1 /*
2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3 %                                                                             %
4 %                                                                             %
5 %                                                                             %
6 %           RRRR    EEEEE   SSSSS   AAA   M   M  PPPP   L      EEEEE          %
7 %           R   R   E       SS     A   A  MM MM  P   P  L      E              %
8 %           RRRR    EEE      SSS   AAAAA  M M M  PPPP   L      EEE            %
9 %           R R     E          SS  A   A  M   M  P      L      E              %
10 %           R  R    EEEEE   SSSSS  A   A  M   M  P      LLLLL  EEEEE          %
11 %                                                                             %
12 %                                                                             %
13 %                      MagickCore Pixel Resampling Methods                    %
14 %                                                                             %
15 %                              Software Design                                %
16 %                                   Cristy                                    %
17 %                              Anthony Thyssen                                %
18 %                                August 2007                                  %
19 %                                                                             %
20 %                                                                             %
21 %  Copyright 1999-2019 ImageMagick Studio LLC, a non-profit organization      %
22 %  dedicated to making software imaging solutions freely available.           %
23 %                                                                             %
24 %  You may not use this file except in compliance with the License.  You may  %
25 %  obtain a copy of the License at                                            %
26 %                                                                             %
27 %    https://imagemagick.org/script/license.php                               %
28 %                                                                             %
29 %  Unless required by applicable law or agreed to in writing, software        %
30 %  distributed under the License is distributed on an "AS IS" BASIS,          %
31 %  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.   %
32 %  See the License for the specific language governing permissions and        %
33 %  limitations under the License.                                             %
34 %                                                                             %
35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
36 %
37 %
38 */
39 
40 /*
41   Include declarations.
42 */
43 #include "MagickCore/studio.h"
44 #include "MagickCore/artifact.h"
45 #include "MagickCore/color-private.h"
46 #include "MagickCore/cache.h"
47 #include "MagickCore/draw.h"
48 #include "MagickCore/exception-private.h"
49 #include "MagickCore/gem.h"
50 #include "MagickCore/image.h"
51 #include "MagickCore/image-private.h"
52 #include "MagickCore/log.h"
53 #include "MagickCore/magick.h"
54 #include "MagickCore/memory_.h"
55 #include "MagickCore/memory-private.h"
56 #include "MagickCore/pixel.h"
57 #include "MagickCore/pixel-accessor.h"
58 #include "MagickCore/quantum.h"
59 #include "MagickCore/random_.h"
60 #include "MagickCore/resample.h"
61 #include "MagickCore/resize.h"
62 #include "MagickCore/resize-private.h"
63 #include "MagickCore/resource_.h"
64 #include "MagickCore/token.h"
65 #include "MagickCore/transform.h"
66 #include "MagickCore/signature-private.h"
67 #include "MagickCore/utility.h"
68 #include "MagickCore/utility-private.h"
69 #include "MagickCore/option.h"
70 /*
71   EWA Resampling Options
72 */
73 
74 /* select ONE resampling method */
75 #define EWA 1                 /* Normal EWA handling - raw or clamped */
76                               /* if 0 then use "High Quality EWA" */
77 #define EWA_CLAMP 1           /* EWA Clamping from Nicolas Robidoux */
78 
79 #define FILTER_LUT 1          /* Use a LUT rather then direct filter calls */
80 
81 /* output debugging information */
82 #define DEBUG_ELLIPSE 0       /* output ellipse info for debug */
83 #define DEBUG_HIT_MISS 0      /* output hit/miss pixels (as gnuplot commands) */
84 #define DEBUG_NO_PIXEL_HIT 0  /* Make pixels that fail to hit anything - RED */
85 
86 #if ! FILTER_DIRECT
87 #define WLUT_WIDTH 1024       /* size of the filter cache */
88 #endif
89 
90 /*
91   Typedef declarations.
92 */
93 struct _ResampleFilter
94 {
95   CacheView
96     *view;
97 
98   Image
99     *image;
100 
101   ExceptionInfo
102     *exception;
103 
104   MagickBooleanType
105     debug;
106 
107   /* Information about image being resampled */
108   ssize_t
109     image_area;
110 
111   PixelInterpolateMethod
112     interpolate;
113 
114   VirtualPixelMethod
115     virtual_pixel;
116 
117   FilterType
118     filter;
119 
120   /* processing settings needed */
121   MagickBooleanType
122     limit_reached,
123     do_interpolate,
124     average_defined;
125 
126   PixelInfo
127     average_pixel;
128 
129   /* current ellipitical area being resampled around center point */
130   double
131     A, B, C,
132     Vlimit, Ulimit, Uwidth, slope;
133 
134 #if FILTER_LUT
135   /* LUT of weights for filtered average in elliptical area */
136   double
137     filter_lut[WLUT_WIDTH];
138 #else
139   /* Use a Direct call to the filter functions */
140   ResizeFilter
141     *filter_def;
142 
143   double
144     F;
145 #endif
146 
147   /* the practical working support of the filter */
148   double
149     support;
150 
151   size_t
152     signature;
153 };
154 
155 /*
156 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
157 %                                                                             %
158 %                                                                             %
159 %                                                                             %
160 %   A c q u i r e R e s a m p l e I n f o                                     %
161 %                                                                             %
162 %                                                                             %
163 %                                                                             %
164 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
165 %
166 %  AcquireResampleFilter() initializes the information resample needs do to a
167 %  scaled lookup of a color from an image, using area sampling.
168 %
169 %  The algorithm is based on a Elliptical Weighted Average, where the pixels
170 %  found in a large elliptical area is averaged together according to a
171 %  weighting (filter) function.  For more details see "Fundamentals of Texture
172 %  Mapping and Image Warping" a master's thesis by Paul.S.Heckbert, June 17,
173 %  1989.  Available for free from, http://www.cs.cmu.edu/~ph/
174 %
175 %  As EWA resampling (or any sort of resampling) can require a lot of
176 %  calculations to produce a distorted scaling of the source image for each
177 %  output pixel, the ResampleFilter structure generated holds that information
178 %  between individual image resampling.
179 %
180 %  This function will make the appropriate AcquireCacheView() calls
181 %  to view the image, calling functions do not need to open a cache view.
182 %
183 %  Usage Example...
184 %      resample_filter=AcquireResampleFilter(image,exception);
185 %      SetResampleFilter(resample_filter, GaussianFilter);
186 %      for (y=0; y < (ssize_t) image->rows; y++) {
187 %        for (x=0; x < (ssize_t) image->columns; x++) {
188 %          u= ....;   v= ....;
189 %          ScaleResampleFilter(resample_filter, ... scaling vectors ...);
190 %          (void) ResamplePixelColor(resample_filter,u,v,&pixel);
191 %          ... assign resampled pixel value ...
192 %        }
193 %      }
194 %      DestroyResampleFilter(resample_filter);
195 %
196 %  The format of the AcquireResampleFilter method is:
197 %
198 %     ResampleFilter *AcquireResampleFilter(const Image *image,
199 %       ExceptionInfo *exception)
200 %
201 %  A description of each parameter follows:
202 %
203 %    o image: the image.
204 %
205 %    o exception: return any errors or warnings in this structure.
206 %
207 */
AcquireResampleFilter(const Image * image,ExceptionInfo * exception)208 MagickExport ResampleFilter *AcquireResampleFilter(const Image *image,
209   ExceptionInfo *exception)
210 {
211   register ResampleFilter
212     *resample_filter;
213 
214   assert(image != (Image *) NULL);
215   assert(image->signature == MagickCoreSignature);
216   if (image->debug != MagickFalse)
217     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
218   assert(exception != (ExceptionInfo *) NULL);
219   assert(exception->signature == MagickCoreSignature);
220   resample_filter=(ResampleFilter *) AcquireCriticalMemory(sizeof(
221     *resample_filter));
222   (void) memset(resample_filter,0,sizeof(*resample_filter));
223   resample_filter->exception=exception;
224   resample_filter->image=ReferenceImage((Image *) image);
225   resample_filter->view=AcquireVirtualCacheView(resample_filter->image,
226     exception);
227   resample_filter->debug=IsEventLogging();
228   resample_filter->image_area=(ssize_t) (image->columns*image->rows);
229   resample_filter->average_defined=MagickFalse;
230   resample_filter->signature=MagickCoreSignature;
231   SetResampleFilter(resample_filter,image->filter);
232   (void) SetResampleFilterInterpolateMethod(resample_filter,image->interpolate);
233   (void) SetResampleFilterVirtualPixelMethod(resample_filter,
234     GetImageVirtualPixelMethod(image));
235   return(resample_filter);
236 }
237 
238 /*
239 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
240 %                                                                             %
241 %                                                                             %
242 %                                                                             %
243 %   D e s t r o y R e s a m p l e I n f o                                     %
244 %                                                                             %
245 %                                                                             %
246 %                                                                             %
247 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
248 %
249 %  DestroyResampleFilter() finalizes and cleans up the resampling
250 %  resample_filter as returned by AcquireResampleFilter(), freeing any memory
251 %  or other information as needed.
252 %
253 %  The format of the DestroyResampleFilter method is:
254 %
255 %      ResampleFilter *DestroyResampleFilter(ResampleFilter *resample_filter)
256 %
257 %  A description of each parameter follows:
258 %
259 %    o resample_filter: resampling information structure
260 %
261 */
DestroyResampleFilter(ResampleFilter * resample_filter)262 MagickExport ResampleFilter *DestroyResampleFilter(
263   ResampleFilter *resample_filter)
264 {
265   assert(resample_filter != (ResampleFilter *) NULL);
266   assert(resample_filter->signature == MagickCoreSignature);
267   assert(resample_filter->image != (Image *) NULL);
268   if (resample_filter->debug != MagickFalse)
269     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",
270       resample_filter->image->filename);
271   resample_filter->view=DestroyCacheView(resample_filter->view);
272   resample_filter->image=DestroyImage(resample_filter->image);
273 #if ! FILTER_LUT
274   resample_filter->filter_def=DestroyResizeFilter(resample_filter->filter_def);
275 #endif
276   resample_filter->signature=(~MagickCoreSignature);
277   resample_filter=(ResampleFilter *) RelinquishMagickMemory(resample_filter);
278   return(resample_filter);
279 }
280 
281 /*
282 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
283 %                                                                             %
284 %                                                                             %
285 %                                                                             %
286 %   R e s a m p l e P i x e l C o l o r                                       %
287 %                                                                             %
288 %                                                                             %
289 %                                                                             %
290 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
291 %
292 %  ResamplePixelColor() samples the pixel values surrounding the location
293 %  given using an elliptical weighted average, at the scale previously
294 %  calculated, and in the most efficent manner possible for the
295 %  VirtualPixelMethod setting.
296 %
297 %  The format of the ResamplePixelColor method is:
298 %
299 %     MagickBooleanType ResamplePixelColor(ResampleFilter *resample_filter,
300 %       const double u0,const double v0,PixelInfo *pixel,
301 %       ExceptionInfo *exception)
302 %
303 %  A description of each parameter follows:
304 %
305 %    o resample_filter: the resample filter.
306 %
307 %    o u0,v0: A double representing the center of the area to resample,
308 %        The distortion transformed transformed x,y coordinate.
309 %
310 %    o pixel: the resampled pixel is returned here.
311 %
312 %    o exception: return any errors or warnings in this structure.
313 %
314 */
ResamplePixelColor(ResampleFilter * resample_filter,const double u0,const double v0,PixelInfo * pixel,ExceptionInfo * exception)315 MagickExport MagickBooleanType ResamplePixelColor(
316   ResampleFilter *resample_filter,const double u0,const double v0,
317   PixelInfo *pixel,ExceptionInfo *exception)
318 {
319   MagickBooleanType
320     status;
321 
322   ssize_t u,v, v1, v2, uw, hit;
323   double u1;
324   double U,V,Q,DQ,DDQ;
325   double divisor_c,divisor_m;
326   register double weight;
327   register const Quantum *pixels;
328   assert(resample_filter != (ResampleFilter *) NULL);
329   assert(resample_filter->signature == MagickCoreSignature);
330 
331   status=MagickTrue;
332   /* GetPixelInfo(resample_filter->image,pixel); */
333   if ( resample_filter->do_interpolate ) {
334     status=InterpolatePixelInfo(resample_filter->image,resample_filter->view,
335       resample_filter->interpolate,u0,v0,pixel,resample_filter->exception);
336     return(status);
337   }
338 
339 #if DEBUG_ELLIPSE
340   (void) FormatLocaleFile(stderr, "u0=%lf; v0=%lf;\n", u0, v0);
341 #endif
342 
343   /*
344     Does resample area Miss the image Proper?
345     If and that area a simple solid color - then simply return that color!
346     This saves a lot of calculation when resampling outside the bounds of
347     the source image.
348 
349     However it probably should be expanded to image bounds plus the filters
350     scaled support size.
351   */
352   hit = 0;
353   switch ( resample_filter->virtual_pixel ) {
354     case BackgroundVirtualPixelMethod:
355     case TransparentVirtualPixelMethod:
356     case BlackVirtualPixelMethod:
357     case GrayVirtualPixelMethod:
358     case WhiteVirtualPixelMethod:
359     case MaskVirtualPixelMethod:
360       if ( resample_filter->limit_reached
361            || u0 + resample_filter->Ulimit < 0.0
362            || u0 - resample_filter->Ulimit > (double) resample_filter->image->columns-1.0
363            || v0 + resample_filter->Vlimit < 0.0
364            || v0 - resample_filter->Vlimit > (double) resample_filter->image->rows-1.0
365            )
366         hit++;
367       break;
368 
369     case UndefinedVirtualPixelMethod:
370     case EdgeVirtualPixelMethod:
371       if (    ( u0 + resample_filter->Ulimit < 0.0 && v0 + resample_filter->Vlimit < 0.0 )
372            || ( u0 + resample_filter->Ulimit < 0.0
373                 && v0 - resample_filter->Vlimit > (double) resample_filter->image->rows-1.0 )
374            || ( u0 - resample_filter->Ulimit > (double) resample_filter->image->columns-1.0
375                 && v0 + resample_filter->Vlimit < 0.0 )
376            || ( u0 - resample_filter->Ulimit > (double) resample_filter->image->columns-1.0
377                 && v0 - resample_filter->Vlimit > (double) resample_filter->image->rows-1.0 )
378            )
379         hit++;
380       break;
381     case HorizontalTileVirtualPixelMethod:
382       if (    v0 + resample_filter->Vlimit < 0.0
383            || v0 - resample_filter->Vlimit > (double) resample_filter->image->rows-1.0
384            )
385         hit++;  /* outside the horizontally tiled images. */
386       break;
387     case VerticalTileVirtualPixelMethod:
388       if (    u0 + resample_filter->Ulimit < 0.0
389            || u0 - resample_filter->Ulimit > (double) resample_filter->image->columns-1.0
390            )
391         hit++;  /* outside the vertically tiled images. */
392       break;
393     case DitherVirtualPixelMethod:
394       if (    ( u0 + resample_filter->Ulimit < -32.0 && v0 + resample_filter->Vlimit < -32.0 )
395            || ( u0 + resample_filter->Ulimit < -32.0
396                 && v0 - resample_filter->Vlimit > (double) resample_filter->image->rows+31.0 )
397            || ( u0 - resample_filter->Ulimit > (double) resample_filter->image->columns+31.0
398                 && v0 + resample_filter->Vlimit < -32.0 )
399            || ( u0 - resample_filter->Ulimit > (double) resample_filter->image->columns+31.0
400                 && v0 - resample_filter->Vlimit > (double) resample_filter->image->rows+31.0 )
401            )
402         hit++;
403       break;
404     case TileVirtualPixelMethod:
405     case MirrorVirtualPixelMethod:
406     case RandomVirtualPixelMethod:
407     case HorizontalTileEdgeVirtualPixelMethod:
408     case VerticalTileEdgeVirtualPixelMethod:
409     case CheckerTileVirtualPixelMethod:
410       /* resampling of area is always needed - no VP limits */
411       break;
412   }
413   if ( hit ) {
414     /* The area being resampled is simply a solid color
415      * just return a single lookup color.
416      *
417      * Should this return the users requested interpolated color?
418      */
419     status=InterpolatePixelInfo(resample_filter->image,resample_filter->view,
420       IntegerInterpolatePixel,u0,v0,pixel,resample_filter->exception);
421     return(status);
422   }
423 
424   /*
425     When Scaling limits reached, return an 'averaged' result.
426   */
427   if ( resample_filter->limit_reached ) {
428     switch ( resample_filter->virtual_pixel ) {
429       /*  This is always handled by the above, so no need.
430         case BackgroundVirtualPixelMethod:
431         case ConstantVirtualPixelMethod:
432         case TransparentVirtualPixelMethod:
433         case GrayVirtualPixelMethod,
434         case WhiteVirtualPixelMethod
435         case MaskVirtualPixelMethod:
436       */
437       case UndefinedVirtualPixelMethod:
438       case EdgeVirtualPixelMethod:
439       case DitherVirtualPixelMethod:
440       case HorizontalTileEdgeVirtualPixelMethod:
441       case VerticalTileEdgeVirtualPixelMethod:
442         /* We need an average edge pixel, from the correct edge!
443            How should I calculate an average edge color?
444            Just returning an averaged neighbourhood,
445            works well in general, but falls down for TileEdge methods.
446            This needs to be done properly!!!!!!
447         */
448         status=InterpolatePixelInfo(resample_filter->image,
449           resample_filter->view,AverageInterpolatePixel,u0,v0,pixel,
450           resample_filter->exception);
451         break;
452       case HorizontalTileVirtualPixelMethod:
453       case VerticalTileVirtualPixelMethod:
454         /* just return the background pixel - Is there more direct way? */
455         status=InterpolatePixelInfo(resample_filter->image,
456           resample_filter->view,IntegerInterpolatePixel,-1.0,-1.0,pixel,
457           resample_filter->exception);
458         break;
459       case TileVirtualPixelMethod:
460       case MirrorVirtualPixelMethod:
461       case RandomVirtualPixelMethod:
462       case CheckerTileVirtualPixelMethod:
463       default:
464         /* generate a average color of the WHOLE image */
465         if ( resample_filter->average_defined == MagickFalse ) {
466           Image
467             *average_image;
468 
469           CacheView
470             *average_view;
471 
472           GetPixelInfo(resample_filter->image,(PixelInfo *)
473             &resample_filter->average_pixel);
474           resample_filter->average_defined=MagickTrue;
475 
476           /* Try to get an averaged pixel color of whole image */
477           average_image=ResizeImage(resample_filter->image,1,1,BoxFilter,
478             resample_filter->exception);
479           if (average_image == (Image *) NULL)
480             {
481               *pixel=resample_filter->average_pixel; /* FAILED */
482               break;
483             }
484           average_view=AcquireVirtualCacheView(average_image,exception);
485           pixels=GetCacheViewVirtualPixels(average_view,0,0,1,1,
486             resample_filter->exception);
487           if (pixels == (const Quantum *) NULL) {
488             average_view=DestroyCacheView(average_view);
489             average_image=DestroyImage(average_image);
490             *pixel=resample_filter->average_pixel; /* FAILED */
491             break;
492           }
493           GetPixelInfoPixel(resample_filter->image,pixels,
494             &(resample_filter->average_pixel));
495           average_view=DestroyCacheView(average_view);
496           average_image=DestroyImage(average_image);
497 
498           if ( resample_filter->virtual_pixel == CheckerTileVirtualPixelMethod )
499             {
500               /* CheckerTile is a alpha blend of the image's average pixel
501                  color and the current background color */
502 
503               /* image's average pixel color */
504               weight = QuantumScale*((double)
505                 resample_filter->average_pixel.alpha);
506               resample_filter->average_pixel.red *= weight;
507               resample_filter->average_pixel.green *= weight;
508               resample_filter->average_pixel.blue *= weight;
509               divisor_c = weight;
510 
511               /* background color */
512               weight = QuantumScale*((double)
513                 resample_filter->image->background_color.alpha);
514               resample_filter->average_pixel.red +=
515                       weight*resample_filter->image->background_color.red;
516               resample_filter->average_pixel.green +=
517                       weight*resample_filter->image->background_color.green;
518               resample_filter->average_pixel.blue +=
519                       weight*resample_filter->image->background_color.blue;
520               resample_filter->average_pixel.alpha +=
521                       resample_filter->image->background_color.alpha;
522               divisor_c += weight;
523 
524               /* alpha blend */
525               resample_filter->average_pixel.red /= divisor_c;
526               resample_filter->average_pixel.green /= divisor_c;
527               resample_filter->average_pixel.blue /= divisor_c;
528               resample_filter->average_pixel.alpha /= 2; /* 50% blend */
529 
530             }
531         }
532         *pixel=resample_filter->average_pixel;
533         break;
534     }
535     return(status);
536   }
537 
538   /*
539     Initialize weighted average data collection
540   */
541   hit = 0;
542   divisor_c = 0.0;
543   divisor_m = 0.0;
544   pixel->red = pixel->green = pixel->blue = 0.0;
545   if (pixel->colorspace == CMYKColorspace)
546     pixel->black = 0.0;
547   if (pixel->alpha_trait != UndefinedPixelTrait)
548     pixel->alpha = 0.0;
549 
550   /*
551     Determine the parellelogram bounding box fitted to the ellipse
552     centered at u0,v0.  This area is bounding by the lines...
553   */
554   v1 = (ssize_t)ceil(v0 - resample_filter->Vlimit);  /* range of scan lines */
555   v2 = (ssize_t)floor(v0 + resample_filter->Vlimit);
556 
557   /* scan line start and width accross the parallelogram */
558   u1 = u0 + (v1-v0)*resample_filter->slope - resample_filter->Uwidth;
559   uw = (ssize_t)(2.0*resample_filter->Uwidth)+1;
560 
561 #if DEBUG_ELLIPSE
562   (void) FormatLocaleFile(stderr, "v1=%ld; v2=%ld\n", (long)v1, (long)v2);
563   (void) FormatLocaleFile(stderr, "u1=%ld; uw=%ld\n", (long)u1, (long)uw);
564 #else
565 # define DEBUG_HIT_MISS 0 /* only valid if DEBUG_ELLIPSE is enabled */
566 #endif
567 
568   /*
569     Do weighted resampling of all pixels,  within the scaled ellipse,
570     bound by a Parellelogram fitted to the ellipse.
571   */
572   DDQ = 2*resample_filter->A;
573   for( v=v1; v<=v2;  v++ ) {
574 #if DEBUG_HIT_MISS
575     long uu = ceil(u1);   /* actual pixel location (for debug only) */
576     (void) FormatLocaleFile(stderr, "# scan line from pixel %ld, %ld\n", (long)uu, (long)v);
577 #endif
578     u = (ssize_t)ceil(u1);        /* first pixel in scanline */
579     u1 += resample_filter->slope; /* start of next scan line */
580 
581 
582     /* location of this first pixel, relative to u0,v0 */
583     U = (double)u-u0;
584     V = (double)v-v0;
585 
586     /* Q = ellipse quotent ( if Q<F then pixel is inside ellipse) */
587     Q = (resample_filter->A*U + resample_filter->B*V)*U + resample_filter->C*V*V;
588     DQ = resample_filter->A*(2.0*U+1) + resample_filter->B*V;
589 
590     /* get the scanline of pixels for this v */
591     pixels=GetCacheViewVirtualPixels(resample_filter->view,u,v,(size_t) uw,
592       1,resample_filter->exception);
593     if (pixels == (const Quantum *) NULL)
594       return(MagickFalse);
595 
596     /* count up the weighted pixel colors */
597     for( u=0; u<uw; u++ ) {
598 #if FILTER_LUT
599       /* Note that the ellipse has been pre-scaled so F = WLUT_WIDTH */
600       if ( Q < (double)WLUT_WIDTH ) {
601         weight = resample_filter->filter_lut[(int)Q];
602 #else
603       /* Note that the ellipse has been pre-scaled so F = support^2 */
604       if ( Q < (double)resample_filter->F ) {
605         weight = GetResizeFilterWeight(resample_filter->filter_def,
606              sqrt(Q));    /* a SquareRoot!  Arrggghhhhh... */
607 #endif
608 
609         pixel->alpha  += weight*GetPixelAlpha(resample_filter->image,pixels);
610         divisor_m += weight;
611 
612         if (pixel->alpha_trait != UndefinedPixelTrait)
613           weight *= QuantumScale*((double) GetPixelAlpha(resample_filter->image,pixels));
614         pixel->red   += weight*GetPixelRed(resample_filter->image,pixels);
615         pixel->green += weight*GetPixelGreen(resample_filter->image,pixels);
616         pixel->blue  += weight*GetPixelBlue(resample_filter->image,pixels);
617         if (pixel->colorspace == CMYKColorspace)
618           pixel->black += weight*GetPixelBlack(resample_filter->image,pixels);
619         divisor_c += weight;
620 
621         hit++;
622 #if DEBUG_HIT_MISS
623         /* mark the pixel according to hit/miss of the ellipse */
624         (void) FormatLocaleFile(stderr, "set arrow from %lf,%lf to %lf,%lf nohead ls 3\n",
625                      (long)uu-.1,(double)v-.1,(long)uu+.1,(long)v+.1);
626         (void) FormatLocaleFile(stderr, "set arrow from %lf,%lf to %lf,%lf nohead ls 3\n",
627                      (long)uu+.1,(double)v-.1,(long)uu-.1,(long)v+.1);
628       } else {
629         (void) FormatLocaleFile(stderr, "set arrow from %lf,%lf to %lf,%lf nohead ls 1\n",
630                      (long)uu-.1,(double)v-.1,(long)uu+.1,(long)v+.1);
631         (void) FormatLocaleFile(stderr, "set arrow from %lf,%lf to %lf,%lf nohead ls 1\n",
632                      (long)uu+.1,(double)v-.1,(long)uu-.1,(long)v+.1);
633       }
634       uu++;
635 #else
636       }
637 #endif
638       pixels+=GetPixelChannels(resample_filter->image);
639       Q += DQ;
640       DQ += DDQ;
641     }
642   }
643 #if DEBUG_ELLIPSE
644   (void) FormatLocaleFile(stderr, "Hit=%ld;  Total=%ld;\n", (long)hit, (long)uw*(v2-v1) );
645 #endif
646 
647   /*
648     Result sanity check -- this should NOT happen
649   */
650   if ( hit == 0 || divisor_m <= MagickEpsilon || divisor_c <= MagickEpsilon ) {
651     /* not enough pixels, or bad weighting in resampling,
652        resort to direct interpolation */
653 #if DEBUG_NO_PIXEL_HIT
654     pixel->alpha = pixel->red = pixel->green = pixel->blue = 0;
655     pixel->red = QuantumRange; /* show pixels for which EWA fails */
656 #else
657     status=InterpolatePixelInfo(resample_filter->image,
658       resample_filter->view,resample_filter->interpolate,u0,v0,pixel,
659       resample_filter->exception);
660 #endif
661     return status;
662   }
663 
664   /*
665     Finialize results of resampling
666   */
667   divisor_m = 1.0/divisor_m;
668   if (pixel->alpha_trait != UndefinedPixelTrait)
669     pixel->alpha = (double) ClampToQuantum(divisor_m*pixel->alpha);
670   divisor_c = 1.0/divisor_c;
671   pixel->red   = (double) ClampToQuantum(divisor_c*pixel->red);
672   pixel->green = (double) ClampToQuantum(divisor_c*pixel->green);
673   pixel->blue  = (double) ClampToQuantum(divisor_c*pixel->blue);
674   if (pixel->colorspace == CMYKColorspace)
675     pixel->black = (double) ClampToQuantum(divisor_c*pixel->black);
676   return(MagickTrue);
677 }
678 
679 #if EWA && EWA_CLAMP
680 /*
681 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
682 %                                                                             %
683 %                                                                             %
684 %                                                                             %
685 -   C l a m p U p A x e s                                                     %
686 %                                                                             %
687 %                                                                             %
688 %                                                                             %
689 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
690 %
691 % ClampUpAxes() function converts the input vectors into a major and
692 % minor axis unit vectors, and their magnitude.  This allows us to
693 % ensure that the ellipse generated is never smaller than the unit
694 % circle and thus never too small for use in EWA resampling.
695 %
696 % This purely mathematical 'magic' was provided by Professor Nicolas
697 % Robidoux and his Masters student Chantal Racette.
698 %
699 % Reference: "We Recommend Singular Value Decomposition", David Austin
700 %   http://www.ams.org/samplings/feature-column/fcarc-svd
701 %
702 % By generating major and minor axis vectors, we can actually use the
703 % ellipse in its "canonical form", by remapping the dx,dy of the
704 % sampled point into distances along the major and minor axis unit
705 % vectors.
706 %
707 % Reference: http://en.wikipedia.org/wiki/Ellipse#Canonical_form
708 */
ClampUpAxes(const double dux,const double dvx,const double duy,const double dvy,double * major_mag,double * minor_mag,double * major_unit_x,double * major_unit_y,double * minor_unit_x,double * minor_unit_y)709 static inline void ClampUpAxes(const double dux,
710 			       const double dvx,
711 			       const double duy,
712 			       const double dvy,
713 			       double *major_mag,
714 			       double *minor_mag,
715 			       double *major_unit_x,
716 			       double *major_unit_y,
717 			       double *minor_unit_x,
718 			       double *minor_unit_y)
719 {
720   /*
721    * ClampUpAxes takes an input 2x2 matrix
722    *
723    * [ a b ] = [ dux duy ]
724    * [ c d ] = [ dvx dvy ]
725    *
726    * and computes from it the major and minor axis vectors [major_x,
727    * major_y] and [minor_x,minor_y] of the smallest ellipse containing
728    * both the unit disk and the ellipse which is the image of the unit
729    * disk by the linear transformation
730    *
731    * [ dux duy ] [S] = [s]
732    * [ dvx dvy ] [T] = [t]
733    *
734    * (The vector [S,T] is the difference between a position in output
735    * space and [X,Y]; the vector [s,t] is the difference between a
736    * position in input space and [x,y].)
737    */
738   /*
739    * Output:
740    *
741    * major_mag is the half-length of the major axis of the "new"
742    * ellipse.
743    *
744    * minor_mag is the half-length of the minor axis of the "new"
745    * ellipse.
746    *
747    * major_unit_x is the x-coordinate of the major axis direction vector
748    * of both the "old" and "new" ellipses.
749    *
750    * major_unit_y is the y-coordinate of the major axis direction vector.
751    *
752    * minor_unit_x is the x-coordinate of the minor axis direction vector.
753    *
754    * minor_unit_y is the y-coordinate of the minor axis direction vector.
755    *
756    * Unit vectors are useful for computing projections, in particular,
757    * to compute the distance between a point in output space and the
758    * center of a unit disk in output space, using the position of the
759    * corresponding point [s,t] in input space. Following the clamping,
760    * the square of this distance is
761    *
762    * ( ( s * major_unit_x + t * major_unit_y ) / major_mag )^2
763    * +
764    * ( ( s * minor_unit_x + t * minor_unit_y ) / minor_mag )^2
765    *
766    * If such distances will be computed for many [s,t]'s, it makes
767    * sense to actually compute the reciprocal of major_mag and
768    * minor_mag and multiply them by the above unit lengths.
769    *
770    * Now, if you want to modify the input pair of tangent vectors so
771    * that it defines the modified ellipse, all you have to do is set
772    *
773    * newdux = major_mag * major_unit_x
774    * newdvx = major_mag * major_unit_y
775    * newduy = minor_mag * minor_unit_x = minor_mag * -major_unit_y
776    * newdvy = minor_mag * minor_unit_y = minor_mag *  major_unit_x
777    *
778    * and use these tangent vectors as if they were the original ones.
779    * Usually, this is a drastic change in the tangent vectors even if
780    * the singular values are not clamped; for example, the minor axis
781    * vector always points in a direction which is 90 degrees
782    * counterclockwise from the direction of the major axis vector.
783    */
784   /*
785    * Discussion:
786    *
787    * GOAL: Fix things so that the pullback, in input space, of a disk
788    * of radius r in output space is an ellipse which contains, at
789    * least, a disc of radius r. (Make this hold for any r>0.)
790    *
791    * ESSENCE OF THE METHOD: Compute the product of the first two
792    * factors of an SVD of the linear transformation defining the
793    * ellipse and make sure that both its columns have norm at least 1.
794    * Because rotations and reflexions map disks to themselves, it is
795    * not necessary to compute the third (rightmost) factor of the SVD.
796    *
797    * DETAILS: Find the singular values and (unit) left singular
798    * vectors of Jinv, clampling up the singular values to 1, and
799    * multiply the unit left singular vectors by the new singular
800    * values in order to get the minor and major ellipse axis vectors.
801    *
802    * Image resampling context:
803    *
804    * The Jacobian matrix of the transformation at the output point
805    * under consideration is defined as follows:
806    *
807    * Consider the transformation (x,y) -> (X,Y) from input locations
808    * to output locations. (Anthony Thyssen, elsewhere in resample.c,
809    * uses the notation (u,v) -> (x,y).)
810    *
811    * The Jacobian matrix of the transformation at (x,y) is equal to
812    *
813    *   J = [ A, B ] = [ dX/dx, dX/dy ]
814    *       [ C, D ]   [ dY/dx, dY/dy ]
815    *
816    * that is, the vector [A,C] is the tangent vector corresponding to
817    * input changes in the horizontal direction, and the vector [B,D]
818    * is the tangent vector corresponding to input changes in the
819    * vertical direction.
820    *
821    * In the context of resampling, it is natural to use the inverse
822    * Jacobian matrix Jinv because resampling is generally performed by
823    * pulling pixel locations in the output image back to locations in
824    * the input image. Jinv is
825    *
826    *   Jinv = [ a, b ] = [ dx/dX, dx/dY ]
827    *          [ c, d ]   [ dy/dX, dy/dY ]
828    *
829    * Note: Jinv can be computed from J with the following matrix
830    * formula:
831    *
832    *   Jinv = 1/(A*D-B*C) [  D, -B ]
833    *                      [ -C,  A ]
834    *
835    * What we do is modify Jinv so that it generates an ellipse which
836    * is as close as possible to the original but which contains the
837    * unit disk. This can be accomplished as follows:
838    *
839    * Let
840    *
841    *   Jinv = U Sigma V^T
842    *
843    * be an SVD decomposition of Jinv. (The SVD is not unique, but the
844    * final ellipse does not depend on the particular SVD.)
845    *
846    * We could clamp up the entries of the diagonal matrix Sigma so
847    * that they are at least 1, and then set
848    *
849    *   Jinv = U newSigma V^T.
850    *
851    * However, we do not need to compute V for the following reason:
852    * V^T is an orthogonal matrix (that is, it represents a combination
853    * of rotations and reflexions) so that it maps the unit circle to
854    * itself. For this reason, the exact value of V does not affect the
855    * final ellipse, and we can choose V to be the identity
856    * matrix. This gives
857    *
858    *   Jinv = U newSigma.
859    *
860    * In the end, we return the two diagonal entries of newSigma
861    * together with the two columns of U.
862    */
863   /*
864    * ClampUpAxes was written by Nicolas Robidoux and Chantal Racette
865    * of Laurentian University with insightful suggestions from Anthony
866    * Thyssen and funding from the National Science and Engineering
867    * Research Council of Canada. It is distinguished from its
868    * predecessors by its efficient handling of degenerate cases.
869    *
870    * The idea of clamping up the EWA ellipse's major and minor axes so
871    * that the result contains the reconstruction kernel filter support
872    * is taken from Andreas Gustaffson's Masters thesis "Interactive
873    * Image Warping", Helsinki University of Technology, Faculty of
874    * Information Technology, 59 pages, 1993 (see Section 3.6).
875    *
876    * The use of the SVD to clamp up the singular values of the
877    * Jacobian matrix of the pullback transformation for EWA resampling
878    * is taken from the astrophysicist Craig DeForest.  It is
879    * implemented in his PDL::Transform code (PDL = Perl Data
880    * Language).
881    */
882   const double a = dux;
883   const double b = duy;
884   const double c = dvx;
885   const double d = dvy;
886   /*
887    * n is the matrix Jinv * transpose(Jinv). Eigenvalues of n are the
888    * squares of the singular values of Jinv.
889    */
890   const double aa = a*a;
891   const double bb = b*b;
892   const double cc = c*c;
893   const double dd = d*d;
894   /*
895    * Eigenvectors of n are left singular vectors of Jinv.
896    */
897   const double n11 = aa+bb;
898   const double n12 = a*c+b*d;
899   const double n21 = n12;
900   const double n22 = cc+dd;
901   const double det = a*d-b*c;
902   const double twice_det = det+det;
903   const double frobenius_squared = n11+n22;
904   const double discriminant =
905     (frobenius_squared+twice_det)*(frobenius_squared-twice_det);
906   /*
907    * In exact arithmetic, discriminant can't be negative. In floating
908    * point, it can, because of the bad conditioning of SVD
909    * decompositions done through the associated normal matrix.
910    */
911   const double sqrt_discriminant =
912     sqrt(discriminant > 0.0 ? discriminant : 0.0);
913   /*
914    * s1 is the largest singular value of the inverse Jacobian
915    * matrix. In other words, its reciprocal is the smallest singular
916    * value of the Jacobian matrix itself.
917    * If s1 = 0, both singular values are 0, and any orthogonal pair of
918    * left and right factors produces a singular decomposition of Jinv.
919    */
920   /*
921    * Initially, we only compute the squares of the singular values.
922    */
923   const double s1s1 = 0.5*(frobenius_squared+sqrt_discriminant);
924   /*
925    * s2 the smallest singular value of the inverse Jacobian
926    * matrix. Its reciprocal is the largest singular value of the
927    * Jacobian matrix itself.
928    */
929   const double s2s2 = 0.5*(frobenius_squared-sqrt_discriminant);
930   const double s1s1minusn11 = s1s1-n11;
931   const double s1s1minusn22 = s1s1-n22;
932   /*
933    * u1, the first column of the U factor of a singular decomposition
934    * of Jinv, is a (non-normalized) left singular vector corresponding
935    * to s1. It has entries u11 and u21. We compute u1 from the fact
936    * that it is an eigenvector of n corresponding to the eigenvalue
937    * s1^2.
938    */
939   const double s1s1minusn11_squared = s1s1minusn11*s1s1minusn11;
940   const double s1s1minusn22_squared = s1s1minusn22*s1s1minusn22;
941   /*
942    * The following selects the largest row of n-s1^2 I as the one
943    * which is used to find the eigenvector. If both s1^2-n11 and
944    * s1^2-n22 are zero, n-s1^2 I is the zero matrix.  In that case,
945    * any vector is an eigenvector; in addition, norm below is equal to
946    * zero, and, in exact arithmetic, this is the only case in which
947    * norm = 0. So, setting u1 to the simple but arbitrary vector [1,0]
948    * if norm = 0 safely takes care of all cases.
949    */
950   const double temp_u11 =
951     ( (s1s1minusn11_squared>=s1s1minusn22_squared) ? n12 : s1s1minusn22 );
952   const double temp_u21 =
953     ( (s1s1minusn11_squared>=s1s1minusn22_squared) ? s1s1minusn11 : n21 );
954   const double norm = sqrt(temp_u11*temp_u11+temp_u21*temp_u21);
955   /*
956    * Finalize the entries of first left singular vector (associated
957    * with the largest singular value).
958    */
959   const double u11 = ( (norm>0.0) ? temp_u11/norm : 1.0 );
960   const double u21 = ( (norm>0.0) ? temp_u21/norm : 0.0 );
961   /*
962    * Clamp the singular values up to 1.
963    */
964   *major_mag = ( (s1s1<=1.0) ? 1.0 : sqrt(s1s1) );
965   *minor_mag = ( (s2s2<=1.0) ? 1.0 : sqrt(s2s2) );
966   /*
967    * Return the unit major and minor axis direction vectors.
968    */
969   *major_unit_x = u11;
970   *major_unit_y = u21;
971   *minor_unit_x = -u21;
972   *minor_unit_y = u11;
973 }
974 
975 #endif
976 /*
977 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
978 %                                                                             %
979 %                                                                             %
980 %                                                                             %
981 %   S c a l e R e s a m p l e F i l t e r                                     %
982 %                                                                             %
983 %                                                                             %
984 %                                                                             %
985 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
986 %
987 %  ScaleResampleFilter() does all the calculations needed to resample an image
988 %  at a specific scale, defined by two scaling vectors.  This not using
989 %  a orthogonal scaling, but two distorted scaling vectors, to allow the
990 %  generation of a angled ellipse.
991 %
992 %  As only two deritive scaling vectors are used the center of the ellipse
993 %  must be the center of the lookup.  That is any curvature that the
994 %  distortion may produce is discounted.
995 %
996 %  The input vectors are produced by either finding the derivitives of the
997 %  distortion function, or the partial derivitives from a distortion mapping.
998 %  They do not need to be the orthogonal dx,dy scaling vectors, but can be
999 %  calculated from other derivatives.  For example you could use  dr,da/r
1000 %  polar coordinate vector scaling vectors
1001 %
1002 %  If   u,v =  DistortEquation(x,y)   OR   u = Fu(x,y); v = Fv(x,y)
1003 %  Then the scaling vectors are determined from the deritives...
1004 %      du/dx, dv/dx     and    du/dy, dv/dy
1005 %  If the resulting scaling vectors is othogonally aligned then...
1006 %      dv/dx = 0   and   du/dy  =  0
1007 %  Producing an othogonally alligned ellipse in source space for the area to
1008 %  be resampled.
1009 %
1010 %  Note that scaling vectors are different to argument order.  Argument order
1011 %  is the general order the deritives are extracted from the distortion
1012 %  equations, and not the scaling vectors. As such the middle two vaules
1013 %  may be swapped from what you expect.  Caution is advised.
1014 %
1015 %  WARNING: It is assumed that any SetResampleFilter() method call will
1016 %  always be performed before the ScaleResampleFilter() method, so that the
1017 %  size of the ellipse will match the support for the resampling filter being
1018 %  used.
1019 %
1020 %  The format of the ScaleResampleFilter method is:
1021 %
1022 %     void ScaleResampleFilter(const ResampleFilter *resample_filter,
1023 %       const double dux,const double duy,const double dvx,const double dvy)
1024 %
1025 %  A description of each parameter follows:
1026 %
1027 %    o resample_filter: the resampling resample_filterrmation defining the
1028 %      image being resampled
1029 %
1030 %    o dux,duy,dvx,dvy:
1031 %         The deritives or scaling vectors defining the EWA ellipse.
1032 %         NOTE: watch the order, which is based on the order deritives
1033 %         are usally determined from distortion equations (see above).
1034 %         The middle two values may need to be swapped if you are thinking
1035 %         in terms of scaling vectors.
1036 %
1037 */
ScaleResampleFilter(ResampleFilter * resample_filter,const double dux,const double duy,const double dvx,const double dvy)1038 MagickExport void ScaleResampleFilter(ResampleFilter *resample_filter,
1039   const double dux,const double duy,const double dvx,const double dvy)
1040 {
1041   double A,B,C,F;
1042 
1043   assert(resample_filter != (ResampleFilter *) NULL);
1044   assert(resample_filter->signature == MagickCoreSignature);
1045 
1046   resample_filter->limit_reached = MagickFalse;
1047 
1048   /* A 'point' filter forces use of interpolation instead of area sampling */
1049   if ( resample_filter->filter == PointFilter )
1050     return; /* EWA turned off - nothing to do */
1051 
1052 #if DEBUG_ELLIPSE
1053   (void) FormatLocaleFile(stderr, "# -----\n" );
1054   (void) FormatLocaleFile(stderr, "dux=%lf; dvx=%lf;   duy=%lf; dvy=%lf;\n",
1055        dux, dvx, duy, dvy);
1056 #endif
1057 
1058   /* Find Ellipse Coefficents such that
1059         A*u^2 + B*u*v + C*v^2 = F
1060      With u,v relative to point around which we are resampling.
1061      And the given scaling dx,dy vectors in u,v space
1062          du/dx,dv/dx   and  du/dy,dv/dy
1063   */
1064 #if EWA
1065   /* Direct conversion of derivatives into elliptical coefficients
1066      However when magnifying images, the scaling vectors will be small
1067      resulting in a ellipse that is too small to sample properly.
1068      As such we need to clamp the major/minor axis to a minumum of 1.0
1069      to prevent it getting too small.
1070   */
1071 #if EWA_CLAMP
1072   { double major_mag,
1073            minor_mag,
1074            major_x,
1075            major_y,
1076            minor_x,
1077            minor_y;
1078 
1079   ClampUpAxes(dux,dvx,duy,dvy, &major_mag, &minor_mag,
1080                 &major_x, &major_y, &minor_x, &minor_y);
1081   major_x *= major_mag;  major_y *= major_mag;
1082   minor_x *= minor_mag;  minor_y *= minor_mag;
1083 #if DEBUG_ELLIPSE
1084   (void) FormatLocaleFile(stderr, "major_x=%lf; major_y=%lf;  minor_x=%lf; minor_y=%lf;\n",
1085         major_x, major_y, minor_x, minor_y);
1086 #endif
1087   A = major_y*major_y+minor_y*minor_y;
1088   B = -2.0*(major_x*major_y+minor_x*minor_y);
1089   C = major_x*major_x+minor_x*minor_x;
1090   F = major_mag*minor_mag;
1091   F *= F; /* square it */
1092   }
1093 #else /* raw unclamped EWA */
1094   A = dvx*dvx+dvy*dvy;
1095   B = -2.0*(dux*dvx+duy*dvy);
1096   C = dux*dux+duy*duy;
1097   F = dux*dvy-duy*dvx;
1098   F *= F; /* square it */
1099 #endif /* EWA_CLAMP */
1100 
1101 #else /* HQ_EWA */
1102   /*
1103     This Paul Heckbert's "Higher Quality EWA" formula, from page 60 in his
1104     thesis, which adds a unit circle to the elliptical area so as to do both
1105     Reconstruction and Prefiltering of the pixels in the resampling.  It also
1106     means it is always likely to have at least 4 pixels within the area of the
1107     ellipse, for weighted averaging.  No scaling will result with F == 4.0 and
1108     a circle of radius 2.0, and F smaller than this means magnification is
1109     being used.
1110 
1111     NOTE: This method produces a very blury result at near unity scale while
1112     producing perfect results for strong minitification and magnifications.
1113 
1114     However filter support is fixed to 2.0 (no good for Windowed Sinc filters)
1115   */
1116   A = dvx*dvx+dvy*dvy+1;
1117   B = -2.0*(dux*dvx+duy*dvy);
1118   C = dux*dux+duy*duy+1;
1119   F = A*C - B*B/4;
1120 #endif
1121 
1122 #if DEBUG_ELLIPSE
1123   (void) FormatLocaleFile(stderr, "A=%lf; B=%lf; C=%lf; F=%lf\n", A,B,C,F);
1124 
1125   /* Figure out the various information directly about the ellipse.
1126      This information currently not needed at this time, but may be
1127      needed later for better limit determination.
1128 
1129      It is also good to have as a record for future debugging
1130   */
1131   { double alpha, beta, gamma, Major, Minor;
1132     double Eccentricity, Ellipse_Area, Ellipse_Angle;
1133 
1134     alpha = A+C;
1135     beta  = A-C;
1136     gamma = sqrt(beta*beta + B*B );
1137 
1138     if ( alpha - gamma <= MagickEpsilon )
1139       Major=MagickMaximumValue;
1140     else
1141       Major=sqrt(2*F/(alpha - gamma));
1142     Minor = sqrt(2*F/(alpha + gamma));
1143 
1144     (void) FormatLocaleFile(stderr, "# Major=%lf; Minor=%lf\n", Major, Minor );
1145 
1146     /* other information about ellipse include... */
1147     Eccentricity = Major/Minor;
1148     Ellipse_Area = MagickPI*Major*Minor;
1149     Ellipse_Angle = atan2(B, A-C);
1150 
1151     (void) FormatLocaleFile(stderr, "# Angle=%lf   Area=%lf\n",
1152          (double) RadiansToDegrees(Ellipse_Angle), Ellipse_Area);
1153   }
1154 #endif
1155 
1156   /* If one or both of the scaling vectors is impossibly large
1157      (producing a very large raw F value), we may as well not bother
1158      doing any form of resampling since resampled area is very large.
1159      In this case some alternative means of pixel sampling, such as
1160      the average of the whole image is needed to get a reasonable
1161      result. Calculate only as needed.
1162   */
1163   if ( (4*A*C - B*B) > MagickMaximumValue ) {
1164     resample_filter->limit_reached = MagickTrue;
1165     return;
1166   }
1167 
1168   /* Scale ellipse to match the filters support
1169      (that is, multiply F by the square of the support)
1170      Simplier to just multiply it by the support twice!
1171   */
1172   F *= resample_filter->support;
1173   F *= resample_filter->support;
1174 
1175   /* Orthogonal bounds of the ellipse */
1176   resample_filter->Ulimit = sqrt(C*F/(A*C-0.25*B*B));
1177   resample_filter->Vlimit = sqrt(A*F/(A*C-0.25*B*B));
1178 
1179   /* Horizontally aligned parallelogram fitted to Ellipse */
1180   resample_filter->Uwidth = sqrt(F/A); /* Half of the parallelogram width */
1181   resample_filter->slope = -B/(2.0*A); /* Reciprocal slope of the parallelogram */
1182 
1183 #if DEBUG_ELLIPSE
1184   (void) FormatLocaleFile(stderr, "Ulimit=%lf; Vlimit=%lf; UWidth=%lf; Slope=%lf;\n",
1185            resample_filter->Ulimit, resample_filter->Vlimit,
1186            resample_filter->Uwidth, resample_filter->slope );
1187 #endif
1188 
1189   /* Check the absolute area of the parallelogram involved.
1190    * This limit needs more work, as it is too slow for larger images
1191    * with tiled views of the horizon.
1192   */
1193   if ( (resample_filter->Uwidth * resample_filter->Vlimit)
1194          > (4.0*resample_filter->image_area)) {
1195     resample_filter->limit_reached = MagickTrue;
1196     return;
1197   }
1198 
1199   /* Scale ellipse formula to directly index the Filter Lookup Table */
1200   { register double scale;
1201 #if FILTER_LUT
1202     /* scale so that F = WLUT_WIDTH; -- hardcoded */
1203     scale = (double)WLUT_WIDTH/F;
1204 #else
1205     /* scale so that F = resample_filter->F (support^2) */
1206     scale = resample_filter->F/F;
1207 #endif
1208     resample_filter->A = A*scale;
1209     resample_filter->B = B*scale;
1210     resample_filter->C = C*scale;
1211   }
1212 }
1213 
1214 /*
1215 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1216 %                                                                             %
1217 %                                                                             %
1218 %                                                                             %
1219 %   S e t R e s a m p l e F i l t e r                                         %
1220 %                                                                             %
1221 %                                                                             %
1222 %                                                                             %
1223 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1224 %
1225 %  SetResampleFilter() set the resampling filter lookup table based on a
1226 %  specific filter.  Note that the filter is used as a radial filter not as a
1227 %  two pass othogonally aligned resampling filter.
1228 %
1229 %  The format of the SetResampleFilter method is:
1230 %
1231 %    void SetResampleFilter(ResampleFilter *resample_filter,
1232 %      const FilterType filter)
1233 %
1234 %  A description of each parameter follows:
1235 %
1236 %    o resample_filter: resampling resample_filterrmation structure
1237 %
1238 %    o filter: the resize filter for elliptical weighting LUT
1239 %
1240 */
SetResampleFilter(ResampleFilter * resample_filter,const FilterType filter)1241 MagickExport void SetResampleFilter(ResampleFilter *resample_filter,
1242   const FilterType filter)
1243 {
1244   ResizeFilter
1245      *resize_filter;
1246 
1247   assert(resample_filter != (ResampleFilter *) NULL);
1248   assert(resample_filter->signature == MagickCoreSignature);
1249 
1250   resample_filter->do_interpolate = MagickFalse;
1251   resample_filter->filter = filter;
1252 
1253   /* Default cylindrical filter is a Cubic Keys filter */
1254   if ( filter == UndefinedFilter )
1255     resample_filter->filter = RobidouxFilter;
1256 
1257   if ( resample_filter->filter == PointFilter ) {
1258     resample_filter->do_interpolate = MagickTrue;
1259     return;  /* EWA turned off - nothing more to do */
1260   }
1261 
1262   resize_filter = AcquireResizeFilter(resample_filter->image,
1263     resample_filter->filter,MagickTrue,resample_filter->exception);
1264   if (resize_filter == (ResizeFilter *) NULL) {
1265     (void) ThrowMagickException(resample_filter->exception,GetMagickModule(),
1266          ModuleError, "UnableToSetFilteringValue",
1267          "Fall back to Interpolated 'Point' filter");
1268     resample_filter->filter = PointFilter;
1269     resample_filter->do_interpolate = MagickTrue;
1270     return;  /* EWA turned off - nothing more to do */
1271   }
1272 
1273   /* Get the practical working support for the filter,
1274    * after any API call blur factors have been accoded for.
1275    */
1276 #if EWA
1277   resample_filter->support = GetResizeFilterSupport(resize_filter);
1278 #else
1279   resample_filter->support = 2.0;  /* fixed support size for HQ-EWA */
1280 #endif
1281 
1282 #if FILTER_LUT
1283   /* Fill the LUT with the weights from the selected filter function */
1284   { register int
1285        Q;
1286     double
1287        r_scale;
1288 
1289     /* Scale radius so the filter LUT covers the full support range */
1290     r_scale = resample_filter->support*sqrt(1.0/(double)WLUT_WIDTH);
1291     for(Q=0; Q<WLUT_WIDTH; Q++)
1292       resample_filter->filter_lut[Q] = (double)
1293            GetResizeFilterWeight(resize_filter,sqrt((double)Q)*r_scale);
1294 
1295     /* finished with the resize filter */
1296     resize_filter = DestroyResizeFilter(resize_filter);
1297   }
1298 #else
1299   /* save the filter and the scaled ellipse bounds needed for filter */
1300   resample_filter->filter_def = resize_filter;
1301   resample_filter->F = resample_filter->support*resample_filter->support;
1302 #endif
1303 
1304   /*
1305     Adjust the scaling of the default unit circle
1306     This assumes that any real scaling changes will always
1307     take place AFTER the filter method has been initialized.
1308   */
1309   ScaleResampleFilter(resample_filter, 1.0, 0.0, 0.0, 1.0);
1310 
1311 #if 0
1312   /*
1313     This is old code kept as a reference only. Basically it generates
1314     a Gaussian bell curve, with sigma = 0.5 if the support is 2.0
1315 
1316     Create Normal Gaussian 2D Filter Weighted Lookup Table.
1317     A normal EWA guassual lookup would use   exp(Q*ALPHA)
1318     where  Q = distance squared from 0.0 (center) to 1.0 (edge)
1319     and    ALPHA = -4.0*ln(2.0)  ==>  -2.77258872223978123767
1320     The table is of length 1024, and equates to support radius of 2.0
1321     thus needs to be scaled by  ALPHA*4/1024 and any blur factor squared
1322 
1323     The it comes from reference code provided by Fred Weinhaus.
1324   */
1325   r_scale = -2.77258872223978123767/(WLUT_WIDTH*blur*blur);
1326   for(Q=0; Q<WLUT_WIDTH; Q++)
1327     resample_filter->filter_lut[Q] = exp((double)Q*r_scale);
1328   resample_filter->support = WLUT_WIDTH;
1329 #endif
1330 
1331 #if FILTER_LUT
1332 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1333   #pragma omp single
1334 #endif
1335   {
1336     if (IsStringTrue(GetImageArtifact(resample_filter->image,
1337         "resample:verbose")) != MagickFalse)
1338       {
1339         register int
1340           Q;
1341         double
1342           r_scale;
1343 
1344         /* Debug output of the filter weighting LUT
1345           Gnuplot the LUT data, the x scale index has been adjusted
1346             plot [0:2][-.2:1] "lut.dat" with lines
1347           The filter values should be normalized for comparision
1348         */
1349         printf("#\n");
1350         printf("# Resampling Filter LUT (%d values) for '%s' filter\n",
1351                    WLUT_WIDTH, CommandOptionToMnemonic(MagickFilterOptions,
1352                    resample_filter->filter) );
1353         printf("#\n");
1354         printf("# Note: values in table are using a squared radius lookup.\n");
1355         printf("# As such its distribution is not uniform.\n");
1356         printf("#\n");
1357         printf("# The X value is the support distance for the Y weight\n");
1358         printf("# so you can use gnuplot to plot this cylindrical filter\n");
1359         printf("#    plot [0:2][-.2:1] \"lut.dat\" with lines\n");
1360         printf("#\n");
1361 
1362         /* Scale radius so the filter LUT covers the full support range */
1363         r_scale = resample_filter->support*sqrt(1.0/(double)WLUT_WIDTH);
1364         for(Q=0; Q<WLUT_WIDTH; Q++)
1365           printf("%8.*g %.*g\n",
1366               GetMagickPrecision(),sqrt((double)Q)*r_scale,
1367               GetMagickPrecision(),resample_filter->filter_lut[Q] );
1368         printf("\n\n"); /* generate a 'break' in gnuplot if multiple outputs */
1369       }
1370     /* Output the above once only for each image, and each setting
1371     (void) DeleteImageArtifact(resample_filter->image,"resample:verbose");
1372     */
1373   }
1374 #endif /* FILTER_LUT */
1375   return;
1376 }
1377 
1378 /*
1379 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1380 %                                                                             %
1381 %                                                                             %
1382 %                                                                             %
1383 %   S e t R e s a m p l e F i l t e r I n t e r p o l a t e M e t h o d       %
1384 %                                                                             %
1385 %                                                                             %
1386 %                                                                             %
1387 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1388 %
1389 %  SetResampleFilterInterpolateMethod() sets the resample filter interpolation
1390 %  method.
1391 %
1392 %  The format of the SetResampleFilterInterpolateMethod method is:
1393 %
1394 %      MagickBooleanType SetResampleFilterInterpolateMethod(
1395 %        ResampleFilter *resample_filter,const InterpolateMethod method)
1396 %
1397 %  A description of each parameter follows:
1398 %
1399 %    o resample_filter: the resample filter.
1400 %
1401 %    o method: the interpolation method.
1402 %
1403 */
SetResampleFilterInterpolateMethod(ResampleFilter * resample_filter,const PixelInterpolateMethod method)1404 MagickExport MagickBooleanType SetResampleFilterInterpolateMethod(
1405   ResampleFilter *resample_filter,const PixelInterpolateMethod method)
1406 {
1407   assert(resample_filter != (ResampleFilter *) NULL);
1408   assert(resample_filter->signature == MagickCoreSignature);
1409   assert(resample_filter->image != (Image *) NULL);
1410   if (resample_filter->debug != MagickFalse)
1411     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",
1412       resample_filter->image->filename);
1413   resample_filter->interpolate=method;
1414   return(MagickTrue);
1415 }
1416 
1417 /*
1418 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1419 %                                                                             %
1420 %                                                                             %
1421 %                                                                             %
1422 %   S e t R e s a m p l e F i l t e r V i r t u a l P i x e l M e t h o d     %
1423 %                                                                             %
1424 %                                                                             %
1425 %                                                                             %
1426 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1427 %
1428 %  SetResampleFilterVirtualPixelMethod() changes the virtual pixel method
1429 %  associated with the specified resample filter.
1430 %
1431 %  The format of the SetResampleFilterVirtualPixelMethod method is:
1432 %
1433 %      MagickBooleanType SetResampleFilterVirtualPixelMethod(
1434 %        ResampleFilter *resample_filter,const VirtualPixelMethod method)
1435 %
1436 %  A description of each parameter follows:
1437 %
1438 %    o resample_filter: the resample filter.
1439 %
1440 %    o method: the virtual pixel method.
1441 %
1442 */
SetResampleFilterVirtualPixelMethod(ResampleFilter * resample_filter,const VirtualPixelMethod method)1443 MagickExport MagickBooleanType SetResampleFilterVirtualPixelMethod(
1444   ResampleFilter *resample_filter,const VirtualPixelMethod method)
1445 {
1446   assert(resample_filter != (ResampleFilter *) NULL);
1447   assert(resample_filter->signature == MagickCoreSignature);
1448   assert(resample_filter->image != (Image *) NULL);
1449   if (resample_filter->debug != MagickFalse)
1450     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",
1451       resample_filter->image->filename);
1452   resample_filter->virtual_pixel=method;
1453   if (method != UndefinedVirtualPixelMethod)
1454     (void) SetCacheViewVirtualPixelMethod(resample_filter->view,method);
1455   return(MagickTrue);
1456 }
1457