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 format of the DeskewImage method is:
 196 %
 197 %      Image *DeskewImage(const Image *image,const double threshold,
 198 %        ExceptionInfo *exception)
 199 %
 200 %  A description of each parameter follows:
 201 %
 202 %    o image: the image.
 203 %
 204 %    o threshold: separate background from foreground.
 205 %
 206 %    o exception: return any errors or warnings in this structure.
 207 %
 208 */
 209
 210 typedef struct _RadonInfo
 211 {
 212   CacheType
 213     type;
 214
 215   size_t
 216     width,
 217     height;
 218
 219   MagickSizeType
 220     length;
 221
 222   MagickBooleanType
 223     mapped;
 224
 225   char
 226     path[MaxTextExtent];
 227
 228   int
 229     file;
 230
 231   unsigned short
 232     *cells;
 233 } RadonInfo;
 234
 235 static RadonInfo *DestroyRadonInfo(RadonInfo *radon_info)
 236 {
 237   assert(radon_info != (RadonInfo *) NULL);
 238   switch (radon_info->type)
 239   {
 240     case MemoryCache:
 241     {
 242       if (radon_info->mapped == MagickFalse)
 243         radon_info->cells=(unsigned short *) RelinquishMagickMemory(
 244           radon_info->cells);
 245       else
 246         radon_info->cells=(unsigned short *) UnmapBlob(radon_info->cells,
 247           (size_t) radon_info->length);
 248       RelinquishMagickResource(MemoryResource,radon_info->length);
 249       break;
 250     }
 251     case MapCache:
 252     {
 253       radon_info->cells=(unsigned short *) UnmapBlob(radon_info->cells,(size_t)
 254         radon_info->length);
 255       RelinquishMagickResource(MapResource,radon_info->length);
 256     }
 257     case DiskCache:
 258     {
 259       if (radon_info->file != -1)
 260         (void) close(radon_info->file);
 261       (void) RelinquishUniqueFileResource(radon_info->path);
 262       RelinquishMagickResource(DiskResource,radon_info->length);
 263       break;
 264     }
 265     default:
 266       break;
 267   }
 268   return((RadonInfo *) RelinquishMagickMemory(radon_info));
 269 }
 270
 271 static MagickBooleanType ResetRadonCells(RadonInfo *radon_info)
 272 {
 273   register ssize_t
 274     x;
 275
 276   ssize_t
 277     count,
 278     y;
 279
 280   unsigned short
 281     value;
 282
 283   if (radon_info->type != DiskCache)
 284     {
 285       (void) ResetMagickMemory(radon_info->cells,0,(size_t) radon_info->length);
 286       return(MagickTrue);
 287     }
 288   value=0;
 289   (void) lseek(radon_info->file,0,SEEK_SET);
 290   for (y=0; y < (ssize_t) radon_info->height; y++)
 291   {
 292     for (x=0; x < (ssize_t) radon_info->width; x++)
 293     {
 294       count=write(radon_info->file,&value,sizeof(*radon_info->cells));
 295       if (count != (ssize_t) sizeof(*radon_info->cells))
 296         break;
 297     }
 298     if (x < (ssize_t) radon_info->width)
 299       break;
 300   }
 301   return(y < (ssize_t) radon_info->height ? MagickFalse : MagickTrue);
 302 }
 303
 304 static RadonInfo *AcquireRadonInfo(const Image *image,const size_t width,
 305   const size_t height,ExceptionInfo *exception)
 306 {
 307   MagickBooleanType
 308     status;
 309
 310   RadonInfo
 311     *radon_info;
 312
 313   radon_info=(RadonInfo *) AcquireMagickMemory(sizeof(*radon_info));
 314   if (radon_info == (RadonInfo *) NULL)
 315     return((RadonInfo *) NULL);
 316   (void) ResetMagickMemory(radon_info,0,sizeof(*radon_info));
 317   radon_info->width=width;
 318   radon_info->height=height;
 319   radon_info->length=(MagickSizeType) width*height*sizeof(*radon_info->cells);
 320   radon_info->type=MemoryCache;
 321   status=AcquireMagickResource(AreaResource,radon_info->length);
 322   if ((status != MagickFalse) &&
 323       (radon_info->length == (MagickSizeType) ((size_t) radon_info->length)))
 324     {
 325       status=AcquireMagickResource(MemoryResource,radon_info->length);
 326       if (status != MagickFalse)
 327         {
 328           radon_info->mapped=MagickFalse;
 329           radon_info->cells=(unsigned short *) AcquireMagickMemory((size_t)
 330             radon_info->length);
 331           if (radon_info->cells == (unsigned short *) NULL)
 332             {
 333               radon_info->mapped=MagickTrue;
 334               radon_info->cells=(unsigned short *) MapBlob(-1,IOMode,0,(size_t)
 335                 radon_info->length);
 336             }
 337           if (radon_info->cells == (unsigned short *) NULL)
 338             RelinquishMagickResource(MemoryResource,radon_info->length);
 339         }
 340     }
 341   radon_info->file=(-1);
 342   if (radon_info->cells == (unsigned short *) NULL)
 343     {
 344       status=AcquireMagickResource(DiskResource,radon_info->length);
 345       if (status == MagickFalse)
 346         {
 347           (void) ThrowMagickException(exception,GetMagickModule(),CacheError,
 348             "CacheResourcesExhausted","`%s'",image->filename);
 349           return(DestroyRadonInfo(radon_info));
 350         }
 351       radon_info->type=DiskCache;
 352       (void) AcquireMagickResource(MemoryResource,radon_info->length);
 353       radon_info->file=AcquireUniqueFileResource(radon_info->path);
 354       if (radon_info->file == -1)
 355         return(DestroyRadonInfo(radon_info));
 356       status=AcquireMagickResource(MapResource,radon_info->length);
 357       if (status != MagickFalse)
 358         {
 359           status=ResetRadonCells(radon_info);
 360           if (status != MagickFalse)
 361             {
 362               radon_info->cells=(unsigned short *) MapBlob(radon_info->file,
 363                 IOMode,0,(size_t) radon_info->length);
 364               if (radon_info->cells != (unsigned short *) NULL)
 365                 radon_info->type=MapCache;
 366               else
 367                 RelinquishMagickResource(MapResource,radon_info->length);
 368             }
 369         }
 370     }
 371   return(radon_info);
 372 }
 373
 374 static inline size_t MagickMin(const size_t x,const size_t y)
 375 {
 376   if (x < y)
 377     return(x);
 378   return(y);
 379 }
 380
 381 static inline ssize_t ReadRadonCell(const RadonInfo *radon_info,
 382   const MagickOffsetType offset,const size_t length,unsigned char *buffer)
 383 {
 384   register ssize_t
 385     i;
 386
 387   ssize_t
 388     count;
 389
 390 #if !defined(MAGICKCORE_HAVE_PPREAD)
 391 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 392   #pragma omp critical (MagickCore_ReadRadonCell)
 393 #endif
 394   {
 395     i=(-1);
 396     if (lseek(radon_info->file,offset,SEEK_SET) >= 0)
 397       {
 398 #endif
 399         count=0;
 400         for (i=0; i < (ssize_t) length; i+=count)
 401         {
 402 #if !defined(MAGICKCORE_HAVE_PPREAD)
 403           count=read(radon_info->file,buffer+i,MagickMin(length-i,(size_t)
 404             SSIZE_MAX));
 405 #else
 406           count=pread(radon_info->file,buffer+i,MagickMin(length-i,(size_t)
 407             SSIZE_MAX),offset+i);
 408 #endif
 409           if (count > 0)
 410             continue;
 411           count=0;
 412           if (errno != EINTR)
 413             {
 414               i=(-1);
 415               break;
 416             }
 417         }
 418 #if !defined(MAGICKCORE_HAVE_PPREAD)
 419       }
 420   }
 421 #endif
 422   return(i);
 423 }
 424
 425 static inline ssize_t WriteRadonCell(const RadonInfo *radon_info,
 426   const MagickOffsetType offset,const size_t length,const unsigned char *buffer)
 427 {
 428   register ssize_t
 429     i;
 430
 431   ssize_t
 432     count;
 433
 434 #if !defined(MAGICKCORE_HAVE_PWRITE)
 435 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 436   #pragma omp critical (MagickCore_WriteRadonCell)
 437 #endif
 438   {
 439     if (lseek(radon_info->file,offset,SEEK_SET) >= 0)
 440       {
 441 #endif
 442         count=0;
 443         for (i=0; i < (ssize_t) length; i+=count)
 444         {
 445 #if !defined(MAGICKCORE_HAVE_PWRITE)
 446           count=write(radon_info->file,buffer+i,MagickMin(length-i,(size_t)
 447             SSIZE_MAX));
 448 #else
 449           count=pwrite(radon_info->file,buffer+i,MagickMin(length-i,(size_t)
 450             SSIZE_MAX),offset+i);
 451 #endif
 452           if (count > 0)
 453             continue;
 454           count=0;
 455           if (errno != EINTR)
 456             {
 457               i=(-1);
 458               break;
 459             }
 460         }
 461 #if !defined(MAGICKCORE_HAVE_PWRITE)
 462       }
 463   }
 464 #endif
 465   return(i);
 466 }
 467
 468 static inline unsigned short GetRadonCell(const RadonInfo *radon_info,
 469   const ssize_t x,const ssize_t y)
 470 {
 471   MagickOffsetType
 472     i;
 473
 474   unsigned short
 475     value;
 476
 477   i=(MagickOffsetType) radon_info->height*x+y;
 478   if ((i < 0) ||
 479       ((MagickSizeType) (i*sizeof(*radon_info->cells)) >= radon_info->length))
 480     return(0);
 481   if (radon_info->type != DiskCache)
 482     return(radon_info->cells[i]);
 483   value=0;
 484   (void) ReadRadonCell(radon_info,i*sizeof(*radon_info->cells),
 485     sizeof(*radon_info->cells),(unsigned char *) &value);
 486   return(value);
 487 }
 488
 489 static inline MagickBooleanType SetRadonCell(const RadonInfo *radon_info,
 490   const ssize_t x,const ssize_t y,const unsigned short value)
 491 {
 492   MagickOffsetType
 493     i;
 494
 495   ssize_t
 496     count;
 497
 498   i=(MagickOffsetType) radon_info->height*x+y;
 499   if ((i < 0) ||
 500       ((MagickSizeType) (i*sizeof(*radon_info->cells)) >= radon_info->length))
 501     return(MagickFalse);
 502   if (radon_info->type != DiskCache)
 503     {
 504       radon_info->cells[i]=value;
 505       return(MagickTrue);
 506     }
 507   count=WriteRadonCell(radon_info,i*sizeof(*radon_info->cells),
 508     sizeof(*radon_info->cells),(const unsigned char *) &value);
 509   if (count != (ssize_t) sizeof(*radon_info->cells))
 510     return(MagickFalse);
 511   return(MagickTrue);
 512 }
 513
 514 static void RadonProjection(const Image *image,RadonInfo *source_cells,
 515   RadonInfo *destination_cells,const ssize_t sign,size_t *projection)
 516 {
 517   RadonInfo
 518     *swap;
 519
 520   register ssize_t
 521     x;
 522
 523   register RadonInfo
 524     *p,
 525     *q;
 526
 527   size_t
 528     step;
 529
 530   p=source_cells;
 531   q=destination_cells;
 532   for (step=1; step < p->width; step*=2)
 533   {
 534     for (x=0; x < (ssize_t) p->width; x+=2*(ssize_t) step)
 535     {
 536       register ssize_t
 537         i;
 538
 539       ssize_t
 540         y;
 541
 542       unsigned short
 543         cell;
 544
 545       for (i=0; i < (ssize_t) step; i++)
 546       {
 547         for (y=0; y < (ssize_t) (p->height-i-1); y++)
 548         {
 549           cell=GetRadonCell(p,x+i,y);
 550           (void) SetRadonCell(q,x+2*i,y,cell+GetRadonCell(p,x+i+(ssize_t)
 551             step,y+i));
 552           (void) SetRadonCell(q,x+2*i+1,y,cell+GetRadonCell(p,x+i+(ssize_t)
 553             step,y+i+1));
 554         }
 555         for ( ; y < (ssize_t) (p->height-i); y++)
 556         {
 557           cell=GetRadonCell(p,x+i,y);
 558           (void) SetRadonCell(q,x+2*i,y,cell+GetRadonCell(p,x+i+(ssize_t) step,
 559             y+i));
 560           (void) SetRadonCell(q,x+2*i+1,y,cell);
 561         }
 562         for ( ; y < (ssize_t) p->height; y++)
 563         {
 564           cell=GetRadonCell(p,x+i,y);
 565           (void) SetRadonCell(q,x+2*i,y,cell);
 566           (void) SetRadonCell(q,x+2*i+1,y,cell);
 567         }
 568       }
 569     }
 570     swap=p;
 571     p=q;
 572     q=swap;
 573   }
 574 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 575   #pragma omp parallel for schedule(static,4) \
 576     magick_threads(image,image,p->width,1)
 577 #endif
 578   for (x=0; x < (ssize_t) p->width; x++)
 579   {
 580     register ssize_t
 581       y;
 582
 583     size_t
 584       sum;
 585
 586     sum=0;
 587     for (y=0; y < (ssize_t) (p->height-1); y++)
 588     {
 589       ssize_t
 590         delta;
 591
 592       delta=GetRadonCell(p,x,y)-(ssize_t) GetRadonCell(p,x,y+1);
 593       sum+=delta*delta;
 594     }
 595     projection[p->width+sign*x-1]=sum;
 596   }
 597 }
 598
 599 static MagickBooleanType RadonTransform(const Image *image,
 600   const double threshold,size_t *projection,ExceptionInfo *exception)
 601 {
 602   CacheView
 603     *image_view;
 604
 605   MagickBooleanType
 606     status;
 607
 608   RadonInfo
 609     *destination_cells,
 610     *source_cells;
 611
 612   register ssize_t
 613     i;
 614
 615   size_t
 616     count,
 617     width;
 618
 619   ssize_t
 620     y;
 621
 622   unsigned char
 623     byte;
 624
 625   unsigned short
 626     bits[256];
 627
 628   for (width=1; width < ((image->columns+7)/8); width<<=1) ;
 629   source_cells=AcquireRadonInfo(image,width,image->rows,exception);
 630   destination_cells=AcquireRadonInfo(image,width,image->rows,exception);
 631   if ((source_cells == (RadonInfo *) NULL) ||
 632       (destination_cells == (RadonInfo *) NULL))
 633     {
 634       if (destination_cells != (RadonInfo *) NULL)
 635         destination_cells=DestroyRadonInfo(destination_cells);
 636       if (source_cells != (RadonInfo *) NULL)
 637         source_cells=DestroyRadonInfo(source_cells);
 638       return(MagickFalse);
 639     }
 640   if (ResetRadonCells(source_cells) == MagickFalse)
 641     {
 642       destination_cells=DestroyRadonInfo(destination_cells);
 643       source_cells=DestroyRadonInfo(source_cells);
 644       return(MagickFalse);
 645     }
 646   for (i=0; i < 256; i++)
 647   {
 648     byte=(unsigned char) i;
 649     for (count=0; byte != 0; byte>>=1)
 650       count+=byte & 0x01;
 651     bits[i]=(unsigned short) count;
 652   }
 653   status=MagickTrue;
 654   image_view=AcquireVirtualCacheView(image,exception);
 655 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 656   #pragma omp parallel for schedule(static,4) shared(status) \
 657     magick_threads(image,image,image->rows,1)
 658 #endif
 659   for (y=0; y < (ssize_t) image->rows; y++)
 660   {
 661     register const Quantum
 662       *restrict p;
 663
 664     register ssize_t
 665       i,
 666       x;
 667
 668     size_t
 669       bit,
 670       byte;
 671
 672     if (status == MagickFalse)
 673       continue;
 674     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 675     if (p == (const Quantum *) NULL)
 676       {
 677         status=MagickFalse;
 678         continue;
 679       }
 680     bit=0;
 681     byte=0;
 682     i=(ssize_t) (image->columns+7)/8;
 683     for (x=0; x < (ssize_t) image->columns; x++)
 684     {
 685       byte<<=1;
 686       if (GetPixelIntensity(image,p) < threshold)
 687         byte|=0x01;
 688       bit++;
 689       if (bit == 8)
 690         {
 691           (void) SetRadonCell(source_cells,--i,y,bits[byte]);
 692           bit=0;
 693           byte=0;
 694         }
 695       p+=GetPixelChannels(image);
 696     }
 697     if (bit != 0)
 698       {
 699         byte<<=(8-bit);
 700         (void) SetRadonCell(source_cells,--i,y,bits[byte]);
 701       }
 702   }
 703   RadonProjection(image,source_cells,destination_cells,-1,projection);
 704   (void) ResetRadonCells(source_cells);
 705 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 706   #pragma omp parallel for schedule(static,4) shared(status) \
 707     magick_threads(image,image,image->rows,1)
 708 #endif
 709   for (y=0; y < (ssize_t) image->rows; y++)
 710   {
 711     register const Quantum
 712       *restrict p;
 713
 714     register ssize_t
 715       i,
 716       x;
 717
 718     size_t
 719       bit,
 720       byte;
 721
 722     if (status == MagickFalse)
 723       continue;
 724     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 725     if (p == (const Quantum *) NULL)
 726       {
 727         status=MagickFalse;
 728         continue;
 729       }
 730     bit=0;
 731     byte=0;
 732     i=0;
 733     for (x=0; x < (ssize_t) image->columns; x++)
 734     {
 735       byte<<=1;
 736       if (GetPixelIntensity(image,p) < threshold)
 737         byte|=0x01;
 738       bit++;
 739       if (bit == 8)
 740         {
 741           (void) SetRadonCell(source_cells,i++,y,bits[byte]);
 742           bit=0;
 743           byte=0;
 744         }
 745       p+=GetPixelChannels(image);
 746     }
 747     if (bit != 0)
 748       {
 749         byte<<=(8-bit);
 750         (void) SetRadonCell(source_cells,i++,y,bits[byte]);
 751       }
 752   }
 753   RadonProjection(image,source_cells,destination_cells,1,projection);
 754   image_view=DestroyCacheView(image_view);
 755   destination_cells=DestroyRadonInfo(destination_cells);
 756   source_cells=DestroyRadonInfo(source_cells);
 757   return(MagickTrue);
 758 }
 759
 760 static void GetImageBackgroundColor(Image *image,const ssize_t offset,
 761   ExceptionInfo *exception)
 762 {
 763   CacheView
 764     *image_view;
 765
 766   PixelInfo
 767     background;
 768
 769   double
 770     count;
 771
 772   ssize_t
 773     y;
 774
 775   /*
 776     Compute average background color.
 777   */
 778   if (offset <= 0)
 779     return;
 780   GetPixelInfo(image,&background);
 781   count=0.0;
 782   image_view=AcquireVirtualCacheView(image,exception);
 783   for (y=0; y < (ssize_t) image->rows; y++)
 784   {
 785     register const Quantum
 786       *restrict p;
 787
 788     register ssize_t
 789       x;
 790
 791     if ((y >= offset) && (y < ((ssize_t) image->rows-offset)))
 792       continue;
 793     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 794     if (p == (const Quantum *) NULL)
 795       continue;
 796     for (x=0; x < (ssize_t) image->columns; x++)
 797     {
 798       if ((x >= offset) && (x < ((ssize_t) image->columns-offset)))
 799         continue;
 800       background.red+=QuantumScale*GetPixelRed(image,p);
 801       background.green+=QuantumScale*GetPixelGreen(image,p);
 802       background.blue+=QuantumScale*GetPixelBlue(image,p);
 803       if ((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0)
 804         background.alpha+=QuantumScale*GetPixelAlpha(image,p);
 805       count++;
 806       p+=GetPixelChannels(image);
 807     }
 808   }
 809   image_view=DestroyCacheView(image_view);
 810   image->background_color.red=(double) ClampToQuantum(QuantumRange*
 811     background.red/count);
 812   image->background_color.green=(double) ClampToQuantum(QuantumRange*
 813     background.green/count);
 814   image->background_color.blue=(double) ClampToQuantum(QuantumRange*
 815     background.blue/count);
 816   if ((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0)
 817     image->background_color.alpha=(double) ClampToQuantum(QuantumRange*
 818       background.alpha/count);
 819 }
 820
 821 MagickExport Image *DeskewImage(const Image *image,const double threshold,
 822   ExceptionInfo *exception)
 823 {
 824   AffineMatrix
 825     affine_matrix;
 826
 827   const char
 828     *artifact;
 829
 830   double
 831     degrees;
 832
 833   Image
 834     *clone_image,
 835     *crop_image,
 836     *deskew_image,
 837     *median_image;
 838
 839   MagickBooleanType
 840     status;
 841
 842   RectangleInfo
 843     geometry;
 844
 845   register ssize_t
 846     i;
 847
 848   size_t
 849     max_projection,
 850     *projection,
 851     width;
 852
 853   ssize_t
 854     skew;
 855
 856   /*
 857     Compute deskew angle.
 858   */
 859   for (width=1; width < ((image->columns+7)/8); width<<=1) ;
 860   projection=(size_t *) AcquireQuantumMemory((size_t) (2*width-1),
 861     sizeof(*projection));
 862   if (projection == (size_t *) NULL)
 863     ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
 864   status=RadonTransform(image,threshold,projection,exception);
 865   if (status == MagickFalse)
 866     {
 867       projection=(size_t *) RelinquishMagickMemory(projection);
 868       ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
 869     }
 870   max_projection=0;
 871   skew=0;
 872   for (i=0; i < (ssize_t) (2*width-1); i++)
 873   {
 874     if (projection[i] > max_projection)
 875       {
 876         skew=i-(ssize_t) width+1;
 877         max_projection=projection[i];
 878       }
 879   }
 880   projection=(size_t *) RelinquishMagickMemory(projection);
 881   /*
 882     Deskew image.
 883   */
 884   clone_image=CloneImage(image,0,0,MagickTrue,exception);
 885   if (clone_image == (Image *) NULL)
 886     return((Image *) NULL);
 887   (void) SetImageVirtualPixelMethod(clone_image,BackgroundVirtualPixelMethod,
 888     exception);
 889   degrees=RadiansToDegrees(-atan((double) skew/width/8));
 890   if (image->debug != MagickFalse)
 891     (void) LogMagickEvent(TransformEvent,GetMagickModule(),
 892       "  Deskew angle: %g",degrees);
 893   affine_matrix.sx=cos(DegreesToRadians(fmod((double) degrees,360.0)));
 894   affine_matrix.rx=sin(DegreesToRadians(fmod((double) degrees,360.0)));
 895   affine_matrix.ry=(-sin(DegreesToRadians(fmod((double) degrees,360.0))));
 896   affine_matrix.sy=cos(DegreesToRadians(fmod((double) degrees,360.0)));
 897   affine_matrix.tx=0.0;
 898   affine_matrix.ty=0.0;
 899   artifact=GetImageArtifact(image,"deskew:auto-crop");
 900   if (artifact == (const char *) NULL)
 901     {
 902       deskew_image=AffineTransformImage(clone_image,&affine_matrix,exception);
 903       clone_image=DestroyImage(clone_image);
 904       return(deskew_image);
 905     }
 906   /*
 907     Auto-crop image.
 908   */
 909   GetImageBackgroundColor(clone_image,(ssize_t) StringToLong(artifact),
 910     exception);
 911   deskew_image=AffineTransformImage(clone_image,&affine_matrix,exception);
 912   clone_image=DestroyImage(clone_image);
 913   if (deskew_image == (Image *) NULL)
 914     return((Image *) NULL);
 915   median_image=StatisticImage(deskew_image,MedianStatistic,3,3,exception);
 916   if (median_image == (Image *) NULL)
 917     {
 918       deskew_image=DestroyImage(deskew_image);
 919       return((Image *) NULL);
 920     }
 921   geometry=GetImageBoundingBox(median_image,exception);
 922   median_image=DestroyImage(median_image);
 923   if (image->debug != MagickFalse)
 924     (void) LogMagickEvent(TransformEvent,GetMagickModule(),"  Deskew geometry: "
 925       "%.20gx%.20g%+.20g%+.20g",(double) geometry.width,(double)
 926       geometry.height,(double) geometry.x,(double) geometry.y);
 927   crop_image=CropImage(deskew_image,&geometry,exception);
 928   deskew_image=DestroyImage(deskew_image);
 929   return(crop_image);
 930 }
 931 \f
 932 /*
 933 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 934 %                                                                             %
 935 %                                                                             %
 936 %                                                                             %
 937 %   I n t e g r a l R o t a t e I m a g e                                     %
 938 %                                                                             %
 939 %                                                                             %
 940 %                                                                             %
 941 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 942 %
 943 %  IntegralRotateImage() rotates the image an integral of 90 degrees.  It
 944 %  allocates the memory necessary for the new Image structure and returns a
 945 %  pointer to the rotated image.
 946 %
 947 %  The format of the IntegralRotateImage method is:
 948 %
 949 %      Image *IntegralRotateImage(const Image *image,size_t rotations,
 950 %        ExceptionInfo *exception)
 951 %
 952 %  A description of each parameter follows.
 953 %
 954 %    o image: the image.
 955 %
 956 %    o rotations: Specifies the number of 90 degree rotations.
 957 %
 958 */
 959 MagickExport Image *IntegralRotateImage(const Image *image,size_t rotations,
 960   ExceptionInfo *exception)
 961 {
 962 #define RotateImageTag  "Rotate/Image"
 963
 964   CacheView
 965     *image_view,
 966     *rotate_view;
 967
 968   Image
 969     *rotate_image;
 970
 971   MagickBooleanType
 972     status;
 973
 974   MagickOffsetType
 975     progress;
 976
 977   RectangleInfo
 978     page;
 979
 980   ssize_t
 981     y;
 982
 983   /*
 984     Initialize rotated image attributes.
 985   */
 986   assert(image != (Image *) NULL);
 987   page=image->page;
 988   rotations%=4;
 989   if (rotations == 0)
 990     return(CloneImage(image,0,0,MagickTrue,exception));
 991   if ((rotations == 1) || (rotations == 3))
 992     rotate_image=CloneImage(image,image->rows,image->columns,MagickTrue,
 993       exception);
 994   else
 995     rotate_image=CloneImage(image,image->columns,image->rows,MagickTrue,
 996       exception);
 997   if (rotate_image == (Image *) NULL)
 998     return((Image *) NULL);
 999   /*
1000     Integral rotate the image.
1001   */
1002   status=MagickTrue;
1003   progress=0;
1004   image_view=AcquireVirtualCacheView(image,exception);
1005   rotate_view=AcquireAuthenticCacheView(rotate_image,exception);
1006   switch (rotations)
1007   {
1008     case 0:
1009     {
1010       /*
1011         Rotate 0 degrees.
1012       */
1013       break;
1014     }
1015     case 1:
1016     {
1017       size_t
1018         tile_height,
1019         tile_width;
1020
1021       ssize_t
1022         tile_y;
1023
1024       /*
1025         Rotate 90 degrees.
1026       */
1027       GetPixelCacheTileSize(image,&tile_width,&tile_height);
1028       tile_width=image->columns;
1029 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1030       #pragma omp parallel for schedule(static,4) \
1031         magick_threads(image,image,image->rows/tile_height,1)
1032 #endif
1033       for (tile_y=0; tile_y < (ssize_t) image->rows; tile_y+=(ssize_t) tile_height)
1034       {
1035         register ssize_t
1036           tile_x;
1037
1038         if (status == MagickFalse)
1039           continue;
1040         tile_x=0;
1041         for ( ; tile_x < (ssize_t) image->columns; tile_x+=(ssize_t) tile_width)
1042         {
1043           MagickBooleanType
1044             sync;
1045
1046           register const Quantum
1047             *restrict p;
1048
1049           register Quantum
1050             *restrict q;
1051
1052           register ssize_t
1053             y;
1054
1055           size_t
1056             height,
1057             width;
1058
1059           width=tile_width;
1060           if ((tile_x+(ssize_t) tile_width) > (ssize_t) image->columns)
1061             width=(size_t) (tile_width-(tile_x+tile_width-image->columns));
1062           height=tile_height;
1063           if ((tile_y+(ssize_t) tile_height) > (ssize_t) image->rows)
1064             height=(size_t) (tile_height-(tile_y+tile_height-image->rows));
1065           p=GetCacheViewVirtualPixels(image_view,tile_x,tile_y,width,height,
1066             exception);
1067           if (p == (const Quantum *) NULL)
1068             {
1069               status=MagickFalse;
1070               break;
1071             }
1072           for (y=0; y < (ssize_t) width; y++)
1073           {
1074             register const Quantum
1075               *restrict tile_pixels;
1076
1077             register ssize_t
1078               x;
1079
1080             if (status == MagickFalse)
1081               continue;
1082             q=QueueCacheViewAuthenticPixels(rotate_view,(ssize_t)
1083               (rotate_image->columns-(tile_y+height)),y+tile_x,height,1,
1084               exception);
1085             if (q == (Quantum *) NULL)
1086               {
1087                 status=MagickFalse;
1088                 continue;
1089               }
1090             tile_pixels=p+((height-1)*width+y)*GetPixelChannels(image);
1091             for (x=0; x < (ssize_t) height; x++)
1092             {
1093               register ssize_t
1094                 i;
1095
1096               if (GetPixelMask(image,tile_pixels) != 0)
1097                 {
1098                   tile_pixels-=width*GetPixelChannels(image);
1099                   q+=GetPixelChannels(rotate_image);
1100                   continue;
1101                 }
1102               for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1103               {
1104                 PixelChannel
1105                   channel;
1106
1107                 PixelTrait
1108                   rotate_traits,
1109                   traits;
1110
1111                 channel=GetPixelChannelChannel(image,i);
1112                 traits=GetPixelChannelTraits(image,channel);
1113                 rotate_traits=GetPixelChannelTraits(rotate_image,channel);
1114                 if ((traits == UndefinedPixelTrait) ||
1115                     (rotate_traits == UndefinedPixelTrait))
1116                   continue;
1117                 SetPixelChannel(rotate_image,channel,tile_pixels[i],q);
1118               }
1119               tile_pixels-=width*GetPixelChannels(image);
1120               q+=GetPixelChannels(rotate_image);
1121             }
1122             sync=SyncCacheViewAuthenticPixels(rotate_view,exception);
1123             if (sync == MagickFalse)
1124               status=MagickFalse;
1125           }
1126         }
1127         if (image->progress_monitor != (MagickProgressMonitor) NULL)
1128           {
1129             MagickBooleanType
1130               proceed;
1131
1132 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1133             #pragma omp critical (MagickCore_IntegralRotateImage)
1134 #endif
1135             proceed=SetImageProgress(image,RotateImageTag,progress+=tile_height,
1136               image->rows);
1137             if (proceed == MagickFalse)
1138               status=MagickFalse;
1139           }
1140       }
1141       (void) SetImageProgress(image,RotateImageTag,(MagickOffsetType)
1142         image->rows-1,image->rows);
1143       Swap(page.width,page.height);
1144       Swap(page.x,page.y);
1145       if (page.width != 0)
1146         page.x=(ssize_t) (page.width-rotate_image->columns-page.x);
1147       break;
1148     }
1149     case 2:
1150     {
1151       /*
1152         Rotate 180 degrees.
1153       */
1154 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1155       #pragma omp parallel for schedule(static,4) \
1156         magick_threads(image,image,1,1)
1157 #endif
1158       for (y=0; y < (ssize_t) image->rows; y++)
1159       {
1160         MagickBooleanType
1161           sync;
1162
1163         register const Quantum
1164           *restrict p;
1165
1166         register Quantum
1167           *restrict q;
1168
1169         register ssize_t
1170           x;
1171
1172         if (status == MagickFalse)
1173           continue;
1174         p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
1175         q=QueueCacheViewAuthenticPixels(rotate_view,0,(ssize_t) (image->rows-y-
1176           1),image->columns,1,exception);
1177         if ((p == (const Quantum *) NULL) || (q == (Quantum *) NULL))
1178           {
1179             status=MagickFalse;
1180             continue;
1181           }
1182         q+=GetPixelChannels(rotate_image)*image->columns;
1183         for (x=0; x < (ssize_t) image->columns; x++)
1184         {
1185           register ssize_t
1186             i;
1187
1188           q-=GetPixelChannels(rotate_image);
1189           if (GetPixelMask(image,p) != 0)
1190             {
1191               p+=GetPixelChannels(image);
1192               continue;
1193             }
1194           for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1195           {
1196             PixelChannel
1197               channel;
1198
1199             PixelTrait
1200               rotate_traits,
1201               traits;
1202
1203             channel=GetPixelChannelChannel(image,i);
1204             traits=GetPixelChannelTraits(image,channel);
1205             rotate_traits=GetPixelChannelTraits(rotate_image,channel);
1206             if ((traits == UndefinedPixelTrait) ||
1207                 (rotate_traits == UndefinedPixelTrait))
1208               continue;
1209             SetPixelChannel(rotate_image,channel,p[i],q);
1210           }
1211           p+=GetPixelChannels(image);
1212         }
1213         sync=SyncCacheViewAuthenticPixels(rotate_view,exception);
1214         if (sync == MagickFalse)
1215           status=MagickFalse;
1216         if (image->progress_monitor != (MagickProgressMonitor) NULL)
1217           {
1218             MagickBooleanType
1219               proceed;
1220
1221 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1222             #pragma omp critical (MagickCore_IntegralRotateImage)
1223 #endif
1224             proceed=SetImageProgress(image,RotateImageTag,progress++,
1225               image->rows);
1226             if (proceed == MagickFalse)
1227               status=MagickFalse;
1228           }
1229       }
1230       (void) SetImageProgress(image,RotateImageTag,(MagickOffsetType)
1231         image->rows-1,image->rows);
1232       Swap(page.width,page.height);
1233       Swap(page.x,page.y);
1234       if (page.width != 0)
1235         page.x=(ssize_t) (page.width-rotate_image->columns-page.x);
1236       break;
1237     }
1238     case 3:
1239     {
1240       size_t
1241         tile_height,
1242         tile_width;
1243
1244       ssize_t
1245         tile_y;
1246
1247       /*
1248         Rotate 270 degrees.
1249       */
1250       GetPixelCacheTileSize(image,&tile_width,&tile_height);
1251       tile_width=image->columns;
1252 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1253       #pragma omp parallel for schedule(static,4) \
1254         magick_threads(image,image,image->rows/tile_height,1)
1255 #endif
1256       for (tile_y=0; tile_y < (ssize_t) image->rows; tile_y+=(ssize_t) tile_height)
1257       {
1258         register ssize_t
1259           tile_x;
1260
1261         if (status == MagickFalse)
1262           continue;
1263         tile_x=0;
1264         for ( ; tile_x < (ssize_t) image->columns; tile_x+=(ssize_t) tile_width)
1265         {
1266           MagickBooleanType
1267             sync;
1268
1269           register const Quantum
1270             *restrict p;
1271
1272           register Quantum
1273             *restrict q;
1274
1275           register ssize_t
1276             y;
1277
1278           size_t
1279             height,
1280             width;
1281
1282           width=tile_width;
1283           if ((tile_x+(ssize_t) tile_width) > (ssize_t) image->columns)
1284             width=(size_t) (tile_width-(tile_x+tile_width-image->columns));
1285           height=tile_height;
1286           if ((tile_y+(ssize_t) tile_height) > (ssize_t) image->rows)
1287             height=(size_t) (tile_height-(tile_y+tile_height-image->rows));
1288           p=GetCacheViewVirtualPixels(image_view,tile_x,tile_y,width,height,
1289             exception);
1290           if (p == (const Quantum *) NULL)
1291             {
1292               status=MagickFalse;
1293               break;
1294             }
1295           for (y=0; y < (ssize_t) width; y++)
1296           {
1297             register const Quantum
1298               *restrict tile_pixels;
1299
1300             register ssize_t
1301               x;
1302
1303             if (status == MagickFalse)
1304               continue;
1305             q=QueueCacheViewAuthenticPixels(rotate_view,tile_y,(ssize_t) (y+
1306               rotate_image->rows-(tile_x+width)),height,1,exception);
1307             if (q == (Quantum *) NULL)
1308               {
1309                 status=MagickFalse;
1310                 continue;
1311               }
1312             tile_pixels=p+((width-1)-y)*GetPixelChannels(image);
1313             for (x=0; x < (ssize_t) height; x++)
1314             {
1315               register ssize_t
1316                 i;
1317
1318               if (GetPixelMask(image,tile_pixels) != 0)
1319                 {
1320                   tile_pixels+=width*GetPixelChannels(image);
1321                   q+=GetPixelChannels(rotate_image);
1322                   continue;
1323                 }
1324               for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1325               {
1326                 PixelChannel
1327                   channel;
1328
1329                 PixelTrait
1330                   rotate_traits,
1331                   traits;
1332
1333                 channel=GetPixelChannelChannel(image,i);
1334                 traits=GetPixelChannelTraits(image,channel);
1335                 rotate_traits=GetPixelChannelTraits(rotate_image,channel);
1336                 if ((traits == UndefinedPixelTrait) ||
1337                     (rotate_traits == UndefinedPixelTrait))
1338                   continue;
1339                 SetPixelChannel(rotate_image,channel,tile_pixels[i],q);
1340               }
1341               tile_pixels+=width*GetPixelChannels(image);
1342               q+=GetPixelChannels(rotate_image);
1343             }
1344 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1345             #pragma omp critical (MagickCore_IntegralRotateImage)
1346 #endif
1347             sync=SyncCacheViewAuthenticPixels(rotate_view,exception);
1348             if (sync == MagickFalse)
1349               status=MagickFalse;
1350           }
1351         }
1352         if (image->progress_monitor != (MagickProgressMonitor) NULL)
1353           {
1354             MagickBooleanType
1355               proceed;
1356
1357             proceed=SetImageProgress(image,RotateImageTag,progress+=tile_height,
1358               image->rows);
1359             if (proceed == MagickFalse)
1360               status=MagickFalse;
1361           }
1362       }
1363       (void) SetImageProgress(image,RotateImageTag,(MagickOffsetType)
1364         image->rows-1,image->rows);
1365       Swap(page.width,page.height);
1366       Swap(page.x,page.y);
1367       if (page.width != 0)
1368         page.x=(ssize_t) (page.width-rotate_image->columns-page.x);
1369       break;
1370     }
1371   }
1372   rotate_view=DestroyCacheView(rotate_view);
1373   image_view=DestroyCacheView(image_view);
1374   rotate_image->type=image->type;
1375   rotate_image->page=page;
1376   if (status == MagickFalse)
1377     rotate_image=DestroyImage(rotate_image);
1378   return(rotate_image);
1379 }
1380 \f
1381 /*
1382 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1383 %                                                                             %
1384 %                                                                             %
1385 %                                                                             %
1386 +   X S h e a r I m a g e                                                     %
1387 %                                                                             %
1388 %                                                                             %
1389 %                                                                             %
1390 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1391 %
1392 %  XShearImage() shears the image in the X direction with a shear angle of
1393 %  'degrees'.  Positive angles shear counter-clockwise (right-hand rule), and
1394 %  negative angles shear clockwise.  Angles are measured relative to a vertical
1395 %  Y-axis.  X shears will widen an image creating 'empty' triangles on the left
1396 %  and right sides of the source image.
1397 %
1398 %  The format of the XShearImage method is:
1399 %
1400 %      MagickBooleanType XShearImage(Image *image,const double degrees,
1401 %        const size_t width,const size_t height,
1402 %        const ssize_t x_offset,const ssize_t y_offset,ExceptionInfo *exception)
1403 %
1404 %  A description of each parameter follows.
1405 %
1406 %    o image: the image.
1407 %
1408 %    o degrees: A double representing the shearing angle along the X
1409 %      axis.
1410 %
1411 %    o width, height, x_offset, y_offset: Defines a region of the image
1412 %      to shear.
1413 %
1414 %    o exception: return any errors or warnings in this structure.
1415 %
1416 */
1417 static MagickBooleanType XShearImage(Image *image,const double degrees,
1418   const size_t width,const size_t height,const ssize_t x_offset,
1419   const ssize_t y_offset,ExceptionInfo *exception)
1420 {
1421 #define XShearImageTag  "XShear/Image"
1422
1423   typedef enum
1424   {
1425     LEFT,
1426     RIGHT
1427   } ShearDirection;
1428
1429   CacheView
1430     *image_view;
1431
1432   MagickBooleanType
1433     status;
1434
1435   MagickOffsetType
1436     progress;
1437
1438   PixelInfo
1439     background;
1440
1441   ssize_t
1442     y;
1443
1444   /*
1445     X shear image.
1446   */
1447   assert(image != (Image *) NULL);
1448   assert(image->signature == MagickSignature);
1449   if (image->debug != MagickFalse)
1450     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1451   status=MagickTrue;
1452   background=image->background_color;
1453   progress=0;
1454   image_view=AcquireAuthenticCacheView(image,exception);
1455 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1456   #pragma omp parallel for schedule(static,4) shared(progress,status) \
1457     magick_threads(image,image,height,1)
1458 #endif
1459   for (y=0; y < (ssize_t) height; y++)
1460   {
1461     PixelInfo
1462       pixel,
1463       source,
1464       destination;
1465
1466     double
1467       area,
1468       displacement;
1469
1470     register Quantum
1471       *restrict p,
1472       *restrict q;
1473
1474     register ssize_t
1475       i;
1476
1477     ShearDirection
1478       direction;
1479
1480     ssize_t
1481       step;
1482
1483     if (status == MagickFalse)
1484       continue;
1485     p=GetCacheViewAuthenticPixels(image_view,0,y_offset+y,image->columns,1,
1486       exception);
1487     if (p == (Quantum *) NULL)
1488       {
1489         status=MagickFalse;
1490         continue;
1491       }
1492     p+=x_offset*GetPixelChannels(image);
1493     displacement=degrees*(double) (y-height/2.0);
1494     if (displacement == 0.0)
1495       continue;
1496     if (displacement > 0.0)
1497       direction=RIGHT;
1498     else
1499       {
1500         displacement*=(-1.0);
1501         direction=LEFT;
1502       }
1503     step=(ssize_t) floor((double) displacement);
1504     area=(double) (displacement-step);
1505     step++;
1506     pixel=background;
1507     GetPixelInfo(image,&source);
1508     GetPixelInfo(image,&destination);
1509     switch (direction)
1510     {
1511       case LEFT:
1512       {
1513         /*
1514           Transfer pixels left-to-right.
1515         */
1516         if (step > x_offset)
1517           break;
1518         q=p-step*GetPixelChannels(image);
1519         for (i=0; i < (ssize_t) width; i++)
1520         {
1521           if ((x_offset+i) < step)
1522             {
1523               p+=GetPixelChannels(image);
1524               GetPixelInfoPixel(image,p,&pixel);
1525               q+=GetPixelChannels(image);
1526               continue;
1527             }
1528           GetPixelInfoPixel(image,p,&source);
1529           CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1530             &source,(double) GetPixelAlpha(image,p),area,&destination);
1531           SetPixelInfoPixel(image,&destination,q);
1532           GetPixelInfoPixel(image,p,&pixel);
1533           p+=GetPixelChannels(image);
1534           q+=GetPixelChannels(image);
1535         }
1536         CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1537           &background,(double) background.alpha,area,&destination);
1538         SetPixelInfoPixel(image,&destination,q);
1539         q+=GetPixelChannels(image);
1540         for (i=0; i < (step-1); i++)
1541         {
1542           SetPixelInfoPixel(image,&background,q);
1543           q+=GetPixelChannels(image);
1544         }
1545         break;
1546       }
1547       case RIGHT:
1548       {
1549         /*
1550           Transfer pixels right-to-left.
1551         */
1552         p+=width*GetPixelChannels(image);
1553         q=p+step*GetPixelChannels(image);
1554         for (i=0; i < (ssize_t) width; i++)
1555         {
1556           p-=GetPixelChannels(image);
1557           q-=GetPixelChannels(image);
1558           if ((size_t) (x_offset+width+step-i) >= image->columns)
1559             continue;
1560           GetPixelInfoPixel(image,p,&source);
1561           CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1562             &source,(double) GetPixelAlpha(image,p),area,&destination);
1563           SetPixelInfoPixel(image,&destination,q);
1564           GetPixelInfoPixel(image,p,&pixel);
1565         }
1566         CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1567           &background,(double) background.alpha,area,&destination);
1568         q-=GetPixelChannels(image);
1569         SetPixelInfoPixel(image,&destination,q);
1570         for (i=0; i < (step-1); i++)
1571         {
1572           q-=GetPixelChannels(image);
1573           SetPixelInfoPixel(image,&background,q);
1574         }
1575         break;
1576       }
1577     }
1578     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
1579       status=MagickFalse;
1580     if (image->progress_monitor != (MagickProgressMonitor) NULL)
1581       {
1582         MagickBooleanType
1583           proceed;
1584
1585 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1586         #pragma omp critical (MagickCore_XShearImage)
1587 #endif
1588         proceed=SetImageProgress(image,XShearImageTag,progress++,height);
1589         if (proceed == MagickFalse)
1590           status=MagickFalse;
1591       }
1592   }
1593   image_view=DestroyCacheView(image_view);
1594   return(status);
1595 }
1596 \f
1597 /*
1598 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1599 %                                                                             %
1600 %                                                                             %
1601 %                                                                             %
1602 +   Y S h e a r I m a g e                                                     %
1603 %                                                                             %
1604 %                                                                             %
1605 %                                                                             %
1606 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1607 %
1608 %  YShearImage shears the image in the Y direction with a shear angle of
1609 %  'degrees'.  Positive angles shear counter-clockwise (right-hand rule), and
1610 %  negative angles shear clockwise.  Angles are measured relative to a
1611 %  horizontal X-axis.  Y shears will increase the height of an image creating
1612 %  'empty' triangles on the top and bottom of the source image.
1613 %
1614 %  The format of the YShearImage method is:
1615 %
1616 %      MagickBooleanType YShearImage(Image *image,const double degrees,
1617 %        const size_t width,const size_t height,
1618 %        const ssize_t x_offset,const ssize_t y_offset,ExceptionInfo *exception)
1619 %
1620 %  A description of each parameter follows.
1621 %
1622 %    o image: the image.
1623 %
1624 %    o degrees: A double representing the shearing angle along the Y
1625 %      axis.
1626 %
1627 %    o width, height, x_offset, y_offset: Defines a region of the image
1628 %      to shear.
1629 %
1630 %    o exception: return any errors or warnings in this structure.
1631 %
1632 */
1633 static MagickBooleanType YShearImage(Image *image,const double degrees,
1634   const size_t width,const size_t height,const ssize_t x_offset,
1635   const ssize_t y_offset,ExceptionInfo *exception)
1636 {
1637 #define YShearImageTag  "YShear/Image"
1638
1639   typedef enum
1640   {
1641     UP,
1642     DOWN
1643   } ShearDirection;
1644
1645   CacheView
1646     *image_view;
1647
1648   MagickBooleanType
1649     status;
1650
1651   MagickOffsetType
1652     progress;
1653
1654   PixelInfo
1655     background;
1656
1657   ssize_t
1658     x;
1659
1660   /*
1661     Y Shear image.
1662   */
1663   assert(image != (Image *) NULL);
1664   assert(image->signature == MagickSignature);
1665   if (image->debug != MagickFalse)
1666     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1667   status=MagickTrue;
1668   progress=0;
1669   background=image->background_color;
1670   image_view=AcquireAuthenticCacheView(image,exception);
1671 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1672   #pragma omp parallel for schedule(static,4) shared(progress,status) \
1673     magick_threads(image,image,width,1)
1674 #endif
1675   for (x=0; x < (ssize_t) width; x++)
1676   {
1677     ssize_t
1678       step;
1679
1680     double
1681       area,
1682       displacement;
1683
1684     PixelInfo
1685       pixel,
1686       source,
1687       destination;
1688
1689     register Quantum
1690       *restrict p,
1691       *restrict q;
1692
1693     register ssize_t
1694       i;
1695
1696     ShearDirection
1697       direction;
1698
1699     if (status == MagickFalse)
1700       continue;
1701     p=GetCacheViewAuthenticPixels(image_view,x_offset+x,0,1,image->rows,
1702       exception);
1703     if (p == (Quantum *) NULL)
1704       {
1705         status=MagickFalse;
1706         continue;
1707       }
1708     p+=y_offset*GetPixelChannels(image);
1709     displacement=degrees*(double) (x-width/2.0);
1710     if (displacement == 0.0)
1711       continue;
1712     if (displacement > 0.0)
1713       direction=DOWN;
1714     else
1715       {
1716         displacement*=(-1.0);
1717         direction=UP;
1718       }
1719     step=(ssize_t) floor((double) displacement);
1720     area=(double) (displacement-step);
1721     step++;
1722     pixel=background;
1723     GetPixelInfo(image,&source);
1724     GetPixelInfo(image,&destination);
1725     switch (direction)
1726     {
1727       case UP:
1728       {
1729         /*
1730           Transfer pixels top-to-bottom.
1731         */
1732         if (step > y_offset)
1733           break;
1734         q=p-step*GetPixelChannels(image);
1735         for (i=0; i < (ssize_t) height; i++)
1736         {
1737           if ((y_offset+i) < step)
1738             {
1739               p+=GetPixelChannels(image);
1740               GetPixelInfoPixel(image,p,&pixel);
1741               q+=GetPixelChannels(image);
1742               continue;
1743             }
1744           GetPixelInfoPixel(image,p,&source);
1745           CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1746             &source,(double) GetPixelAlpha(image,p),area,
1747             &destination);
1748           SetPixelInfoPixel(image,&destination,q);
1749           GetPixelInfoPixel(image,p,&pixel);
1750           p+=GetPixelChannels(image);
1751           q+=GetPixelChannels(image);
1752         }
1753         CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1754           &background,(double) background.alpha,area,&destination);
1755         SetPixelInfoPixel(image,&destination,q);
1756         q+=GetPixelChannels(image);
1757         for (i=0; i < (step-1); i++)
1758         {
1759           SetPixelInfoPixel(image,&background,q);
1760           q+=GetPixelChannels(image);
1761         }
1762         break;
1763       }
1764       case DOWN:
1765       {
1766         /*
1767           Transfer pixels bottom-to-top.
1768         */
1769         p+=height*GetPixelChannels(image);
1770         q=p+step*GetPixelChannels(image);
1771         for (i=0; i < (ssize_t) height; i++)
1772         {
1773           p-=GetPixelChannels(image);
1774           q-=GetPixelChannels(image);
1775           if ((size_t) (y_offset+height+step-i) >= image->rows)
1776             continue;
1777           GetPixelInfoPixel(image,p,&source);
1778           CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1779             &source,(double) GetPixelAlpha(image,p),area,
1780             &destination);
1781           SetPixelInfoPixel(image,&destination,q);
1782           GetPixelInfoPixel(image,p,&pixel);
1783         }
1784         CompositePixelInfoAreaBlend(&pixel,(double) pixel.alpha,
1785           &background,(double) background.alpha,area,&destination);
1786         q-=GetPixelChannels(image);
1787         SetPixelInfoPixel(image,&destination,q);
1788         for (i=0; i < (step-1); i++)
1789         {
1790           q-=GetPixelChannels(image);
1791           SetPixelInfoPixel(image,&background,q);
1792         }
1793         break;
1794       }
1795     }
1796     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
1797       status=MagickFalse;
1798     if (image->progress_monitor != (MagickProgressMonitor) NULL)
1799       {
1800         MagickBooleanType
1801           proceed;
1802
1803 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1804         #pragma omp critical (MagickCore_YShearImage)
1805 #endif
1806         proceed=SetImageProgress(image,YShearImageTag,progress++,image->rows);
1807         if (proceed == MagickFalse)
1808           status=MagickFalse;
1809       }
1810   }
1811   image_view=DestroyCacheView(image_view);
1812   return(status);
1813 }
1814 \f
1815 /*
1816 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1817 %                                                                             %
1818 %                                                                             %
1819 %                                                                             %
1820 %   S h e a r I m a g e                                                       %
1821 %                                                                             %
1822 %                                                                             %
1823 %                                                                             %
1824 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1825 %
1826 %  ShearImage() creates a new image that is a shear_image copy of an existing
1827 %  one.  Shearing slides one edge of an image along the X or Y axis, creating
1828 %  a parallelogram.  An X direction shear slides an edge along the X axis,
1829 %  while a Y direction shear slides an edge along the Y axis.  The amount of
1830 %  the shear is controlled by a shear angle.  For X direction shears, x_shear
1831 %  is measured relative to the Y axis, and similarly, for Y direction shears
1832 %  y_shear is measured relative to the X axis.  Empty triangles left over from
1833 %  shearing the image are filled with the background color defined by member
1834 %  'background_color' of the image..  ShearImage() allocates the memory
1835 %  necessary for the new Image structure and returns a pointer to the new image.
1836 %
1837 %  ShearImage() is based on the paper "A Fast Algorithm for General Raster
1838 %  Rotatation" by Alan W. Paeth.
1839 %
1840 %  The format of the ShearImage method is:
1841 %
1842 %      Image *ShearImage(const Image *image,const double x_shear,
1843 %        const double y_shear,ExceptionInfo *exception)
1844 %
1845 %  A description of each parameter follows.
1846 %
1847 %    o image: the image.
1848 %
1849 %    o x_shear, y_shear: Specifies the number of degrees to shear the image.
1850 %
1851 %    o exception: return any errors or warnings in this structure.
1852 %
1853 */
1854 MagickExport Image *ShearImage(const Image *image,const double x_shear,
1855   const double y_shear,ExceptionInfo *exception)
1856 {
1857   Image
1858     *integral_image,
1859     *shear_image;
1860
1861   ssize_t
1862     x_offset,
1863     y_offset;
1864
1865   MagickBooleanType
1866     status;
1867
1868   PointInfo
1869     shear;
1870
1871   RectangleInfo
1872     border_info;
1873
1874   size_t
1875     y_width;
1876
1877   assert(image != (Image *) NULL);
1878   assert(image->signature == MagickSignature);
1879   if (image->debug != MagickFalse)
1880     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1881   assert(exception != (ExceptionInfo *) NULL);
1882   assert(exception->signature == MagickSignature);
1883   if ((x_shear != 0.0) && (fmod(x_shear,90.0) == 0.0))
1884     ThrowImageException(ImageError,"AngleIsDiscontinuous");
1885   if ((y_shear != 0.0) && (fmod(y_shear,90.0) == 0.0))
1886     ThrowImageException(ImageError,"AngleIsDiscontinuous");
1887   /*
1888     Initialize shear angle.
1889   */
1890   integral_image=CloneImage(image,0,0,MagickTrue,exception);
1891   if (integral_image == (Image *) NULL)
1892     ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
1893   shear.x=(-tan(DegreesToRadians(fmod(x_shear,360.0))));
1894   shear.y=tan(DegreesToRadians(fmod(y_shear,360.0)));
1895   if ((shear.x == 0.0) && (shear.y == 0.0))
1896     return(integral_image);
1897   if (SetImageStorageClass(integral_image,DirectClass,exception) == MagickFalse)
1898     {
1899       integral_image=DestroyImage(integral_image);
1900       return(integral_image);
1901     }
1902   if (integral_image->alpha_trait != BlendPixelTrait)
1903     (void) SetImageAlphaChannel(integral_image,OpaqueAlphaChannel,exception);
1904   /*
1905     Compute image size.
1906   */
1907   y_width=image->columns+(ssize_t) floor(fabs(shear.x)*image->rows+0.5);
1908   x_offset=(ssize_t) ceil((double) image->columns+((fabs(shear.x)*image->rows)-
1909     image->columns)/2.0-0.5);
1910   y_offset=(ssize_t) ceil((double) image->rows+((fabs(shear.y)*y_width)-
1911     image->rows)/2.0-0.5);
1912   /*
1913     Surround image with border.
1914   */
1915   integral_image->border_color=integral_image->background_color;
1916   integral_image->compose=CopyCompositeOp;
1917   border_info.width=(size_t) x_offset;
1918   border_info.height=(size_t) y_offset;
1919   shear_image=BorderImage(integral_image,&border_info,image->compose,exception);
1920   integral_image=DestroyImage(integral_image);
1921   if (shear_image == (Image *) NULL)
1922     ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
1923   /*
1924     Shear the image.
1925   */
1926   if (shear_image->alpha_trait != BlendPixelTrait)
1927     (void) SetImageAlphaChannel(shear_image,OpaqueAlphaChannel,exception);
1928   status=XShearImage(shear_image,shear.x,image->columns,image->rows,x_offset,
1929     (ssize_t) (shear_image->rows-image->rows)/2,exception);
1930   if (status == MagickFalse)
1931     {
1932       shear_image=DestroyImage(shear_image);
1933       return((Image *) NULL);
1934     }
1935   status=YShearImage(shear_image,shear.y,y_width,image->rows,(ssize_t)
1936     (shear_image->columns-y_width)/2,y_offset,exception);
1937   if (status == MagickFalse)
1938     {
1939       shear_image=DestroyImage(shear_image);
1940       return((Image *) NULL);
1941     }
1942   status=CropToFitImage(&shear_image,shear.x,shear.y,(double)
1943     image->columns,(double) image->rows,MagickFalse,exception);
1944   shear_image->compose=image->compose;
1945   shear_image->page.width=0;
1946   shear_image->page.height=0;
1947   if (status == MagickFalse)
1948     shear_image=DestroyImage(shear_image);
1949   return(shear_image);
1950 }
1951 \f
1952 /*
1953 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1954 %                                                                             %
1955 %                                                                             %
1956 %                                                                             %
1957 %   S h e a r R o t a t e I m a g e                                           %
1958 %                                                                             %
1959 %                                                                             %
1960 %                                                                             %
1961 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1962 %
1963 %  ShearRotateImage() creates a new image that is a rotated copy of an existing
1964 %  one.  Positive angles rotate counter-clockwise (right-hand rule), while
1965 %  negative angles rotate clockwise.  Rotated images are usually larger than
1966 %  the originals and have 'empty' triangular corners.  X axis.  Empty
1967 %  triangles left over from shearing the image are filled with the background
1968 %  color defined by member 'background_color' of the image.  ShearRotateImage
1969 %  allocates the memory necessary for the new Image structure and returns a
1970 %  pointer to the new image.
1971 %
1972 %  ShearRotateImage() is based on the paper "A Fast Algorithm for General
1973 %  Raster Rotatation" by Alan W. Paeth.  ShearRotateImage is adapted from a
1974 %  similar method based on the Paeth paper written by Michael Halle of the
1975 %  Spatial Imaging Group, MIT Media Lab.
1976 %
1977 %  The format of the ShearRotateImage method is:
1978 %
1979 %      Image *ShearRotateImage(const Image *image,const double degrees,
1980 %        ExceptionInfo *exception)
1981 %
1982 %  A description of each parameter follows.
1983 %
1984 %    o image: the image.
1985 %
1986 %    o degrees: Specifies the number of degrees to rotate the image.
1987 %
1988 %    o exception: return any errors or warnings in this structure.
1989 %
1990 */
1991 MagickExport Image *ShearRotateImage(const Image *image,const double degrees,
1992   ExceptionInfo *exception)
1993 {
1994   Image
1995     *integral_image,
1996     *rotate_image;
1997
1998   MagickBooleanType
1999     status;
2000
2001   double
2002     angle;
2003
2004   PointInfo
2005     shear;
2006
2007   RectangleInfo
2008     border_info;
2009
2010   size_t
2011     height,
2012     rotations,
2013     width,
2014     y_width;
2015
2016   ssize_t
2017     x_offset,
2018     y_offset;
2019
2020   /*
2021     Adjust rotation angle.
2022   */
2023   assert(image != (Image *) NULL);
2024   assert(image->signature == MagickSignature);
2025   if (image->debug != MagickFalse)
2026     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2027   assert(exception != (ExceptionInfo *) NULL);
2028   assert(exception->signature == MagickSignature);
2029   angle=degrees;
2030   while (angle < -45.0)
2031     angle+=360.0;
2032   for (rotations=0; angle > 45.0; rotations++)
2033     angle-=90.0;
2034   rotations%=4;
2035   /*
2036     Calculate shear equations.
2037   */
2038   integral_image=IntegralRotateImage(image,rotations,exception);
2039   if (integral_image == (Image *) NULL)
2040     ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
2041   shear.x=(-tan((double) DegreesToRadians(angle)/2.0));
2042   shear.y=sin((double) DegreesToRadians(angle));
2043   if ((shear.x == 0.0) && (shear.y == 0.0))
2044     return(integral_image);
2045   if (SetImageStorageClass(integral_image,DirectClass,exception) == MagickFalse)
2046     {
2047       integral_image=DestroyImage(integral_image);
2048       return(integral_image);
2049     }
2050   if (integral_image->alpha_trait != BlendPixelTrait)
2051     (void) SetImageAlphaChannel(integral_image,OpaqueAlphaChannel,exception);
2052   /*
2053     Compute image size.
2054   */
2055   width=image->columns;
2056   height=image->rows;
2057   if ((rotations == 1) || (rotations == 3))
2058     {
2059       width=image->rows;
2060       height=image->columns;
2061     }
2062   y_width=width+(ssize_t) floor(fabs(shear.x)*height+0.5);
2063   x_offset=(ssize_t) ceil((double) width+((fabs(shear.y)*height)-width)/2.0-
2064     0.5);
2065   y_offset=(ssize_t) ceil((double) height+((fabs(shear.y)*y_width)-height)/2.0-
2066     0.5);
2067   /*
2068     Surround image with a border.
2069   */
2070   integral_image->border_color=integral_image->background_color;
2071   integral_image->compose=CopyCompositeOp;
2072   border_info.width=(size_t) x_offset;
2073   border_info.height=(size_t) y_offset;
2074   rotate_image=BorderImage(integral_image,&border_info,image->compose,
2075     exception);
2076   integral_image=DestroyImage(integral_image);
2077   if (rotate_image == (Image *) NULL)
2078     ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
2079   /*
2080     Rotate the image.
2081   */
2082   status=XShearImage(rotate_image,shear.x,width,height,x_offset,(ssize_t)
2083     (rotate_image->rows-height)/2,exception);
2084   if (status == MagickFalse)
2085     {
2086       rotate_image=DestroyImage(rotate_image);
2087       return((Image *) NULL);
2088     }
2089   status=YShearImage(rotate_image,shear.y,y_width,height,(ssize_t)
2090     (rotate_image->columns-y_width)/2,y_offset,exception);
2091   if (status == MagickFalse)
2092     {
2093       rotate_image=DestroyImage(rotate_image);
2094       return((Image *) NULL);
2095     }
2096   status=XShearImage(rotate_image,shear.x,y_width,rotate_image->rows,(ssize_t)
2097     (rotate_image->columns-y_width)/2,0,exception);
2098   if (status == MagickFalse)
2099     {
2100       rotate_image=DestroyImage(rotate_image);
2101       return((Image *) NULL);
2102     }
2103   status=CropToFitImage(&rotate_image,shear.x,shear.y,(double) width,
2104     (double) height,MagickTrue,exception);
2105   rotate_image->compose=image->compose;
2106   rotate_image->page.width=0;
2107   rotate_image->page.height=0;
2108   if (status == MagickFalse)
2109     rotate_image=DestroyImage(rotate_image);
2110   return(rotate_image);
2111 }