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 1999-2011 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 MagickRealType x_shear,const MagickRealType x_shear,
  99 %        const MagickRealType width,const MagickRealType 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 MagickRealType x_shear,const MagickRealType y_shear,
 113   const MagickRealType width,const MagickRealType 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(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(dynamic,4)
 576 #endif
 577   for (x=0; x < (ssize_t) p->width; x++)
 578   {
 579     register ssize_t
 580       y;
 581
 582     size_t
 583       sum;
 584
 585     sum=0;
 586     for (y=0; y < (ssize_t) (p->height-1); y++)
 587     {
 588       ssize_t
 589         delta;
 590
 591       delta=GetRadonCell(p,x,y)-(ssize_t) GetRadonCell(p,x,y+1);
 592       sum+=delta*delta;
 593     }
 594     projection[p->width+sign*x-1]=sum;
 595   }
 596 }
 597
 598 static MagickBooleanType RadonTransform(const Image *image,
 599   const double threshold,size_t *projection,ExceptionInfo *exception)
 600 {
 601   CacheView
 602     *image_view;
 603
 604   MagickBooleanType
 605     status;
 606
 607   RadonInfo
 608     *destination_cells,
 609     *source_cells;
 610
 611   register ssize_t
 612     i;
 613
 614   size_t
 615     count,
 616     width;
 617
 618   ssize_t
 619     y;
 620
 621   unsigned char
 622     byte;
 623
 624   unsigned short
 625     bits[256];
 626
 627   for (width=1; width < ((image->columns+7)/8); width<<=1) ;
 628   source_cells=AcquireRadonInfo(image,width,image->rows,exception);
 629   destination_cells=AcquireRadonInfo(image,width,image->rows,exception);
 630   if ((source_cells == (RadonInfo *) NULL) ||
 631       (destination_cells == (RadonInfo *) NULL))
 632     {
 633       if (destination_cells != (RadonInfo *) NULL)
 634         destination_cells=DestroyRadonInfo(destination_cells);
 635       if (source_cells != (RadonInfo *) NULL)
 636         source_cells=DestroyRadonInfo(source_cells);
 637       return(MagickFalse);
 638     }
 639   if (ResetRadonCells(source_cells) == MagickFalse)
 640     {
 641       destination_cells=DestroyRadonInfo(destination_cells);
 642       source_cells=DestroyRadonInfo(source_cells);
 643       return(MagickFalse);
 644     }
 645   for (i=0; i < 256; i++)
 646   {
 647     byte=(unsigned char) i;
 648     for (count=0; byte != 0; byte>>=1)
 649       count+=byte & 0x01;
 650     bits[i]=(unsigned short) count;
 651   }
 652   status=MagickTrue;
 653   image_view=AcquireCacheView(image);
 654 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 655   #pragma omp parallel for schedule(dynamic,4) shared(status)
 656 #endif
 657   for (y=0; y < (ssize_t) image->rows; y++)
 658   {
 659     register const Quantum
 660       *restrict p;
 661
 662     register ssize_t
 663       i,
 664       x;
 665
 666     size_t
 667       bit,
 668       byte;
 669
 670     if (status == MagickFalse)
 671       continue;
 672     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 673     if (p == (const Quantum *) NULL)
 674       {
 675         status=MagickFalse;
 676         continue;
 677       }
 678     bit=0;
 679     byte=0;
 680     i=(ssize_t) (image->columns+7)/8;
 681     for (x=0; x < (ssize_t) image->columns; x++)
 682     {
 683       byte<<=1;
 684       if ((double) GetPixelIntensity(image,p) < threshold)
 685         byte|=0x01;
 686       bit++;
 687       if (bit == 8)
 688         {
 689           (void) SetRadonCell(source_cells,--i,y,bits[byte]);
 690           bit=0;
 691           byte=0;
 692         }
 693       p+=GetPixelChannels(image);
 694     }
 695     if (bit != 0)
 696       {
 697         byte<<=(8-bit);
 698         (void) SetRadonCell(source_cells,--i,y,bits[byte]);
 699       }
 700   }
 701   RadonProjection(source_cells,destination_cells,-1,projection);
 702   (void) ResetRadonCells(source_cells);
 703 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 704   #pragma omp parallel for schedule(dynamic,4) shared(status)
 705 #endif
 706   for (y=0; y < (ssize_t) image->rows; y++)
 707   {
 708     register const Quantum
 709       *restrict p;
 710
 711     register ssize_t
 712       i,
 713       x;
 714
 715     size_t
 716       bit,
 717       byte;
 718
 719     if (status == MagickFalse)
 720       continue;
 721     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 722     if (p == (const Quantum *) NULL)
 723       {
 724         status=MagickFalse;
 725         continue;
 726       }
 727     bit=0;
 728     byte=0;
 729     i=0;
 730     for (x=0; x < (ssize_t) image->columns; x++)
 731     {
 732       byte<<=1;
 733       if ((double) GetPixelIntensity(image,p) < threshold)
 734         byte|=0x01;
 735       bit++;
 736       if (bit == 8)
 737         {
 738           (void) SetRadonCell(source_cells,i++,y,bits[byte]);
 739           bit=0;
 740           byte=0;
 741         }
 742       p+=GetPixelChannels(image);
 743     }
 744     if (bit != 0)
 745       {
 746         byte<<=(8-bit);
 747         (void) SetRadonCell(source_cells,i++,y,bits[byte]);
 748       }
 749   }
 750   RadonProjection(source_cells,destination_cells,1,projection);
 751   image_view=DestroyCacheView(image_view);
 752   destination_cells=DestroyRadonInfo(destination_cells);
 753   source_cells=DestroyRadonInfo(source_cells);
 754   return(MagickTrue);
 755 }
 756
 757 static void GetImageBackgroundColor(Image *image,const ssize_t offset,
 758   ExceptionInfo *exception)
 759 {
 760   CacheView
 761     *image_view;
 762
 763   PixelInfo
 764     background;
 765
 766   MagickRealType
 767     count;
 768
 769   ssize_t
 770     y;
 771
 772   /*
 773     Compute average background color.
 774   */
 775   if (offset <= 0)
 776     return;
 777   GetPixelInfo(image,&background);
 778   count=0.0;
 779   image_view=AcquireCacheView(image);
 780   for (y=0; y < (ssize_t) image->rows; y++)
 781   {
 782     register const Quantum
 783       *restrict p;
 784
 785     register ssize_t
 786       x;
 787
 788     if ((y >= offset) && (y < ((ssize_t) image->rows-offset)))
 789       continue;
 790     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 791     if (p == (const Quantum *) NULL)
 792       continue;
 793     for (x=0; x < (ssize_t) image->columns; x++)
 794     {
 795       if ((x >= offset) && (x < ((ssize_t) image->columns-offset)))
 796         continue;
 797       background.red+=QuantumScale*GetPixelRed(image,p);
 798       background.green+=QuantumScale*GetPixelGreen(image,p);
 799       background.blue+=QuantumScale*GetPixelBlue(image,p);
 800       if ((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0)
 801         background.alpha+=QuantumScale*GetPixelAlpha(image,p);
 802       count++;
 803       p+=GetPixelChannels(image);
 804     }
 805   }
 806   image_view=DestroyCacheView(image_view);
 807   image->background_color.red=(double) ClampToQuantum((MagickRealType)
 808     QuantumRange*background.red/count);
 809   image->background_color.green=(double) ClampToQuantum((MagickRealType)
 810     QuantumRange*background.green/count);
 811   image->background_color.blue=(double) ClampToQuantum((MagickRealType)
 812     QuantumRange*background.blue/count);
 813   if ((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0)
 814     image->background_color.alpha=(double) ClampToQuantum((MagickRealType)
 815       QuantumRange*background.alpha/count);
 816 }
 817
 818 MagickExport Image *DeskewImage(const Image *image,const double threshold,
 819   ExceptionInfo *exception)
 820 {
 821   AffineMatrix
 822     affine_matrix;
 823
 824   const char
 825     *artifact;
 826
 827   double
 828     degrees;
 829
 830   Image
 831     *clone_image,
 832     *crop_image,
 833     *deskew_image,
 834     *median_image;
 835
 836   MagickBooleanType
 837     status;
 838
 839   RectangleInfo
 840     geometry;
 841
 842   register ssize_t
 843     i;
 844
 845   size_t
 846     max_projection,
 847     *projection,
 848     width;
 849
 850   ssize_t
 851     skew;
 852
 853   /*
 854     Compute deskew angle.
 855   */
 856   for (width=1; width < ((image->columns+7)/8); width<<=1) ;
 857   projection=(size_t *) AcquireQuantumMemory((size_t) (2*width-1),
 858     sizeof(*projection));
 859   if (projection == (size_t *) NULL)
 860     ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
 861   status=RadonTransform(image,threshold,projection,exception);
 862   if (status == MagickFalse)
 863     {
 864       projection=(size_t *) RelinquishMagickMemory(projection);
 865       ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
 866     }
 867   max_projection=0;
 868   skew=0;
 869   for (i=0; i < (ssize_t) (2*width-1); i++)
 870   {
 871     if (projection[i] > max_projection)
 872       {
 873         skew=i-(ssize_t) width+1;
 874         max_projection=projection[i];
 875       }
 876   }
 877   projection=(size_t *) RelinquishMagickMemory(projection);
 878   /*
 879     Deskew image.
 880   */
 881   clone_image=CloneImage(image,0,0,MagickTrue,exception);
 882   if (clone_image == (Image *) NULL)
 883     return((Image *) NULL);
 884   (void) SetImageVirtualPixelMethod(clone_image,BackgroundVirtualPixelMethod);
 885   degrees=RadiansToDegrees(-atan((double) skew/width/8));
 886   if (image->debug != MagickFalse)
 887     (void) LogMagickEvent(TransformEvent,GetMagickModule(),
 888       "  Deskew angle: %g",degrees);
 889   affine_matrix.sx=cos(DegreesToRadians(fmod((double) degrees,360.0)));
 890   affine_matrix.rx=sin(DegreesToRadians(fmod((double) degrees,360.0)));
 891   affine_matrix.ry=(-sin(DegreesToRadians(fmod((double) degrees,360.0))));
 892   affine_matrix.sy=cos(DegreesToRadians(fmod((double) degrees,360.0)));
 893   affine_matrix.tx=0.0;
 894   affine_matrix.ty=0.0;
 895   artifact=GetImageArtifact(image,"deskew:auto-crop");
 896   if (artifact == (const char *) NULL)
 897     {
 898       deskew_image=AffineTransformImage(clone_image,&affine_matrix,exception);
 899       clone_image=DestroyImage(clone_image);
 900       return(deskew_image);
 901     }
 902   /*
 903     Auto-crop image.
 904   */
 905   GetImageBackgroundColor(clone_image,(ssize_t) StringToLong(artifact),
 906     exception);
 907   deskew_image=AffineTransformImage(clone_image,&affine_matrix,exception);
 908   clone_image=DestroyImage(clone_image);
 909   if (deskew_image == (Image *) NULL)
 910     return((Image *) NULL);
 911   median_image=StatisticImage(deskew_image,MedianStatistic,3,3,exception);
 912   if (median_image == (Image *) NULL)
 913     {
 914       deskew_image=DestroyImage(deskew_image);
 915       return((Image *) NULL);
 916     }
 917   geometry=GetImageBoundingBox(median_image,exception);
 918   median_image=DestroyImage(median_image);
 919   if (image->debug != MagickFalse)
 920     (void) LogMagickEvent(TransformEvent,GetMagickModule(),"  Deskew geometry: "
 921       "%.20gx%.20g%+.20g%+.20g",(double) geometry.width,(double)
 922       geometry.height,(double) geometry.x,(double) geometry.y);
 923   crop_image=CropImage(deskew_image,&geometry,exception);
 924   deskew_image=DestroyImage(deskew_image);
 925   return(crop_image);
 926 }
 927 \f
 928 /*
 929 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 930 %                                                                             %
 931 %                                                                             %
 932 %                                                                             %
 933 %   I n t e g r a l R o t a t e I m a g e                                     %
 934 %                                                                             %
 935 %                                                                             %
 936 %                                                                             %
 937 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 938 %
 939 %  IntegralRotateImage() rotates the image an integral of 90 degrees.  It
 940 %  allocates the memory necessary for the new Image structure and returns a
 941 %  pointer to the rotated image.
 942 %
 943 %  The format of the IntegralRotateImage method is:
 944 %
 945 %      Image *IntegralRotateImage(const Image *image,size_t rotations,
 946 %        ExceptionInfo *exception)
 947 %
 948 %  A description of each parameter follows.
 949 %
 950 %    o image: the image.
 951 %
 952 %    o rotations: Specifies the number of 90 degree rotations.
 953 %
 954 */
 955 MagickExport Image *IntegralRotateImage(const Image *image,size_t rotations,
 956   ExceptionInfo *exception)
 957 {
 958 #define RotateImageTag  "Rotate/Image"
 959
 960   CacheView
 961     *image_view,
 962     *rotate_view;
 963
 964   Image
 965     *rotate_image;
 966
 967   MagickBooleanType
 968     status;
 969
 970   MagickOffsetType
 971     progress;
 972
 973   RectangleInfo
 974     page;
 975
 976   ssize_t
 977     y;
 978
 979   /*
 980     Initialize rotated image attributes.
 981   */
 982   assert(image != (Image *) NULL);
 983   page=image->page;
 984   rotations%=4;
 985   if (rotations == 0)
 986     return(CloneImage(image,0,0,MagickTrue,exception));
 987   if ((rotations == 1) || (rotations == 3))
 988     rotate_image=CloneImage(image,image->rows,image->columns,MagickTrue,
 989       exception);
 990   else
 991     rotate_image=CloneImage(image,image->columns,image->rows,MagickTrue,
 992       exception);
 993   if (rotate_image == (Image *) NULL)
 994     return((Image *) NULL);
 995   /*
 996     Integral rotate the image.
 997   */
 998   status=MagickTrue;
 999   progress=0;
1000   image_view=AcquireCacheView(image);
1001   rotate_view=AcquireCacheView(rotate_image);
1002   switch (rotations)
1003   {
1004     case 0:
1005     {
1006       /*
1007         Rotate 0 degrees.
1008       */
1009       break;
1010     }
1011     case 1:
1012     {
1013       size_t
1014         tile_height,
1015         tile_width;
1016
1017       ssize_t
1018         tile_y;
1019
1020       /*
1021         Rotate 90 degrees.
1022       */
1023       GetPixelCacheTileSize(image,&tile_width,&tile_height);
1024       tile_width=image->columns;
1025 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1026       #pragma omp parallel for schedule(dynamic,4) shared(progress, status) omp_throttle(1)
1027 #endif
1028       for (tile_y=0; tile_y < (ssize_t) image->rows; tile_y+=(ssize_t) tile_height)
1029       {
1030         register ssize_t
1031           tile_x;
1032
1033         if (status == MagickFalse)
1034           continue;
1035         tile_x=0;
1036         for ( ; tile_x < (ssize_t) image->columns; tile_x+=(ssize_t) tile_width)
1037         {
1038           MagickBooleanType
1039             sync;
1040
1041           register const Quantum
1042             *restrict p;
1043
1044           register Quantum
1045             *restrict q;
1046
1047           register ssize_t
1048             y;
1049
1050           size_t
1051             height,
1052             width;
1053
1054           width=tile_width;
1055           if ((tile_x+(ssize_t) tile_width) > (ssize_t) image->columns)
1056             width=(size_t) (tile_width-(tile_x+tile_width-image->columns));
1057           height=tile_height;
1058           if ((tile_y+(ssize_t) tile_height) > (ssize_t) image->rows)
1059             height=(size_t) (tile_height-(tile_y+tile_height-image->rows));
1060           p=GetCacheViewVirtualPixels(image_view,tile_x,tile_y,width,height,
1061             exception);
1062           if (p == (const Quantum *) NULL)
1063             {
1064               status=MagickFalse;
1065               break;
1066             }
1067           for (y=0; y < (ssize_t) width; y++)
1068           {
1069             register const Quantum
1070               *restrict tile_pixels;
1071
1072             register ssize_t
1073               x;
1074
1075             if (status == MagickFalse)
1076               continue;
1077             q=QueueCacheViewAuthenticPixels(rotate_view,(ssize_t)
1078               (rotate_image->columns-(tile_y+height)),y+tile_x,height,1,
1079               exception);
1080             if (q == (Quantum *) NULL)
1081               {
1082                 status=MagickFalse;
1083                 continue;
1084               }
1085             tile_pixels=p+((height-1)*width+y)*GetPixelChannels(image);
1086             for (x=0; x < (ssize_t) height; x++)
1087             {
1088               register ssize_t
1089                 i;
1090
1091               for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1092               {
1093                 PixelChannel
1094                   channel;
1095
1096                 PixelTrait
1097                   rotate_traits,
1098                   traits;
1099
1100                 channel=GetPixelChannelMapChannel(image,i);
1101                 traits=GetPixelChannelMapTraits(image,channel);
1102                 rotate_traits=GetPixelChannelMapTraits(rotate_image,channel);
1103                 if ((traits == UndefinedPixelTrait) ||
1104                     (rotate_traits == UndefinedPixelTrait))
1105                   continue;
1106                 SetPixelChannel(rotate_image,channel,tile_pixels[i],q);
1107               }
1108               tile_pixels-=width*GetPixelChannels(image);
1109               q+=GetPixelChannels(rotate_image);
1110             }
1111             sync=SyncCacheViewAuthenticPixels(rotate_view,exception);
1112             if (sync == MagickFalse)
1113               status=MagickFalse;
1114           }
1115         }
1116         if (image->progress_monitor != (MagickProgressMonitor) NULL)
1117           {
1118             MagickBooleanType
1119               proceed;
1120
1121 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1122             #pragma omp critical (MagickCore_IntegralRotateImage)
1123 #endif
1124             proceed=SetImageProgress(image,RotateImageTag,progress+=tile_height,
1125               image->rows);
1126             if (proceed == MagickFalse)
1127               status=MagickFalse;
1128           }
1129       }
1130       (void) SetImageProgress(image,RotateImageTag,(MagickOffsetType)
1131         image->rows-1,image->rows);
1132       Swap(page.width,page.height);
1133       Swap(page.x,page.y);
1134       if (page.width != 0)
1135         page.x=(ssize_t) (page.width-rotate_image->columns-page.x);
1136       break;
1137     }
1138     case 2:
1139     {
1140       /*
1141         Rotate 180 degrees.
1142       */
1143 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1144       #pragma omp parallel for schedule(dynamic,4) shared(progress,status) omp_throttle(1)
1145 #endif
1146       for (y=0; y < (ssize_t) image->rows; y++)
1147       {
1148         MagickBooleanType
1149           sync;
1150
1151         register const Quantum
1152           *restrict p;
1153
1154         register Quantum
1155           *restrict q;
1156
1157         register ssize_t
1158           x;
1159
1160         if (status == MagickFalse)
1161           continue;
1162         p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
1163         q=QueueCacheViewAuthenticPixels(rotate_view,0,(ssize_t) (image->rows-y-
1164           1),image->columns,1,exception);
1165         if ((p == (const Quantum *) NULL) || (q == (Quantum *) NULL))
1166           {
1167             status=MagickFalse;
1168             continue;
1169           }
1170         q+=GetPixelChannels(rotate_image)*image->columns;
1171         for (x=0; x < (ssize_t) image->columns; x++)
1172         {
1173           register ssize_t
1174             i;
1175
1176           q-=GetPixelChannels(rotate_image);
1177           for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1178           {
1179             PixelChannel
1180               channel;
1181
1182             PixelTrait
1183               rotate_traits,
1184               traits;
1185
1186             channel=GetPixelChannelMapChannel(image,i);
1187             traits=GetPixelChannelMapTraits(image,channel);
1188             rotate_traits=GetPixelChannelMapTraits(rotate_image,channel);
1189             if ((traits == UndefinedPixelTrait) ||
1190                 (rotate_traits == UndefinedPixelTrait))
1191               continue;
1192             SetPixelChannel(rotate_image,channel,p[i],q);
1193           }
1194           p+=GetPixelChannels(image);
1195         }
1196         sync=SyncCacheViewAuthenticPixels(rotate_view,exception);
1197         if (sync == MagickFalse)
1198           status=MagickFalse;
1199         if (image->progress_monitor != (MagickProgressMonitor) NULL)
1200           {
1201             MagickBooleanType
1202               proceed;
1203
1204 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1205             #pragma omp critical (MagickCore_IntegralRotateImage)
1206 #endif
1207             proceed=SetImageProgress(image,RotateImageTag,progress++,
1208               image->rows);
1209             if (proceed == MagickFalse)
1210               status=MagickFalse;
1211           }
1212       }
1213       (void) SetImageProgress(image,RotateImageTag,(MagickOffsetType)
1214         image->rows-1,image->rows);
1215       Swap(page.width,page.height);
1216       Swap(page.x,page.y);
1217       if (page.width != 0)
1218         page.x=(ssize_t) (page.width-rotate_image->columns-page.x);
1219       break;
1220     }
1221     case 3:
1222     {
1223       size_t
1224         tile_height,
1225         tile_width;
1226
1227       ssize_t
1228         tile_y;
1229
1230       /*
1231         Rotate 270 degrees.
1232       */
1233       GetPixelCacheTileSize(image,&tile_width,&tile_height);
1234       tile_width=image->columns;
1235 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1236       #pragma omp parallel for schedule(dynamic,4) shared(progress,status) omp_throttle(1)
1237 #endif
1238       for (tile_y=0; tile_y < (ssize_t) image->rows; tile_y+=(ssize_t) tile_height)
1239       {
1240         register ssize_t
1241           tile_x;
1242
1243         if (status == MagickFalse)
1244           continue;
1245         tile_x=0;
1246         for ( ; tile_x < (ssize_t) image->columns; tile_x+=(ssize_t) tile_width)
1247         {
1248           MagickBooleanType
1249             sync;
1250
1251           register const Quantum
1252             *restrict p;
1253
1254           register Quantum
1255             *restrict q;
1256
1257           register ssize_t
1258             y;
1259
1260           size_t
1261             height,
1262             width;
1263
1264           width=tile_width;
1265           if ((tile_x+(ssize_t) tile_width) > (ssize_t) image->columns)
1266             width=(size_t) (tile_width-(tile_x+tile_width-image->columns));
1267           height=tile_height;
1268           if ((tile_y+(ssize_t) tile_height) > (ssize_t) image->rows)
1269             height=(size_t) (tile_height-(tile_y+tile_height-image->rows));
1270           p=GetCacheViewVirtualPixels(image_view,tile_x,tile_y,width,height,
1271             exception);
1272           if (p == (const Quantum *) NULL)
1273             {
1274               status=MagickFalse;
1275               break;
1276             }
1277           for (y=0; y < (ssize_t) width; y++)
1278           {
1279             register const Quantum
1280               *restrict tile_pixels;
1281
1282             register ssize_t
1283               x;
1284
1285             if (status == MagickFalse)
1286               continue;
1287             q=QueueCacheViewAuthenticPixels(rotate_view,tile_y,(ssize_t) (y+
1288               rotate_image->rows-(tile_x+width)),height,1,exception);
1289             if (q == (Quantum *) NULL)
1290               {
1291                 status=MagickFalse;
1292                 continue;
1293               }
1294             tile_pixels=p+((width-1)-y)*GetPixelChannels(image);
1295             for (x=0; x < (ssize_t) height; x++)
1296             {
1297               register ssize_t
1298                 i;
1299
1300               for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1301               {
1302                 PixelChannel
1303                   channel;
1304
1305                 PixelTrait
1306                   rotate_traits,
1307                   traits;
1308
1309                 channel=GetPixelChannelMapChannel(image,i);
1310                 traits=GetPixelChannelMapTraits(image,channel);
1311                 rotate_traits=GetPixelChannelMapTraits(rotate_image,channel);
1312                 if ((traits == UndefinedPixelTrait) ||
1313                     (rotate_traits == UndefinedPixelTrait))
1314                   continue;
1315                 SetPixelChannel(rotate_image,channel,tile_pixels[i],q);
1316               }
1317               tile_pixels+=width*GetPixelChannels(image);
1318               q+=GetPixelChannels(rotate_image);
1319             }
1320             sync=SyncCacheViewAuthenticPixels(rotate_view,exception);
1321             if (sync == MagickFalse)
1322               status=MagickFalse;
1323           }
1324         }
1325         if (image->progress_monitor != (MagickProgressMonitor) NULL)
1326           {
1327             MagickBooleanType
1328               proceed;
1329
1330 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1331             #pragma omp critical (MagickCore_IntegralRotateImage)
1332 #endif
1333             proceed=SetImageProgress(image,RotateImageTag,progress+=tile_height,
1334               image->rows);
1335             if (proceed == MagickFalse)
1336               status=MagickFalse;
1337           }
1338       }
1339       (void) SetImageProgress(image,RotateImageTag,(MagickOffsetType)
1340         image->rows-1,image->rows);
1341       Swap(page.width,page.height);
1342       Swap(page.x,page.y);
1343       if (page.width != 0)
1344         page.x=(ssize_t) (page.width-rotate_image->columns-page.x);
1345       break;
1346     }
1347   }
1348   rotate_view=DestroyCacheView(rotate_view);
1349   image_view=DestroyCacheView(image_view);
1350   rotate_image->type=image->type;
1351   rotate_image->page=page;
1352   if (status == MagickFalse)
1353     rotate_image=DestroyImage(rotate_image);
1354   return(rotate_image);
1355 }
1356 \f
1357 /*
1358 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1359 %                                                                             %
1360 %                                                                             %
1361 %                                                                             %
1362 +   X S h e a r I m a g e                                                     %
1363 %                                                                             %
1364 %                                                                             %
1365 %                                                                             %
1366 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1367 %
1368 %  XShearImage() shears the image in the X direction with a shear angle of
1369 %  'degrees'.  Positive angles shear counter-clockwise (right-hand rule), and
1370 %  negative angles shear clockwise.  Angles are measured relative to a vertical
1371 %  Y-axis.  X shears will widen an image creating 'empty' triangles on the left
1372 %  and right sides of the source image.
1373 %
1374 %  The format of the XShearImage method is:
1375 %
1376 %      MagickBooleanType XShearImage(Image *image,const MagickRealType degrees,
1377 %        const size_t width,const size_t height,
1378 %        const ssize_t x_offset,const ssize_t y_offset,ExceptionInfo *exception)
1379 %
1380 %  A description of each parameter follows.
1381 %
1382 %    o image: the image.
1383 %
1384 %    o degrees: A MagickRealType representing the shearing angle along the X
1385 %      axis.
1386 %
1387 %    o width, height, x_offset, y_offset: Defines a region of the image
1388 %      to shear.
1389 %
1390 %    o exception: return any errors or warnings in this structure.
1391 %
1392 */
1393 static MagickBooleanType XShearImage(Image *image,const MagickRealType degrees,
1394   const size_t width,const size_t height,const ssize_t x_offset,
1395   const ssize_t y_offset,ExceptionInfo *exception)
1396 {
1397 #define XShearImageTag  "XShear/Image"
1398
1399   typedef enum
1400   {
1401     LEFT,
1402     RIGHT
1403   } ShearDirection;
1404
1405   CacheView
1406     *image_view;
1407
1408   MagickBooleanType
1409     status;
1410
1411   MagickOffsetType
1412     progress;
1413
1414   PixelInfo
1415     background;
1416
1417   ssize_t
1418     y;
1419
1420   /*
1421     X shear image.
1422   */
1423   assert(image != (Image *) NULL);
1424   assert(image->signature == MagickSignature);
1425   if (image->debug != MagickFalse)
1426     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1427   status=MagickTrue;
1428   background=image->background_color;
1429   progress=0;
1430   image_view=AcquireCacheView(image);
1431 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1432   #pragma omp parallel for schedule(dynamic,4) shared(progress, status)
1433 #endif
1434   for (y=0; y < (ssize_t) height; y++)
1435   {
1436     PixelInfo
1437       pixel,
1438       source,
1439       destination;
1440
1441     MagickRealType
1442       area,
1443       displacement;
1444
1445     register Quantum
1446       *restrict p,
1447       *restrict q;
1448
1449     register ssize_t
1450       i;
1451
1452     ShearDirection
1453       direction;
1454
1455     ssize_t
1456       step;
1457
1458     if (status == MagickFalse)
1459       continue;
1460     p=GetCacheViewAuthenticPixels(image_view,0,y_offset+y,image->columns,1,
1461       exception);
1462     if (p == (Quantum *) NULL)
1463       {
1464         status=MagickFalse;
1465         continue;
1466       }
1467     p+=x_offset*GetPixelChannels(image);
1468     displacement=degrees*(MagickRealType) (y-height/2.0);
1469     if (displacement == 0.0)
1470       continue;
1471     if (displacement > 0.0)
1472       direction=RIGHT;
1473     else
1474       {
1475         displacement*=(-1.0);
1476         direction=LEFT;
1477       }
1478     step=(ssize_t) floor((double) displacement);
1479     area=(MagickRealType) (displacement-step);
1480     step++;
1481     pixel=background;
1482     GetPixelInfo(image,&source);
1483     GetPixelInfo(image,&destination);
1484     switch (direction)
1485     {
1486       case LEFT:
1487       {
1488         /*
1489           Transfer pixels left-to-right.
1490         */
1491         if (step > x_offset)
1492           break;
1493         q=p-step*GetPixelChannels(image);
1494         for (i=0; i < (ssize_t) width; i++)
1495         {
1496           if ((x_offset+i) < step)
1497             {
1498               p+=GetPixelChannels(image);
1499               GetPixelInfoPixel(image,p,&pixel);
1500               q+=GetPixelChannels(image);
1501               continue;
1502             }
1503           GetPixelInfoPixel(image,p,&source);
1504           CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
1505             &source,(MagickRealType) GetPixelAlpha(image,p),area,&destination);
1506           SetPixelInfoPixel(image,&destination,q);
1507           GetPixelInfoPixel(image,p,&pixel);
1508           p+=GetPixelChannels(image);
1509           q+=GetPixelChannels(image);
1510         }
1511         CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
1512           &background,(MagickRealType) background.alpha,area,&destination);
1513         SetPixelInfoPixel(image,&destination,q);
1514         q+=GetPixelChannels(image);
1515         for (i=0; i < (step-1); i++)
1516         {
1517           SetPixelInfoPixel(image,&background,q);
1518           q+=GetPixelChannels(image);
1519         }
1520         break;
1521       }
1522       case RIGHT:
1523       {
1524         /*
1525           Transfer pixels right-to-left.
1526         */
1527         p+=width*GetPixelChannels(image);
1528         q=p+step*GetPixelChannels(image);
1529         for (i=0; i < (ssize_t) width; i++)
1530         {
1531           p-=GetPixelChannels(image);
1532           q-=GetPixelChannels(image);
1533           if ((size_t) (x_offset+width+step-i) >= image->columns)
1534             continue;
1535           GetPixelInfoPixel(image,p,&source);
1536           CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
1537             &source,(MagickRealType) GetPixelAlpha(image,p),area,&destination);
1538           SetPixelInfoPixel(image,&destination,q);
1539           GetPixelInfoPixel(image,p,&pixel);
1540         }
1541         CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
1542           &background,(MagickRealType) background.alpha,area,&destination);
1543         q-=GetPixelChannels(image);
1544         SetPixelInfoPixel(image,&destination,q);
1545         for (i=0; i < (step-1); i++)
1546         {
1547           q-=GetPixelChannels(image);
1548           SetPixelInfoPixel(image,&background,q);
1549         }
1550         break;
1551       }
1552     }
1553     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
1554       status=MagickFalse;
1555     if (image->progress_monitor != (MagickProgressMonitor) NULL)
1556       {
1557         MagickBooleanType
1558           proceed;
1559
1560 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1561         #pragma omp critical (MagickCore_XShearImage)
1562 #endif
1563         proceed=SetImageProgress(image,XShearImageTag,progress++,height);
1564         if (proceed == MagickFalse)
1565           status=MagickFalse;
1566       }
1567   }
1568   image_view=DestroyCacheView(image_view);
1569   return(status);
1570 }
1571 \f
1572 /*
1573 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1574 %                                                                             %
1575 %                                                                             %
1576 %                                                                             %
1577 +   Y S h e a r I m a g e                                                     %
1578 %                                                                             %
1579 %                                                                             %
1580 %                                                                             %
1581 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1582 %
1583 %  YShearImage shears the image in the Y direction with a shear angle of
1584 %  'degrees'.  Positive angles shear counter-clockwise (right-hand rule), and
1585 %  negative angles shear clockwise.  Angles are measured relative to a
1586 %  horizontal X-axis.  Y shears will increase the height of an image creating
1587 %  'empty' triangles on the top and bottom of the source image.
1588 %
1589 %  The format of the YShearImage method is:
1590 %
1591 %      MagickBooleanType YShearImage(Image *image,const MagickRealType degrees,
1592 %        const size_t width,const size_t height,
1593 %        const ssize_t x_offset,const ssize_t y_offset,ExceptionInfo *exception)
1594 %
1595 %  A description of each parameter follows.
1596 %
1597 %    o image: the image.
1598 %
1599 %    o degrees: A MagickRealType representing the shearing angle along the Y
1600 %      axis.
1601 %
1602 %    o width, height, x_offset, y_offset: Defines a region of the image
1603 %      to shear.
1604 %
1605 %    o exception: return any errors or warnings in this structure.
1606 %
1607 */
1608 static MagickBooleanType YShearImage(Image *image,const MagickRealType degrees,
1609   const size_t width,const size_t height,const ssize_t x_offset,
1610   const ssize_t y_offset,ExceptionInfo *exception)
1611 {
1612 #define YShearImageTag  "YShear/Image"
1613
1614   typedef enum
1615   {
1616     UP,
1617     DOWN
1618   } ShearDirection;
1619
1620   CacheView
1621     *image_view;
1622
1623   MagickBooleanType
1624     status;
1625
1626   MagickOffsetType
1627     progress;
1628
1629   PixelInfo
1630     background;
1631
1632   ssize_t
1633     x;
1634
1635   /*
1636     Y Shear image.
1637   */
1638   assert(image != (Image *) NULL);
1639   assert(image->signature == MagickSignature);
1640   if (image->debug != MagickFalse)
1641     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1642   status=MagickTrue;
1643   progress=0;
1644   background=image->background_color;
1645   image_view=AcquireCacheView(image);
1646 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1647   #pragma omp parallel for schedule(dynamic,4) shared(progress, status)
1648 #endif
1649   for (x=0; x < (ssize_t) width; x++)
1650   {
1651     ssize_t
1652       step;
1653
1654     MagickRealType
1655       area,
1656       displacement;
1657
1658     PixelInfo
1659       pixel,
1660       source,
1661       destination;
1662
1663     register Quantum
1664       *restrict p,
1665       *restrict q;
1666
1667     register ssize_t
1668       i;
1669
1670     ShearDirection
1671       direction;
1672
1673     if (status == MagickFalse)
1674       continue;
1675     p=GetCacheViewAuthenticPixels(image_view,x_offset+x,0,1,image->rows,
1676       exception);
1677     if (p == (Quantum *) NULL)
1678       {
1679         status=MagickFalse;
1680         continue;
1681       }
1682     p+=y_offset*GetPixelChannels(image);
1683     displacement=degrees*(MagickRealType) (x-width/2.0);
1684     if (displacement == 0.0)
1685       continue;
1686     if (displacement > 0.0)
1687       direction=DOWN;
1688     else
1689       {
1690         displacement*=(-1.0);
1691         direction=UP;
1692       }
1693     step=(ssize_t) floor((double) displacement);
1694     area=(MagickRealType) (displacement-step);
1695     step++;
1696     pixel=background;
1697     GetPixelInfo(image,&source);
1698     GetPixelInfo(image,&destination);
1699     switch (direction)
1700     {
1701       case UP:
1702       {
1703         /*
1704           Transfer pixels top-to-bottom.
1705         */
1706         if (step > y_offset)
1707           break;
1708         q=p-step*GetPixelChannels(image);
1709         for (i=0; i < (ssize_t) height; i++)
1710         {
1711           if ((y_offset+i) < step)
1712             {
1713               p+=GetPixelChannels(image);
1714               GetPixelInfoPixel(image,p,&pixel);
1715               q+=GetPixelChannels(image);
1716               continue;
1717             }
1718           GetPixelInfoPixel(image,p,&source);
1719           CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
1720             &source,(MagickRealType) GetPixelAlpha(image,p),area,
1721             &destination);
1722           SetPixelInfoPixel(image,&destination,q);
1723           GetPixelInfoPixel(image,p,&pixel);
1724           p+=GetPixelChannels(image);
1725           q+=GetPixelChannels(image);
1726         }
1727         CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
1728           &background,(MagickRealType) background.alpha,area,&destination);
1729         SetPixelInfoPixel(image,&destination,q);
1730         q+=GetPixelChannels(image);
1731         for (i=0; i < (step-1); i++)
1732         {
1733           SetPixelInfoPixel(image,&background,q);
1734           q+=GetPixelChannels(image);
1735         }
1736         break;
1737       }
1738       case DOWN:
1739       {
1740         /*
1741           Transfer pixels bottom-to-top.
1742         */
1743         p+=height*GetPixelChannels(image);
1744         q=p+step*GetPixelChannels(image);
1745         for (i=0; i < (ssize_t) height; i++)
1746         {
1747           p-=GetPixelChannels(image);
1748           q-=GetPixelChannels(image);
1749           if ((size_t) (y_offset+height+step-i) >= image->rows)
1750             continue;
1751           GetPixelInfoPixel(image,p,&source);
1752           CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
1753             &source,(MagickRealType) GetPixelAlpha(image,p),area,
1754             &destination);
1755           SetPixelInfoPixel(image,&destination,q);
1756           GetPixelInfoPixel(image,p,&pixel);
1757         }
1758         CompositePixelInfoAreaBlend(&pixel,(MagickRealType) pixel.alpha,
1759           &background,(MagickRealType) background.alpha,area,&destination);
1760         q-=GetPixelChannels(image);
1761         SetPixelInfoPixel(image,&destination,q);
1762         for (i=0; i < (step-1); i++)
1763         {
1764           q-=GetPixelChannels(image);
1765           SetPixelInfoPixel(image,&background,q);
1766         }
1767         break;
1768       }
1769     }
1770     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
1771       status=MagickFalse;
1772     if (image->progress_monitor != (MagickProgressMonitor) NULL)
1773       {
1774         MagickBooleanType
1775           proceed;
1776
1777 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1778         #pragma omp critical (MagickCore_YShearImage)
1779 #endif
1780         proceed=SetImageProgress(image,YShearImageTag,progress++,image->rows);
1781         if (proceed == MagickFalse)
1782           status=MagickFalse;
1783       }
1784   }
1785   image_view=DestroyCacheView(image_view);
1786   return(status);
1787 }
1788 \f
1789 /*
1790 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1791 %                                                                             %
1792 %                                                                             %
1793 %                                                                             %
1794 %   S h e a r I m a g e                                                       %
1795 %                                                                             %
1796 %                                                                             %
1797 %                                                                             %
1798 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1799 %
1800 %  ShearImage() creates a new image that is a shear_image copy of an existing
1801 %  one.  Shearing slides one edge of an image along the X or Y axis, creating
1802 %  a parallelogram.  An X direction shear slides an edge along the X axis,
1803 %  while a Y direction shear slides an edge along the Y axis.  The amount of
1804 %  the shear is controlled by a shear angle.  For X direction shears, x_shear
1805 %  is measured relative to the Y axis, and similarly, for Y direction shears
1806 %  y_shear is measured relative to the X axis.  Empty triangles left over from
1807 %  shearing the image are filled with the background color defined by member
1808 %  'background_color' of the image..  ShearImage() allocates the memory
1809 %  necessary for the new Image structure and returns a pointer to the new image.
1810 %
1811 %  ShearImage() is based on the paper "A Fast Algorithm for General Raster
1812 %  Rotatation" by Alan W. Paeth.
1813 %
1814 %  The format of the ShearImage method is:
1815 %
1816 %      Image *ShearImage(const Image *image,const double x_shear,
1817 %        const double y_shear,ExceptionInfo *exception)
1818 %
1819 %  A description of each parameter follows.
1820 %
1821 %    o image: the image.
1822 %
1823 %    o x_shear, y_shear: Specifies the number of degrees to shear the image.
1824 %
1825 %    o exception: return any errors or warnings in this structure.
1826 %
1827 */
1828 MagickExport Image *ShearImage(const Image *image,const double x_shear,
1829   const double y_shear,ExceptionInfo *exception)
1830 {
1831   Image
1832     *integral_image,
1833     *shear_image;
1834
1835   ssize_t
1836     x_offset,
1837     y_offset;
1838
1839   MagickBooleanType
1840     status;
1841
1842   PointInfo
1843     shear;
1844
1845   RectangleInfo
1846     border_info;
1847
1848   size_t
1849     y_width;
1850
1851   assert(image != (Image *) NULL);
1852   assert(image->signature == MagickSignature);
1853   if (image->debug != MagickFalse)
1854     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1855   assert(exception != (ExceptionInfo *) NULL);
1856   assert(exception->signature == MagickSignature);
1857   if ((x_shear != 0.0) && (fmod(x_shear,90.0) == 0.0))
1858     ThrowImageException(ImageError,"AngleIsDiscontinuous");
1859   if ((y_shear != 0.0) && (fmod(y_shear,90.0) == 0.0))
1860     ThrowImageException(ImageError,"AngleIsDiscontinuous");
1861   /*
1862     Initialize shear angle.
1863   */
1864   integral_image=CloneImage(image,0,0,MagickTrue,exception);
1865   if (integral_image == (Image *) NULL)
1866     ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
1867   shear.x=(-tan(DegreesToRadians(fmod(x_shear,360.0))));
1868   shear.y=tan(DegreesToRadians(fmod(y_shear,360.0)));
1869   if ((shear.x == 0.0) && (shear.y == 0.0))
1870     return(integral_image);
1871   if (SetImageStorageClass(integral_image,DirectClass,exception) == MagickFalse)
1872     {
1873       integral_image=DestroyImage(integral_image);
1874       return(integral_image);
1875     }
1876   if (integral_image->matte == MagickFalse)
1877     (void) SetImageAlphaChannel(integral_image,OpaqueAlphaChannel,exception);
1878   /*
1879     Compute image size.
1880   */
1881   y_width=image->columns+(ssize_t) floor(fabs(shear.x)*image->rows+0.5);
1882   x_offset=(ssize_t) ceil((double) image->columns+((fabs(shear.x)*image->rows)-
1883     image->columns)/2.0-0.5);
1884   y_offset=(ssize_t) ceil((double) image->rows+((fabs(shear.y)*y_width)-
1885     image->rows)/2.0-0.5);
1886   /*
1887     Surround image with border.
1888   */
1889   integral_image->border_color=integral_image->background_color;
1890   integral_image->compose=CopyCompositeOp;
1891   border_info.width=(size_t) x_offset;
1892   border_info.height=(size_t) y_offset;
1893   shear_image=BorderImage(integral_image,&border_info,image->compose,exception);
1894   integral_image=DestroyImage(integral_image);
1895   if (shear_image == (Image *) NULL)
1896     ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
1897   /*
1898     Shear the image.
1899   */
1900   if (shear_image->matte == MagickFalse)
1901     (void) SetImageAlphaChannel(shear_image,OpaqueAlphaChannel,exception);
1902   status=XShearImage(shear_image,shear.x,image->columns,image->rows,x_offset,
1903     (ssize_t) (shear_image->rows-image->rows)/2,exception);
1904   if (status == MagickFalse)
1905     {
1906       shear_image=DestroyImage(shear_image);
1907       return((Image *) NULL);
1908     }
1909   status=YShearImage(shear_image,shear.y,y_width,image->rows,(ssize_t)
1910     (shear_image->columns-y_width)/2,y_offset,exception);
1911   if (status == MagickFalse)
1912     {
1913       shear_image=DestroyImage(shear_image);
1914       return((Image *) NULL);
1915     }
1916   status=CropToFitImage(&shear_image,shear.x,shear.y,(MagickRealType)
1917     image->columns,(MagickRealType) image->rows,MagickFalse,exception);
1918   if (status == MagickFalse)
1919     {
1920       shear_image=DestroyImage(shear_image);
1921       return((Image *) NULL);
1922     }
1923   shear_image->compose=image->compose;
1924   shear_image->page.width=0;
1925   shear_image->page.height=0;
1926   return(shear_image);
1927 }
1928 \f
1929 /*
1930 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1931 %                                                                             %
1932 %                                                                             %
1933 %                                                                             %
1934 %   S h e a r R o t a t e I m a g e                                           %
1935 %                                                                             %
1936 %                                                                             %
1937 %                                                                             %
1938 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1939 %
1940 %  ShearRotateImage() creates a new image that is a rotated copy of an existing
1941 %  one.  Positive angles rotate counter-clockwise (right-hand rule), while
1942 %  negative angles rotate clockwise.  Rotated images are usually larger than
1943 %  the originals and have 'empty' triangular corners.  X axis.  Empty
1944 %  triangles left over from shearing the image are filled with the background
1945 %  color defined by member 'background_color' of the image.  ShearRotateImage
1946 %  allocates the memory necessary for the new Image structure and returns a
1947 %  pointer to the new image.
1948 %
1949 %  ShearRotateImage() is based on the paper "A Fast Algorithm for General
1950 %  Raster Rotatation" by Alan W. Paeth.  ShearRotateImage is adapted from a
1951 %  similar method based on the Paeth paper written by Michael Halle of the
1952 %  Spatial Imaging Group, MIT Media Lab.
1953 %
1954 %  The format of the ShearRotateImage method is:
1955 %
1956 %      Image *ShearRotateImage(const Image *image,const double degrees,
1957 %        ExceptionInfo *exception)
1958 %
1959 %  A description of each parameter follows.
1960 %
1961 %    o image: the image.
1962 %
1963 %    o degrees: Specifies the number of degrees to rotate the image.
1964 %
1965 %    o exception: return any errors or warnings in this structure.
1966 %
1967 */
1968 MagickExport Image *ShearRotateImage(const Image *image,const double degrees,
1969   ExceptionInfo *exception)
1970 {
1971   Image
1972     *integral_image,
1973     *rotate_image;
1974
1975   MagickBooleanType
1976     status;
1977
1978   MagickRealType
1979     angle;
1980
1981   PointInfo
1982     shear;
1983
1984   RectangleInfo
1985     border_info;
1986
1987   size_t
1988     height,
1989     rotations,
1990     width,
1991     y_width;
1992
1993   ssize_t
1994     x_offset,
1995     y_offset;
1996
1997   /*
1998     Adjust rotation angle.
1999   */
2000   assert(image != (Image *) NULL);
2001   assert(image->signature == MagickSignature);
2002   if (image->debug != MagickFalse)
2003     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2004   assert(exception != (ExceptionInfo *) NULL);
2005   assert(exception->signature == MagickSignature);
2006   angle=degrees;
2007   while (angle < -45.0)
2008     angle+=360.0;
2009   for (rotations=0; angle > 45.0; rotations++)
2010     angle-=90.0;
2011   rotations%=4;
2012   /*
2013     Calculate shear equations.
2014   */
2015   integral_image=IntegralRotateImage(image,rotations,exception);
2016   if (integral_image == (Image *) NULL)
2017     ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
2018   shear.x=(-tan((double) DegreesToRadians(angle)/2.0));
2019   shear.y=sin((double) DegreesToRadians(angle));
2020   if ((shear.x == 0.0) && (shear.y == 0.0))
2021     return(integral_image);
2022   if (SetImageStorageClass(integral_image,DirectClass,exception) == MagickFalse)
2023     {
2024       integral_image=DestroyImage(integral_image);
2025       return(integral_image);
2026     }
2027   if (integral_image->matte == MagickFalse)
2028     (void) SetImageAlphaChannel(integral_image,OpaqueAlphaChannel,exception);
2029   /*
2030     Compute image size.
2031   */
2032   width=image->columns;
2033   height=image->rows;
2034   if ((rotations == 1) || (rotations == 3))
2035     {
2036       width=image->rows;
2037       height=image->columns;
2038     }
2039   y_width=width+(ssize_t) floor(fabs(shear.x)*height+0.5);
2040   x_offset=(ssize_t) ceil((double) width+((fabs(shear.y)*height)-width)/2.0-
2041     0.5);
2042   y_offset=(ssize_t) ceil((double) height+((fabs(shear.y)*y_width)-height)/2.0-
2043     0.5);
2044   /*
2045     Surround image with a border.
2046   */
2047   integral_image->border_color=integral_image->background_color;
2048   integral_image->compose=CopyCompositeOp;
2049   border_info.width=(size_t) x_offset;
2050   border_info.height=(size_t) y_offset;
2051   rotate_image=BorderImage(integral_image,&border_info,image->compose,
2052     exception);
2053   integral_image=DestroyImage(integral_image);
2054   if (rotate_image == (Image *) NULL)
2055     ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
2056   /*
2057     Rotate the image.
2058   */
2059   status=XShearImage(rotate_image,shear.x,width,height,x_offset,(ssize_t)
2060     (rotate_image->rows-height)/2,exception);
2061   if (status == MagickFalse)
2062     {
2063       rotate_image=DestroyImage(rotate_image);
2064       return((Image *) NULL);
2065     }
2066   status=YShearImage(rotate_image,shear.y,y_width,height,(ssize_t)
2067     (rotate_image->columns-y_width)/2,y_offset,exception);
2068   if (status == MagickFalse)
2069     {
2070       rotate_image=DestroyImage(rotate_image);
2071       return((Image *) NULL);
2072     }
2073   status=XShearImage(rotate_image,shear.x,y_width,rotate_image->rows,(ssize_t)
2074     (rotate_image->columns-y_width)/2,0,exception);
2075   if (status == MagickFalse)
2076     {
2077       rotate_image=DestroyImage(rotate_image);
2078       return((Image *) NULL);
2079     }
2080   status=CropToFitImage(&rotate_image,shear.x,shear.y,(MagickRealType) width,
2081     (MagickRealType) height,MagickTrue,exception);
2082   if (status == MagickFalse)
2083     {
2084       rotate_image=DestroyImage(rotate_image);
2085       return((Image *) NULL);
2086     }
2087   rotate_image->compose=image->compose;
2088   rotate_image->page.width=0;
2089   rotate_image->page.height=0;
2090   return(rotate_image);
2091 }