)
1585 #endif
1586         proceed=SetImageProgress(image,XShearImageTag,progress++,height);
1587         if (proceed == MagickFalse)
1588           status=MagickFalse;
1589       }
1590   }
1591   image_view=DestroyCacheView(image_view);
1592   return(status);
1593 }
1594 \f
1595 /*
1596 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1597 %                                                                             %
1598 %                                                                             %
1599 %                                                                             %
1600 +   Y S h e a r I m a g e                                                     %
1601 %                                                                             %
1602 %                                                                             %
1603 %                                                                             %
1604 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1605 %
1606 %  YShearImage shears the image in the Y direction with a shear angle of
1607 %  'degrees'.  Positive angles shear counter-clockwise (right-hand rule), and
1608 %  negative angles shear clockwise.  Angles are measured relative to a
1609 %  horizontal X-axis.  Y shears will increase the height of an image creating
1610 %  'empty' triangles on the top and bottom of the source image.
1611 %
1612 %  The format of the YShearImage method is:
1613 %
1614 %      MagickBooleanType YShearImage(Image *image,const double degrees,
1615 %        const size_t width,const size_t height,
1616 %        const ssize_t x_offset,const ssize_t y_offset,ExceptionInfo *exception)
1617 %
1618 %  A description of each parameter follows.
1619 %
1620 %    o image: the image.
1621 %
1622 %    o degrees: A double representing the shearing angle along the Y
1623 %      axis.
1624 %
1625 %    o width, height, x_offset, y_offset: Defines a region of the image
1626 %      to shear.
1627 %
1628 %    o exception: return any errors or warnings in this structure.
1629 %
1630 */
1631 static MagickBooleanType YShearImage(Image *image,const double degrees,
1632   const size_t width,const size_t height,const ssize_t x_offset,
1633   const ssize_t y_offset,ExceptionInfo *exception)
1634 {
1635 #define YShearImageTag  "YShear/Image"
1636
1637   typedef enum
1638   {
1639     UP,
1640     DOWN
1641   } ShearDirection;
1642
1643   CacheView
1644     *image_view;
1645
1646   MagickBooleanType
1647     status;
1648
1649   MagickOffsetType
1650     progress;
1651
1652   PixelInfo
1653     background;
1654
1655   ssize_t
1656     x;
1657
1658   /*
1659     Y Shear image.
1660   */
1661   assert(image != (Image *) NULL);
1662   assert(image->signature == MagickSignature);
1663   if (image->debug != MagickFalse)
1664     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1665   status=MagickTrue;
1666   progress=0;
1667   background=image->background_color;
1668   image_view=AcquireAuthenticCacheView(image,exception);
1669 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1670   #pragma omp parallel for schedule(static,4) shared(progress,status) \
1671     magick_threads(image,image,width,1)
1672 #endif
1673   for (x=0; x < (ssize_t) width; x++)
1674   {
1675     ssize_t
1676       step;
1677
1678     double
1679       area,
1680       displacement;
1681
1682     PixelInfo
1683       pixel,
1684       source,
1685       destination;
1686
1687     register Quantum
1688       *restrict p,
1689       *restrict q;
1690
1691     register ssize_t
1692       i;
1693
1694     ShearDirection
1695       direction;
1696
1697     if (status == MagickFalse)
1698       continue;
1699     p=GetCacheViewAuthenticPixels(image_view,x_offset+x,0,1,image->rows,
1700       exception);
1701     if (p == (Quantum *) NULL)
1702       {
1703         status=MagickFalse;
1704         continue;
1705       }
1706     p+=y_offset*GetPixelChannels(image);
1707     displacement=degrees*(double) (x-width/2.0);
1708     if (displacement == 0.0)
1709       continue;
1710     if (displacement > 0.0)
1711       direction=DOWN;
1712     else
1713       {
1714         displacement*=(-1.0);
1715         direction=UP;
1716       }
1717     step=(ssize_t) floor((double) displacement);
1718     area=(double) (displacement-step);
1719     step++;
1720     pixel=background;
1721     GetPixelInfo(image,&source);
1722     GetPixelInfo(image,&destination);
1723     switch (direction)
1724     {
1725       case UP:
1726       {
1727         /*
1728           Transfer pixels top-to-bottom.
1729         */
1730         if (step > y_offset)
1731           break;
1732         q=p-step*GetPixelChannels(image);
1733         for (i=0; i < (ssize_t) height; i++)
1734         {
1735           if ((y_offset+i) < step)
1736             {
1737               p+=GetPixelChannels(image);
1738               GetPixelInfoPixel(image,p,&pixel);
1739               q+=GetPixelChannels(image);
1740               continue;
1741             }
1742           GetPixelInfoPixel(image,p,&source);
1743           CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1744             &source,(double) GetPixelAlpha(image,p),area,
1745             &destination);
1746           SetPixelInfoPixel(image,&destination,q);
1747           GetPixelInfoPixel(image,p,&pixel);
1748           p+=GetPixelChannels(image);
1749           q+=GetPixelChannels(image);
1750         }
1751         CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1752           &background,(double) background.alpha,area,&destination);
1753         SetPixelInfoPixel(image,&destination,q);
1754         q+=GetPixelChannels(image);
1755         for (i=0; i < (step-1); i++)
1756         {
1757           SetPixelInfoPixel(image,&background,q);
1758           q+=GetPixelChannels(image);
1759         }
1760         break;
1761       }
1762       case DOWN:
1763       {
1764         /*
1765           Transfer pixels bottom-to-top.
1766         */
1767         p+=height*GetPixelChannels(image);
1768         q=p+step*GetPixelChannels(image);
1769         for (i=0; i < (ssize_t) height; i++)
1770         {
1771           p-=GetPixelChannels(image);
1772           q-=GetPixelChannels(image);
1773           if ((size_t) (y_offset+height+step-i) >= image->rows)
1774             continue;
1775           GetPixelInfoPixel(image,p,&source);
1776           CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1777             &source,(double) GetPixelAlpha(image,p),area,
1778             &destination);
1779           SetPixelInfoPixel(image,&destination,q);
1780           GetPixelInfoPixel(image,p,&pixel);
1781         }
1782         CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1783           &background,(double) background.alpha,area,&destination);
1784         q-=GetPixelChannels(image);
1785         SetPixelInfoPixel(image,&destination,q);
1786         for (i=0; i < (step-1); i++)
1787         {
1788           q-=GetPixelChannels(image);
1789           SetPixelInfoPixel(image,&background,q);
1790         }
1791         break;
1792       }
1793     }
1794     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
1795       status=MagickFalse;
1796     if (image->progress_monitor != (MagickProgressMonitor) NULL)
1797       {
1798         MagickBooleanType
1799           proceed;
1800
1801 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1802         #pragma omp critical (MagickCore_YShearImage)
1803 #endif
1804         proceed=SetImageProgress(image,YShearImageTag,progress++,image->rows);
1805         if (proceed == MagickFalse)
1806           status=MagickFalse;
1807       }
1808   }
1809   image_view=DestroyCacheView(image_view);
1810   return(status);
1811 }
1812 \f
1813 /*
1814 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1815 %                                                                             %
1816 %                                                                             %
1817 %                                                                             %
1818 %   S h e a r I m a g e                                                       %
1819 %                                                                             %
1820 %                                                                             %
1821 %                                                                             %
1822 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1823 %
1824 %  ShearImage() creates a new image that is a shear_image copy of an existing
1825 %  one.  Shearing slides one edge of an image along the X or Y axis, creating
1826 %  a parallelogram.  An X direction shear slides an edge along the X axis,
1827 %  while a Y direction shear slides an edge along the Y axis.  The amount of
1828 %  the shear is controlled by a shear angle.  For X direction shears, x_shear
1829 %  is measured relative to the Y axis, and similarly, for Y direction shears
1830 %  y_shear is measured relative to the X axis.  Empty triangles left over from
1831 %  shearing the image are filled with the background color defined by member
1832 %  'background_color' of the image..  ShearImage() allocates the memory
1833 %  necessary for the new Image structure and returns a pointer to the new image.
1834 %
1835 %  ShearImage() is based on the paper "A Fast Algorithm for General Raster
1836 %  Rotatation" by Alan W. Paeth.
1837 %
1838 %  The format of the ShearImage method is:
1839 %
1840 %      Image *ShearImage(const Image *image,const double x_shear,
1841 %        const double y_shear,ExceptionInfo *exception)
1842 %
1843 %  A description of each parameter follows.
1844 %
1845 %    o image: the image.
1846 %
1847 %    o x_shear, y_shear: Specifies the number of degrees to shear the image.
1848 %
1849 %    o exception: return any errors or warnings in this structure.
1850 %
1851 */
1852 MagickExport Image *ShearImage(const Image *image,const double x_shear,
1853   const double y_shear,ExceptionInfo *exception)
1854 {
1855   Image
1856     *integral_image,
1857     *shear_image;
1858
1859   ssize_t
1860     x_offset,
1861     y_offset;
1862
1863   MagickBooleanType
1864     status;
1865
1866   PointInfo
1867     shear;
1868
1869   RectangleInfo
1870     border_info;
1871
1872   size_t
1873     y_width;
1874
1875   assert(image != (Image *) NULL);
1876   assert(image->signature == MagickSignature);
1877   if (image->debug != MagickFalse)
1878     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1879   assert(exception != (ExceptionInfo *) NULL);
1880   assert(exception->signature == MagickSignature);
1881   if ((x_shear != 0.0) && (fmod(x_shear,90.0) == 0.0))
1882     ThrowImageException(ImageError,"AngleIsDiscontinuous");
1883   if ((y_shear != 0.0) && (fmod(y_shear,90.0) == 0.0))
1884     ThrowImageException(ImageError,"AngleIsDiscontinuous");
1885   /*
1886     Initialize shear angle.
1887   */
1888   integral_image=CloneImage(image,0,0,MagickTrue,exception);
1889   if (integral_image == (Image *) NULL)
1890     ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
1891   shear.x=(-tan(DegreesToRadians(fmod(x_shear,360.0))));
1892   shear.y=tan(DegreesToRadians(fmod(y_shear,360.0)));
1893   if ((shear.x == 0.0) && (shear.y == 0.0))
1894     return(integral_image);
1895   if (SetImageStorageClass(integral_image,DirectClass,exception) == MagickFalse)
1896     {
1897       integral_image=DestroyImage(integral_image);
1898       return(integral_image);
1899     }
1900   if (integral_image->alpha_trait != BlendPixelTrait)
1901     (void) SetImageAlphaChannel(integral_image,OpaqueAlphaChannel,exception);
1902   /*
1903     Compute image size.
1904   */
1905   y_width=image->columns+(ssize_t) floor(fabs(shear.x)*image->rows+0.5);
1906   x_offset=(ssize_t) ceil((double) image->columns+((fabs(shear.x)*image->rows)-
1907     image->columns)/2.0-0.5);
1908   y_offset=(ssize_t) ceil((double) image->rows+((fabs(shear.y)*y_width)-
1909     image->rows)/2.0-0.5);
1910   /*
1911     Surround image with border.
1912   */
1913   integral_image->border_color=integral_image->background_color;
1914   integral_image->compose=CopyCompositeOp;
1915   border_info.width=(size_t) x_offset;
1916   border_info.height=(size_t) y_offset;
1917   shear_image=BorderImage(integral_image,&border_info,image->compose,exception);
1918   integral_image=DestroyImage(integral_image);
1919   if (shear_image == (Image *) NULL)
1920     ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
1921   /*
1922     Shear the image.
1923   */
1924   if (shear_image->alpha_trait != BlendPixelTrait)
1925     (void) SetImageAlphaChannel(shear_image,OpaqueAlphaChannel,exception);
1926   status=XShearImage(shear_image,shear.x,image->columns,image->rows,x_offset,
1927     (ssize_t) (shear_image->rows-image->rows)/2,exception);
1928   if (status == MagickFalse)
1929     {
1930       shear_image=DestroyImage(shear_image);
1931       return((Image *) NULL);
1932     }
1933   status=YShearImage(shear_image,shear.y,y_width,image->rows,(ssize_t)
1934     (shear_image->columns-y_width)/2,y_offset,exception);
1935   if (status == MagickFalse)
1936     {
1937       shear_image=DestroyImage(shear_image);
1938       return((Image *) NULL);
1939     }
1940   status=CropToFitImage(&shear_image,shear.x,shear.y,(double)
1941     image->columns,(double) image->rows,MagickFalse,exception);
1942   shear_image->compose=image->compose;
1943   shear_image->page.width=0;
1944   shear_image->page.height=0;
1945   if (status == MagickFalse)
1946     shear_image=DestroyImage(shear_image);
1947   return(shear_image);
1948 }
1949 \f
1950 /*
1951 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1952 %                                                                             %
1953 %                                                                             %
1954 %                                                                             %
1955 %   S h e a r R o t a t e I m a g e                                           %
1956 %                                                                             %
1957 %                                                                             %
1958 %                                                                             %
1959 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1960 %
1961 %  ShearRotateImage() creates a new image that is a rotated copy of an existing
1962 %  one.  Positive angles rotate counter-clockwise (right-hand rule), while
1963 %  negative angles rotate clockwise.  Rotated images are usually larger than
1964 %  the originals and have 'empty' triangular corners.  X axis.  Empty
1965 %  triangles left over from shearing the image are filled with the background
1966 %  color defined by member 'background_color' of the image.  ShearRotateImage
1967 %  allocates the memory necessary for the new Image structure and returns a
1968 %  pointer to the new image.
1969 %
1970 %  ShearRotateImage() is based on the paper "A Fast Algorithm for General
1971 %  Raster Rotatation" by Alan W. Paeth.  ShearRotateImage is adapted from a
1972 %  similar method based on the Paeth paper written by Michael Halle of the
1973 %  Spatial Imaging Group, MIT Media Lab.
1974 %
1975 %  The format of the ShearRotateImage method is:
1976 %
1977 %      Image *ShearRotateImage(const Image *image,const double degrees,
1978 %        ExceptionInfo *exception)
1979 %
1980 %  A description of each parameter follows.
1981 %
1982 %    o image: the image.
1983 %
1984 %    o degrees: Specifies the number of degrees to rotate the image.
1985 %
1986 %    o exception: return any errors or warnings in this structure.
1987 %
1988 */
1989 MagickExport Image *ShearRotateImage(const Image *image,const double degrees,
1990   ExceptionInfo *exception)
1991 {
1992   Image
1993     *integral_image,
1994     *rotate_image;
1995
1996   MagickBooleanType
1997     status;
1998
1999   double
2000     angle;
2001
2002   PointInfo
2003     shear;
2004
2005   RectangleInfo
2006     border_info;
2007
2008   size_t
2009     height,
2010     rotations,
2011     width,
2012     y_width;
2013
2014   ssize_t
2015     x_offset,
2016     y_offset;
2017
2018   /*
2019     Adjust rotation angle.
2020   */
2021   assert(image != (Image *) NULL);
2022   assert(image->signature == MagickSignature);
2023   if (image->debug != MagickFalse)
2024     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2025   assert(exception != (ExceptionInfo *) NULL);
2026   assert(exception->signature == MagickSignature);
2027   angle=degrees;
2028   while (angle < -45.0)
2029     angle+=360.0;
2030   for (rotations=0; angle > 45.0; rotations++)
2031     angle-=90.0;
2032   rotations%=4;
2033   /*
2034     Calculate shear equations.
2035   */
2036   integral_image=IntegralRotateImage(image,rotations,exception);
2037   if (integral_image == (Image *) NULL)
2038     ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
2039   shear.x=(-tan((double) DegreesToRadians(angle)/2.0));
2040   shear.y=sin((double) DegreesToRadians(angle));
2041   if ((shear.x == 0.0) && (shear.y == 0.0))
2042     return(integral_image);
2043   if (SetImageStorageClass(integral_image,DirectClass,exception) == MagickFalse)
2044     {
2045       integral_image=DestroyImage(integral_image);
2046       return(integral_image);
2047     }
2048   if (integral_image->alpha_trait != BlendPixelTrait)
2049     (void) SetImageAlphaChannel(integral_image,OpaqueAlphaChannel,exception);
2050   /*
2051     Compute image size.
2052   */
2053   width=image->columns;
2054   height=image->rows;
2055   if ((rotations == 1) || (rotations == 3))
2056     {
2057       width=image->rows;
2058       height=image->columns;
2059     }
2060   y_width=width+(ssize_t) floor(fabs(shear.x)*height+0.5);
2061   x_offset=(ssize_t) ceil((double) width+((fabs(shear.y)*height)-width)/2.0-
2062     0.5);
2063   y_offset=(ssize_t) ceil((double) height+((fabs(shear.y)*y_width)-height)/2.0-
2064     0.5);
2065   /*
2066     Surround image with a border.
2067   */
2068   integral_image->border_color=integral_image->background_color;
2069   integral_image->compose=CopyCompositeOp;
2070   border_info.width=(size_t) x_offset;
2071   border_info.height=(size_t) y_offset;
2072   rotate_image=BorderImage(integral_image,&border_info,image->compose,
2073     exception);
2074   integral_image=DestroyImage(integral_image);
2075   if (rotate_image == (Image *) NULL)
2076     ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
2077   /*
2078     Rotate the image.
2079   */
2080   status=XShearImage(rotate_image,shear.x,width,height,x_offset,(ssize_t)
2081     (rotate_image->rows-height)/2,exception);
2082   if (status == MagickFalse)
2083     {
2084       rotate_image=DestroyImage(rotate_image);
2085       return((Image *) NULL);
2086     }
2087   status=YShearImage(rotate_image,shear.y,y_width,height,(ssize_t)
2088     (rotate_image->columns-y_width)/2,y_offset,exception);
2089   if (status == MagickFalse)
2090     {
2091       rotate_image=DestroyImage(rotate_image);
2092       return((Image *) NULL);
2093     }
2094   status=XShearImage(rotate_image,shear.x,y_width,rotate_image->rows,(ssize_t)
2095     (rotate_image->columns-y_width)/2,0,exception);
2096   if (status == MagickFalse)
2097     {
2098       rotate_image=DestroyImage(rotate_image);
2099       return((Image *) NULL);
2100     }
2101   status=CropToFitImage(&rotate_image,shear.x,shear.y,(double) width,
2102     (double) height,MagickTrue,exception);
2103   rotate_image->compose=image->compose;
2104   rotate_image->page.width=0;
2105   rotate_image->page.height=0;
2106   if (status == MagickFalse)
2107     rotate_image=DestroyImage(rotate_image);
2108   return(rotate_image);
2109 }