MagickCore 7.1.2
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distort.c
1/*
2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3% %
4% %
5% %
6% DDDD IIIII SSSSS TTTTT OOO RRRR TTTTT %
7% D D I SS T O O R R T %
8% D D I SSS T O O RRRR T %
9% D D I SS T O O R R T %
10% DDDD IIIII SSSSS T OOO R R T %
11% %
12% %
13% MagickCore Image Distortion Methods %
14% %
15% Software Design %
16% Cristy %
17% Anthony Thyssen %
18% June 2007 %
19% %
20% %
21% Copyright @ 1999 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/cache.h"
46#include "MagickCore/cache-view.h"
47#include "MagickCore/channel.h"
48#include "MagickCore/colorspace-private.h"
49#include "MagickCore/composite-private.h"
50#include "MagickCore/distort.h"
51#include "MagickCore/exception.h"
52#include "MagickCore/exception-private.h"
53#include "MagickCore/gem.h"
54#include "MagickCore/image.h"
55#include "MagickCore/linked-list.h"
56#include "MagickCore/list.h"
57#include "MagickCore/matrix.h"
58#include "MagickCore/matrix-private.h"
59#include "MagickCore/memory_.h"
60#include "MagickCore/monitor-private.h"
61#include "MagickCore/option.h"
62#include "MagickCore/pixel.h"
63#include "MagickCore/pixel-accessor.h"
64#include "MagickCore/resample.h"
65#include "MagickCore/resample-private.h"
66#include "MagickCore/registry.h"
67#include "MagickCore/resource_.h"
68#include "MagickCore/semaphore.h"
69#include "MagickCore/shear.h"
70#include "MagickCore/string_.h"
71#include "MagickCore/string-private.h"
72#include "MagickCore/thread-private.h"
73#include "MagickCore/token.h"
74#include "MagickCore/transform.h"
75␌
76/*
77 Numerous internal routines for image distortions.
78*/
79static inline void AffineArgsToCoefficients(double *affine)
80{
81 /* map external sx,ry,rx,sy,tx,ty to internal c0,c2,c4,c1,c3,c5 */
82 double tmp[4]; /* note indexes 0 and 5 remain unchanged */
83 tmp[0]=affine[1]; tmp[1]=affine[2]; tmp[2]=affine[3]; tmp[3]=affine[4];
84 affine[3]=tmp[0]; affine[1]=tmp[1]; affine[4]=tmp[2]; affine[2]=tmp[3];
85}
86
87static inline void CoefficientsToAffineArgs(double *coeff)
88{
89 /* map internal c0,c1,c2,c3,c4,c5 to external sx,ry,rx,sy,tx,ty */
90 double tmp[4]; /* note indexes 0 and 5 remain unchanged */
91 tmp[0]=coeff[3]; tmp[1]=coeff[1]; tmp[2]=coeff[4]; tmp[3]=coeff[2];
92 coeff[1]=tmp[0]; coeff[2]=tmp[1]; coeff[3]=tmp[2]; coeff[4]=tmp[3];
93}
94static void InvertAffineCoefficients(const double *coeff,double *inverse)
95{
96 /* From "Digital Image Warping" by George Wolberg, page 50 */
97 double determinant;
98
99 determinant=MagickSafeReciprocal(coeff[0]*coeff[4]-coeff[1]*coeff[3]);
100 inverse[0]=determinant*coeff[4];
101 inverse[1]=determinant*(-coeff[1]);
102 inverse[2]=determinant*(coeff[1]*coeff[5]-coeff[2]*coeff[4]);
103 inverse[3]=determinant*(-coeff[3]);
104 inverse[4]=determinant*coeff[0];
105 inverse[5]=determinant*(coeff[2]*coeff[3]-coeff[0]*coeff[5]);
106}
107
108static void InvertPerspectiveCoefficients(const double *coeff,
109 double *inverse)
110{
111 /* From "Digital Image Warping" by George Wolberg, page 53 */
112 double determinant;
113
114 determinant=MagickSafeReciprocal(coeff[0]*coeff[4]-coeff[3]*coeff[1]);
115 inverse[0]=determinant*(coeff[4]-coeff[7]*coeff[5]);
116 inverse[1]=determinant*(coeff[7]*coeff[2]-coeff[1]);
117 inverse[2]=determinant*(coeff[1]*coeff[5]-coeff[4]*coeff[2]);
118 inverse[3]=determinant*(coeff[6]*coeff[5]-coeff[3]);
119 inverse[4]=determinant*(coeff[0]-coeff[6]*coeff[2]);
120 inverse[5]=determinant*(coeff[3]*coeff[2]-coeff[0]*coeff[5]);
121 inverse[6]=determinant*(coeff[3]*coeff[7]-coeff[6]*coeff[4]);
122 inverse[7]=determinant*(coeff[6]*coeff[1]-coeff[0]*coeff[7]);
123}
124
125/*
126 * Polynomial Term Defining Functions
127 *
128 * Order must either be an integer, or 1.5 to produce
129 * the 2 number_valuesal polynomial function...
130 * affine 1 (3) u = c0 + c1*x + c2*y
131 * bilinear 1.5 (4) u = '' + c3*x*y
132 * quadratic 2 (6) u = '' + c4*x*x + c5*y*y
133 * cubic 3 (10) u = '' + c6*x^3 + c7*x*x*y + c8*x*y*y + c9*y^3
134 * quartic 4 (15) u = '' + c10*x^4 + ... + c14*y^4
135 * quintic 5 (21) u = '' + c15*x^5 + ... + c20*y^5
136 * number in parenthesis minimum number of points needed.
137 * Anything beyond quintic, has not been implemented until
138 * a more automated way of determining terms is found.
139
140 * Note the slight re-ordering of the terms for a quadratic polynomial
141 * which is to allow the use of a bi-linear (order=1.5) polynomial.
142 * All the later polynomials are ordered simply from x^N to y^N
143 */
144static size_t poly_number_terms(double order)
145{
146 /* Return the number of terms for a 2d polynomial */
147 if ( order < 1 || order > 5 ||
148 ( order != floor(order) && (order-1.5) > MagickEpsilon) )
149 return 0; /* invalid polynomial order */
150 return((size_t) floor((order+1)*(order+2)/2));
151}
152
153static double poly_basis_fn(ssize_t n, double x, double y)
154{
155 /* Return the result for this polynomial term */
156 switch(n) {
157 case 0: return( 1.0 ); /* constant */
158 case 1: return( x );
159 case 2: return( y ); /* affine order = 1 terms = 3 */
160 case 3: return( x*y ); /* bilinear order = 1.5 terms = 4 */
161 case 4: return( x*x );
162 case 5: return( y*y ); /* quadratic order = 2 terms = 6 */
163 case 6: return( x*x*x );
164 case 7: return( x*x*y );
165 case 8: return( x*y*y );
166 case 9: return( y*y*y ); /* cubic order = 3 terms = 10 */
167 case 10: return( x*x*x*x );
168 case 11: return( x*x*x*y );
169 case 12: return( x*x*y*y );
170 case 13: return( x*y*y*y );
171 case 14: return( y*y*y*y ); /* quartic order = 4 terms = 15 */
172 case 15: return( x*x*x*x*x );
173 case 16: return( x*x*x*x*y );
174 case 17: return( x*x*x*y*y );
175 case 18: return( x*x*y*y*y );
176 case 19: return( x*y*y*y*y );
177 case 20: return( y*y*y*y*y ); /* quintic order = 5 terms = 21 */
178 }
179 return( 0 ); /* should never happen */
180}
181static const char *poly_basis_str(ssize_t n)
182{
183 /* return the result for this polynomial term */
184 switch(n) {
185 case 0: return(""); /* constant */
186 case 1: return("*ii");
187 case 2: return("*jj"); /* affine order = 1 terms = 3 */
188 case 3: return("*ii*jj"); /* bilinear order = 1.5 terms = 4 */
189 case 4: return("*ii*ii");
190 case 5: return("*jj*jj"); /* quadratic order = 2 terms = 6 */
191 case 6: return("*ii*ii*ii");
192 case 7: return("*ii*ii*jj");
193 case 8: return("*ii*jj*jj");
194 case 9: return("*jj*jj*jj"); /* cubic order = 3 terms = 10 */
195 case 10: return("*ii*ii*ii*ii");
196 case 11: return("*ii*ii*ii*jj");
197 case 12: return("*ii*ii*jj*jj");
198 case 13: return("*ii*jj*jj*jj");
199 case 14: return("*jj*jj*jj*jj"); /* quartic order = 4 terms = 15 */
200 case 15: return("*ii*ii*ii*ii*ii");
201 case 16: return("*ii*ii*ii*ii*jj");
202 case 17: return("*ii*ii*ii*jj*jj");
203 case 18: return("*ii*ii*jj*jj*jj");
204 case 19: return("*ii*jj*jj*jj*jj");
205 case 20: return("*jj*jj*jj*jj*jj"); /* quintic order = 5 terms = 21 */
206 }
207 return( "UNKNOWN" ); /* should never happen */
208}
209static double poly_basis_dx(ssize_t n, double x, double y)
210{
211 /* polynomial term for x derivative */
212 switch(n) {
213 case 0: return( 0.0 ); /* constant */
214 case 1: return( 1.0 );
215 case 2: return( 0.0 ); /* affine order = 1 terms = 3 */
216 case 3: return( y ); /* bilinear order = 1.5 terms = 4 */
217 case 4: return( x );
218 case 5: return( 0.0 ); /* quadratic order = 2 terms = 6 */
219 case 6: return( x*x );
220 case 7: return( x*y );
221 case 8: return( y*y );
222 case 9: return( 0.0 ); /* cubic order = 3 terms = 10 */
223 case 10: return( x*x*x );
224 case 11: return( x*x*y );
225 case 12: return( x*y*y );
226 case 13: return( y*y*y );
227 case 14: return( 0.0 ); /* quartic order = 4 terms = 15 */
228 case 15: return( x*x*x*x );
229 case 16: return( x*x*x*y );
230 case 17: return( x*x*y*y );
231 case 18: return( x*y*y*y );
232 case 19: return( y*y*y*y );
233 case 20: return( 0.0 ); /* quintic order = 5 terms = 21 */
234 }
235 return( 0.0 ); /* should never happen */
236}
237static double poly_basis_dy(ssize_t n, double x, double y)
238{
239 /* polynomial term for y derivative */
240 switch(n) {
241 case 0: return( 0.0 ); /* constant */
242 case 1: return( 0.0 );
243 case 2: return( 1.0 ); /* affine order = 1 terms = 3 */
244 case 3: return( x ); /* bilinear order = 1.5 terms = 4 */
245 case 4: return( 0.0 );
246 case 5: return( y ); /* quadratic order = 2 terms = 6 */
247 default: return( poly_basis_dx(n-1,x,y) ); /* weird but true */
248 }
249 /* NOTE: the only reason that last is not true for 'quadratic'
250 is due to the re-arrangement of terms to allow for 'bilinear'
251 */
252}
253␌
254/*
255%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
256% %
257% %
258% %
259% A f f i n e T r a n s f o r m I m a g e %
260% %
261% %
262% %
263%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
264%
265% AffineTransformImage() transforms an image as dictated by the affine matrix.
266% It allocates the memory necessary for the new Image structure and returns
267% a pointer to the new image.
268%
269% The format of the AffineTransformImage method is:
270%
271% Image *AffineTransformImage(const Image *image,
272% AffineMatrix *affine_matrix,ExceptionInfo *exception)
273%
274% A description of each parameter follows:
275%
276% o image: the image.
277%
278% o affine_matrix: the affine matrix.
279%
280% o exception: return any errors or warnings in this structure.
281%
282*/
283MagickExport Image *AffineTransformImage(const Image *image,
284 const AffineMatrix *affine_matrix,ExceptionInfo *exception)
285{
286 double
287 distort[6];
288
289 Image
290 *deskew_image;
291
292 /*
293 Affine transform image.
294 */
295 assert(image->signature == MagickCoreSignature);
296 assert(affine_matrix != (AffineMatrix *) NULL);
297 assert(exception != (ExceptionInfo *) NULL);
298 assert(exception->signature == MagickCoreSignature);
299 if (IsEventLogging() != MagickFalse)
300 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
301 distort[0]=affine_matrix->sx;
302 distort[1]=affine_matrix->rx;
303 distort[2]=affine_matrix->ry;
304 distort[3]=affine_matrix->sy;
305 distort[4]=affine_matrix->tx;
306 distort[5]=affine_matrix->ty;
307 deskew_image=DistortImage(image,AffineProjectionDistortion,6,distort,
308 MagickTrue,exception);
309 return(deskew_image);
310}
311␌
312/*
313%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
314% %
315% %
316% %
317+ G e n e r a t e C o e f f i c i e n t s %
318% %
319% %
320% %
321%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
322%
323% GenerateCoefficients() takes user provided input arguments and generates
324% the coefficients, needed to apply the specific distortion for either
325% distorting images (generally using control points) or generating a color
326% gradient from sparsely separated color points.
327%
328% The format of the GenerateCoefficients() method is:
329%
330% Image *GenerateCoefficients(const Image *image,DistortMethod method,
331% const size_t number_arguments,const double *arguments,
332% size_t number_values, ExceptionInfo *exception)
333%
334% A description of each parameter follows:
335%
336% o image: the image to be distorted.
337%
338% o method: the method of image distortion/ sparse gradient
339%
340% o number_arguments: the number of arguments given.
341%
342% o arguments: the arguments for this distortion method.
343%
344% o number_values: the style and format of given control points, (caller type)
345% 0: 2 dimensional mapping of control points (Distort)
346% Format: u,v,x,y where u,v is the 'source' of the
347% the color to be plotted, for DistortImage()
348% N: Interpolation of control points with N values (usually r,g,b)
349% Format: x,y,r,g,b mapping x,y to color values r,g,b
350% IN future, variable number of values may be given (1 to N)
351%
352% o exception: return any errors or warnings in this structure
353%
354% Note that the returned array of double values must be freed by the
355% calling method using RelinquishMagickMemory(). This however may change in
356% the future to require a more 'method' specific method.
357%
358% Because of this, this method should not be classed as stable or used
359% outside other MagickCore library methods.
360*/
361
362static inline double MagickRound(double x)
363{
364 /*
365 Round the fraction to nearest integer.
366 */
367 if ((x-floor(x)) < (ceil(x)-x))
368 return(floor(x));
369 return(ceil(x));
370}
371
372static double *GenerateCoefficients(const Image *image,
373 DistortMethod *method,const size_t number_arguments,const double *arguments,
374 size_t number_values,ExceptionInfo *exception)
375{
376 double
377 *coeff;
378
379 size_t
380 i;
381
382 size_t
383 number_coefficients, /* number of coefficients to return (array size) */
384 cp_size, /* number floating point numbers per control point */
385 cp_x,cp_y, /* the x,y indexes for control point */
386 cp_values; /* index of values for this control point */
387 /* number_values Number of values given per control point */
388
389 if ( number_values == 0 ) {
390 /* Image distortion using control points (or other distortion)
391 That is generate a mapping so that x,y->u,v given u,v,x,y
392 */
393 number_values = 2; /* special case: two values of u,v */
394 cp_values = 0; /* the values i,j are BEFORE the destination CP x,y */
395 cp_x = 2; /* location of x,y in input control values */
396 cp_y = 3;
397 /* NOTE: cp_values, also used for later 'reverse map distort' tests */
398 }
399 else {
400 cp_x = 0; /* location of x,y in input control values */
401 cp_y = 1;
402 cp_values = 2; /* and the other values are after x,y */
403 /* Typically in this case the values are R,G,B color values */
404 }
405 cp_size = number_values+2; /* each CP definition involves this many numbers */
406
407 /* If not enough control point pairs are found for specific distortions
408 fall back to Affine distortion (allowing 0 to 3 point pairs)
409 */
410 if ( number_arguments < 4*cp_size &&
411 ( *method == BilinearForwardDistortion
412 || *method == BilinearReverseDistortion
413 || *method == PerspectiveDistortion
414 ) )
415 *method = AffineDistortion;
416
417 number_coefficients=0;
418 switch (*method) {
419 case AffineDistortion:
420 case RigidAffineDistortion:
421 /* also BarycentricColorInterpolate: */
422 number_coefficients=3*number_values;
423 break;
424 case PolynomialDistortion:
425 /* number of coefficients depend on the given polynomial 'order' */
426 i = poly_number_terms(arguments[0]);
427 number_coefficients = 2 + i*number_values;
428 if ( i == 0 ) {
429 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
430 "InvalidArgument","%s : '%s'","Polynomial",
431 "Invalid order, should be integer 1 to 5, or 1.5");
432 return((double *) NULL);
433 }
434 if ( number_arguments < 1+i*cp_size ) {
435 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
436 "InvalidArgument", "%s : 'require at least %.20g CPs'",
437 "Polynomial", (double) i);
438 return((double *) NULL);
439 }
440 break;
441 case BilinearReverseDistortion:
442 number_coefficients=4*number_values;
443 break;
444 /*
445 The rest are constants as they are only used for image distorts
446 */
447 case BilinearForwardDistortion:
448 number_coefficients=10; /* 2*4 coeff plus 2 constants */
449 cp_x = 0; /* Reverse src/dest coords for forward mapping */
450 cp_y = 1;
451 cp_values = 2;
452 break;
453#if 0
454 case QuadrilateralDistortion:
455 number_coefficients=19; /* BilinearForward + BilinearReverse */
456#endif
457 break;
458 case ShepardsDistortion:
459 number_coefficients=1; /* The power factor to use */
460 break;
461 case ArcDistortion:
462 number_coefficients=5;
463 break;
464 case ScaleRotateTranslateDistortion:
465 case AffineProjectionDistortion:
466 case Plane2CylinderDistortion:
467 case Cylinder2PlaneDistortion:
468 number_coefficients=6;
469 break;
470 case PolarDistortion:
471 case DePolarDistortion:
472 number_coefficients=8;
473 break;
474 case PerspectiveDistortion:
475 case PerspectiveProjectionDistortion:
476 number_coefficients=9;
477 break;
478 case BarrelDistortion:
479 case BarrelInverseDistortion:
480 number_coefficients=10;
481 break;
482 default:
483 perror("unknown method given"); /* just fail assertion */
484 }
485
486 /* allocate the array of coefficients needed */
487 coeff=(double *) AcquireQuantumMemory(number_coefficients,sizeof(*coeff));
488 if (coeff == (double *) NULL)
489 {
490 (void) ThrowMagickException(exception,GetMagickModule(),
491 ResourceLimitError,"MemoryAllocationFailed","%s",
492 "GenerateCoefficients");
493 return((double *) NULL);
494 }
495
496 /* zero out coefficients array */
497 for (i=0; i < number_coefficients; i++)
498 coeff[i] = 0.0;
499
500 switch (*method)
501 {
502 case AffineDistortion:
503 {
504 /* Affine Distortion
505 v = c0*x + c1*y + c2
506 for each 'value' given
507
508 Input Arguments are sets of control points...
509 For Distort Images u,v, x,y ...
510 For Sparse Gradients x,y, r,g,b ...
511 */
512 if ( number_arguments%cp_size != 0 ||
513 number_arguments < cp_size ) {
514 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
515 "InvalidArgument", "%s : 'require at least %.20g CPs'",
516 "Affine", 1.0);
517 coeff=(double *) RelinquishMagickMemory(coeff);
518 return((double *) NULL);
519 }
520 /* handle special cases of not enough arguments */
521 if ( number_arguments == cp_size ) {
522 /* Only 1 CP Set Given */
523 if ( cp_values == 0 ) {
524 /* image distortion - translate the image */
525 coeff[0] = 1.0;
526 coeff[2] = arguments[0] - arguments[2];
527 coeff[4] = 1.0;
528 coeff[5] = arguments[1] - arguments[3];
529 }
530 else {
531 /* sparse gradient - use the values directly */
532 for (i=0; i<number_values; i++)
533 coeff[i*3+2] = arguments[cp_values+i];
534 }
535 }
536 else {
537 /* 2 or more points (usually 3) given.
538 Solve a least squares simultaneous equation for coefficients.
539 */
540 double
541 **matrix,
542 **vectors,
543 terms[3];
544
545 MagickBooleanType
546 status;
547
548 /* create matrix, and a fake vectors matrix */
549 matrix=AcquireMagickMatrix(3UL,3UL);
550 vectors=(double **) AcquireQuantumMemory(number_values,
551 sizeof(*vectors));
552 if (matrix == (double **) NULL || vectors == (double **) NULL)
553 {
554 matrix = RelinquishMagickMatrix(matrix, 3UL);
555 vectors = (double **) RelinquishMagickMemory(vectors);
556 coeff = (double *) RelinquishMagickMemory(coeff);
557 (void) ThrowMagickException(exception,GetMagickModule(),
558 ResourceLimitError,"MemoryAllocationFailed",
559 "%s", "DistortCoefficients");
560 return((double *) NULL);
561 }
562 /* fake a number_values x3 vectors matrix from coefficients array */
563 for (i=0; i < number_values; i++)
564 vectors[i] = &(coeff[i*3]);
565 /* Add given control point pairs for least squares solving */
566 for (i=0; i < number_arguments; i+=cp_size) {
567 terms[0] = arguments[i+cp_x]; /* x */
568 terms[1] = arguments[i+cp_y]; /* y */
569 terms[2] = 1; /* 1 */
570 LeastSquaresAddTerms(matrix,vectors,terms,
571 &(arguments[i+cp_values]),3UL,number_values);
572 }
573 if ( number_arguments == 2*cp_size ) {
574 /* Only two pairs were given, but we need 3 to solve the affine.
575 Fake extra coordinates by rotating p1 around p0 by 90 degrees.
576 x2 = x0 - (y1-y0) y2 = y0 + (x1-x0)
577 */
578 terms[0] = arguments[cp_x]
579 - ( arguments[cp_size+cp_y] - arguments[cp_y] ); /* x2 */
580 terms[1] = arguments[cp_y] +
581 + ( arguments[cp_size+cp_x] - arguments[cp_x] ); /* y2 */
582 terms[2] = 1; /* 1 */
583 if ( cp_values == 0 ) {
584 /* Image Distortion - rotate the u,v coordinates too */
585 double
586 uv2[2];
587 uv2[0] = arguments[0] - arguments[5] + arguments[1]; /* u2 */
588 uv2[1] = arguments[1] + arguments[4] - arguments[0]; /* v2 */
589 LeastSquaresAddTerms(matrix,vectors,terms,uv2,3UL,2UL);
590 }
591 else {
592 /* Sparse Gradient - use values of p0 for linear gradient */
593 LeastSquaresAddTerms(matrix,vectors,terms,
594 &(arguments[cp_values]),3UL,number_values);
595 }
596 }
597 /* Solve for LeastSquares Coefficients */
598 status=GaussJordanElimination(matrix,vectors,3UL,number_values);
599 matrix = RelinquishMagickMatrix(matrix, 3UL);
600 vectors = (double **) RelinquishMagickMemory(vectors);
601 if ( status == MagickFalse ) {
602 coeff = (double *) RelinquishMagickMemory(coeff);
603 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
604 "InvalidArgument","%s : 'Unsolvable Matrix'",
605 CommandOptionToMnemonic(MagickDistortOptions, *method) );
606 return((double *) NULL);
607 }
608 }
609 return(coeff);
610 }
611 case RigidAffineDistortion:
612 {
613 double
614 inverse[6],
615 **matrix,
616 terms[5],
617 *vectors[1];
618
619 MagickBooleanType
620 status;
621
622 /*
623 Rigid affine (also known as a Euclidean transform), restricts affine
624 coefficients to 4 (S, R, Tx, Ty) with Sy=Sx and Ry = -Rx so that one has
625 only scale, rotation and translation. No skew.
626 */
627 if (((number_arguments % cp_size) != 0) || (number_arguments < cp_size))
628 {
629 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
630 "InvalidArgument", "%s : 'require at least %.20g CPs'",
631 CommandOptionToMnemonic(MagickDistortOptions,*method),2.0);
632 coeff=(double *) RelinquishMagickMemory(coeff);
633 return((double *) NULL);
634 }
635 /*
636 Rigid affine requires a 4x4 least-squares matrix (zeroed).
637 */
638 matrix=AcquireMagickMatrix(4UL,4UL);
639 if (matrix == (double **) NULL)
640 {
641 coeff=(double *) RelinquishMagickMemory(coeff);
642 (void) ThrowMagickException(exception,GetMagickModule(),
643 ResourceLimitError,"MemoryAllocationFailed","%s",
644 CommandOptionToMnemonic(MagickDistortOptions,*method));
645 return((double *) NULL);
646 }
647 /*
648 Add control points for least squares solving.
649 */
650 vectors[0]=(&(coeff[0]));
651 for (i=0; i < number_arguments; i+=4)
652 {
653 terms[0]=arguments[i+0];
654 terms[1]=(-arguments[i+1]);
655 terms[2]=1.0;
656 terms[3]=0.0;
657 LeastSquaresAddTerms(matrix,vectors,terms,&(arguments[i+2]),4UL,1UL);
658 terms[0]=arguments[i+1];
659 terms[1]=arguments[i+0];
660 terms[2]=0.0;
661 terms[3]=1.0;
662 LeastSquaresAddTerms(matrix,vectors,terms,&(arguments[i+3]),4UL,1UL);
663 }
664 /*
665 Solve for least-squares coefficients.
666 */
667 status=GaussJordanElimination(matrix,vectors,4UL,1UL);
668 matrix=RelinquishMagickMatrix(matrix,4UL);
669 if (status == MagickFalse)
670 {
671 coeff=(double *) RelinquishMagickMemory(coeff);
672 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
673 "InvalidArgument","%s : 'Unsolvable Matrix'",
674 CommandOptionToMnemonic(MagickDistortOptions,*method));
675 return((double *) NULL);
676 }
677 /*
678 Convert (S, R, Tx, Ty) to an affine projection.
679 */
680 inverse[0]=coeff[0];
681 inverse[1]=coeff[1];
682 inverse[2]=(-coeff[1]);
683 inverse[3]=coeff[0];
684 inverse[4]=coeff[2];
685 inverse[5]=coeff[3];
686 AffineArgsToCoefficients(inverse);
687 InvertAffineCoefficients(inverse,coeff);
688 *method=AffineDistortion;
689 return(coeff);
690 }
691 case AffineProjectionDistortion:
692 {
693 /*
694 Arguments: Affine Matrix (forward mapping)
695 Arguments sx, rx, ry, sy, tx, ty
696 Where u = sx*x + ry*y + tx
697 v = rx*x + sy*y + ty
698
699 Returns coefficients (in there inverse form) ordered as...
700 sx ry tx rx sy ty
701
702 AffineProjection Distortion Notes...
703 + Will only work with a 2 number_values for Image Distortion
704 + Can not be used for generating a sparse gradient (interpolation)
705 */
706 double inverse[8];
707 if (number_arguments != 6) {
708 coeff = (double *) RelinquishMagickMemory(coeff);
709 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
710 "InvalidArgument","%s : 'Needs 6 coeff values'",
711 CommandOptionToMnemonic(MagickDistortOptions, *method) );
712 return((double *) NULL);
713 }
714 /* FUTURE: trap test for sx*sy-rx*ry == 0 (determinant = 0, no inverse) */
715 for(i=0; i<6UL; i++ )
716 inverse[i] = arguments[i];
717 AffineArgsToCoefficients(inverse); /* map into coefficients */
718 InvertAffineCoefficients(inverse, coeff); /* invert */
719 *method = AffineDistortion;
720
721 return(coeff);
722 }
723 case ScaleRotateTranslateDistortion:
724 {
725 /* Scale, Rotate and Translate Distortion
726 An alternative Affine Distortion
727 Argument options, by number of arguments given:
728 7: x,y, sx,sy, a, nx,ny
729 6: x,y, s, a, nx,ny
730 5: x,y, sx,sy, a
731 4: x,y, s, a
732 3: x,y, a
733 2: s, a
734 1: a
735 Where actions are (in order of application)
736 x,y 'center' of transforms (default = image center)
737 sx,sy scale image by this amount (default = 1)
738 a angle of rotation (argument required)
739 nx,ny move 'center' here (default = x,y or no movement)
740 And convert to affine mapping coefficients
741
742 ScaleRotateTranslate Distortion Notes...
743 + Does not use a set of CPs in any normal way
744 + Will only work with a 2 number_valuesal Image Distortion
745 + Cannot be used for generating a sparse gradient (interpolation)
746 */
747 double
748 cosine, sine,
749 x,y,sx,sy,a,nx,ny;
750
751 /* set default center, and default scale */
752 x = nx = (double)(image->columns)/2.0 + (double)image->page.x;
753 y = ny = (double)(image->rows)/2.0 + (double)image->page.y;
754 sx = sy = 1.0;
755 switch ( number_arguments ) {
756 case 0:
757 coeff = (double *) RelinquishMagickMemory(coeff);
758 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
759 "InvalidArgument","%s : 'Needs at least 1 argument'",
760 CommandOptionToMnemonic(MagickDistortOptions, *method) );
761 return((double *) NULL);
762 case 1:
763 a = arguments[0];
764 break;
765 case 2:
766 sx = sy = arguments[0];
767 a = arguments[1];
768 break;
769 default:
770 x = nx = arguments[0];
771 y = ny = arguments[1];
772 switch ( number_arguments ) {
773 case 3:
774 a = arguments[2];
775 break;
776 case 4:
777 sx = sy = arguments[2];
778 a = arguments[3];
779 break;
780 case 5:
781 sx = arguments[2];
782 sy = arguments[3];
783 a = arguments[4];
784 break;
785 case 6:
786 sx = sy = arguments[2];
787 a = arguments[3];
788 nx = arguments[4];
789 ny = arguments[5];
790 break;
791 case 7:
792 sx = arguments[2];
793 sy = arguments[3];
794 a = arguments[4];
795 nx = arguments[5];
796 ny = arguments[6];
797 break;
798 default:
799 coeff = (double *) RelinquishMagickMemory(coeff);
800 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
801 "InvalidArgument","%s : 'Too Many Arguments (7 or less)'",
802 CommandOptionToMnemonic(MagickDistortOptions, *method) );
803 return((double *) NULL);
804 }
805 break;
806 }
807 /* Trap if sx or sy == 0 -- image is scaled out of existence! */
808 if ( fabs(sx) < MagickEpsilon || fabs(sy) < MagickEpsilon ) {
809 coeff = (double *) RelinquishMagickMemory(coeff);
810 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
811 "InvalidArgument","%s : 'Zero Scale Given'",
812 CommandOptionToMnemonic(MagickDistortOptions, *method) );
813 return((double *) NULL);
814 }
815 /* Save the given arguments as an affine distortion */
816 a=DegreesToRadians(a); cosine=cos(a); sine=sin(a);
817
818 *method = AffineDistortion;
819 coeff[0]=cosine/sx;
820 coeff[1]=sine/sx;
821 coeff[2]=x-nx*coeff[0]-ny*coeff[1];
822 coeff[3]=(-sine)/sy;
823 coeff[4]=cosine/sy;
824 coeff[5]=y-nx*coeff[3]-ny*coeff[4];
825 return(coeff);
826 }
827 case PerspectiveDistortion:
828 { /*
829 Perspective Distortion (a ratio of affine distortions)
830
831 p(x,y) c0*x + c1*y + c2
832 u = ------ = ------------------
833 r(x,y) c6*x + c7*y + 1
834
835 q(x,y) c3*x + c4*y + c5
836 v = ------ = ------------------
837 r(x,y) c6*x + c7*y + 1
838
839 c8 = Sign of 'r', or the denominator affine, for the actual image.
840 This determines what part of the distorted image is 'ground'
841 side of the horizon, the other part is 'sky' or invalid.
842 Valid values are +1.0 or -1.0 only.
843
844 Input Arguments are sets of control points...
845 For Distort Images u,v, x,y ...
846 For Sparse Gradients x,y, r,g,b ...
847
848 Perspective Distortion Notes...
849 + Can be thought of as ratio of 3 affine transformations
850 + Not separable: r() or c6 and c7 are used by both equations
851 + All 8 coefficients must be determined simultaneously
852 + Will only work with a 2 number_valuesal Image Distortion
853 + Can not be used for generating a sparse gradient (interpolation)
854 + It is not linear, but is simple to generate an inverse
855 + All lines within an image remain lines.
856 + but distances between points may vary.
857 */
858 double
859 **matrix,
860 *vectors[1],
861 terms[8];
862
863 size_t
864 cp_u = cp_values,
865 cp_v = cp_values+1;
866
867 MagickBooleanType
868 status;
869
870 if ( number_arguments%cp_size != 0 ||
871 number_arguments < cp_size*4 ) {
872 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
873 "InvalidArgument", "%s : 'require at least %.20g CPs'",
874 CommandOptionToMnemonic(MagickDistortOptions, *method), 4.0);
875 coeff=(double *) RelinquishMagickMemory(coeff);
876 return((double *) NULL);
877 }
878 /* fake 1x8 vectors matrix directly using the coefficients array */
879 vectors[0] = &(coeff[0]);
880 /* 8x8 least-squares matrix (zeroed) */
881 matrix = AcquireMagickMatrix(8UL,8UL);
882 if (matrix == (double **) NULL) {
883 coeff=(double *) RelinquishMagickMemory(coeff);
884 (void) ThrowMagickException(exception,GetMagickModule(),
885 ResourceLimitError,"MemoryAllocationFailed",
886 "%s", "DistortCoefficients");
887 return((double *) NULL);
888 }
889 /* Add control points for least squares solving */
890 for (i=0; i < number_arguments; i+=4) {
891 terms[0]=arguments[i+cp_x]; /* c0*x */
892 terms[1]=arguments[i+cp_y]; /* c1*y */
893 terms[2]=1.0; /* c2*1 */
894 terms[3]=0.0;
895 terms[4]=0.0;
896 terms[5]=0.0;
897 terms[6]=-terms[0]*arguments[i+cp_u]; /* 1/(c6*x) */
898 terms[7]=-terms[1]*arguments[i+cp_u]; /* 1/(c7*y) */
899 LeastSquaresAddTerms(matrix,vectors,terms,&(arguments[i+cp_u]),
900 8UL,1UL);
901
902 terms[0]=0.0;
903 terms[1]=0.0;
904 terms[2]=0.0;
905 terms[3]=arguments[i+cp_x]; /* c3*x */
906 terms[4]=arguments[i+cp_y]; /* c4*y */
907 terms[5]=1.0; /* c5*1 */
908 terms[6]=-terms[3]*arguments[i+cp_v]; /* 1/(c6*x) */
909 terms[7]=-terms[4]*arguments[i+cp_v]; /* 1/(c7*y) */
910 LeastSquaresAddTerms(matrix,vectors,terms,&(arguments[i+cp_v]),
911 8UL,1UL);
912 }
913 /* Solve for LeastSquares Coefficients */
914 status=GaussJordanElimination(matrix,vectors,8UL,1UL);
915 matrix = RelinquishMagickMatrix(matrix, 8UL);
916 if ( status == MagickFalse ) {
917 coeff = (double *) RelinquishMagickMemory(coeff);
918 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
919 "InvalidArgument","%s : 'Unsolvable Matrix'",
920 CommandOptionToMnemonic(MagickDistortOptions, *method) );
921 return((double *) NULL);
922 }
923 /*
924 Calculate 9'th coefficient! The ground-sky determination.
925 What is sign of the 'ground' in r() denominator affine function?
926 Just use any valid image coordinate (first control point) in
927 destination for determination of what part of view is 'ground'.
928 */
929 coeff[8] = coeff[6]*arguments[cp_x]
930 + coeff[7]*arguments[cp_y] + 1.0;
931 coeff[8] = (coeff[8] < 0.0) ? -1.0 : +1.0;
932
933 return(coeff);
934 }
935 case PerspectiveProjectionDistortion:
936 {
937 /*
938 Arguments: Perspective Coefficients (forward mapping)
939 */
940 if (number_arguments != 8) {
941 coeff = (double *) RelinquishMagickMemory(coeff);
942 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
943 "InvalidArgument", "%s : 'Needs 8 coefficient values'",
944 CommandOptionToMnemonic(MagickDistortOptions, *method));
945 return((double *) NULL);
946 }
947 /* FUTURE: trap test c0*c4-c3*c1 == 0 (determinate = 0, no inverse) */
948 InvertPerspectiveCoefficients(arguments, coeff);
949 /*
950 Calculate 9'th coefficient! The ground-sky determination.
951 What is sign of the 'ground' in r() denominator affine function?
952 Just use any valid image coordinate in destination for determination.
953 For a forward mapped perspective the images 0,0 coord will map to
954 c2,c5 in the distorted image, so set the sign of denominator of that.
955 */
956 coeff[8] = coeff[6]*arguments[2]
957 + coeff[7]*arguments[5] + 1.0;
958 coeff[8] = (coeff[8] < 0.0) ? -1.0 : +1.0;
959 *method = PerspectiveDistortion;
960
961 return(coeff);
962 }
963 case BilinearForwardDistortion:
964 case BilinearReverseDistortion:
965 {
966 /* Bilinear Distortion (Forward mapping)
967 v = c0*x + c1*y + c2*x*y + c3;
968 for each 'value' given
969
970 This is actually a simple polynomial Distortion! The difference
971 however is when we need to reverse the above equation to generate a
972 BilinearForwardDistortion (see below).
973
974 Input Arguments are sets of control points...
975 For Distort Images u,v, x,y ...
976 For Sparse Gradients x,y, r,g,b ...
977
978 */
979 double
980 **matrix,
981 **vectors,
982 terms[4];
983
984 MagickBooleanType
985 status;
986
987 /* check the number of arguments */
988 if ( number_arguments%cp_size != 0 ||
989 number_arguments < cp_size*4 ) {
990 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
991 "InvalidArgument", "%s : 'require at least %.20g CPs'",
992 CommandOptionToMnemonic(MagickDistortOptions, *method), 4.0);
993 coeff=(double *) RelinquishMagickMemory(coeff);
994 return((double *) NULL);
995 }
996 /* create matrix, and a fake vectors matrix */
997 matrix=AcquireMagickMatrix(4UL,4UL);
998 vectors=(double **) AcquireQuantumMemory(number_values,sizeof(*vectors));
999 if (matrix == (double **) NULL || vectors == (double **) NULL)
1000 {
1001 matrix = RelinquishMagickMatrix(matrix, 4UL);
1002 vectors = (double **) RelinquishMagickMemory(vectors);
1003 coeff = (double *) RelinquishMagickMemory(coeff);
1004 (void) ThrowMagickException(exception,GetMagickModule(),
1005 ResourceLimitError,"MemoryAllocationFailed",
1006 "%s", "DistortCoefficients");
1007 return((double *) NULL);
1008 }
1009 /* fake a number_values x4 vectors matrix from coefficients array */
1010 for (i=0; i < number_values; i++)
1011 vectors[i] = &(coeff[i*4]);
1012 /* Add given control point pairs for least squares solving */
1013 for (i=0; i < number_arguments; i+=cp_size) {
1014 terms[0] = arguments[i+cp_x]; /* x */
1015 terms[1] = arguments[i+cp_y]; /* y */
1016 terms[2] = terms[0]*terms[1]; /* x*y */
1017 terms[3] = 1; /* 1 */
1018 LeastSquaresAddTerms(matrix,vectors,terms,
1019 &(arguments[i+cp_values]),4UL,number_values);
1020 }
1021 /* Solve for LeastSquares Coefficients */
1022 status=GaussJordanElimination(matrix,vectors,4UL,number_values);
1023 matrix = RelinquishMagickMatrix(matrix, 4UL);
1024 vectors = (double **) RelinquishMagickMemory(vectors);
1025 if ( status == MagickFalse ) {
1026 coeff = (double *) RelinquishMagickMemory(coeff);
1027 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1028 "InvalidArgument","%s : 'Unsolvable Matrix'",
1029 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1030 return((double *) NULL);
1031 }
1032 if ( *method == BilinearForwardDistortion ) {
1033 /* Bilinear Forward Mapped Distortion
1034
1035 The above least-squares solved for coefficients but in the forward
1036 direction, due to changes to indexing constants.
1037
1038 i = c0*x + c1*y + c2*x*y + c3;
1039 j = c4*x + c5*y + c6*x*y + c7;
1040
1041 where i,j are in the destination image, NOT the source.
1042
1043 Reverse Pixel mapping however needs to use reverse of these
1044 functions. It required a full page of algebra to work out the
1045 reversed mapping formula, but resolves down to the following...
1046
1047 c8 = c0*c5-c1*c4;
1048 c9 = 2*(c2*c5-c1*c6); // '2*a' in the quadratic formula
1049
1050 i = i - c3; j = j - c7;
1051 b = c6*i - c2*j + c8; // So that a*y^2 + b*y + c == 0
1052 c = c4*i - c0*j; // y = ( -b +- sqrt(bb - 4ac) ) / (2*a)
1053
1054 r = b*b - c9*(c+c);
1055 if ( c9 != 0 )
1056 y = ( -b + sqrt(r) ) / c9;
1057 else
1058 y = -c/b;
1059
1060 x = ( i - c1*y) / ( c1 - c2*y );
1061
1062 NB: if 'r' is negative there is no solution!
1063 NB: the sign of the sqrt() should be negative if image becomes
1064 flipped or flopped, or crosses over itself.
1065 NB: technically coefficient c5 is not needed, anymore,
1066 but kept for completeness.
1067
1068 See Anthony Thyssen <A.Thyssen@griffith.edu.au>
1069 or Fred Weinhaus <fmw@alink.net> for more details.
1070
1071 */
1072 coeff[8] = coeff[0]*coeff[5] - coeff[1]*coeff[4];
1073 coeff[9] = 2*(coeff[2]*coeff[5] - coeff[1]*coeff[6]);
1074 }
1075 return(coeff);
1076 }
1077#if 0
1078 case QuadrilateralDistortion:
1079 {
1080 /* Map a Quadrilateral to a unit square using BilinearReverse
1081 Then map that unit square back to the final Quadrilateral
1082 using BilinearForward.
1083
1084 Input Arguments are sets of control points...
1085 For Distort Images u,v, x,y ...
1086 For Sparse Gradients x,y, r,g,b ...
1087
1088 */
1089 /* UNDER CONSTRUCTION */
1090 return(coeff);
1091 }
1092#endif
1093
1094 case PolynomialDistortion:
1095 {
1096 /* Polynomial Distortion
1097
1098 First two coefficients are used to hole global polynomial information
1099 c0 = Order of the polynomial being created
1100 c1 = number_of_terms in one polynomial equation
1101
1102 Rest of the coefficients map to the equations....
1103 v = c0 + c1*x + c2*y + c3*x*y + c4*x^2 + c5*y^2 + c6*x^3 + ...
1104 for each 'value' (number_values of them) given.
1105 As such total coefficients = 2 + number_terms * number_values
1106
1107 Input Arguments are sets of control points...
1108 For Distort Images order [u,v, x,y] ...
1109 For Sparse Gradients order [x,y, r,g,b] ...
1110
1111 Polynomial Distortion Notes...
1112 + UNDER DEVELOPMENT -- Do not expect this to remain as is.
1113 + Currently polynomial is a reversed mapped distortion.
1114 + Order 1.5 is fudged to map into a bilinear distortion.
1115 though it is not the same order as that distortion.
1116 */
1117 double
1118 **matrix,
1119 **vectors,
1120 *terms;
1121
1122 size_t
1123 nterms; /* number of polynomial terms per number_values */
1124
1125 ssize_t
1126 j;
1127
1128 MagickBooleanType
1129 status;
1130
1131 /* first two coefficients hold polynomial order information */
1132 coeff[0] = arguments[0];
1133 coeff[1] = (double) poly_number_terms(arguments[0]);
1134 nterms = (size_t) coeff[1];
1135
1136 /* create matrix, a fake vectors matrix, and least sqs terms */
1137 matrix=AcquireMagickMatrix(nterms,nterms);
1138 vectors=(double **) AcquireQuantumMemory(number_values,
1139 sizeof(*vectors));
1140 terms=(double *) AcquireQuantumMemory(nterms,sizeof(*terms));
1141 if ((matrix == (double **) NULL) || (vectors == (double **) NULL) ||
1142 (terms == (double *) NULL))
1143 {
1144 matrix = RelinquishMagickMatrix(matrix, nterms);
1145 vectors = (double **) RelinquishMagickMemory(vectors);
1146 terms = (double *) RelinquishMagickMemory(terms);
1147 coeff = (double *) RelinquishMagickMemory(coeff);
1148 (void) ThrowMagickException(exception,GetMagickModule(),
1149 ResourceLimitError,"MemoryAllocationFailed",
1150 "%s", "DistortCoefficients");
1151 return((double *) NULL);
1152 }
1153 /* fake a number_values x3 vectors matrix from coefficients array */
1154 for (i=0; i < number_values; i++)
1155 vectors[i] = &(coeff[2+i*nterms]);
1156 /* Add given control point pairs for least squares solving */
1157 for (i=1; i < number_arguments; i+=cp_size) { /* NB: start = 1 not 0 */
1158 for (j=0; j < (ssize_t) nterms; j++)
1159 terms[j] = poly_basis_fn(j,arguments[i+cp_x],arguments[i+cp_y]);
1160 LeastSquaresAddTerms(matrix,vectors,terms,
1161 &(arguments[i+cp_values]),nterms,number_values);
1162 }
1163 terms = (double *) RelinquishMagickMemory(terms);
1164 /* Solve for LeastSquares Coefficients */
1165 status=GaussJordanElimination(matrix,vectors,nterms,number_values);
1166 matrix = RelinquishMagickMatrix(matrix, nterms);
1167 vectors = (double **) RelinquishMagickMemory(vectors);
1168 if ( status == MagickFalse ) {
1169 coeff = (double *) RelinquishMagickMemory(coeff);
1170 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1171 "InvalidArgument","%s : 'Unsolvable Matrix'",
1172 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1173 return((double *) NULL);
1174 }
1175 return(coeff);
1176 }
1177 case ArcDistortion:
1178 {
1179 /* Arc Distortion
1180 Args: arc_width rotate top_edge_radius bottom_edge_radius
1181 All but first argument are optional
1182 arc_width The angle over which to arc the image side-to-side
1183 rotate Angle to rotate image from vertical center
1184 top_radius Set top edge of source image at this radius
1185 bottom_radius Set bottom edge to this radius (radial scaling)
1186
1187 By default, if the radii arguments are nor provided the image radius
1188 is calculated so the horizontal center-line is fits the given arc
1189 without scaling.
1190
1191 The output image size is ALWAYS adjusted to contain the whole image,
1192 and an offset is given to position image relative to the 0,0 point of
1193 the origin, allowing users to use relative positioning onto larger
1194 background (via -flatten).
1195
1196 The arguments are converted to these coefficients
1197 c0: angle for center of source image
1198 c1: angle scale for mapping to source image
1199 c2: radius for top of source image
1200 c3: radius scale for mapping source image
1201 c4: centerline of arc within source image
1202
1203 Note the coefficients use a center angle, so asymptotic join is
1204 furthest from both sides of the source image. This also means that
1205 for arc angles greater than 360 the sides of the image will be
1206 trimmed equally.
1207
1208 Arc Distortion Notes...
1209 + Does not use a set of CPs
1210 + Will only work with Image Distortion
1211 + Can not be used for generating a sparse gradient (interpolation)
1212 */
1213 if ( number_arguments >= 1 && arguments[0] < MagickEpsilon ) {
1214 coeff = (double *) RelinquishMagickMemory(coeff);
1215 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1216 "InvalidArgument","%s : 'Arc Angle Too Small'",
1217 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1218 return((double *) NULL);
1219 }
1220 if ( number_arguments >= 3 && arguments[2] < MagickEpsilon ) {
1221 coeff = (double *) RelinquishMagickMemory(coeff);
1222 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1223 "InvalidArgument","%s : 'Outer Radius Too Small'",
1224 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1225 return((double *) NULL);
1226 }
1227 coeff[0] = -MagickPI2; /* -90, place at top! */
1228 if ( number_arguments >= 1 )
1229 coeff[1] = DegreesToRadians(arguments[0]);
1230 else
1231 coeff[1] = MagickPI2; /* zero arguments - center is at top */
1232 if ( number_arguments >= 2 )
1233 coeff[0] += DegreesToRadians(arguments[1]);
1234 coeff[0] /= Magick2PI; /* normalize radians */
1235 coeff[0] -= MagickRound(coeff[0]);
1236 coeff[0] *= Magick2PI; /* de-normalize back to radians */
1237 coeff[3] = (double)image->rows-1;
1238 coeff[2] = (double)image->columns/coeff[1] + coeff[3]/2.0;
1239 if ( number_arguments >= 3 ) {
1240 if ( number_arguments >= 4 )
1241 coeff[3] = arguments[2] - arguments[3];
1242 else
1243 coeff[3] *= arguments[2]/coeff[2];
1244 coeff[2] = arguments[2];
1245 }
1246 coeff[4] = ((double)image->columns-1.0)/2.0;
1247
1248 return(coeff);
1249 }
1250 case PolarDistortion:
1251 case DePolarDistortion:
1252 {
1253 /* (De)Polar Distortion (same set of arguments)
1254 Args: Rmax, Rmin, Xcenter,Ycenter, Afrom,Ato
1255 DePolar can also have the extra arguments of Width, Height
1256
1257 Coefficients 0 to 5 is the sanitized version first 6 input args
1258 Coefficient 6 is the angle to coord ratio and visa-versa
1259 Coefficient 7 is the radius to coord ratio and visa-versa
1260
1261 WARNING: It is possible for Radius max<min and/or Angle from>to
1262 */
1263 if ( number_arguments == 3
1264 || ( number_arguments > 6 && *method == PolarDistortion )
1265 || number_arguments > 8 ) {
1266 (void) ThrowMagickException(exception,GetMagickModule(),
1267 OptionError,"InvalidArgument", "%s : number of arguments",
1268 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1269 coeff=(double *) RelinquishMagickMemory(coeff);
1270 return((double *) NULL);
1271 }
1272 /* Rmax - if 0 calculate appropriate value */
1273 if ( number_arguments >= 1 )
1274 coeff[0] = arguments[0];
1275 else
1276 coeff[0] = 0.0;
1277 /* Rmin - usually 0 */
1278 coeff[1] = number_arguments >= 2 ? arguments[1] : 0.0;
1279 /* Center X,Y */
1280 if ( number_arguments >= 4 ) {
1281 coeff[2] = arguments[2];
1282 coeff[3] = arguments[3];
1283 }
1284 else { /* center of actual image */
1285 coeff[2] = (double)(image->columns)/2.0+image->page.x;
1286 coeff[3] = (double)(image->rows)/2.0+image->page.y;
1287 }
1288 /* Angle from,to - about polar center 0 is downward */
1289 coeff[4] = -MagickPI;
1290 if ( number_arguments >= 5 )
1291 coeff[4] = DegreesToRadians(arguments[4]);
1292 coeff[5] = coeff[4];
1293 if ( number_arguments >= 6 )
1294 coeff[5] = DegreesToRadians(arguments[5]);
1295 if ( fabs(coeff[4]-coeff[5]) < MagickEpsilon )
1296 coeff[5] += Magick2PI; /* same angle is a full circle */
1297 /* if radius 0 or negative, its a special value... */
1298 if ( coeff[0] < MagickEpsilon ) {
1299 /* Use closest edge if radius == 0 */
1300 if ( fabs(coeff[0]) < MagickEpsilon ) {
1301 coeff[0]=MagickMin(fabs(coeff[2]-image->page.x),
1302 fabs(coeff[3]-image->page.y));
1303 coeff[0]=MagickMin(coeff[0],
1304 fabs(coeff[2]-image->page.x-image->columns));
1305 coeff[0]=MagickMin(coeff[0],
1306 fabs(coeff[3]-image->page.y-image->rows));
1307 }
1308 /* furthest diagonal if radius == -1 */
1309 if ( fabs(-1.0-coeff[0]) < MagickEpsilon ) {
1310 double rx,ry;
1311 rx = coeff[2]-image->page.x;
1312 ry = coeff[3]-image->page.y;
1313 coeff[0] = rx*rx+ry*ry;
1314 ry = coeff[3]-image->page.y-image->rows;
1315 coeff[0] = MagickMax(coeff[0],rx*rx+ry*ry);
1316 rx = coeff[2]-image->page.x-image->columns;
1317 coeff[0] = MagickMax(coeff[0],rx*rx+ry*ry);
1318 ry = coeff[3]-image->page.y;
1319 coeff[0] = MagickMax(coeff[0],rx*rx+ry*ry);
1320 coeff[0] = sqrt(coeff[0]);
1321 }
1322 }
1323 /* IF Rmax <= 0 or Rmin < 0 OR Rmax < Rmin, THEN error */
1324 if ( coeff[0] < MagickEpsilon || coeff[1] < -MagickEpsilon
1325 || (coeff[0]-coeff[1]) < MagickEpsilon ) {
1326 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1327 "InvalidArgument", "%s : Invalid Radius",
1328 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1329 coeff=(double *) RelinquishMagickMemory(coeff);
1330 return((double *) NULL);
1331 }
1332 /* conversion ratios */
1333 if ( *method == PolarDistortion ) {
1334 coeff[6]=(double) image->columns/(coeff[5]-coeff[4]);
1335 coeff[7]=(double) image->rows/(coeff[0]-coeff[1]);
1336 }
1337 else { /* *method == DePolarDistortion */
1338 coeff[6]=(coeff[5]-coeff[4])/image->columns;
1339 coeff[7]=(coeff[0]-coeff[1])/image->rows;
1340 }
1341 return(coeff);
1342 }
1343 case Cylinder2PlaneDistortion:
1344 case Plane2CylinderDistortion:
1345 {
1346 /* 3D Cylinder to/from a Tangential Plane
1347
1348 Projection between a cylinder and flat plain from a point on the
1349 center line of the cylinder.
1350
1351 The two surfaces coincide in 3D space at the given centers of
1352 distortion (perpendicular to projection point) on both images.
1353
1354 Args: FOV_arc_width
1355 Coefficients: FOV(radians), Radius, center_x,y, dest_center_x,y
1356
1357 FOV (Field Of View) the angular field of view of the distortion,
1358 across the width of the image, in degrees. The centers are the
1359 points of least distortion in the input and resulting images.
1360
1361 These centers are however determined later.
1362
1363 Coeff 0 is the FOV angle of view of image width in radians
1364 Coeff 1 is calculated radius of cylinder.
1365 Coeff 2,3 center of distortion of input image
1366 Coefficients 4,5 Center of Distortion of dest (determined later)
1367 */
1368 if ( arguments[0] < MagickEpsilon || arguments[0] > 160.0 ) {
1369 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1370 "InvalidArgument", "%s : Invalid FOV Angle",
1371 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1372 coeff=(double *) RelinquishMagickMemory(coeff);
1373 return((double *) NULL);
1374 }
1375 coeff[0] = DegreesToRadians(arguments[0]);
1376 if ( *method == Cylinder2PlaneDistortion )
1377 /* image is curved around cylinder, so FOV angle (in radians)
1378 * scales directly to image X coordinate, according to its radius.
1379 */
1380 coeff[1] = (double) image->columns/coeff[0];
1381 else
1382 /* radius is distance away from an image with this angular FOV */
1383 coeff[1] = (double) image->columns / ( 2 * tan(coeff[0]/2) );
1384
1385 coeff[2] = (double)(image->columns)/2.0+image->page.x;
1386 coeff[3] = (double)(image->rows)/2.0+image->page.y;
1387 coeff[4] = coeff[2];
1388 coeff[5] = coeff[3]; /* assuming image size is the same */
1389 return(coeff);
1390 }
1391 case BarrelDistortion:
1392 case BarrelInverseDistortion:
1393 {
1394 /* Barrel Distortion
1395 Rs=(A*Rd^3 + B*Rd^2 + C*Rd + D)*Rd
1396 BarrelInv Distortion
1397 Rs=Rd/(A*Rd^3 + B*Rd^2 + C*Rd + D)
1398
1399 Where Rd is the normalized radius from corner to middle of image
1400 Input Arguments are one of the following forms (number of arguments)...
1401 3: A,B,C
1402 4: A,B,C,D
1403 5: A,B,C X,Y
1404 6: A,B,C,D X,Y
1405 8: Ax,Bx,Cx,Dx Ay,By,Cy,Dy
1406 10: Ax,Bx,Cx,Dx Ay,By,Cy,Dy X,Y
1407
1408 Returns 10 coefficient values, which are de-normalized (pixel scale)
1409 Ax, Bx, Cx, Dx, Ay, By, Cy, Dy, Xc, Yc
1410 */
1411 /* Radius de-normalization scaling factor */
1412 double
1413 rscale = 2.0/MagickMin((double) image->columns,(double) image->rows);
1414
1415 /* sanity check number of args must = 3,4,5,6,8,10 or error */
1416 if ( (number_arguments < 3) || (number_arguments == 7) ||
1417 (number_arguments == 9) || (number_arguments > 10) )
1418 {
1419 coeff=(double *) RelinquishMagickMemory(coeff);
1420 (void) ThrowMagickException(exception,GetMagickModule(),
1421 OptionError,"InvalidArgument", "%s : number of arguments",
1422 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1423 return((double *) NULL);
1424 }
1425 /* A,B,C,D coefficients */
1426 coeff[0] = arguments[0];
1427 coeff[1] = arguments[1];
1428 coeff[2] = arguments[2];
1429 if ((number_arguments == 3) || (number_arguments == 5) )
1430 coeff[3] = 1.0 - coeff[0] - coeff[1] - coeff[2];
1431 else
1432 coeff[3] = arguments[3];
1433 /* de-normalize the coefficients */
1434 coeff[0] *= pow(rscale,3.0);
1435 coeff[1] *= rscale*rscale;
1436 coeff[2] *= rscale;
1437 /* Y coefficients: as given OR same as X coefficients */
1438 if ( number_arguments >= 8 ) {
1439 coeff[4] = arguments[4] * pow(rscale,3.0);
1440 coeff[5] = arguments[5] * rscale*rscale;
1441 coeff[6] = arguments[6] * rscale;
1442 coeff[7] = arguments[7];
1443 }
1444 else {
1445 coeff[4] = coeff[0];
1446 coeff[5] = coeff[1];
1447 coeff[6] = coeff[2];
1448 coeff[7] = coeff[3];
1449 }
1450 /* X,Y Center of Distortion (image coordinates) */
1451 if ( number_arguments == 5 ) {
1452 coeff[8] = arguments[3];
1453 coeff[9] = arguments[4];
1454 }
1455 else if ( number_arguments == 6 ) {
1456 coeff[8] = arguments[4];
1457 coeff[9] = arguments[5];
1458 }
1459 else if ( number_arguments == 10 ) {
1460 coeff[8] = arguments[8];
1461 coeff[9] = arguments[9];
1462 }
1463 else {
1464 /* center of the image provided (image coordinates) */
1465 coeff[8] = (double)image->columns/2.0 + image->page.x;
1466 coeff[9] = (double)image->rows/2.0 + image->page.y;
1467 }
1468 return(coeff);
1469 }
1470 case ShepardsDistortion:
1471 {
1472 /* Shepards Distortion input arguments are the coefficients!
1473 Just check the number of arguments is valid!
1474 Args: u1,v1, x1,y1, ...
1475 OR : u1,v1, r1,g1,c1, ...
1476 */
1477 if ( number_arguments%cp_size != 0 ||
1478 number_arguments < cp_size ) {
1479 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1480 "InvalidArgument", "%s : 'requires CP's (4 numbers each)'",
1481 CommandOptionToMnemonic(MagickDistortOptions, *method));
1482 coeff=(double *) RelinquishMagickMemory(coeff);
1483 return((double *) NULL);
1484 }
1485 /* User defined weighting power for Shepard's Method */
1486 { const char *artifact=GetImageArtifact(image,"shepards:power");
1487 if ( artifact != (const char *) NULL ) {
1488 coeff[0]=StringToDouble(artifact,(char **) NULL) / 2.0;
1489 if ( coeff[0] < MagickEpsilon ) {
1490 (void) ThrowMagickException(exception,GetMagickModule(),
1491 OptionError,"InvalidArgument","%s", "-define shepards:power" );
1492 coeff=(double *) RelinquishMagickMemory(coeff);
1493 return((double *) NULL);
1494 }
1495 }
1496 else
1497 coeff[0]=1.0; /* Default power of 2 (Inverse Squared) */
1498 }
1499 return(coeff);
1500 }
1501 default:
1502 break;
1503 }
1504 /* you should never reach this point */
1505 perror("no method handler"); /* just fail assertion */
1506 return((double *) NULL);
1507}
1508␌
1509/*
1510%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1511% %
1512% %
1513% %
1514+ D i s t o r t R e s i z e I m a g e %
1515% %
1516% %
1517% %
1518%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1519%
1520% DistortResizeImage() resize image using the equivalent but slower image
1521% distortion operator. The filter is applied using a EWA cylindrical
1522% resampling. But like resize the final image size is limited to whole pixels
1523% with no effects by virtual-pixels on the result.
1524%
1525% Note that images containing a transparency channel will be twice as slow to
1526% resize as images one without transparency.
1527%
1528% The format of the DistortResizeImage method is:
1529%
1530% Image *DistortResizeImage(const Image *image,const size_t columns,
1531% const size_t rows,ExceptionInfo *exception)
1532%
1533% A description of each parameter follows:
1534%
1535% o image: the image.
1536%
1537% o columns: the number of columns in the resized image.
1538%
1539% o rows: the number of rows in the resized image.
1540%
1541% o exception: return any errors or warnings in this structure.
1542%
1543*/
1544MagickExport Image *DistortResizeImage(const Image *image,const size_t columns,
1545 const size_t rows,ExceptionInfo *exception)
1546{
1547#define DistortResizeImageTag "Distort/Image"
1548
1549 Image
1550 *resize_image,
1551 *tmp_image;
1552
1553 RectangleInfo
1554 crop_area;
1555
1556 double
1557 distort_args[12];
1558
1559 VirtualPixelMethod
1560 vp_save;
1561
1562 /*
1563 Distort resize image.
1564 */
1565 assert(image != (const Image *) NULL);
1566 assert(image->signature == MagickCoreSignature);
1567 assert(exception != (ExceptionInfo *) NULL);
1568 assert(exception->signature == MagickCoreSignature);
1569 if (IsEventLogging() != MagickFalse)
1570 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1571 if ((columns == 0) || (rows == 0))
1572 return((Image *) NULL);
1573 /* Do not short-circuit this resize if final image size is unchanged */
1574
1575 (void) memset(distort_args,0,sizeof(distort_args));
1576 distort_args[4]=(double) image->columns;
1577 distort_args[6]=(double) columns;
1578 distort_args[9]=(double) image->rows;
1579 distort_args[11]=(double) rows;
1580
1581 vp_save=GetImageVirtualPixelMethod(image);
1582
1583 tmp_image=CloneImage(image,0,0,MagickTrue,exception);
1584 if (tmp_image == (Image *) NULL)
1585 return((Image *) NULL);
1586 (void) SetImageVirtualPixelMethod(tmp_image,TransparentVirtualPixelMethod,
1587 exception);
1588
1589 if ((image->alpha_trait & BlendPixelTrait) == 0)
1590 {
1591 /*
1592 Image has no alpha channel, so we are free to use it.
1593 */
1594 (void) SetImageAlphaChannel(tmp_image,SetAlphaChannel,exception);
1595 resize_image=DistortImage(tmp_image,AffineDistortion,12,distort_args,
1596 MagickTrue,exception),
1597 tmp_image=DestroyImage(tmp_image);
1598 if (resize_image == (Image *) NULL)
1599 return((Image *) NULL);
1600 (void) SetImageAlphaChannel(resize_image,OffAlphaChannel,exception);
1601 }
1602 else
1603 {
1604 /*
1605 Image has transparency so handle colors and alpha separately.
1606 Basically we need to separate Virtual-Pixel alpha in the resized
1607 image, so only the actual original images alpha channel is used.
1608
1609 distort alpha channel separately
1610 */
1611 Image
1612 *resize_alpha;
1613
1614 (void) SetImageAlphaChannel(tmp_image,ExtractAlphaChannel,exception);
1615 (void) SetImageAlphaChannel(tmp_image,OpaqueAlphaChannel,exception);
1616 resize_alpha=DistortImage(tmp_image,AffineDistortion,12,distort_args,
1617 MagickTrue,exception),
1618 tmp_image=DestroyImage(tmp_image);
1619 if (resize_alpha == (Image *) NULL)
1620 return((Image *) NULL);
1621
1622 /* distort the actual image containing alpha + VP alpha */
1623 tmp_image=CloneImage(image,0,0,MagickTrue,exception);
1624 if (tmp_image == (Image *) NULL)
1625 return((Image *) NULL);
1626 (void) SetImageVirtualPixelMethod(tmp_image,
1627 TransparentVirtualPixelMethod,exception);
1628 resize_image=DistortImage(tmp_image,AffineDistortion,12,distort_args,
1629 MagickTrue,exception),
1630 tmp_image=DestroyImage(tmp_image);
1631 if (resize_image == (Image *) NULL)
1632 {
1633 resize_alpha=DestroyImage(resize_alpha);
1634 return((Image *) NULL);
1635 }
1636 /* replace resize images alpha with the separately distorted alpha */
1637 (void) SetImageAlphaChannel(resize_image,OffAlphaChannel,exception);
1638 (void) SetImageAlphaChannel(resize_alpha,OffAlphaChannel,exception);
1639 (void) CompositeImage(resize_image,resize_alpha,CopyAlphaCompositeOp,
1640 MagickTrue,0,0,exception);
1641 resize_alpha=DestroyImage(resize_alpha);
1642 resize_image->alpha_trait=image->alpha_trait;
1643 resize_image->compose=image->compose;
1644 }
1645 (void) SetImageVirtualPixelMethod(resize_image,vp_save,exception);
1646
1647 /*
1648 Clean up the results of the Distortion
1649 */
1650 crop_area.width=columns;
1651 crop_area.height=rows;
1652 crop_area.x=0;
1653 crop_area.y=0;
1654
1655 tmp_image=resize_image;
1656 resize_image=CropImage(tmp_image,&crop_area,exception);
1657 tmp_image=DestroyImage(tmp_image);
1658 if (resize_image != (Image *) NULL)
1659 {
1660 resize_image->page.width=0;
1661 resize_image->page.height=0;
1662 }
1663 return(resize_image);
1664}
1665␌
1666/*
1667%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1668% %
1669% %
1670% %
1671% D i s t o r t I m a g e %
1672% %
1673% %
1674% %
1675%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1676%
1677% DistortImage() distorts an image using various distortion methods, by
1678% mapping color lookups of the source image to a new destination image
1679% usually of the same size as the source image, unless 'bestfit' is set to
1680% true.
1681%
1682% If 'bestfit' is enabled, and distortion allows it, the destination image is
1683% adjusted to ensure the whole source 'image' will just fit within the final
1684% destination image, which will be sized and offset accordingly. Also in
1685% many cases the virtual offset of the source image will be taken into
1686% account in the mapping.
1687%
1688% If the '-verbose' control option has been set print to standard error the
1689% equivalent '-fx' formula with coefficients for the function, if practical.
1690%
1691% The format of the DistortImage() method is:
1692%
1693% Image *DistortImage(const Image *image,const DistortMethod method,
1694% const size_t number_arguments,const double *arguments,
1695% MagickBooleanType bestfit, ExceptionInfo *exception)
1696%
1697% A description of each parameter follows:
1698%
1699% o image: the image to be distorted.
1700%
1701% o method: the method of image distortion.
1702%
1703% ArcDistortion always ignores source image offset, and always
1704% 'bestfit' the destination image with the top left corner offset
1705% relative to the polar mapping center.
1706%
1707% Affine, Perspective, and Bilinear, do least squares fitting of the
1708% distortion when more than the minimum number of control point pairs
1709% are provided.
1710%
1711% Perspective, and Bilinear, fall back to a Affine distortion when less
1712% than 4 control point pairs are provided. While Affine distortions
1713% let you use any number of control point pairs, that is Zero pairs is
1714% a No-Op (viewport only) distortion, one pair is a translation and
1715% two pairs of control points do a scale-rotate-translate, without any
1716% shearing.
1717%
1718% o number_arguments: the number of arguments given.
1719%
1720% o arguments: an array of floating point arguments for this method.
1721%
1722% o bestfit: Attempt to 'bestfit' the size of the resulting image.
1723% This also forces the resulting image to be a 'layered' virtual
1724% canvas image. Can be overridden using 'distort:viewport' setting.
1725%
1726% o exception: return any errors or warnings in this structure
1727%
1728% Extra Controls from Image meta-data (artifacts)...
1729%
1730% o "verbose"
1731% Output to stderr alternatives, internal coefficients, and FX
1732% equivalents for the distortion operation (if feasible).
1733% This forms an extra check of the distortion method, and allows users
1734% access to the internal constants IM calculates for the distortion.
1735%
1736% o "distort:viewport"
1737% Directly set the output image canvas area and offset to use for the
1738% resulting image, rather than use the original images canvas, or a
1739% calculated 'bestfit' canvas.
1740%
1741% o "distort:scale"
1742% Scale the size of the output canvas by this amount to provide a
1743% method of Zooming, and for super-sampling the results.
1744%
1745% Other settings that can effect results include
1746%
1747% o 'interpolate' For source image lookups (scale enlargements)
1748%
1749% o 'filter' Set filter to use for area-resampling (scale shrinking).
1750% Set to 'point' to turn off and use 'interpolate' lookup
1751% instead
1752%
1753*/
1754MagickExport Image *DistortImage(const Image *image, DistortMethod method,
1755 const size_t number_arguments,const double *arguments,
1756 MagickBooleanType bestfit,ExceptionInfo *exception)
1757{
1758#define DistortImageTag "Distort/Image"
1759
1760 double
1761 *coeff,
1762 output_scaling;
1763
1764 Image
1765 *distort_image;
1766
1767 RectangleInfo
1768 geometry; /* geometry of the distorted space viewport */
1769
1770 MagickBooleanType
1771 viewport_given;
1772
1773 PixelInfo
1774 invalid; /* the color to assign when distort result is invalid */
1775
1776 assert(image != (Image *) NULL);
1777 assert(image->signature == MagickCoreSignature);
1778 assert(exception != (ExceptionInfo *) NULL);
1779 assert(exception->signature == MagickCoreSignature);
1780 if (IsEventLogging() != MagickFalse)
1781 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1782 /*
1783 Handle Special Compound Distortions
1784 */
1785 if ( method == ResizeDistortion )
1786 {
1787 if ( number_arguments != 2 )
1788 {
1789 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1790 "InvalidArgument","%s : '%s'","Resize",
1791 "Invalid number of args: 2 only");
1792 return((Image *) NULL);
1793 }
1794 distort_image=DistortResizeImage(image,(size_t)arguments[0],
1795 (size_t)arguments[1], exception);
1796 return(distort_image);
1797 }
1798
1799 /*
1800 Convert input arguments (usually as control points for reverse mapping)
1801 into mapping coefficients to apply the distortion.
1802
1803 Note that some distortions are mapped to other distortions,
1804 and as such do not require specific code after this point.
1805 */
1806 coeff = GenerateCoefficients(image, &method, number_arguments,
1807 arguments, 0, exception);
1808 if ( coeff == (double *) NULL )
1809 return((Image *) NULL);
1810
1811 /*
1812 Determine the size and offset for a 'bestfit' destination.
1813 Usually the four corners of the source image is enough.
1814 */
1815
1816 /* default output image bounds, when no 'bestfit' is requested */
1817 geometry.width=image->columns;
1818 geometry.height=image->rows;
1819 geometry.x=0;
1820 geometry.y=0;
1821
1822 if ( method == ArcDistortion ) {
1823 bestfit = MagickTrue; /* always calculate a 'best fit' viewport */
1824 }
1825
1826 /* Work out the 'best fit', (required for ArcDistortion) */
1827 if ( bestfit ) {
1828 PointInfo
1829 s,d,min,max; /* source, dest coords --mapping--> min, max coords */
1830
1831 MagickBooleanType
1832 fix_bounds = MagickTrue; /* enlarge bounds for VP handling */
1833
1834 s.x=s.y=min.x=max.x=min.y=max.y=0.0; /* keep compiler happy */
1835
1836/* defines to figure out the bounds of the distorted image */
1837#define InitalBounds(p) \
1838{ \
1839 /* printf("%lg,%lg -> %lg,%lg\n", s.x,s.y, d.x,d.y); */ \
1840 min.x = max.x = p.x; \
1841 min.y = max.y = p.y; \
1842}
1843#define ExpandBounds(p) \
1844{ \
1845 /* printf("%lg,%lg -> %lg,%lg\n", s.x,s.y, d.x,d.y); */ \
1846 min.x = MagickMin(min.x,p.x); \
1847 max.x = MagickMax(max.x,p.x); \
1848 min.y = MagickMin(min.y,p.y); \
1849 max.y = MagickMax(max.y,p.y); \
1850}
1851
1852 switch (method)
1853 {
1854 case AffineDistortion:
1855 case RigidAffineDistortion:
1856 { double inverse[6];
1857 InvertAffineCoefficients(coeff, inverse);
1858 s.x = (double) image->page.x;
1859 s.y = (double) image->page.y;
1860 d.x = inverse[0]*s.x+inverse[1]*s.y+inverse[2];
1861 d.y = inverse[3]*s.x+inverse[4]*s.y+inverse[5];
1862 InitalBounds(d);
1863 s.x = (double) image->page.x+image->columns;
1864 s.y = (double) image->page.y;
1865 d.x = inverse[0]*s.x+inverse[1]*s.y+inverse[2];
1866 d.y = inverse[3]*s.x+inverse[4]*s.y+inverse[5];
1867 ExpandBounds(d);
1868 s.x = (double) image->page.x;
1869 s.y = (double) image->page.y+image->rows;
1870 d.x = inverse[0]*s.x+inverse[1]*s.y+inverse[2];
1871 d.y = inverse[3]*s.x+inverse[4]*s.y+inverse[5];
1872 ExpandBounds(d);
1873 s.x = (double) image->page.x+image->columns;
1874 s.y = (double) image->page.y+image->rows;
1875 d.x = inverse[0]*s.x+inverse[1]*s.y+inverse[2];
1876 d.y = inverse[3]*s.x+inverse[4]*s.y+inverse[5];
1877 ExpandBounds(d);
1878 break;
1879 }
1880 case PerspectiveDistortion:
1881 { double inverse[8], scale;
1882 InvertPerspectiveCoefficients(coeff, inverse);
1883 s.x = (double) image->page.x;
1884 s.y = (double) image->page.y;
1885 scale=inverse[6]*s.x+inverse[7]*s.y+1.0;
1886 scale=MagickSafeReciprocal(scale);
1887 d.x = scale*(inverse[0]*s.x+inverse[1]*s.y+inverse[2]);
1888 d.y = scale*(inverse[3]*s.x+inverse[4]*s.y+inverse[5]);
1889 InitalBounds(d);
1890 s.x = (double) image->page.x+image->columns;
1891 s.y = (double) image->page.y;
1892 scale=inverse[6]*s.x+inverse[7]*s.y+1.0;
1893 scale=MagickSafeReciprocal(scale);
1894 d.x = scale*(inverse[0]*s.x+inverse[1]*s.y+inverse[2]);
1895 d.y = scale*(inverse[3]*s.x+inverse[4]*s.y+inverse[5]);
1896 ExpandBounds(d);
1897 s.x = (double) image->page.x;
1898 s.y = (double) image->page.y+image->rows;
1899 scale=inverse[6]*s.x+inverse[7]*s.y+1.0;
1900 scale=MagickSafeReciprocal(scale);
1901 d.x = scale*(inverse[0]*s.x+inverse[1]*s.y+inverse[2]);
1902 d.y = scale*(inverse[3]*s.x+inverse[4]*s.y+inverse[5]);
1903 ExpandBounds(d);
1904 s.x = (double) image->page.x+image->columns;
1905 s.y = (double) image->page.y+image->rows;
1906 scale=inverse[6]*s.x+inverse[7]*s.y+1.0;
1907 scale=MagickSafeReciprocal(scale);
1908 d.x = scale*(inverse[0]*s.x+inverse[1]*s.y+inverse[2]);
1909 d.y = scale*(inverse[3]*s.x+inverse[4]*s.y+inverse[5]);
1910 ExpandBounds(d);
1911 break;
1912 }
1913 case ArcDistortion:
1914 { double a, ca, sa;
1915 /* Forward Map Corners */
1916 a = coeff[0]-coeff[1]/2; ca = cos(a); sa = sin(a);
1917 d.x = coeff[2]*ca;
1918 d.y = coeff[2]*sa;
1919 InitalBounds(d);
1920 d.x = (coeff[2]-coeff[3])*ca;
1921 d.y = (coeff[2]-coeff[3])*sa;
1922 ExpandBounds(d);
1923 a = coeff[0]+coeff[1]/2; ca = cos(a); sa = sin(a);
1924 d.x = coeff[2]*ca;
1925 d.y = coeff[2]*sa;
1926 ExpandBounds(d);
1927 d.x = (coeff[2]-coeff[3])*ca;
1928 d.y = (coeff[2]-coeff[3])*sa;
1929 ExpandBounds(d);
1930 /* Orthogonal points along top of arc */
1931 for( a=(double) (ceil((double) ((coeff[0]-coeff[1]/2.0)/MagickPI2))*MagickPI2);
1932 a<(coeff[0]+coeff[1]/2.0); a+=MagickPI2 ) {
1933 ca = cos(a); sa = sin(a);
1934 d.x = coeff[2]*ca;
1935 d.y = coeff[2]*sa;
1936 ExpandBounds(d);
1937 }
1938 /*
1939 Convert the angle_to_width and radius_to_height
1940 to appropriate scaling factors, to allow faster processing
1941 in the mapping function.
1942 */
1943 coeff[1] = (double) (Magick2PI*image->columns/coeff[1]);
1944 coeff[3] = (double)image->rows/coeff[3];
1945 break;
1946 }
1947 case PolarDistortion:
1948 {
1949 if (number_arguments < 2)
1950 coeff[2] = coeff[3] = 0.0;
1951 min.x = coeff[2]-coeff[0];
1952 max.x = coeff[2]+coeff[0];
1953 min.y = coeff[3]-coeff[0];
1954 max.y = coeff[3]+coeff[0];
1955 /* should be about 1.0 if Rmin = 0 */
1956 coeff[7]=(double) geometry.height/(coeff[0]-coeff[1]);
1957 break;
1958 }
1959 case DePolarDistortion:
1960 {
1961 /* direct calculation as it needs to tile correctly
1962 * for reversibility in a DePolar-Polar cycle */
1963 fix_bounds = MagickFalse;
1964 geometry.x = geometry.y = 0;
1965 geometry.height = (size_t) ceil(coeff[0]-coeff[1]);
1966 geometry.width = (size_t) ceil((coeff[0]-coeff[1])*
1967 (coeff[5]-coeff[4])*0.5);
1968 /* correct scaling factors relative to new size */
1969 coeff[6]=(coeff[5]-coeff[4]) * MagickSafeReciprocal(
1970 (double) geometry.width); /* changed width */
1971 coeff[7]=(coeff[0]-coeff[1]) * MagickSafeReciprocal(
1972 (double) geometry.height); /* should be about 1.0 */
1973 break;
1974 }
1975 case Cylinder2PlaneDistortion:
1976 {
1977 /* direct calculation so center of distortion is either a pixel
1978 * center, or pixel edge. This allows for reversibility of the
1979 * distortion */
1980 geometry.x = geometry.y = 0;
1981 geometry.width = (size_t) ceil( 2.0*coeff[1]*tan(coeff[0]/2.0) );
1982 geometry.height = (size_t) ceil( 2.0*coeff[3]/cos(coeff[0]/2.0) );
1983 /* correct center of distortion relative to new size */
1984 coeff[4] = (double) geometry.width/2.0;
1985 coeff[5] = (double) geometry.height/2.0;
1986 fix_bounds = MagickFalse;
1987 break;
1988 }
1989 case Plane2CylinderDistortion:
1990 {
1991 /* direct calculation center is either pixel center, or pixel edge
1992 * so as to allow reversibility of the image distortion */
1993 geometry.x = geometry.y = 0;
1994 geometry.width = (size_t) ceil(coeff[0]*coeff[1]); /* FOV * radius */
1995 geometry.height = (size_t) (2*coeff[3]); /* input image height */
1996 /* correct center of distortion relative to new size */
1997 coeff[4] = (double) geometry.width/2.0;
1998 coeff[5] = (double) geometry.height/2.0;
1999 fix_bounds = MagickFalse;
2000 break;
2001 }
2002 case ShepardsDistortion:
2003 case BilinearForwardDistortion:
2004 case BilinearReverseDistortion:
2005#if 0
2006 case QuadrilateralDistortion:
2007#endif
2008 case PolynomialDistortion:
2009 case BarrelDistortion:
2010 case BarrelInverseDistortion:
2011 default:
2012 /* no calculated bestfit available for these distortions */
2013 bestfit = MagickFalse;
2014 fix_bounds = MagickFalse;
2015 break;
2016 }
2017
2018 /* Set the output image geometry to calculated 'bestfit'.
2019 Yes this tends to 'over do' the file image size, ON PURPOSE!
2020 Do not do this for DePolar which needs to be exact for virtual tiling.
2021 */
2022 if ( fix_bounds ) {
2023 geometry.x = (ssize_t) floor(min.x-0.5);
2024 geometry.y = (ssize_t) floor(min.y-0.5);
2025 geometry.width=(size_t) ceil(max.x-geometry.x+0.5);
2026 geometry.height=(size_t) ceil(max.y-geometry.y+0.5);
2027 }
2028
2029 } /* end bestfit destination image calculations */
2030
2031 /* The user provided a 'viewport' expert option which may
2032 overrides some parts of the current output image geometry.
2033 This also overrides its default 'bestfit' setting.
2034 */
2035 { const char *artifact=GetImageArtifact(image,"distort:viewport");
2036 viewport_given = MagickFalse;
2037 if ( artifact != (const char *) NULL ) {
2038 MagickStatusType flags=ParseAbsoluteGeometry(artifact,&geometry);
2039 if (flags==NoValue)
2040 (void) ThrowMagickException(exception,GetMagickModule(),
2041 OptionWarning,"InvalidSetting","'%s' '%s'",
2042 "distort:viewport",artifact);
2043 else
2044 viewport_given = MagickTrue;
2045 }
2046 }
2047
2048 /* Verbose output */
2049 if (IsStringTrue(GetImageArtifact(image,"verbose")) != MagickFalse) {
2050 ssize_t
2051 i;
2052 char image_gen[MagickPathExtent];
2053 const char *lookup;
2054
2055 /* Set destination image size and virtual offset */
2056 if ( bestfit || viewport_given ) {
2057 (void) FormatLocaleString(image_gen,MagickPathExtent,
2058 " -size %.20gx%.20g -page %+.20g%+.20g xc: +insert \\\n",
2059 (double) geometry.width,(double) geometry.height,(double) geometry.x,
2060 (double) geometry.y);
2061 lookup="v.p{xx-v.page.x-0.5,yy-v.page.y-0.5}";
2062 }
2063 else {
2064 image_gen[0] = '\0'; /* no destination to generate */
2065 lookup = "p{xx-page.x-0.5,yy-page.y-0.5}"; /* simplify lookup */
2066 }
2067
2068 switch (method)
2069 {
2070 case AffineDistortion:
2071 case RigidAffineDistortion:
2072 {
2073 double
2074 *inverse;
2075
2076 inverse=(double *) AcquireQuantumMemory(6,sizeof(*inverse));
2077 if (inverse == (double *) NULL)
2078 {
2079 coeff=(double *) RelinquishMagickMemory(coeff);
2080 (void) ThrowMagickException(exception,GetMagickModule(),
2081 ResourceLimitError,"MemoryAllocationFailed","%s","DistortImages");
2082 return((Image *) NULL);
2083 }
2084 InvertAffineCoefficients(coeff, inverse);
2085 CoefficientsToAffineArgs(inverse);
2086 (void) FormatLocaleFile(stderr, "Affine projection:\n");
2087 (void) FormatLocaleFile(stderr,
2088 " -distort AffineProjection \\\n '");
2089 for (i=0; i < 5; i++)
2090 (void) FormatLocaleFile(stderr, "%.*g,",GetMagickPrecision(),
2091 inverse[i]);
2092 (void) FormatLocaleFile(stderr, "%.*g'\n",GetMagickPrecision(),
2093 inverse[5]);
2094 (void) FormatLocaleFile(stderr,
2095 "Equivalent scale, rotation(deg), translation:\n");
2096 (void) FormatLocaleFile(stderr," %.*g,%.*g,%.*g,%.*g\n",
2097 GetMagickPrecision(),sqrt(inverse[0]*inverse[0]+
2098 inverse[1]*inverse[1]),GetMagickPrecision(),
2099 RadiansToDegrees(atan2(inverse[1],inverse[0])),
2100 GetMagickPrecision(),inverse[4],GetMagickPrecision(),inverse[5]);
2101 inverse=(double *) RelinquishMagickMemory(inverse);
2102 (void) FormatLocaleFile(stderr,"Affine distort, FX equivalent:\n");
2103 (void) FormatLocaleFile(stderr, "%s", image_gen);
2104 (void) FormatLocaleFile(stderr,
2105 " -fx 'ii=i+page.x+0.5; jj=j+page.y+0.5;\n");
2106 (void) FormatLocaleFile(stderr," xx=%+.*g*ii %+.*g*jj %+.*g;\n",
2107 GetMagickPrecision(),coeff[0],GetMagickPrecision(),coeff[1],
2108 GetMagickPrecision(),coeff[2]);
2109 (void) FormatLocaleFile(stderr," yy=%+.*g*ii %+.*g*jj %+.*g;\n",
2110 GetMagickPrecision(),coeff[3],GetMagickPrecision(),coeff[4],
2111 GetMagickPrecision(),coeff[5]);
2112 (void) FormatLocaleFile(stderr," %s' \\\n",lookup);
2113 break;
2114 }
2115 case PerspectiveDistortion:
2116 {
2117 double
2118 *inverse;
2119
2120 inverse=(double *) AcquireQuantumMemory(8,sizeof(*inverse));
2121 if (inverse == (double *) NULL)
2122 {
2123 coeff=(double *) RelinquishMagickMemory(coeff);
2124 (void) ThrowMagickException(exception,GetMagickModule(),
2125 ResourceLimitError,"MemoryAllocationFailed","%s",
2126 "DistortCoefficients");
2127 return((Image *) NULL);
2128 }
2129 InvertPerspectiveCoefficients(coeff, inverse);
2130 (void) FormatLocaleFile(stderr,"Perspective Projection:\n");
2131 (void) FormatLocaleFile(stderr,
2132 " -distort PerspectiveProjection \\\n '");
2133 for (i=0; i < 4; i++)
2134 (void) FormatLocaleFile(stderr, "%.*g, ",GetMagickPrecision(),
2135 inverse[i]);
2136 (void) FormatLocaleFile(stderr, "\n ");
2137 for ( ; i < 7; i++)
2138 (void) FormatLocaleFile(stderr, "%.*g, ",GetMagickPrecision(),
2139 inverse[i]);
2140 (void) FormatLocaleFile(stderr, "%.*g'\n",GetMagickPrecision(),
2141 inverse[7]);
2142 inverse=(double *) RelinquishMagickMemory(inverse);
2143 (void) FormatLocaleFile(stderr,"Perspective Distort, FX Equivalent:\n");
2144 (void) FormatLocaleFile(stderr,"%.1024s",image_gen);
2145 (void) FormatLocaleFile(stderr,
2146 " -fx 'ii=i+page.x+0.5; jj=j+page.y+0.5;\n");
2147 (void) FormatLocaleFile(stderr," rr=%+.*g*ii %+.*g*jj + 1;\n",
2148 GetMagickPrecision(),coeff[6],GetMagickPrecision(),coeff[7]);
2149 (void) FormatLocaleFile(stderr,
2150 " xx=(%+.*g*ii %+.*g*jj %+.*g)/rr;\n",
2151 GetMagickPrecision(),coeff[0],GetMagickPrecision(),coeff[1],
2152 GetMagickPrecision(),coeff[2]);
2153 (void) FormatLocaleFile(stderr,
2154 " yy=(%+.*g*ii %+.*g*jj %+.*g)/rr;\n",
2155 GetMagickPrecision(),coeff[3],GetMagickPrecision(),coeff[4],
2156 GetMagickPrecision(),coeff[5]);
2157 (void) FormatLocaleFile(stderr," rr%s0 ? %s : blue' \\\n",
2158 coeff[8] < 0.0 ? "<" : ">", lookup);
2159 break;
2160 }
2161 case BilinearForwardDistortion:
2162 {
2163 (void) FormatLocaleFile(stderr,"BilinearForward Mapping Equations:\n");
2164 (void) FormatLocaleFile(stderr,"%s", image_gen);
2165 (void) FormatLocaleFile(stderr," i = %+lf*x %+lf*y %+lf*x*y %+lf;\n",
2166 coeff[0],coeff[1],coeff[2],coeff[3]);
2167 (void) FormatLocaleFile(stderr," j = %+lf*x %+lf*y %+lf*x*y %+lf;\n",
2168 coeff[4],coeff[5],coeff[6],coeff[7]);
2169#if 0
2170 /* for debugging */
2171 (void) FormatLocaleFile(stderr, " c8 = %+lf c9 = 2*a = %+lf;\n",
2172 coeff[8], coeff[9]);
2173#endif
2174 (void) FormatLocaleFile(stderr,
2175 "BilinearForward Distort, FX Equivalent:\n");
2176 (void) FormatLocaleFile(stderr,"%s", image_gen);
2177 (void) FormatLocaleFile(stderr,
2178 " -fx 'ii=i+page.x%+lf; jj=j+page.y%+lf;\n",0.5-coeff[3],0.5-
2179 coeff[7]);
2180 (void) FormatLocaleFile(stderr," bb=%lf*ii %+lf*jj %+lf;\n",
2181 coeff[6], -coeff[2], coeff[8]);
2182 /* Handle Special degenerate (non-quadratic) or trapezoidal case */
2183 if (coeff[9] != 0)
2184 {
2185 (void) FormatLocaleFile(stderr,
2186 " rt=bb*bb %+lf*(%lf*ii%+lf*jj);\n",-2*coeff[9],coeff[4],
2187 -coeff[0]);
2188 (void) FormatLocaleFile(stderr,
2189 " yy=( -bb + sqrt(rt) ) / %lf;\n",coeff[9]);
2190 }
2191 else
2192 (void) FormatLocaleFile(stderr," yy=(%lf*ii%+lf*jj)/bb;\n",
2193 -coeff[4],coeff[0]);
2194 (void) FormatLocaleFile(stderr,
2195 " xx=(ii %+lf*yy)/(%lf %+lf*yy);\n",-coeff[1],coeff[0],
2196 coeff[2]);
2197 if ( coeff[9] != 0 )
2198 (void) FormatLocaleFile(stderr," (rt < 0 ) ? red : %s'\n",
2199 lookup);
2200 else
2201 (void) FormatLocaleFile(stderr," %s' \\\n", lookup);
2202 break;
2203 }
2204 case BilinearReverseDistortion:
2205 {
2206#if 0
2207 (void) FormatLocaleFile(stderr, "Polynomial Projection Distort:\n");
2208 (void) FormatLocaleFile(stderr, " -distort PolynomialProjection \\\n");
2209 (void) FormatLocaleFile(stderr, " '1.5, %lf, %lf, %lf, %lf,\n",
2210 coeff[3], coeff[0], coeff[1], coeff[2]);
2211 (void) FormatLocaleFile(stderr, " %lf, %lf, %lf, %lf'\n",
2212 coeff[7], coeff[4], coeff[5], coeff[6]);
2213#endif
2214 (void) FormatLocaleFile(stderr,
2215 "BilinearReverse Distort, FX Equivalent:\n");
2216 (void) FormatLocaleFile(stderr,"%s", image_gen);
2217 (void) FormatLocaleFile(stderr,
2218 " -fx 'ii=i+page.x+0.5; jj=j+page.y+0.5;\n");
2219 (void) FormatLocaleFile(stderr,
2220 " xx=%+lf*ii %+lf*jj %+lf*ii*jj %+lf;\n",coeff[0],coeff[1],
2221 coeff[2], coeff[3]);
2222 (void) FormatLocaleFile(stderr,
2223 " yy=%+lf*ii %+lf*jj %+lf*ii*jj %+lf;\n",coeff[4],coeff[5],
2224 coeff[6], coeff[7]);
2225 (void) FormatLocaleFile(stderr," %s' \\\n", lookup);
2226 break;
2227 }
2228 case PolynomialDistortion:
2229 {
2230 size_t nterms = (size_t) coeff[1];
2231 (void) FormatLocaleFile(stderr,
2232 "Polynomial (order %lg, terms %lu), FX Equivalent\n",coeff[0],
2233 (unsigned long) nterms);
2234 (void) FormatLocaleFile(stderr,"%s", image_gen);
2235 (void) FormatLocaleFile(stderr,
2236 " -fx 'ii=i+page.x+0.5; jj=j+page.y+0.5;\n");
2237 (void) FormatLocaleFile(stderr, " xx =");
2238 for (i=0; i < (ssize_t) nterms; i++)
2239 {
2240 if ((i != 0) && (i%4 == 0))
2241 (void) FormatLocaleFile(stderr, "\n ");
2242 (void) FormatLocaleFile(stderr," %+lf%s",coeff[2+i],
2243 poly_basis_str(i));
2244 }
2245 (void) FormatLocaleFile(stderr,";\n yy =");
2246 for (i=0; i < (ssize_t) nterms; i++)
2247 {
2248 if ((i != 0) && (i%4 == 0))
2249 (void) FormatLocaleFile(stderr,"\n ");
2250 (void) FormatLocaleFile(stderr," %+lf%s",coeff[2+i+(int) nterms],
2251 poly_basis_str(i));
2252 }
2253 (void) FormatLocaleFile(stderr,";\n %s' \\\n", lookup);
2254 break;
2255 }
2256 case ArcDistortion:
2257 {
2258 (void) FormatLocaleFile(stderr,"Arc Distort, Internal Coefficients:\n");
2259 for (i=0; i < 5; i++)
2260 (void) FormatLocaleFile(stderr,
2261 " c%.20g = %+lf\n",(double) i,coeff[i]);
2262 (void) FormatLocaleFile(stderr,"Arc Distort, FX Equivalent:\n");
2263 (void) FormatLocaleFile(stderr,"%s", image_gen);
2264 (void) FormatLocaleFile(stderr," -fx 'ii=i+page.x; jj=j+page.y;\n");
2265 (void) FormatLocaleFile(stderr," xx=(atan2(jj,ii)%+lf)/(2*pi);\n",
2266 -coeff[0]);
2267 (void) FormatLocaleFile(stderr," xx=xx-round(xx);\n");
2268 (void) FormatLocaleFile(stderr," xx=xx*%lf %+lf;\n",coeff[1],
2269 coeff[4]);
2270 (void) FormatLocaleFile(stderr,
2271 " yy=(%lf - hypot(ii,jj)) * %lf;\n",coeff[2],coeff[3]);
2272 (void) FormatLocaleFile(stderr," v.p{xx-.5,yy-.5}' \\\n");
2273 break;
2274 }
2275 case PolarDistortion:
2276 {
2277 (void) FormatLocaleFile(stderr,"Polar Distort, Internal Coefficients\n");
2278 for (i=0; i < 8; i++)
2279 (void) FormatLocaleFile(stderr," c%.20g = %+lf\n",(double) i,
2280 coeff[i]);
2281 (void) FormatLocaleFile(stderr,"Polar Distort, FX Equivalent:\n");
2282 (void) FormatLocaleFile(stderr,"%s", image_gen);
2283 (void) FormatLocaleFile(stderr,
2284 " -fx 'ii=i+page.x%+lf; jj=j+page.y%+lf;\n",-coeff[2],-coeff[3]);
2285 (void) FormatLocaleFile(stderr," xx=(atan2(ii,jj)%+lf)/(2*pi);\n",
2286 -(coeff[4]+coeff[5])/2 );
2287 (void) FormatLocaleFile(stderr," xx=xx-round(xx);\n");
2288 (void) FormatLocaleFile(stderr," xx=xx*2*pi*%lf + v.w/2;\n",
2289 coeff[6] );
2290 (void) FormatLocaleFile(stderr," yy=(hypot(ii,jj)%+lf)*%lf;\n",
2291 -coeff[1],coeff[7] );
2292 (void) FormatLocaleFile(stderr," v.p{xx-.5,yy-.5}' \\\n");
2293 break;
2294 }
2295 case DePolarDistortion:
2296 {
2297 (void) FormatLocaleFile(stderr,
2298 "DePolar Distort, Internal Coefficients\n");
2299 for (i=0; i < 8; i++)
2300 (void) FormatLocaleFile(stderr," c%.20g = %+lf\n",(double) i,
2301 coeff[i]);
2302 (void) FormatLocaleFile(stderr,"DePolar Distort, FX Equivalent:\n");
2303 (void) FormatLocaleFile(stderr,"%s", image_gen);
2304 (void) FormatLocaleFile(stderr," -fx 'aa=(i+.5)*%lf %+lf;\n",
2305 coeff[6],+coeff[4]);
2306 (void) FormatLocaleFile(stderr," rr=(j+.5)*%lf %+lf;\n",
2307 coeff[7],+coeff[1]);
2308 (void) FormatLocaleFile(stderr," xx=rr*sin(aa) %+lf;\n",
2309 coeff[2]);
2310 (void) FormatLocaleFile(stderr," yy=rr*cos(aa) %+lf;\n",
2311 coeff[3]);
2312 (void) FormatLocaleFile(stderr," v.p{xx-.5,yy-.5}' \\\n");
2313 break;
2314 }
2315 case Cylinder2PlaneDistortion:
2316 {
2317 (void) FormatLocaleFile(stderr,
2318 "Cylinder to Plane Distort, Internal Coefficients\n");
2319 (void) FormatLocaleFile(stderr," cylinder_radius = %+lf\n",coeff[1]);
2320 (void) FormatLocaleFile(stderr,
2321 "Cylinder to Plane Distort, FX Equivalent:\n");
2322 (void) FormatLocaleFile(stderr, "%s", image_gen);
2323 (void) FormatLocaleFile(stderr,
2324 " -fx 'ii=i+page.x%+lf+0.5; jj=j+page.y%+lf+0.5;\n",-coeff[4],
2325 -coeff[5]);
2326 (void) FormatLocaleFile(stderr," aa=atan(ii/%+lf);\n",coeff[1]);
2327 (void) FormatLocaleFile(stderr," xx=%lf*aa%+lf;\n",
2328 coeff[1],coeff[2]);
2329 (void) FormatLocaleFile(stderr," yy=jj*cos(aa)%+lf;\n",coeff[3]);
2330 (void) FormatLocaleFile(stderr," %s' \\\n", lookup);
2331 break;
2332 }
2333 case Plane2CylinderDistortion:
2334 {
2335 (void) FormatLocaleFile(stderr,
2336 "Plane to Cylinder Distort, Internal Coefficients\n");
2337 (void) FormatLocaleFile(stderr," cylinder_radius = %+lf\n",coeff[1]);
2338 (void) FormatLocaleFile(stderr,
2339 "Plane to Cylinder Distort, FX Equivalent:\n");
2340 (void) FormatLocaleFile(stderr,"%s", image_gen);
2341 (void) FormatLocaleFile(stderr,
2342 " -fx 'ii=i+page.x%+lf+0.5; jj=j+page.y%+lf+0.5;\n",-coeff[4],
2343 -coeff[5]);
2344 (void) FormatLocaleFile(stderr," ii=ii/%+lf;\n",coeff[1]);
2345 (void) FormatLocaleFile(stderr," xx=%lf*tan(ii)%+lf;\n",coeff[1],
2346 coeff[2] );
2347 (void) FormatLocaleFile(stderr," yy=jj/cos(ii)%+lf;\n",coeff[3]);
2348 (void) FormatLocaleFile(stderr," %s' \\\n", lookup);
2349 break;
2350 }
2351 case BarrelDistortion:
2352 case BarrelInverseDistortion:
2353 {
2354 double
2355 xc,
2356 yc;
2357
2358 /*
2359 NOTE: This does the barrel roll in pixel coords not image coords
2360 The internal distortion must do it in image coordinates,
2361 so that is what the center coeff (8,9) is given in.
2362 */
2363 xc=((double)image->columns-1.0)/2.0+image->page.x;
2364 yc=((double)image->rows-1.0)/2.0+image->page.y;
2365 (void) FormatLocaleFile(stderr, "Barrel%s Distort, FX Equivalent:\n",
2366 method == BarrelDistortion ? "" : "Inv");
2367 (void) FormatLocaleFile(stderr, "%s", image_gen);
2368 if ( fabs(coeff[8]-xc-0.5) < 0.1 && fabs(coeff[9]-yc-0.5) < 0.1 )
2369 (void) FormatLocaleFile(stderr," -fx 'xc=(w-1)/2; yc=(h-1)/2;\n");
2370 else
2371 (void) FormatLocaleFile(stderr," -fx 'xc=%lf; yc=%lf;\n",coeff[8]-
2372 0.5,coeff[9]-0.5);
2373 (void) FormatLocaleFile(stderr,
2374 " ii=i-xc; jj=j-yc; rr=hypot(ii,jj);\n");
2375 (void) FormatLocaleFile(stderr,
2376 " ii=ii%s(%lf*rr*rr*rr %+lf*rr*rr %+lf*rr %+lf);\n",
2377 method == BarrelDistortion ? "*" : "/",coeff[0],coeff[1],coeff[2],
2378 coeff[3]);
2379 (void) FormatLocaleFile(stderr,
2380 " jj=jj%s(%lf*rr*rr*rr %+lf*rr*rr %+lf*rr %+lf);\n",
2381 method == BarrelDistortion ? "*" : "/",coeff[4],coeff[5],coeff[6],
2382 coeff[7]);
2383 (void) FormatLocaleFile(stderr," p{ii+xc,jj+yc}' \\\n");
2384 break;
2385 }
2386 default:
2387 break;
2388 }
2389 }
2390 /*
2391 The user provided a 'scale' expert option will scale the output image size,
2392 by the factor given allowing for super-sampling of the distorted image
2393 space. Any scaling factors must naturally be halved as a result.
2394 */
2395 { const char *artifact;
2396 artifact=GetImageArtifact(image,"distort:scale");
2397 output_scaling = 1.0;
2398 if (artifact != (const char *) NULL) {
2399 output_scaling = fabs(StringToDouble(artifact,(char **) NULL));
2400 geometry.width=(size_t) (output_scaling*geometry.width+0.5);
2401 geometry.height=(size_t) (output_scaling*geometry.height+0.5);
2402 geometry.x=(ssize_t) (output_scaling*geometry.x+0.5);
2403 geometry.y=(ssize_t) (output_scaling*geometry.y+0.5);
2404 if ( output_scaling < 0.1 ) {
2405 coeff = (double *) RelinquishMagickMemory(coeff);
2406 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
2407 "InvalidArgument","%s", "-set option:distort:scale" );
2408 return((Image *) NULL);
2409 }
2410 output_scaling = 1/output_scaling;
2411 }
2412 }
2413#define ScaleFilter(F,A,B,C,D) \
2414 ScaleResampleFilter( (F), \
2415 output_scaling*(A), output_scaling*(B), \
2416 output_scaling*(C), output_scaling*(D) )
2417
2418 /*
2419 Initialize the distort image attributes.
2420 */
2421 distort_image=CloneImage(image,geometry.width,geometry.height,MagickTrue,
2422 exception);
2423 if (distort_image == (Image *) NULL)
2424 {
2425 coeff=(double *) RelinquishMagickMemory(coeff);
2426 return((Image *) NULL);
2427 }
2428 /* if image is ColorMapped - change it to DirectClass */
2429 if (SetImageStorageClass(distort_image,DirectClass,exception) == MagickFalse)
2430 {
2431 coeff=(double *) RelinquishMagickMemory(coeff);
2432 distort_image=DestroyImage(distort_image);
2433 return((Image *) NULL);
2434 }
2435 if ((IsPixelInfoGray(&distort_image->background_color) == MagickFalse) &&
2436 (IsGrayColorspace(distort_image->colorspace) != MagickFalse))
2437 (void) SetImageColorspace(distort_image,sRGBColorspace,exception);
2438 if (distort_image->background_color.alpha_trait != UndefinedPixelTrait)
2439 distort_image->alpha_trait=BlendPixelTrait;
2440 distort_image->page.x=geometry.x;
2441 distort_image->page.y=geometry.y;
2442 ConformPixelInfo(distort_image,&distort_image->matte_color,&invalid,
2443 exception);
2444
2445 { /* ----- MAIN CODE -----
2446 Sample the source image to each pixel in the distort image.
2447 */
2448 CacheView
2449 *distort_view;
2450
2451 MagickBooleanType
2452 status;
2453
2454 MagickOffsetType
2455 progress;
2456
2457 PixelInfo
2458 zero;
2459
2460 ResampleFilter
2461 **magick_restrict resample_filter;
2462
2463 ssize_t
2464 j;
2465
2466 status=MagickTrue;
2467 progress=0;
2468 GetPixelInfo(distort_image,&zero);
2469 resample_filter=AcquireResampleFilterTLS(image,UndefinedVirtualPixelMethod,
2470 MagickFalse,exception);
2471 distort_view=AcquireAuthenticCacheView(distort_image,exception);
2472#if defined(MAGICKCORE_OPENMP_SUPPORT)
2473 #pragma omp parallel for schedule(static) shared(progress,status) \
2474 magick_number_threads(image,distort_image,distort_image->rows,1)
2475#endif
2476 for (j=0; j < (ssize_t) distort_image->rows; j++)
2477 {
2478 const int
2479 id = GetOpenMPThreadId();
2480
2481 double
2482 validity; /* how mathematically valid is this the mapping */
2483
2484 MagickBooleanType
2485 sync;
2486
2487 PixelInfo
2488 pixel; /* pixel color to assign to distorted image */
2489
2490 PointInfo
2491 d,
2492 s; /* transform destination image x,y to source image x,y */
2493
2494 ssize_t
2495 i;
2496
2497 Quantum
2498 *magick_restrict q;
2499
2500 q=QueueCacheViewAuthenticPixels(distort_view,0,j,distort_image->columns,1,
2501 exception);
2502 if (q == (Quantum *) NULL)
2503 {
2504 status=MagickFalse;
2505 continue;
2506 }
2507 pixel=zero;
2508
2509 /* Define constant scaling vectors for Affine Distortions
2510 Other methods are either variable, or use interpolated lookup
2511 */
2512 switch (method)
2513 {
2514 case AffineDistortion:
2515 case RigidAffineDistortion:
2516 ScaleFilter( resample_filter[id],
2517 coeff[0], coeff[1],
2518 coeff[3], coeff[4] );
2519 break;
2520 default:
2521 break;
2522 }
2523
2524 /* Initialize default pixel validity
2525 * negative: pixel is invalid output 'matte_color'
2526 * 0.0 to 1.0: antialiased, mix with resample output
2527 * 1.0 or greater: use resampled output.
2528 */
2529 validity = 1.0;
2530
2531 for (i=0; i < (ssize_t) distort_image->columns; i++)
2532 {
2533 /* map pixel coordinate to distortion space coordinate */
2534 d.x = (double) (geometry.x+i+0.5)*output_scaling;
2535 d.y = (double) (geometry.y+j+0.5)*output_scaling;
2536 s = d; /* default is a no-op mapping */
2537 switch (method)
2538 {
2539 case AffineDistortion:
2540 case RigidAffineDistortion:
2541 {
2542 s.x=coeff[0]*d.x+coeff[1]*d.y+coeff[2];
2543 s.y=coeff[3]*d.x+coeff[4]*d.y+coeff[5];
2544 /* Affine partial derivatives are constant -- set above */
2545 break;
2546 }
2547 case PerspectiveDistortion:
2548 {
2549 double
2550 p,n,r,abs_r,abs_c6,abs_c7,scale;
2551 /* perspective is a ratio of affines */
2552 p=coeff[0]*d.x+coeff[1]*d.y+coeff[2];
2553 n=coeff[3]*d.x+coeff[4]*d.y+coeff[5];
2554 r=coeff[6]*d.x+coeff[7]*d.y+1.0;
2555 /* Pixel Validity -- is it a 'sky' or 'ground' pixel */
2556 validity = (r*coeff[8] < 0.0) ? 0.0 : 1.0;
2557 /* Determine horizon anti-alias blending */
2558 abs_r = fabs(r)*2;
2559 abs_c6 = fabs(coeff[6]);
2560 abs_c7 = fabs(coeff[7]);
2561 if ( abs_c6 > abs_c7 ) {
2562 if ( abs_r < abs_c6*output_scaling )
2563 validity = 0.5 - coeff[8]*r/(coeff[6]*output_scaling);
2564 }
2565 else if ( abs_r < abs_c7*output_scaling )
2566 validity = 0.5 - coeff[8]*r/(coeff[7]*output_scaling);
2567 /* Perspective Sampling Point (if valid) */
2568 if ( validity > 0.0 ) {
2569 /* divide by r affine, for perspective scaling */
2570 scale = 1.0/r;
2571 s.x = p*scale;
2572 s.y = n*scale;
2573 /* Perspective Partial Derivatives or Scaling Vectors */
2574 scale *= scale;
2575 ScaleFilter( resample_filter[id],
2576 (r*coeff[0] - p*coeff[6])*scale,
2577 (r*coeff[1] - p*coeff[7])*scale,
2578 (r*coeff[3] - n*coeff[6])*scale,
2579 (r*coeff[4] - n*coeff[7])*scale );
2580 }
2581 break;
2582 }
2583 case BilinearReverseDistortion:
2584 {
2585 /* Reversed Mapped is just a simple polynomial */
2586 s.x=coeff[0]*d.x+coeff[1]*d.y+coeff[2]*d.x*d.y+coeff[3];
2587 s.y=coeff[4]*d.x+coeff[5]*d.y
2588 +coeff[6]*d.x*d.y+coeff[7];
2589 /* Bilinear partial derivatives of scaling vectors */
2590 ScaleFilter( resample_filter[id],
2591 coeff[0] + coeff[2]*d.y,
2592 coeff[1] + coeff[2]*d.x,
2593 coeff[4] + coeff[6]*d.y,
2594 coeff[5] + coeff[6]*d.x );
2595 break;
2596 }
2597 case BilinearForwardDistortion:
2598 {
2599 /* Forward mapped needs reversed polynomial equations
2600 * which unfortunately requires a square root! */
2601 double b,c;
2602 d.x -= coeff[3]; d.y -= coeff[7];
2603 b = coeff[6]*d.x - coeff[2]*d.y + coeff[8];
2604 c = coeff[4]*d.x - coeff[0]*d.y;
2605
2606 validity = 1.0;
2607 /* Handle Special degenerate (non-quadratic) case
2608 * Currently without horizon anti-aliasing */
2609 if ( fabs(coeff[9]) < MagickEpsilon )
2610 s.y = -c/b;
2611 else {
2612 c = b*b - 2*coeff[9]*c;
2613 if ( c < 0.0 )
2614 validity = 0.0;
2615 else
2616 s.y = ( -b + sqrt(c) )/coeff[9];
2617 }
2618 if ( validity > 0.0 )
2619 s.x = ( d.x - coeff[1]*s.y) / ( coeff[0] + coeff[2]*s.y );
2620
2621 /* NOTE: the sign of the square root should be -ve for parts
2622 where the source image becomes 'flipped' or 'mirrored'.
2623 FUTURE: Horizon handling
2624 FUTURE: Scaling factors or Derivatives (how?)
2625 */
2626 break;
2627 }
2628#if 0
2629 case BilinearDistortion:
2630 /* Bilinear mapping of any Quadrilateral to any Quadrilateral */
2631 /* UNDER DEVELOPMENT */
2632 break;
2633#endif
2634 case PolynomialDistortion:
2635 {
2636 /* multi-ordered polynomial */
2637 ssize_t
2638 k;
2639
2640 ssize_t
2641 nterms=(ssize_t)coeff[1];
2642
2643 PointInfo
2644 du,dv; /* the du,dv vectors from unit dx,dy -- derivatives */
2645
2646 s.x=s.y=du.x=du.y=dv.x=dv.y=0.0;
2647 for(k=0; k < nterms; k++) {
2648 s.x += poly_basis_fn(k,d.x,d.y)*coeff[2+k];
2649 du.x += poly_basis_dx(k,d.x,d.y)*coeff[2+k];
2650 du.y += poly_basis_dy(k,d.x,d.y)*coeff[2+k];
2651 s.y += poly_basis_fn(k,d.x,d.y)*coeff[2+k+nterms];
2652 dv.x += poly_basis_dx(k,d.x,d.y)*coeff[2+k+nterms];
2653 dv.y += poly_basis_dy(k,d.x,d.y)*coeff[2+k+nterms];
2654 }
2655 ScaleFilter( resample_filter[id], du.x,du.y,dv.x,dv.y );
2656 break;
2657 }
2658 case ArcDistortion:
2659 {
2660 /* what is the angle and radius in the destination image */
2661 s.x = (double) ((atan2(d.y,d.x) - coeff[0])/Magick2PI);
2662 s.x -= MagickRound(s.x); /* angle */
2663 s.y = hypot(d.x,d.y); /* radius */
2664
2665 /* Arc Distortion Partial Scaling Vectors
2666 Are derived by mapping the perpendicular unit vectors
2667 dR and dA*R*2PI rather than trying to map dx and dy
2668 The results is a very simple orthogonal aligned ellipse.
2669 */
2670 if ( s.y > MagickEpsilon )
2671 ScaleFilter( resample_filter[id],
2672 (double) (coeff[1]/(Magick2PI*s.y)), 0, 0, coeff[3] );
2673 else
2674 ScaleFilter( resample_filter[id],
2675 distort_image->columns*2, 0, 0, coeff[3] );
2676
2677 /* now scale the angle and radius for source image lookup point */
2678 s.x = s.x*coeff[1] + coeff[4] + image->page.x +0.5;
2679 s.y = (coeff[2] - s.y) * coeff[3] + image->page.y;
2680 break;
2681 }
2682 case PolarDistortion:
2683 { /* 2D Cartesian to Polar View */
2684 d.x -= coeff[2];
2685 d.y -= coeff[3];
2686 s.x = atan2(d.x,d.y) - (coeff[4]+coeff[5])/2;
2687 s.x /= Magick2PI;
2688 s.x -= MagickRound(s.x);
2689 s.x *= Magick2PI; /* angle - relative to centerline */
2690 s.y = hypot(d.x,d.y); /* radius */
2691
2692 /* Polar Scaling vectors are based on mapping dR and dA vectors
2693 This results in very simple orthogonal scaling vectors
2694 */
2695 if ( s.y > MagickEpsilon )
2696 ScaleFilter( resample_filter[id],
2697 (double) (coeff[6]/(Magick2PI*s.y)), 0, 0, coeff[7] );
2698 else
2699 ScaleFilter( resample_filter[id],
2700 distort_image->columns*2, 0, 0, coeff[7] );
2701
2702 /* now finish mapping radius/angle to source x,y coords */
2703 s.x = s.x*coeff[6] + (double)image->columns/2.0 + image->page.x;
2704 s.y = (s.y-coeff[1])*coeff[7] + image->page.y;
2705 break;
2706 }
2707 case DePolarDistortion:
2708 { /* @D Polar to Cartesian */
2709 /* ignore all destination virtual offsets */
2710 d.x = ((double)i+0.5)*output_scaling*coeff[6]+coeff[4];
2711 d.y = ((double)j+0.5)*output_scaling*coeff[7]+coeff[1];
2712 s.x = d.y*sin(d.x) + coeff[2];
2713 s.y = d.y*cos(d.x) + coeff[3];
2714 /* derivatives are useless - better to use SuperSampling */
2715 break;
2716 }
2717 case Cylinder2PlaneDistortion:
2718 { /* 3D Cylinder to Tangential Plane */
2719 double ax, cx;
2720 /* relative to center of distortion */
2721 d.x -= coeff[4]; d.y -= coeff[5];
2722 d.x /= coeff[1]; /* x' = x/r */
2723 ax=atan(d.x); /* aa = atan(x/r) = u/r */
2724 cx=cos(ax); /* cx = cos(atan(x/r)) = 1/sqrt(x^2+u^2) */
2725 s.x = coeff[1]*ax; /* u = r*atan(x/r) */
2726 s.y = d.y*cx; /* v = y*cos(u/r) */
2727 /* derivatives... (see personal notes) */
2728 ScaleFilter( resample_filter[id],
2729 1.0/(1.0+d.x*d.x), 0.0, -d.x*s.y*cx*cx/coeff[1], s.y/d.y );
2730#if 0
2731if ( i == 0 && j == 0 ) {
2732 fprintf(stderr, "x=%lf y=%lf u=%lf v=%lf\n", d.x*coeff[1], d.y, s.x, s.y);
2733 fprintf(stderr, "phi = %lf\n", (double)(ax * 180.0/MagickPI) );
2734 fprintf(stderr, "du/dx=%lf du/dx=%lf dv/dx=%lf dv/dy=%lf\n",
2735 1.0/(1.0+d.x*d.x), 0.0, -d.x*s.y*cx*cx/coeff[1], s.y/d.y );
2736 fflush(stderr); }
2737#endif
2738 /* add center of distortion in source */
2739 s.x += coeff[2]; s.y += coeff[3];
2740 break;
2741 }
2742 case Plane2CylinderDistortion:
2743 { /* 3D Cylinder to Tangential Plane */
2744 /* relative to center of distortion */
2745 d.x -= coeff[4]; d.y -= coeff[5];
2746
2747 /* is pixel valid - horizon of a infinite Virtual-Pixel Plane
2748 * (see Anthony Thyssen's personal note) */
2749 validity = (double) (coeff[1]*MagickPI2 - fabs(d.x))/output_scaling + 0.5;
2750
2751 if ( validity > 0.0 ) {
2752 double cx,tx;
2753 d.x /= coeff[1]; /* x'= x/r */
2754 cx = 1/cos(d.x); /* cx = 1/cos(x/r) */
2755 tx = tan(d.x); /* tx = tan(x/r) */
2756 s.x = coeff[1]*tx; /* u = r * tan(x/r) */
2757 s.y = d.y*cx; /* v = y / cos(x/r) */
2758 /* derivatives... (see Anthony Thyssen's personal notes) */
2759 ScaleFilter( resample_filter[id],
2760 cx*cx, 0.0, s.y*cx/coeff[1], cx );
2761#if 0
2762/*if ( i == 0 && j == 0 )*/
2763if ( d.x == 0.5 && d.y == 0.5 ) {
2764 fprintf(stderr, "x=%lf y=%lf u=%lf v=%lf\n", d.x*coeff[1], d.y, s.x, s.y);
2765 fprintf(stderr, "radius = %lf phi = %lf validity = %lf\n",
2766 coeff[1], (double)(d.x * 180.0/MagickPI), validity );
2767 fprintf(stderr, "du/dx=%lf du/dx=%lf dv/dx=%lf dv/dy=%lf\n",
2768 cx*cx, 0.0, s.y*cx/coeff[1], cx);
2769 fflush(stderr); }
2770#endif
2771 }
2772 /* add center of distortion in source */
2773 s.x += coeff[2]; s.y += coeff[3];
2774 break;
2775 }
2776 case BarrelDistortion:
2777 case BarrelInverseDistortion:
2778 { /* Lens Barrel Distortion Correction */
2779 double r,fx,fy,gx,gy;
2780 /* Radial Polynomial Distortion (de-normalized) */
2781 d.x -= coeff[8];
2782 d.y -= coeff[9];
2783 r = sqrt(d.x*d.x+d.y*d.y);
2784 if ( r > MagickEpsilon ) {
2785 fx = ((coeff[0]*r + coeff[1])*r + coeff[2])*r + coeff[3];
2786 fy = ((coeff[4]*r + coeff[5])*r + coeff[6])*r + coeff[7];
2787 gx = ((3*coeff[0]*r + 2*coeff[1])*r + coeff[2])/r;
2788 gy = ((3*coeff[4]*r + 2*coeff[5])*r + coeff[6])/r;
2789 /* adjust functions and scaling for 'inverse' form */
2790 if ( method == BarrelInverseDistortion ) {
2791 fx = 1/fx; fy = 1/fy;
2792 gx *= -fx*fx; gy *= -fy*fy;
2793 }
2794 /* Set the source pixel to lookup and EWA derivative vectors */
2795 s.x = d.x*fx + coeff[8];
2796 s.y = d.y*fy + coeff[9];
2797 ScaleFilter( resample_filter[id],
2798 gx*d.x*d.x + fx, gx*d.x*d.y,
2799 gy*d.x*d.y, gy*d.y*d.y + fy );
2800 }
2801 else {
2802 /* Special handling to avoid divide by zero when r==0
2803 **
2804 ** The source and destination pixels match in this case
2805 ** which was set at the top of the loop using s = d;
2806 ** otherwise... s.x=coeff[8]; s.y=coeff[9];
2807 */
2808 if ( method == BarrelDistortion )
2809 ScaleFilter( resample_filter[id],
2810 coeff[3], 0, 0, coeff[7] );
2811 else /* method == BarrelInverseDistortion */
2812 /* FUTURE, trap for D==0 causing division by zero */
2813 ScaleFilter( resample_filter[id],
2814 1.0/coeff[3], 0, 0, 1.0/coeff[7] );
2815 }
2816 break;
2817 }
2818 case ShepardsDistortion:
2819 { /* Shepards Method, or Inverse Weighted Distance for
2820 displacement around the destination image control points
2821 The input arguments are the coefficients to the function.
2822 This is more of a 'displacement' function rather than an
2823 absolute distortion function.
2824
2825 Note: We can not determine derivatives using shepards method
2826 so only a point sample interpolation can be used.
2827 */
2828 double
2829 denominator;
2830
2831 size_t
2832 k;
2833
2834 denominator = s.x = s.y = 0;
2835 for(k=0; k<number_arguments; k+=4) {
2836 double weight =
2837 ((double)d.x-arguments[k+2])*((double)d.x-arguments[k+2])
2838 + ((double)d.y-arguments[k+3])*((double)d.y-arguments[k+3]);
2839 weight = pow(weight,coeff[0]); /* shepards power factor */
2840 weight = ( weight < 1.0 ) ? 1.0 : 1.0/weight;
2841
2842 s.x += (arguments[ k ]-arguments[k+2])*weight;
2843 s.y += (arguments[k+1]-arguments[k+3])*weight;
2844 denominator += weight;
2845 }
2846 s.x /= denominator;
2847 s.y /= denominator;
2848 s.x += d.x; /* make it as relative displacement */
2849 s.y += d.y;
2850 break;
2851 }
2852 default:
2853 break; /* use the default no-op given above */
2854 }
2855 /* map virtual canvas location back to real image coordinate */
2856 if ( bestfit && method != ArcDistortion ) {
2857 s.x -= image->page.x;
2858 s.y -= image->page.y;
2859 }
2860 s.x -= 0.5;
2861 s.y -= 0.5;
2862
2863 if ( validity <= 0.0 ) {
2864 /* result of distortion is an invalid pixel - don't resample */
2865 SetPixelViaPixelInfo(distort_image,&invalid,q);
2866 }
2867 else {
2868 /* resample the source image to find its correct color */
2869 status=ResamplePixelColor(resample_filter[id],s.x,s.y,&pixel,
2870 exception);
2871 if (status == MagickFalse)
2872 SetPixelViaPixelInfo(distort_image,&invalid,q);
2873 else
2874 {
2875 /* if validity between 0.0 & 1.0 mix result with invalid pixel */
2876 if ( validity < 1.0 ) {
2877 /* Do a blend of sample color and invalid pixel */
2878 /* should this be a 'Blend', or an 'Over' compose */
2879 CompositePixelInfoBlend(&pixel,validity,&invalid,(1.0-validity),
2880 &pixel);
2881 }
2882 SetPixelViaPixelInfo(distort_image,&pixel,q);
2883 }
2884 }
2885 q+=(ptrdiff_t) GetPixelChannels(distort_image);
2886 }
2887 sync=SyncCacheViewAuthenticPixels(distort_view,exception);
2888 if (sync == MagickFalse)
2889 status=MagickFalse;
2890 if (image->progress_monitor != (MagickProgressMonitor) NULL)
2891 {
2892 MagickBooleanType
2893 proceed;
2894
2895#if defined(MAGICKCORE_OPENMP_SUPPORT)
2896 #pragma omp atomic
2897#endif
2898 progress++;
2899 proceed=SetImageProgress(image,DistortImageTag,progress,image->rows);
2900 if (proceed == MagickFalse)
2901 status=MagickFalse;
2902 }
2903 }
2904 distort_view=DestroyCacheView(distort_view);
2905 resample_filter=DestroyResampleFilterTLS(resample_filter);
2906
2907 if (status == MagickFalse)
2908 distort_image=DestroyImage(distort_image);
2909 }
2910
2911 /* Arc does not return an offset unless 'bestfit' is in effect
2912 And the user has not provided an overriding 'viewport'.
2913 */
2914 if ( method == ArcDistortion && !bestfit && !viewport_given ) {
2915 distort_image->page.x = 0;
2916 distort_image->page.y = 0;
2917 }
2918 coeff=(double *) RelinquishMagickMemory(coeff);
2919 return(distort_image);
2920}
2921␌
2922/*
2923%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2924% %
2925% %
2926% %
2927% R o t a t e I m a g e %
2928% %
2929% %
2930% %
2931%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2932%
2933% RotateImage() creates a new image that is a rotated copy of an existing
2934% one. Positive angles rotate counter-clockwise (right-hand rule), while
2935% negative angles rotate clockwise. Rotated images are usually larger than
2936% the originals and have 'empty' triangular corners. X axis. Empty
2937% triangles left over from shearing the image are filled with the background
2938% color defined by member 'background_color' of the image. RotateImage
2939% allocates the memory necessary for the new Image structure and returns a
2940% pointer to the new image.
2941%
2942% The format of the RotateImage method is:
2943%
2944% Image *RotateImage(const Image *image,const double degrees,
2945% ExceptionInfo *exception)
2946%
2947% A description of each parameter follows.
2948%
2949% o image: the image.
2950%
2951% o degrees: Specifies the number of degrees to rotate the image.
2952%
2953% o exception: return any errors or warnings in this structure.
2954%
2955*/
2956MagickExport Image *RotateImage(const Image *image,const double degrees,
2957 ExceptionInfo *exception)
2958{
2959 Image
2960 *distort_image,
2961 *rotate_image;
2962
2963 double
2964 angle;
2965
2966 PointInfo
2967 shear;
2968
2969 size_t
2970 rotations;
2971
2972 /*
2973 Adjust rotation angle.
2974 */
2975 assert(image != (Image *) NULL);
2976 assert(image->signature == MagickCoreSignature);
2977 if (IsEventLogging() != MagickFalse)
2978 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2979 assert(exception != (ExceptionInfo *) NULL);
2980 assert(exception->signature == MagickCoreSignature);
2981 angle=fmod(degrees,360.0);
2982 while (angle < -45.0)
2983 angle+=360.0;
2984 for (rotations=0; angle > 45.0; rotations++)
2985 angle-=90.0;
2986 rotations%=4;
2987 shear.x=(-tan((double) DegreesToRadians(angle)/2.0));
2988 shear.y=sin((double) DegreesToRadians(angle));
2989 if ((fabs(shear.x) < MagickEpsilon) && (fabs(shear.y) < MagickEpsilon))
2990 return(IntegralRotateImage(image,rotations,exception));
2991 distort_image=CloneImage(image,0,0,MagickTrue,exception);
2992 if (distort_image == (Image *) NULL)
2993 return((Image *) NULL);
2994 (void) SetImageVirtualPixelMethod(distort_image,BackgroundVirtualPixelMethod,
2995 exception);
2996 rotate_image=DistortImage(distort_image,ScaleRotateTranslateDistortion,1,
2997 &degrees,MagickTrue,exception);
2998 distort_image=DestroyImage(distort_image);
2999 return(rotate_image);
3000}
3001␌
3002/*
3003%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3004% %
3005% %
3006% %
3007% S p a r s e C o l o r I m a g e %
3008% %
3009% %
3010% %
3011%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3012%
3013% SparseColorImage(), given a set of coordinates, interpolates the colors
3014% found at those coordinates, across the whole image, using various methods.
3015%
3016% The format of the SparseColorImage() method is:
3017%
3018% Image *SparseColorImage(const Image *image,
3019% const SparseColorMethod method,const size_t number_arguments,
3020% const double *arguments,ExceptionInfo *exception)
3021%
3022% A description of each parameter follows:
3023%
3024% o image: the image to be filled in.
3025%
3026% o method: the method to fill in the gradient between the control points.
3027%
3028% The methods used for SparseColor() are often simular to methods
3029% used for DistortImage(), and even share the same code for determination
3030% of the function coefficients, though with more dimensions (or resulting
3031% values).
3032%
3033% o number_arguments: the number of arguments given.
3034%
3035% o arguments: array of floating point arguments for this method--
3036% x,y,color_values-- with color_values given as normalized values.
3037%
3038% o exception: return any errors or warnings in this structure
3039%
3040*/
3041MagickExport Image *SparseColorImage(const Image *image,
3042 const SparseColorMethod method,const size_t number_arguments,
3043 const double *arguments,ExceptionInfo *exception)
3044{
3045#define SparseColorTag "Distort/SparseColor"
3046
3047 double
3048 *coeff;
3049
3050 Image
3051 *sparse_image;
3052
3053 size_t
3054 number_colors;
3055
3056 SparseColorMethod
3057 sparse_method;
3058
3059 assert(image != (Image *) NULL);
3060 assert(image->signature == MagickCoreSignature);
3061 assert(exception != (ExceptionInfo *) NULL);
3062 assert(exception->signature == MagickCoreSignature);
3063 if (IsEventLogging() != MagickFalse)
3064 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
3065
3066 /* Determine number of color values needed per control point */
3067 number_colors=0;
3068 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
3069 number_colors++;
3070 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
3071 number_colors++;
3072 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
3073 number_colors++;
3074 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
3075 (image->colorspace == CMYKColorspace))
3076 number_colors++;
3077 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
3078 (image->alpha_trait != UndefinedPixelTrait))
3079 number_colors++;
3080
3081 /*
3082 Convert input arguments into mapping coefficients, in this case
3083 we are mapping (distorting) colors, rather than coordinates.
3084 */
3085 { DistortMethod
3086 distort_method;
3087
3088 distort_method=(DistortMethod) method;
3089 if ( distort_method >= SentinelDistortion )
3090 distort_method = ShepardsDistortion; /* Pretend to be Shepards */
3091 coeff = GenerateCoefficients(image, &distort_method, number_arguments,
3092 arguments, number_colors, exception);
3093 if ( coeff == (double *) NULL )
3094 return((Image *) NULL);
3095 /*
3096 Note some Distort Methods may fall back to other simpler methods,
3097 Currently the only fallback of concern is Bilinear to Affine
3098 (Barycentric), which is also sparse_colr method. This also ensures
3099 correct two and one color Barycentric handling.
3100 */
3101 sparse_method = (SparseColorMethod) distort_method;
3102 if ( distort_method == ShepardsDistortion )
3103 sparse_method = method; /* return non-distort methods to normal */
3104 if ( sparse_method == InverseColorInterpolate )
3105 coeff[0]=0.5; /* sqrt() the squared distance for inverse */
3106 }
3107
3108 /* Verbose output */
3109 if (IsStringTrue(GetImageArtifact(image,"verbose")) != MagickFalse) {
3110
3111 switch (sparse_method) {
3112 case BarycentricColorInterpolate:
3113 {
3114 ssize_t x=0;
3115 (void) FormatLocaleFile(stderr, "Barycentric Sparse Color:\n");
3116 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
3117 (void) FormatLocaleFile(stderr, " -channel R -fx '%+lf*i %+lf*j %+lf' \\\n",
3118 coeff[x], coeff[x+1], coeff[x+2]),x+=3;
3119 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
3120 (void) FormatLocaleFile(stderr, " -channel G -fx '%+lf*i %+lf*j %+lf' \\\n",
3121 coeff[x], coeff[x+1], coeff[x+2]),x+=3;
3122 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
3123 (void) FormatLocaleFile(stderr, " -channel B -fx '%+lf*i %+lf*j %+lf' \\\n",
3124 coeff[x], coeff[x+1], coeff[x+2]),x+=3;
3125 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
3126 (image->colorspace == CMYKColorspace))
3127 (void) FormatLocaleFile(stderr, " -channel K -fx '%+lf*i %+lf*j %+lf' \\\n",
3128 coeff[x], coeff[x+1], coeff[x+2]),x+=3;
3129 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
3130 (image->alpha_trait != UndefinedPixelTrait))
3131 (void) FormatLocaleFile(stderr, " -channel A -fx '%+lf*i %+lf*j %+lf' \\\n",
3132 coeff[x], coeff[x+1], coeff[x+2]),x+=3;
3133 break;
3134 }
3135 case BilinearColorInterpolate:
3136 {
3137 ssize_t x=0;
3138 (void) FormatLocaleFile(stderr, "Bilinear Sparse Color\n");
3139 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
3140 (void) FormatLocaleFile(stderr, " -channel R -fx '%+lf*i %+lf*j %+lf*i*j %+lf;\n",
3141 coeff[ x ], coeff[x+1],
3142 coeff[x+2], coeff[x+3]),x+=4;
3143 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
3144 (void) FormatLocaleFile(stderr, " -channel G -fx '%+lf*i %+lf*j %+lf*i*j %+lf;\n",
3145 coeff[ x ], coeff[x+1],
3146 coeff[x+2], coeff[x+3]),x+=4;
3147 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
3148 (void) FormatLocaleFile(stderr, " -channel B -fx '%+lf*i %+lf*j %+lf*i*j %+lf;\n",
3149 coeff[ x ], coeff[x+1],
3150 coeff[x+2], coeff[x+3]),x+=4;
3151 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
3152 (image->colorspace == CMYKColorspace))
3153 (void) FormatLocaleFile(stderr, " -channel K -fx '%+lf*i %+lf*j %+lf*i*j %+lf;\n",
3154 coeff[ x ], coeff[x+1],
3155 coeff[x+2], coeff[x+3]),x+=4;
3156 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
3157 (image->alpha_trait != UndefinedPixelTrait))
3158 (void) FormatLocaleFile(stderr, " -channel A -fx '%+lf*i %+lf*j %+lf*i*j %+lf;\n",
3159 coeff[ x ], coeff[x+1],
3160 coeff[x+2], coeff[x+3]),x+=4;
3161 break;
3162 }
3163 default:
3164 /* sparse color method is too complex for FX emulation */
3165 break;
3166 }
3167 }
3168
3169 /* Generate new image for generated interpolated gradient.
3170 * ASIDE: Actually we could have just replaced the colors of the original
3171 * image, but IM Core policy, is if storage class could change then clone
3172 * the image.
3173 */
3174
3175 sparse_image=CloneImage(image,0,0,MagickTrue,exception);
3176 if (sparse_image == (Image *) NULL)
3177 return((Image *) NULL);
3178 if (SetImageStorageClass(sparse_image,DirectClass,exception) == MagickFalse)
3179 { /* if image is ColorMapped - change it to DirectClass */
3180 sparse_image=DestroyImage(sparse_image);
3181 return((Image *) NULL);
3182 }
3183 if (IsGrayColorspace(sparse_image->colorspace) != MagickFalse)
3184 (void) SetImageColorspace(sparse_image,sRGBColorspace,exception);
3185 { /* ----- MAIN CODE ----- */
3186 CacheView
3187 *sparse_view;
3188
3189 MagickBooleanType
3190 status;
3191
3192 MagickOffsetType
3193 progress;
3194
3195 ssize_t
3196 j;
3197
3198 status=MagickTrue;
3199 progress=0;
3200 sparse_view=AcquireAuthenticCacheView(sparse_image,exception);
3201#if defined(MAGICKCORE_OPENMP_SUPPORT)
3202 #pragma omp parallel for schedule(static) shared(progress,status) \
3203 magick_number_threads(image,sparse_image,sparse_image->rows,1)
3204#endif
3205 for (j=0; j < (ssize_t) sparse_image->rows; j++)
3206 {
3207 MagickBooleanType
3208 sync;
3209
3210 PixelInfo
3211 pixel; /* pixel to assign to distorted image */
3212
3213 Quantum
3214 *magick_restrict q;
3215
3216 ssize_t
3217 i;
3218
3219 q=GetCacheViewAuthenticPixels(sparse_view,0,j,sparse_image->columns,1,
3220 exception);
3221 if (q == (Quantum *) NULL)
3222 {
3223 status=MagickFalse;
3224 continue;
3225 }
3226 GetPixelInfo(sparse_image,&pixel);
3227 for (i=0; i < (ssize_t) sparse_image->columns; i++)
3228 {
3229 GetPixelInfoPixel(sparse_image,q,&pixel);
3230 switch (sparse_method)
3231 {
3232 case BarycentricColorInterpolate:
3233 {
3234 ssize_t x=0;
3235 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3236 pixel.red = coeff[x]*i +coeff[x+1]*j
3237 +coeff[x+2], x+=3;
3238 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3239 pixel.green = coeff[x]*i +coeff[x+1]*j
3240 +coeff[x+2], x+=3;
3241 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3242 pixel.blue = coeff[x]*i +coeff[x+1]*j
3243 +coeff[x+2], x+=3;
3244 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3245 (sparse_image->colorspace == CMYKColorspace))
3246 pixel.black = coeff[x]*i +coeff[x+1]*j
3247 +coeff[x+2], x+=3;
3248 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3249 (sparse_image->alpha_trait != UndefinedPixelTrait))
3250 pixel.alpha = coeff[x]*i +coeff[x+1]*j
3251 +coeff[x+2], x+=3;
3252 break;
3253 }
3254 case BilinearColorInterpolate:
3255 {
3256 ssize_t x=0;
3257 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3258 pixel.red = coeff[x]*i + coeff[x+1]*j +
3259 coeff[x+2]*i*j + coeff[x+3], x+=4;
3260 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3261 pixel.green = coeff[x]*i + coeff[x+1]*j +
3262 coeff[x+2]*i*j + coeff[x+3], x+=4;
3263 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3264 pixel.blue = coeff[x]*i + coeff[x+1]*j +
3265 coeff[x+2]*i*j + coeff[x+3], x+=4;
3266 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3267 (image->colorspace == CMYKColorspace))
3268 pixel.black = coeff[x]*i + coeff[x+1]*j +
3269 coeff[x+2]*i*j + coeff[x+3], x+=4;
3270 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3271 (sparse_image->alpha_trait != UndefinedPixelTrait))
3272 pixel.alpha = coeff[x]*i + coeff[x+1]*j +
3273 coeff[x+2]*i*j + coeff[x+3], x+=4;
3274 break;
3275 }
3276 case InverseColorInterpolate:
3277 case ShepardsColorInterpolate:
3278 { /* Inverse (Squared) Distance weights average (IDW) */
3279 double
3280 denominator;
3281
3282 size_t
3283 k;
3284
3285 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3286 pixel.red=0.0;
3287 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3288 pixel.green=0.0;
3289 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3290 pixel.blue=0.0;
3291 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3292 (image->colorspace == CMYKColorspace))
3293 pixel.black=0.0;
3294 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3295 (sparse_image->alpha_trait != UndefinedPixelTrait))
3296 pixel.alpha=0.0;
3297 denominator = 0.0;
3298 for (k=0; k<number_arguments; k+=2+number_colors)
3299 {
3300 double weight =
3301 ((double) i-arguments[ k ])*((double) i-arguments[ k ])
3302 + ((double) j-arguments[k+1])*((double) j-arguments[k+1]);
3303 ssize_t x = (ssize_t) k+2;
3304
3305 weight = pow(weight,coeff[0]); /* inverse of power factor */
3306 weight = ( weight < 1.0 ) ? 1.0 : 1.0/weight;
3307 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3308 pixel.red += arguments[x++]*weight;
3309 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3310 pixel.green += arguments[x++]*weight;
3311 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3312 pixel.blue += arguments[x++]*weight;
3313 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3314 (image->colorspace == CMYKColorspace))
3315 pixel.black += arguments[x++]*weight;
3316 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3317 (sparse_image->alpha_trait != UndefinedPixelTrait))
3318 pixel.alpha += arguments[x++]*weight;
3319 denominator += weight;
3320 }
3321 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3322 pixel.red/=denominator;
3323 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3324 pixel.green/=denominator;
3325 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3326 pixel.blue/=denominator;
3327 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3328 (image->colorspace == CMYKColorspace))
3329 pixel.black/=denominator;
3330 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3331 (sparse_image->alpha_trait != UndefinedPixelTrait))
3332 pixel.alpha/=denominator;
3333 break;
3334 }
3335 case ManhattanColorInterpolate:
3336 {
3337 double
3338 minimum = MagickMaximumValue;
3339
3340 size_t
3341 k;
3342
3343 /*
3344 Just use the closest control point you can find!
3345 */
3346 for (k=0; k<number_arguments; k+=2+number_colors)
3347 {
3348 double distance = fabs((double)i-arguments[ k ])+
3349 fabs((double)j-arguments[k+1]);
3350 if ( distance < minimum ) {
3351 ssize_t x=(ssize_t) k+2;
3352 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3353 pixel.red=arguments[x++];
3354 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3355 pixel.green=arguments[x++];
3356 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3357 pixel.blue=arguments[x++];
3358 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3359 (image->colorspace == CMYKColorspace))
3360 pixel.black=arguments[x++];
3361 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3362 (sparse_image->alpha_trait != UndefinedPixelTrait))
3363 pixel.alpha=arguments[x++];
3364 minimum = distance;
3365 }
3366 }
3367 break;
3368 }
3369 case VoronoiColorInterpolate:
3370 default:
3371 {
3372 double
3373 minimum = MagickMaximumValue;
3374
3375 size_t
3376 k;
3377
3378 /*
3379 Just use the closest control point you can find!
3380 */
3381 for (k=0; k<number_arguments; k+=2+number_colors) {
3382 double distance =
3383 ((double) i-arguments[ k ])*((double) i-arguments[ k ])
3384 + ((double) j-arguments[k+1])*((double) j-arguments[k+1]);
3385 if ( distance < minimum ) {
3386 ssize_t x = (ssize_t) k+2;
3387 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3388 pixel.red=arguments[x++];
3389 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3390 pixel.green=arguments[x++];
3391 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3392 pixel.blue=arguments[x++];
3393 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3394 (image->colorspace == CMYKColorspace))
3395 pixel.black=arguments[x++];
3396 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3397 (sparse_image->alpha_trait != UndefinedPixelTrait))
3398 pixel.alpha=arguments[x++];
3399 minimum = distance;
3400 }
3401 }
3402 break;
3403 }
3404 }
3405 /* set the color directly back into the source image */
3406 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3407 pixel.red=(MagickRealType) ClampPixel((double) QuantumRange*
3408 pixel.red);
3409 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3410 pixel.green=(MagickRealType) ClampPixel((double) QuantumRange*
3411 pixel.green);
3412 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3413 pixel.blue=(MagickRealType) ClampPixel((double) QuantumRange*
3414 pixel.blue);
3415 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3416 (image->colorspace == CMYKColorspace))
3417 pixel.black=(MagickRealType) ClampPixel((double) QuantumRange*
3418 pixel.black);
3419 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3420 (image->alpha_trait != UndefinedPixelTrait))
3421 pixel.alpha=(MagickRealType) ClampPixel((double) QuantumRange*
3422 pixel.alpha);
3423 SetPixelViaPixelInfo(sparse_image,&pixel,q);
3424 q+=(ptrdiff_t) GetPixelChannels(sparse_image);
3425 }
3426 sync=SyncCacheViewAuthenticPixels(sparse_view,exception);
3427 if (sync == MagickFalse)
3428 status=MagickFalse;
3429 if (image->progress_monitor != (MagickProgressMonitor) NULL)
3430 {
3431 MagickBooleanType
3432 proceed;
3433
3434#if defined(MAGICKCORE_OPENMP_SUPPORT)
3435 #pragma omp atomic
3436#endif
3437 progress++;
3438 proceed=SetImageProgress(image,SparseColorTag,progress,image->rows);
3439 if (proceed == MagickFalse)
3440 status=MagickFalse;
3441 }
3442 }
3443 sparse_view=DestroyCacheView(sparse_view);
3444 if (status == MagickFalse)
3445 sparse_image=DestroyImage(sparse_image);
3446 }
3447 coeff = (double *) RelinquishMagickMemory(coeff);
3448 return(sparse_image);
3449}