MagickCore 7.1.2-22
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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/license/ %
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(CastDoubleToSizeT(floor((order+1.0)*(order+2.0)/2.0)));
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 (((number_arguments-1) % cp_size) != 0)) {
436 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
437 "InvalidArgument", "%s : 'require at least %.20g CPs'",
438 "Polynomial", (double) i);
439 return((double *) NULL);
440 }
441 break;
442 case BilinearReverseDistortion:
443 number_coefficients=4*number_values;
444 break;
445 /*
446 The rest are constants as they are only used for image distorts
447 */
448 case BilinearForwardDistortion:
449 number_coefficients=10; /* 2*4 coeff plus 2 constants */
450 cp_x = 0; /* Reverse src/dest coords for forward mapping */
451 cp_y = 1;
452 cp_values = 2;
453 break;
454#if 0
455 case QuadrilateralDistortion:
456 number_coefficients=19; /* BilinearForward + BilinearReverse */
457#endif
458 break;
459 case ShepardsDistortion:
460 number_coefficients=1; /* The power factor to use */
461 break;
462 case ArcDistortion:
463 number_coefficients=5;
464 break;
465 case ScaleRotateTranslateDistortion:
466 case AffineProjectionDistortion:
467 case Plane2CylinderDistortion:
468 case Cylinder2PlaneDistortion:
469 number_coefficients=6;
470 break;
471 case PolarDistortion:
472 case DePolarDistortion:
473 number_coefficients=8;
474 break;
475 case PerspectiveDistortion:
476 case PerspectiveProjectionDistortion:
477 number_coefficients=9;
478 break;
479 case BarrelDistortion:
480 case BarrelInverseDistortion:
481 number_coefficients=10;
482 break;
483 default:
484 perror("unknown method given"); /* just fail assertion */
485 }
486
487 /* allocate the array of coefficients needed */
488 coeff=(double *) AcquireQuantumMemory(number_coefficients,sizeof(*coeff));
489 if (coeff == (double *) NULL)
490 {
491 (void) ThrowMagickException(exception,GetMagickModule(),
492 ResourceLimitError,"MemoryAllocationFailed","%s",
493 "GenerateCoefficients");
494 return((double *) NULL);
495 }
496
497 /* zero out coefficients array */
498 for (i=0; i < number_coefficients; i++)
499 coeff[i] = 0.0;
500
501 switch (*method)
502 {
503 case AffineDistortion:
504 {
505 /* Affine Distortion
506 v = c0*x + c1*y + c2
507 for each 'value' given
508
509 Input Arguments are sets of control points...
510 For Distort Images u,v, x,y ...
511 For Sparse Gradients x,y, r,g,b ...
512 */
513 if ( number_arguments%cp_size != 0 ||
514 number_arguments < cp_size ) {
515 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
516 "InvalidArgument", "%s : 'require at least %.20g CPs'",
517 "Affine", 1.0);
518 coeff=(double *) RelinquishMagickMemory(coeff);
519 return((double *) NULL);
520 }
521 /* handle special cases of not enough arguments */
522 if ( number_arguments == cp_size ) {
523 /* Only 1 CP Set Given */
524 if ( cp_values == 0 ) {
525 /* image distortion - translate the image */
526 coeff[0] = 1.0;
527 coeff[2] = arguments[0] - arguments[2];
528 coeff[4] = 1.0;
529 coeff[5] = arguments[1] - arguments[3];
530 }
531 else {
532 /* sparse gradient - use the values directly */
533 for (i=0; i<number_values; i++)
534 coeff[i*3+2] = arguments[cp_values+i];
535 }
536 }
537 else {
538 /* 2 or more points (usually 3) given.
539 Solve a least squares simultaneous equation for coefficients.
540 */
541 double
542 **matrix,
543 **vectors,
544 terms[3];
545
546 MagickBooleanType
547 status;
548
549 /* create matrix, and a fake vectors matrix */
550 matrix=AcquireMagickMatrix(3UL,3UL);
551 vectors=(double **) AcquireQuantumMemory(number_values,
552 sizeof(*vectors));
553 if (matrix == (double **) NULL || vectors == (double **) NULL)
554 {
555 matrix = RelinquishMagickMatrix(matrix, 3UL);
556 vectors = (double **) RelinquishMagickMemory(vectors);
557 coeff = (double *) RelinquishMagickMemory(coeff);
558 (void) ThrowMagickException(exception,GetMagickModule(),
559 ResourceLimitError,"MemoryAllocationFailed",
560 "%s", "DistortCoefficients");
561 return((double *) NULL);
562 }
563 /* fake a number_values x3 vectors matrix from coefficients array */
564 for (i=0; i < number_values; i++)
565 vectors[i] = &(coeff[i*3]);
566 /* Add given control point pairs for least squares solving */
567 for (i=0; i < number_arguments; i+=cp_size) {
568 terms[0] = arguments[i+cp_x]; /* x */
569 terms[1] = arguments[i+cp_y]; /* y */
570 terms[2] = 1; /* 1 */
571 LeastSquaresAddTerms(matrix,vectors,terms,
572 &(arguments[i+cp_values]),3UL,number_values);
573 }
574 if ( number_arguments == 2*cp_size ) {
575 /* Only two pairs were given, but we need 3 to solve the affine.
576 Fake extra coordinates by rotating p1 around p0 by 90 degrees.
577 x2 = x0 - (y1-y0) y2 = y0 + (x1-x0)
578 */
579 terms[0] = arguments[cp_x]
580 - ( arguments[cp_size+cp_y] - arguments[cp_y] ); /* x2 */
581 terms[1] = arguments[cp_y] +
582 + ( arguments[cp_size+cp_x] - arguments[cp_x] ); /* y2 */
583 terms[2] = 1; /* 1 */
584 if ( cp_values == 0 ) {
585 /* Image Distortion - rotate the u,v coordinates too */
586 double
587 uv2[2];
588 uv2[0] = arguments[0] - arguments[5] + arguments[1]; /* u2 */
589 uv2[1] = arguments[1] + arguments[4] - arguments[0]; /* v2 */
590 LeastSquaresAddTerms(matrix,vectors,terms,uv2,3UL,2UL);
591 }
592 else {
593 /* Sparse Gradient - use values of p0 for linear gradient */
594 LeastSquaresAddTerms(matrix,vectors,terms,
595 &(arguments[cp_values]),3UL,number_values);
596 }
597 }
598 /* Solve for LeastSquares Coefficients */
599 status=GaussJordanElimination(matrix,vectors,3UL,number_values);
600 matrix = RelinquishMagickMatrix(matrix, 3UL);
601 vectors = (double **) RelinquishMagickMemory(vectors);
602 if ( status == MagickFalse ) {
603 coeff = (double *) RelinquishMagickMemory(coeff);
604 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
605 "InvalidArgument","%s : 'Unsolvable Matrix'",
606 CommandOptionToMnemonic(MagickDistortOptions, *method) );
607 return((double *) NULL);
608 }
609 }
610 return(coeff);
611 }
612 case RigidAffineDistortion:
613 {
614 double
615 inverse[6],
616 **matrix,
617 terms[5],
618 *vectors[1];
619
620 MagickBooleanType
621 status;
622
623 /*
624 Rigid affine (also known as a Euclidean transform), restricts affine
625 coefficients to 4 (S, R, Tx, Ty) with Sy=Sx and Ry = -Rx so that one has
626 only scale, rotation and translation. No skew.
627 */
628 if (((number_arguments % cp_size) != 0) || (number_arguments < cp_size))
629 {
630 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
631 "InvalidArgument", "%s : 'require at least %.20g CPs'",
632 CommandOptionToMnemonic(MagickDistortOptions,*method),2.0);
633 coeff=(double *) RelinquishMagickMemory(coeff);
634 return((double *) NULL);
635 }
636 /*
637 Rigid affine requires a 4x4 least-squares matrix (zeroed).
638 */
639 matrix=AcquireMagickMatrix(4UL,4UL);
640 if (matrix == (double **) NULL)
641 {
642 coeff=(double *) RelinquishMagickMemory(coeff);
643 (void) ThrowMagickException(exception,GetMagickModule(),
644 ResourceLimitError,"MemoryAllocationFailed","%s",
645 CommandOptionToMnemonic(MagickDistortOptions,*method));
646 return((double *) NULL);
647 }
648 /*
649 Add control points for least squares solving.
650 */
651 vectors[0]=(&(coeff[0]));
652 for (i=0; i < number_arguments; i+=4)
653 {
654 terms[0]=arguments[i+0];
655 terms[1]=(-arguments[i+1]);
656 terms[2]=1.0;
657 terms[3]=0.0;
658 LeastSquaresAddTerms(matrix,vectors,terms,&(arguments[i+2]),4UL,1UL);
659 terms[0]=arguments[i+1];
660 terms[1]=arguments[i+0];
661 terms[2]=0.0;
662 terms[3]=1.0;
663 LeastSquaresAddTerms(matrix,vectors,terms,&(arguments[i+3]),4UL,1UL);
664 }
665 /*
666 Solve for least-squares coefficients.
667 */
668 status=GaussJordanElimination(matrix,vectors,4UL,1UL);
669 matrix=RelinquishMagickMatrix(matrix,4UL);
670 if (status == MagickFalse)
671 {
672 coeff=(double *) RelinquishMagickMemory(coeff);
673 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
674 "InvalidArgument","%s : 'Unsolvable Matrix'",
675 CommandOptionToMnemonic(MagickDistortOptions,*method));
676 return((double *) NULL);
677 }
678 /*
679 Convert (S, R, Tx, Ty) to an affine projection.
680 */
681 inverse[0]=coeff[0];
682 inverse[1]=coeff[1];
683 inverse[2]=(-coeff[1]);
684 inverse[3]=coeff[0];
685 inverse[4]=coeff[2];
686 inverse[5]=coeff[3];
687 AffineArgsToCoefficients(inverse);
688 InvertAffineCoefficients(inverse,coeff);
689 *method=AffineDistortion;
690 return(coeff);
691 }
692 case AffineProjectionDistortion:
693 {
694 /*
695 Arguments: Affine Matrix (forward mapping)
696 Arguments sx, rx, ry, sy, tx, ty
697 Where u = sx*x + ry*y + tx
698 v = rx*x + sy*y + ty
699
700 Returns coefficients (in there inverse form) ordered as...
701 sx ry tx rx sy ty
702
703 AffineProjection Distortion Notes...
704 + Will only work with a 2 number_values for Image Distortion
705 + Can not be used for generating a sparse gradient (interpolation)
706 */
707 double inverse[8];
708 if (number_arguments != 6) {
709 coeff = (double *) RelinquishMagickMemory(coeff);
710 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
711 "InvalidArgument","%s : 'Needs 6 coeff values'",
712 CommandOptionToMnemonic(MagickDistortOptions, *method) );
713 return((double *) NULL);
714 }
715 /* FUTURE: trap test for sx*sy-rx*ry == 0 (determinant = 0, no inverse) */
716 for(i=0; i<6UL; i++ )
717 inverse[i] = arguments[i];
718 AffineArgsToCoefficients(inverse); /* map into coefficients */
719 InvertAffineCoefficients(inverse, coeff); /* invert */
720 *method = AffineDistortion;
721
722 return(coeff);
723 }
724 case ScaleRotateTranslateDistortion:
725 {
726 /* Scale, Rotate and Translate Distortion
727 An alternative Affine Distortion
728 Argument options, by number of arguments given:
729 7: x,y, sx,sy, a, nx,ny
730 6: x,y, s, a, nx,ny
731 5: x,y, sx,sy, a
732 4: x,y, s, a
733 3: x,y, a
734 2: s, a
735 1: a
736 Where actions are (in order of application)
737 x,y 'center' of transforms (default = image center)
738 sx,sy scale image by this amount (default = 1)
739 a angle of rotation (argument required)
740 nx,ny move 'center' here (default = x,y or no movement)
741 And convert to affine mapping coefficients
742
743 ScaleRotateTranslate Distortion Notes...
744 + Does not use a set of CPs in any normal way
745 + Will only work with a 2 number_valuesal Image Distortion
746 + Cannot be used for generating a sparse gradient (interpolation)
747 */
748 double
749 cosine, sine,
750 x,y,sx,sy,a,nx,ny;
751
752 /* set default center, and default scale */
753 x = nx = (double)(image->columns)/2.0 + (double)image->page.x;
754 y = ny = (double)(image->rows)/2.0 + (double)image->page.y;
755 sx = sy = 1.0;
756 switch ( number_arguments ) {
757 case 0:
758 coeff = (double *) RelinquishMagickMemory(coeff);
759 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
760 "InvalidArgument","%s : 'Needs at least 1 argument'",
761 CommandOptionToMnemonic(MagickDistortOptions, *method) );
762 return((double *) NULL);
763 case 1:
764 a = arguments[0];
765 break;
766 case 2:
767 sx = sy = arguments[0];
768 a = arguments[1];
769 break;
770 default:
771 x = nx = arguments[0];
772 y = ny = arguments[1];
773 switch ( number_arguments ) {
774 case 3:
775 a = arguments[2];
776 break;
777 case 4:
778 sx = sy = arguments[2];
779 a = arguments[3];
780 break;
781 case 5:
782 sx = arguments[2];
783 sy = arguments[3];
784 a = arguments[4];
785 break;
786 case 6:
787 sx = sy = arguments[2];
788 a = arguments[3];
789 nx = arguments[4];
790 ny = arguments[5];
791 break;
792 case 7:
793 sx = arguments[2];
794 sy = arguments[3];
795 a = arguments[4];
796 nx = arguments[5];
797 ny = arguments[6];
798 break;
799 default:
800 coeff = (double *) RelinquishMagickMemory(coeff);
801 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
802 "InvalidArgument","%s : 'Too Many Arguments (7 or less)'",
803 CommandOptionToMnemonic(MagickDistortOptions, *method) );
804 return((double *) NULL);
805 }
806 break;
807 }
808 /* Trap if sx or sy == 0 -- image is scaled out of existence! */
809 if ( fabs(sx) < MagickEpsilon || fabs(sy) < MagickEpsilon ) {
810 coeff = (double *) RelinquishMagickMemory(coeff);
811 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
812 "InvalidArgument","%s : 'Zero Scale Given'",
813 CommandOptionToMnemonic(MagickDistortOptions, *method) );
814 return((double *) NULL);
815 }
816 /* Save the given arguments as an affine distortion */
817 a=DegreesToRadians(a); cosine=cos(a); sine=sin(a);
818
819 *method = AffineDistortion;
820 coeff[0]=cosine/sx;
821 coeff[1]=sine/sx;
822 coeff[2]=x-nx*coeff[0]-ny*coeff[1];
823 coeff[3]=(-sine)/sy;
824 coeff[4]=cosine/sy;
825 coeff[5]=y-nx*coeff[3]-ny*coeff[4];
826 return(coeff);
827 }
828 case PerspectiveDistortion:
829 { /*
830 Perspective Distortion (a ratio of affine distortions)
831
832 p(x,y) c0*x + c1*y + c2
833 u = ------ = ------------------
834 r(x,y) c6*x + c7*y + 1
835
836 q(x,y) c3*x + c4*y + c5
837 v = ------ = ------------------
838 r(x,y) c6*x + c7*y + 1
839
840 c8 = Sign of 'r', or the denominator affine, for the actual image.
841 This determines what part of the distorted image is 'ground'
842 side of the horizon, the other part is 'sky' or invalid.
843 Valid values are +1.0 or -1.0 only.
844
845 Input Arguments are sets of control points...
846 For Distort Images u,v, x,y ...
847 For Sparse Gradients x,y, r,g,b ...
848
849 Perspective Distortion Notes...
850 + Can be thought of as ratio of 3 affine transformations
851 + Not separable: r() or c6 and c7 are used by both equations
852 + All 8 coefficients must be determined simultaneously
853 + Will only work with a 2 number_valuesal Image Distortion
854 + Can not be used for generating a sparse gradient (interpolation)
855 + It is not linear, but is simple to generate an inverse
856 + All lines within an image remain lines.
857 + but distances between points may vary.
858 */
859 double
860 **matrix,
861 *vectors[1],
862 terms[8];
863
864 size_t
865 cp_u = cp_values,
866 cp_v = cp_values+1;
867
868 MagickBooleanType
869 status;
870
871 if ( number_arguments%cp_size != 0 ||
872 number_arguments < cp_size*4 ) {
873 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
874 "InvalidArgument", "%s : 'require at least %.20g CPs'",
875 CommandOptionToMnemonic(MagickDistortOptions, *method), 4.0);
876 coeff=(double *) RelinquishMagickMemory(coeff);
877 return((double *) NULL);
878 }
879 /* fake 1x8 vectors matrix directly using the coefficients array */
880 vectors[0] = &(coeff[0]);
881 /* 8x8 least-squares matrix (zeroed) */
882 matrix = AcquireMagickMatrix(8UL,8UL);
883 if (matrix == (double **) NULL) {
884 coeff=(double *) RelinquishMagickMemory(coeff);
885 (void) ThrowMagickException(exception,GetMagickModule(),
886 ResourceLimitError,"MemoryAllocationFailed",
887 "%s", "DistortCoefficients");
888 return((double *) NULL);
889 }
890 /* Add control points for least squares solving */
891 for (i=0; i < number_arguments; i+=4) {
892 terms[0]=arguments[i+cp_x]; /* c0*x */
893 terms[1]=arguments[i+cp_y]; /* c1*y */
894 terms[2]=1.0; /* c2*1 */
895 terms[3]=0.0;
896 terms[4]=0.0;
897 terms[5]=0.0;
898 terms[6]=-terms[0]*arguments[i+cp_u]; /* 1/(c6*x) */
899 terms[7]=-terms[1]*arguments[i+cp_u]; /* 1/(c7*y) */
900 LeastSquaresAddTerms(matrix,vectors,terms,&(arguments[i+cp_u]),
901 8UL,1UL);
902
903 terms[0]=0.0;
904 terms[1]=0.0;
905 terms[2]=0.0;
906 terms[3]=arguments[i+cp_x]; /* c3*x */
907 terms[4]=arguments[i+cp_y]; /* c4*y */
908 terms[5]=1.0; /* c5*1 */
909 terms[6]=-terms[3]*arguments[i+cp_v]; /* 1/(c6*x) */
910 terms[7]=-terms[4]*arguments[i+cp_v]; /* 1/(c7*y) */
911 LeastSquaresAddTerms(matrix,vectors,terms,&(arguments[i+cp_v]),
912 8UL,1UL);
913 }
914 /* Solve for LeastSquares Coefficients */
915 status=GaussJordanElimination(matrix,vectors,8UL,1UL);
916 matrix = RelinquishMagickMatrix(matrix, 8UL);
917 if ( status == MagickFalse ) {
918 coeff = (double *) RelinquishMagickMemory(coeff);
919 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
920 "InvalidArgument","%s : 'Unsolvable Matrix'",
921 CommandOptionToMnemonic(MagickDistortOptions, *method) );
922 return((double *) NULL);
923 }
924 /*
925 Calculate 9'th coefficient! The ground-sky determination.
926 What is sign of the 'ground' in r() denominator affine function?
927 Just use any valid image coordinate (first control point) in
928 destination for determination of what part of view is 'ground'.
929 */
930 coeff[8] = coeff[6]*arguments[cp_x]
931 + coeff[7]*arguments[cp_y] + 1.0;
932 coeff[8] = (coeff[8] < 0.0) ? -1.0 : +1.0;
933
934 return(coeff);
935 }
936 case PerspectiveProjectionDistortion:
937 {
938 /*
939 Arguments: Perspective Coefficients (forward mapping)
940 */
941 if (number_arguments != 8) {
942 coeff = (double *) RelinquishMagickMemory(coeff);
943 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
944 "InvalidArgument", "%s : 'Needs 8 coefficient values'",
945 CommandOptionToMnemonic(MagickDistortOptions, *method));
946 return((double *) NULL);
947 }
948 /* FUTURE: trap test c0*c4-c3*c1 == 0 (determinate = 0, no inverse) */
949 InvertPerspectiveCoefficients(arguments, coeff);
950 /*
951 Calculate 9'th coefficient! The ground-sky determination.
952 What is sign of the 'ground' in r() denominator affine function?
953 Just use any valid image coordinate in destination for determination.
954 For a forward mapped perspective the images 0,0 coord will map to
955 c2,c5 in the distorted image, so set the sign of denominator of that.
956 */
957 coeff[8] = coeff[6]*arguments[2]
958 + coeff[7]*arguments[5] + 1.0;
959 coeff[8] = (coeff[8] < 0.0) ? -1.0 : +1.0;
960 *method = PerspectiveDistortion;
961
962 return(coeff);
963 }
964 case BilinearForwardDistortion:
965 case BilinearReverseDistortion:
966 {
967 /* Bilinear Distortion (Forward mapping)
968 v = c0*x + c1*y + c2*x*y + c3;
969 for each 'value' given
970
971 This is actually a simple polynomial Distortion! The difference
972 however is when we need to reverse the above equation to generate a
973 BilinearForwardDistortion (see below).
974
975 Input Arguments are sets of control points...
976 For Distort Images u,v, x,y ...
977 For Sparse Gradients x,y, r,g,b ...
978
979 */
980 double
981 **matrix,
982 **vectors,
983 terms[4];
984
985 MagickBooleanType
986 status;
987
988 /* check the number of arguments */
989 if ( number_arguments%cp_size != 0 ||
990 number_arguments < cp_size*4 ) {
991 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
992 "InvalidArgument", "%s : 'require at least %.20g CPs'",
993 CommandOptionToMnemonic(MagickDistortOptions, *method), 4.0);
994 coeff=(double *) RelinquishMagickMemory(coeff);
995 return((double *) NULL);
996 }
997 /* create matrix, and a fake vectors matrix */
998 matrix=AcquireMagickMatrix(4UL,4UL);
999 vectors=(double **) AcquireQuantumMemory(number_values,sizeof(*vectors));
1000 if (matrix == (double **) NULL || vectors == (double **) NULL)
1001 {
1002 matrix = RelinquishMagickMatrix(matrix, 4UL);
1003 vectors = (double **) RelinquishMagickMemory(vectors);
1004 coeff = (double *) RelinquishMagickMemory(coeff);
1005 (void) ThrowMagickException(exception,GetMagickModule(),
1006 ResourceLimitError,"MemoryAllocationFailed",
1007 "%s", "DistortCoefficients");
1008 return((double *) NULL);
1009 }
1010 /* fake a number_values x4 vectors matrix from coefficients array */
1011 for (i=0; i < number_values; i++)
1012 vectors[i] = &(coeff[i*4]);
1013 /* Add given control point pairs for least squares solving */
1014 for (i=0; i < number_arguments; i+=cp_size) {
1015 terms[0] = arguments[i+cp_x]; /* x */
1016 terms[1] = arguments[i+cp_y]; /* y */
1017 terms[2] = terms[0]*terms[1]; /* x*y */
1018 terms[3] = 1; /* 1 */
1019 LeastSquaresAddTerms(matrix,vectors,terms,
1020 &(arguments[i+cp_values]),4UL,number_values);
1021 }
1022 /* Solve for LeastSquares Coefficients */
1023 status=GaussJordanElimination(matrix,vectors,4UL,number_values);
1024 matrix = RelinquishMagickMatrix(matrix, 4UL);
1025 vectors = (double **) RelinquishMagickMemory(vectors);
1026 if ( status == MagickFalse ) {
1027 coeff = (double *) RelinquishMagickMemory(coeff);
1028 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1029 "InvalidArgument","%s : 'Unsolvable Matrix'",
1030 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1031 return((double *) NULL);
1032 }
1033 if ( *method == BilinearForwardDistortion ) {
1034 /* Bilinear Forward Mapped Distortion
1035
1036 The above least-squares solved for coefficients but in the forward
1037 direction, due to changes to indexing constants.
1038
1039 i = c0*x + c1*y + c2*x*y + c3;
1040 j = c4*x + c5*y + c6*x*y + c7;
1041
1042 where i,j are in the destination image, NOT the source.
1043
1044 Reverse Pixel mapping however needs to use reverse of these
1045 functions. It required a full page of algebra to work out the
1046 reversed mapping formula, but resolves down to the following...
1047
1048 c8 = c0*c5-c1*c4;
1049 c9 = 2*(c2*c5-c1*c6); // '2*a' in the quadratic formula
1050
1051 i = i - c3; j = j - c7;
1052 b = c6*i - c2*j + c8; // So that a*y^2 + b*y + c == 0
1053 c = c4*i - c0*j; // y = ( -b +- sqrt(bb - 4ac) ) / (2*a)
1054
1055 r = b*b - c9*(c+c);
1056 if ( c9 != 0 )
1057 y = ( -b + sqrt(r) ) / c9;
1058 else
1059 y = -c/b;
1060
1061 x = ( i - c1*y) / ( c1 - c2*y );
1062
1063 NB: if 'r' is negative there is no solution!
1064 NB: the sign of the sqrt() should be negative if image becomes
1065 flipped or flopped, or crosses over itself.
1066 NB: technically coefficient c5 is not needed, anymore,
1067 but kept for completeness.
1068
1069 See Anthony Thyssen <A.Thyssen@griffith.edu.au>
1070 or Fred Weinhaus <fmw@alink.net> for more details.
1071
1072 */
1073 coeff[8] = coeff[0]*coeff[5] - coeff[1]*coeff[4];
1074 coeff[9] = 2*(coeff[2]*coeff[5] - coeff[1]*coeff[6]);
1075 }
1076 return(coeff);
1077 }
1078#if 0
1079 case QuadrilateralDistortion:
1080 {
1081 /* Map a Quadrilateral to a unit square using BilinearReverse
1082 Then map that unit square back to the final Quadrilateral
1083 using BilinearForward.
1084
1085 Input Arguments are sets of control points...
1086 For Distort Images u,v, x,y ...
1087 For Sparse Gradients x,y, r,g,b ...
1088
1089 */
1090 /* UNDER CONSTRUCTION */
1091 return(coeff);
1092 }
1093#endif
1094
1095 case PolynomialDistortion:
1096 {
1097 /* Polynomial Distortion
1098
1099 First two coefficients are used to hole global polynomial information
1100 c0 = Order of the polynomial being created
1101 c1 = number_of_terms in one polynomial equation
1102
1103 Rest of the coefficients map to the equations....
1104 v = c0 + c1*x + c2*y + c3*x*y + c4*x^2 + c5*y^2 + c6*x^3 + ...
1105 for each 'value' (number_values of them) given.
1106 As such total coefficients = 2 + number_terms * number_values
1107
1108 Input Arguments are sets of control points...
1109 For Distort Images order [u,v, x,y] ...
1110 For Sparse Gradients order [x,y, r,g,b] ...
1111
1112 Polynomial Distortion Notes...
1113 + UNDER DEVELOPMENT -- Do not expect this to remain as is.
1114 + Currently polynomial is a reversed mapped distortion.
1115 + Order 1.5 is fudged to map into a bilinear distortion.
1116 though it is not the same order as that distortion.
1117 */
1118 double
1119 **matrix,
1120 **vectors,
1121 *terms;
1122
1123 size_t
1124 nterms; /* number of polynomial terms per number_values */
1125
1126 ssize_t
1127 j;
1128
1129 MagickBooleanType
1130 status;
1131
1132 /* first two coefficients hold polynomial order information */
1133 coeff[0] = arguments[0];
1134 coeff[1] = (double) poly_number_terms(arguments[0]);
1135 nterms = CastDoubleToSizeT(coeff[1]);
1136
1137 /* create matrix, a fake vectors matrix, and least sqs terms */
1138 matrix=AcquireMagickMatrix(nterms,nterms);
1139 vectors=(double **) AcquireQuantumMemory(number_values,
1140 sizeof(*vectors));
1141 terms=(double *) AcquireQuantumMemory(nterms,sizeof(*terms));
1142 if ((matrix == (double **) NULL) || (vectors == (double **) NULL) ||
1143 (terms == (double *) NULL))
1144 {
1145 matrix = RelinquishMagickMatrix(matrix, nterms);
1146 vectors = (double **) RelinquishMagickMemory(vectors);
1147 terms = (double *) RelinquishMagickMemory(terms);
1148 coeff = (double *) RelinquishMagickMemory(coeff);
1149 (void) ThrowMagickException(exception,GetMagickModule(),
1150 ResourceLimitError,"MemoryAllocationFailed",
1151 "%s", "DistortCoefficients");
1152 return((double *) NULL);
1153 }
1154 /* fake a number_values x3 vectors matrix from coefficients array */
1155 for (i=0; i < number_values; i++)
1156 vectors[i] = &(coeff[2+i*nterms]);
1157 /* Add given control point pairs for least squares solving */
1158 for (i=1; i < number_arguments; i+=cp_size) { /* NB: start = 1 not 0 */
1159 for (j=0; j < (ssize_t) nterms; j++)
1160 terms[j] = poly_basis_fn(j,arguments[i+cp_x],arguments[i+cp_y]);
1161 LeastSquaresAddTerms(matrix,vectors,terms,
1162 &(arguments[i+cp_values]),nterms,number_values);
1163 }
1164 terms = (double *) RelinquishMagickMemory(terms);
1165 /* Solve for LeastSquares Coefficients */
1166 status=GaussJordanElimination(matrix,vectors,nterms,number_values);
1167 matrix = RelinquishMagickMatrix(matrix, nterms);
1168 vectors = (double **) RelinquishMagickMemory(vectors);
1169 if ( status == MagickFalse ) {
1170 coeff = (double *) RelinquishMagickMemory(coeff);
1171 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1172 "InvalidArgument","%s : 'Unsolvable Matrix'",
1173 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1174 return((double *) NULL);
1175 }
1176 return(coeff);
1177 }
1178 case ArcDistortion:
1179 {
1180 /* Arc Distortion
1181 Args: arc_width rotate top_edge_radius bottom_edge_radius
1182 All but first argument are optional
1183 arc_width The angle over which to arc the image side-to-side
1184 rotate Angle to rotate image from vertical center
1185 top_radius Set top edge of source image at this radius
1186 bottom_radius Set bottom edge to this radius (radial scaling)
1187
1188 By default, if the radii arguments are nor provided the image radius
1189 is calculated so the horizontal center-line is fits the given arc
1190 without scaling.
1191
1192 The output image size is ALWAYS adjusted to contain the whole image,
1193 and an offset is given to position image relative to the 0,0 point of
1194 the origin, allowing users to use relative positioning onto larger
1195 background (via -flatten).
1196
1197 The arguments are converted to these coefficients
1198 c0: angle for center of source image
1199 c1: angle scale for mapping to source image
1200 c2: radius for top of source image
1201 c3: radius scale for mapping source image
1202 c4: centerline of arc within source image
1203
1204 Note the coefficients use a center angle, so asymptotic join is
1205 furthest from both sides of the source image. This also means that
1206 for arc angles greater than 360 the sides of the image will be
1207 trimmed equally.
1208
1209 Arc Distortion Notes...
1210 + Does not use a set of CPs
1211 + Will only work with Image Distortion
1212 + Can not be used for generating a sparse gradient (interpolation)
1213 */
1214 if ( number_arguments >= 1 && arguments[0] < MagickEpsilon ) {
1215 coeff = (double *) RelinquishMagickMemory(coeff);
1216 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1217 "InvalidArgument","%s : 'Arc Angle Too Small'",
1218 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1219 return((double *) NULL);
1220 }
1221 if ( number_arguments >= 3 && arguments[2] < MagickEpsilon ) {
1222 coeff = (double *) RelinquishMagickMemory(coeff);
1223 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1224 "InvalidArgument","%s : 'Outer Radius Too Small'",
1225 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1226 return((double *) NULL);
1227 }
1228 coeff[0] = -MagickPI2; /* -90, place at top! */
1229 if ( number_arguments >= 1 )
1230 coeff[1] = DegreesToRadians(arguments[0]);
1231 else
1232 coeff[1] = MagickPI2; /* zero arguments - center is at top */
1233 if ( number_arguments >= 2 )
1234 coeff[0] += DegreesToRadians(arguments[1]);
1235 coeff[0] /= Magick2PI; /* normalize radians */
1236 coeff[0] -= MagickRound(coeff[0]);
1237 coeff[0] *= Magick2PI; /* de-normalize back to radians */
1238 coeff[3] = (double)image->rows-1;
1239 coeff[2] = (double)image->columns/coeff[1] + coeff[3]/2.0;
1240 if ( number_arguments >= 3 ) {
1241 if ( number_arguments >= 4 )
1242 coeff[3] = arguments[2] - arguments[3];
1243 else
1244 coeff[3] *= arguments[2]/coeff[2];
1245 coeff[2] = arguments[2];
1246 }
1247 coeff[4] = ((double)image->columns-1.0)/2.0;
1248
1249 return(coeff);
1250 }
1251 case PolarDistortion:
1252 case DePolarDistortion:
1253 {
1254 /* (De)Polar Distortion (same set of arguments)
1255 Args: Rmax, Rmin, Xcenter,Ycenter, Afrom,Ato
1256 DePolar can also have the extra arguments of Width, Height
1257
1258 Coefficients 0 to 5 is the sanitized version first 6 input args
1259 Coefficient 6 is the angle to coord ratio and visa-versa
1260 Coefficient 7 is the radius to coord ratio and visa-versa
1261
1262 WARNING: It is possible for Radius max<min and/or Angle from>to
1263 */
1264 if ( number_arguments == 3
1265 || ( number_arguments > 6 && *method == PolarDistortion )
1266 || number_arguments > 8 ) {
1267 (void) ThrowMagickException(exception,GetMagickModule(),
1268 OptionError,"InvalidArgument", "%s : number of arguments",
1269 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1270 coeff=(double *) RelinquishMagickMemory(coeff);
1271 return((double *) NULL);
1272 }
1273 /* Rmax - if 0 calculate appropriate value */
1274 if ( number_arguments >= 1 )
1275 coeff[0] = arguments[0];
1276 else
1277 coeff[0] = 0.0;
1278 /* Rmin - usually 0 */
1279 coeff[1] = number_arguments >= 2 ? arguments[1] : 0.0;
1280 /* Center X,Y */
1281 if ( number_arguments >= 4 ) {
1282 coeff[2] = arguments[2];
1283 coeff[3] = arguments[3];
1284 }
1285 else { /* center of actual image */
1286 coeff[2] = (double)(image->columns)/2.0+image->page.x;
1287 coeff[3] = (double)(image->rows)/2.0+image->page.y;
1288 }
1289 /* Angle from,to - about polar center 0 is downward */
1290 coeff[4] = -MagickPI;
1291 if ( number_arguments >= 5 )
1292 coeff[4] = DegreesToRadians(arguments[4]);
1293 coeff[5] = coeff[4];
1294 if ( number_arguments >= 6 )
1295 coeff[5] = DegreesToRadians(arguments[5]);
1296 if ( fabs(coeff[4]-coeff[5]) < MagickEpsilon )
1297 coeff[5] += Magick2PI; /* same angle is a full circle */
1298 /* if radius 0 or negative, its a special value... */
1299 if ( coeff[0] < MagickEpsilon ) {
1300 /* Use closest edge if radius == 0 */
1301 if ( fabs(coeff[0]) < MagickEpsilon ) {
1302 coeff[0]=MagickMin(fabs(coeff[2]-image->page.x),
1303 fabs(coeff[3]-image->page.y));
1304 coeff[0]=MagickMin(coeff[0],
1305 fabs(coeff[2]-image->page.x-image->columns));
1306 coeff[0]=MagickMin(coeff[0],
1307 fabs(coeff[3]-image->page.y-image->rows));
1308 }
1309 /* furthest diagonal if radius == -1 */
1310 if ( fabs(-1.0-coeff[0]) < MagickEpsilon ) {
1311 double rx,ry;
1312 rx = coeff[2]-image->page.x;
1313 ry = coeff[3]-image->page.y;
1314 coeff[0] = rx*rx+ry*ry;
1315 ry = coeff[3]-image->page.y-image->rows;
1316 coeff[0] = MagickMax(coeff[0],rx*rx+ry*ry);
1317 rx = coeff[2]-image->page.x-image->columns;
1318 coeff[0] = MagickMax(coeff[0],rx*rx+ry*ry);
1319 ry = coeff[3]-image->page.y;
1320 coeff[0] = MagickMax(coeff[0],rx*rx+ry*ry);
1321 coeff[0] = sqrt(coeff[0]);
1322 }
1323 }
1324 /* IF Rmax <= 0 or Rmin < 0 OR Rmax < Rmin, THEN error */
1325 if ( coeff[0] < MagickEpsilon || coeff[1] < -MagickEpsilon
1326 || (coeff[0]-coeff[1]) < MagickEpsilon ) {
1327 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1328 "InvalidArgument", "%s : Invalid Radius",
1329 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1330 coeff=(double *) RelinquishMagickMemory(coeff);
1331 return((double *) NULL);
1332 }
1333 /* conversion ratios */
1334 if ( *method == PolarDistortion ) {
1335 coeff[6]=(double) image->columns/(coeff[5]-coeff[4]);
1336 coeff[7]=(double) image->rows/(coeff[0]-coeff[1]);
1337 }
1338 else { /* *method == DePolarDistortion */
1339 coeff[6]=(coeff[5]-coeff[4])/image->columns;
1340 coeff[7]=(coeff[0]-coeff[1])/image->rows;
1341 }
1342 return(coeff);
1343 }
1344 case Cylinder2PlaneDistortion:
1345 case Plane2CylinderDistortion:
1346 {
1347 /* 3D Cylinder to/from a Tangential Plane
1348
1349 Projection between a cylinder and flat plain from a point on the
1350 center line of the cylinder.
1351
1352 The two surfaces coincide in 3D space at the given centers of
1353 distortion (perpendicular to projection point) on both images.
1354
1355 Args: FOV_arc_width
1356 Coefficients: FOV(radians), Radius, center_x,y, dest_center_x,y
1357
1358 FOV (Field Of View) the angular field of view of the distortion,
1359 across the width of the image, in degrees. The centers are the
1360 points of least distortion in the input and resulting images.
1361
1362 These centers are however determined later.
1363
1364 Coeff 0 is the FOV angle of view of image width in radians
1365 Coeff 1 is calculated radius of cylinder.
1366 Coeff 2,3 center of distortion of input image
1367 Coefficients 4,5 Center of Distortion of dest (determined later)
1368 */
1369 if ( arguments[0] < MagickEpsilon || arguments[0] > 160.0 ) {
1370 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1371 "InvalidArgument", "%s : Invalid FOV Angle",
1372 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1373 coeff=(double *) RelinquishMagickMemory(coeff);
1374 return((double *) NULL);
1375 }
1376 coeff[0] = DegreesToRadians(arguments[0]);
1377 if ( *method == Cylinder2PlaneDistortion )
1378 /* image is curved around cylinder, so FOV angle (in radians)
1379 * scales directly to image X coordinate, according to its radius.
1380 */
1381 coeff[1] = (double) image->columns/coeff[0];
1382 else
1383 /* radius is distance away from an image with this angular FOV */
1384 coeff[1] = (double) image->columns / ( 2 * tan(coeff[0]/2) );
1385
1386 coeff[2] = (double)(image->columns)/2.0+image->page.x;
1387 coeff[3] = (double)(image->rows)/2.0+image->page.y;
1388 coeff[4] = coeff[2];
1389 coeff[5] = coeff[3]; /* assuming image size is the same */
1390 return(coeff);
1391 }
1392 case BarrelDistortion:
1393 case BarrelInverseDistortion:
1394 {
1395 /* Barrel Distortion
1396 Rs=(A*Rd^3 + B*Rd^2 + C*Rd + D)*Rd
1397 BarrelInv Distortion
1398 Rs=Rd/(A*Rd^3 + B*Rd^2 + C*Rd + D)
1399
1400 Where Rd is the normalized radius from corner to middle of image
1401 Input Arguments are one of the following forms (number of arguments)...
1402 3: A,B,C
1403 4: A,B,C,D
1404 5: A,B,C X,Y
1405 6: A,B,C,D X,Y
1406 8: Ax,Bx,Cx,Dx Ay,By,Cy,Dy
1407 10: Ax,Bx,Cx,Dx Ay,By,Cy,Dy X,Y
1408
1409 Returns 10 coefficient values, which are de-normalized (pixel scale)
1410 Ax, Bx, Cx, Dx, Ay, By, Cy, Dy, Xc, Yc
1411 */
1412 /* Radius de-normalization scaling factor */
1413 double
1414 rscale = 2.0/MagickMin((double) image->columns,(double) image->rows);
1415
1416 /* sanity check number of args must = 3,4,5,6,8,10 or error */
1417 if ( (number_arguments < 3) || (number_arguments == 7) ||
1418 (number_arguments == 9) || (number_arguments > 10) )
1419 {
1420 coeff=(double *) RelinquishMagickMemory(coeff);
1421 (void) ThrowMagickException(exception,GetMagickModule(),
1422 OptionError,"InvalidArgument", "%s : number of arguments",
1423 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1424 return((double *) NULL);
1425 }
1426 /* A,B,C,D coefficients */
1427 coeff[0] = arguments[0];
1428 coeff[1] = arguments[1];
1429 coeff[2] = arguments[2];
1430 if ((number_arguments == 3) || (number_arguments == 5) )
1431 coeff[3] = 1.0 - coeff[0] - coeff[1] - coeff[2];
1432 else
1433 coeff[3] = arguments[3];
1434 /* de-normalize the coefficients */
1435 coeff[0] *= pow(rscale,3.0);
1436 coeff[1] *= rscale*rscale;
1437 coeff[2] *= rscale;
1438 /* Y coefficients: as given OR same as X coefficients */
1439 if ( number_arguments >= 8 ) {
1440 coeff[4] = arguments[4] * pow(rscale,3.0);
1441 coeff[5] = arguments[5] * rscale*rscale;
1442 coeff[6] = arguments[6] * rscale;
1443 coeff[7] = arguments[7];
1444 }
1445 else {
1446 coeff[4] = coeff[0];
1447 coeff[5] = coeff[1];
1448 coeff[6] = coeff[2];
1449 coeff[7] = coeff[3];
1450 }
1451 /* X,Y Center of Distortion (image coordinates) */
1452 if ( number_arguments == 5 ) {
1453 coeff[8] = arguments[3];
1454 coeff[9] = arguments[4];
1455 }
1456 else if ( number_arguments == 6 ) {
1457 coeff[8] = arguments[4];
1458 coeff[9] = arguments[5];
1459 }
1460 else if ( number_arguments == 10 ) {
1461 coeff[8] = arguments[8];
1462 coeff[9] = arguments[9];
1463 }
1464 else {
1465 /* center of the image provided (image coordinates) */
1466 coeff[8] = (double)image->columns/2.0 + image->page.x;
1467 coeff[9] = (double)image->rows/2.0 + image->page.y;
1468 }
1469 return(coeff);
1470 }
1471 case ShepardsDistortion:
1472 {
1473 /* Shepards Distortion input arguments are the coefficients!
1474 Just check the number of arguments is valid!
1475 Args: u1,v1, x1,y1, ...
1476 OR : u1,v1, r1,g1,c1, ...
1477 */
1478 if ( number_arguments%cp_size != 0 ||
1479 number_arguments < cp_size ) {
1480 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1481 "InvalidArgument", "%s : 'requires CP's (4 numbers each)'",
1482 CommandOptionToMnemonic(MagickDistortOptions, *method));
1483 coeff=(double *) RelinquishMagickMemory(coeff);
1484 return((double *) NULL);
1485 }
1486 /* User defined weighting power for Shepard's Method */
1487 { const char *artifact=GetImageArtifact(image,"shepards:power");
1488 if ( artifact != (const char *) NULL ) {
1489 coeff[0]=StringToDouble(artifact,(char **) NULL) / 2.0;
1490 if ( coeff[0] < MagickEpsilon ) {
1491 (void) ThrowMagickException(exception,GetMagickModule(),
1492 OptionError,"InvalidArgument","%s", "-define shepards:power" );
1493 coeff=(double *) RelinquishMagickMemory(coeff);
1494 return((double *) NULL);
1495 }
1496 }
1497 else
1498 coeff[0]=1.0; /* Default power of 2 (Inverse Squared) */
1499 }
1500 return(coeff);
1501 }
1502 default:
1503 break;
1504 }
1505 /* you should never reach this point */
1506 perror("no method handler"); /* just fail assertion */
1507 return((double *) NULL);
1508}
1509␌
1510/*
1511%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1512% %
1513% %
1514% %
1515+ D i s t o r t R e s i z e I m a g e %
1516% %
1517% %
1518% %
1519%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1520%
1521% DistortResizeImage() resize image using the equivalent but slower image
1522% distortion operator. The filter is applied using a EWA cylindrical
1523% resampling. But like resize the final image size is limited to whole pixels
1524% with no effects by virtual-pixels on the result.
1525%
1526% Note that images containing a transparency channel will be twice as slow to
1527% resize as images one without transparency.
1528%
1529% The format of the DistortResizeImage method is:
1530%
1531% Image *DistortResizeImage(const Image *image,const size_t columns,
1532% const size_t rows,ExceptionInfo *exception)
1533%
1534% A description of each parameter follows:
1535%
1536% o image: the image.
1537%
1538% o columns: the number of columns in the resized image.
1539%
1540% o rows: the number of rows in the resized image.
1541%
1542% o exception: return any errors or warnings in this structure.
1543%
1544*/
1545MagickExport Image *DistortResizeImage(const Image *image,const size_t columns,
1546 const size_t rows,ExceptionInfo *exception)
1547{
1548#define DistortResizeImageTag "Distort/Image"
1549
1550 Image
1551 *resize_image,
1552 *tmp_image;
1553
1554 RectangleInfo
1555 crop_area;
1556
1557 double
1558 distort_args[12];
1559
1560 VirtualPixelMethod
1561 vp_save;
1562
1563 /*
1564 Distort resize image.
1565 */
1566 assert(image != (const Image *) NULL);
1567 assert(image->signature == MagickCoreSignature);
1568 assert(exception != (ExceptionInfo *) NULL);
1569 assert(exception->signature == MagickCoreSignature);
1570 if (IsEventLogging() != MagickFalse)
1571 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1572 if ((columns == 0) || (rows == 0))
1573 return((Image *) NULL);
1574 /* Do not short-circuit this resize if final image size is unchanged */
1575
1576 (void) memset(distort_args,0,sizeof(distort_args));
1577 distort_args[4]=(double) image->columns;
1578 distort_args[6]=(double) columns;
1579 distort_args[9]=(double) image->rows;
1580 distort_args[11]=(double) rows;
1581
1582 vp_save=GetImageVirtualPixelMethod(image);
1583
1584 tmp_image=CloneImage(image,0,0,MagickTrue,exception);
1585 if (tmp_image == (Image *) NULL)
1586 return((Image *) NULL);
1587 (void) SetImageVirtualPixelMethod(tmp_image,TransparentVirtualPixelMethod,
1588 exception);
1589
1590 if ((image->alpha_trait & BlendPixelTrait) == 0)
1591 {
1592 /*
1593 Image has no alpha channel, so we are free to use it.
1594 */
1595 (void) SetImageAlphaChannel(tmp_image,SetAlphaChannel,exception);
1596 resize_image=DistortImage(tmp_image,AffineDistortion,12,distort_args,
1597 MagickTrue,exception),
1598 tmp_image=DestroyImage(tmp_image);
1599 if (resize_image == (Image *) NULL)
1600 return((Image *) NULL);
1601 (void) SetImageAlphaChannel(resize_image,OffAlphaChannel,exception);
1602 }
1603 else
1604 {
1605 /*
1606 Image has transparency so handle colors and alpha separately.
1607 Basically we need to separate Virtual-Pixel alpha in the resized
1608 image, so only the actual original images alpha channel is used.
1609
1610 distort alpha channel separately
1611 */
1612 Image
1613 *resize_alpha;
1614
1615 (void) SetImageAlphaChannel(tmp_image,ExtractAlphaChannel,exception);
1616 (void) SetImageAlphaChannel(tmp_image,OpaqueAlphaChannel,exception);
1617 resize_alpha=DistortImage(tmp_image,AffineDistortion,12,distort_args,
1618 MagickTrue,exception),
1619 tmp_image=DestroyImage(tmp_image);
1620 if (resize_alpha == (Image *) NULL)
1621 return((Image *) NULL);
1622
1623 /* distort the actual image containing alpha + VP alpha */
1624 tmp_image=CloneImage(image,0,0,MagickTrue,exception);
1625 if (tmp_image == (Image *) NULL)
1626 return((Image *) NULL);
1627 (void) SetImageVirtualPixelMethod(tmp_image,
1628 TransparentVirtualPixelMethod,exception);
1629 resize_image=DistortImage(tmp_image,AffineDistortion,12,distort_args,
1630 MagickTrue,exception),
1631 tmp_image=DestroyImage(tmp_image);
1632 if (resize_image == (Image *) NULL)
1633 {
1634 resize_alpha=DestroyImage(resize_alpha);
1635 return((Image *) NULL);
1636 }
1637 /* replace resize images alpha with the separately distorted alpha */
1638 (void) SetImageAlphaChannel(resize_image,OffAlphaChannel,exception);
1639 (void) SetImageAlphaChannel(resize_alpha,OffAlphaChannel,exception);
1640 (void) CompositeImage(resize_image,resize_alpha,CopyAlphaCompositeOp,
1641 MagickTrue,0,0,exception);
1642 resize_alpha=DestroyImage(resize_alpha);
1643 resize_image->alpha_trait=image->alpha_trait;
1644 resize_image->compose=image->compose;
1645 }
1646 (void) SetImageVirtualPixelMethod(resize_image,vp_save,exception);
1647
1648 /*
1649 Clean up the results of the Distortion
1650 */
1651 crop_area.width=columns;
1652 crop_area.height=rows;
1653 crop_area.x=0;
1654 crop_area.y=0;
1655
1656 tmp_image=resize_image;
1657 resize_image=CropImage(tmp_image,&crop_area,exception);
1658 tmp_image=DestroyImage(tmp_image);
1659 if (resize_image != (Image *) NULL)
1660 {
1661 resize_image->page.width=0;
1662 resize_image->page.height=0;
1663 }
1664 return(resize_image);
1665}
1666␌
1667/*
1668%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1669% %
1670% %
1671% %
1672% D i s t o r t I m a g e %
1673% %
1674% %
1675% %
1676%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1677%
1678% DistortImage() distorts an image using various distortion methods, by
1679% mapping color lookups of the source image to a new destination image
1680% usually of the same size as the source image, unless 'bestfit' is set to
1681% true.
1682%
1683% If 'bestfit' is enabled, and distortion allows it, the destination image is
1684% adjusted to ensure the whole source 'image' will just fit within the final
1685% destination image, which will be sized and offset accordingly. Also in
1686% many cases the virtual offset of the source image will be taken into
1687% account in the mapping.
1688%
1689% If the '-verbose' control option has been set print to standard error the
1690% equivalent '-fx' formula with coefficients for the function, if practical.
1691%
1692% The format of the DistortImage() method is:
1693%
1694% Image *DistortImage(const Image *image,const DistortMethod method,
1695% const size_t number_arguments,const double *arguments,
1696% MagickBooleanType bestfit, ExceptionInfo *exception)
1697%
1698% A description of each parameter follows:
1699%
1700% o image: the image to be distorted.
1701%
1702% o method: the method of image distortion.
1703%
1704% ArcDistortion always ignores source image offset, and always
1705% 'bestfit' the destination image with the top left corner offset
1706% relative to the polar mapping center.
1707%
1708% Affine, Perspective, and Bilinear, do least squares fitting of the
1709% distortion when more than the minimum number of control point pairs
1710% are provided.
1711%
1712% Perspective, and Bilinear, fall back to a Affine distortion when less
1713% than 4 control point pairs are provided. While Affine distortions
1714% let you use any number of control point pairs, that is Zero pairs is
1715% a No-Op (viewport only) distortion, one pair is a translation and
1716% two pairs of control points do a scale-rotate-translate, without any
1717% shearing.
1718%
1719% o number_arguments: the number of arguments given.
1720%
1721% o arguments: an array of floating point arguments for this method.
1722%
1723% o bestfit: Attempt to 'bestfit' the size of the resulting image.
1724% This also forces the resulting image to be a 'layered' virtual
1725% canvas image. Can be overridden using 'distort:viewport' setting.
1726%
1727% o exception: return any errors or warnings in this structure
1728%
1729% Extra Controls from Image meta-data (artifacts)...
1730%
1731% o "verbose"
1732% Output to stderr alternatives, internal coefficients, and FX
1733% equivalents for the distortion operation (if feasible).
1734% This forms an extra check of the distortion method, and allows users
1735% access to the internal constants IM calculates for the distortion.
1736%
1737% o "distort:viewport"
1738% Directly set the output image canvas area and offset to use for the
1739% resulting image, rather than use the original images canvas, or a
1740% calculated 'bestfit' canvas.
1741%
1742% o "distort:scale"
1743% Scale the size of the output canvas by this amount to provide a
1744% method of Zooming, and for super-sampling the results.
1745%
1746% Other settings that can effect results include
1747%
1748% o 'interpolate' For source image lookups (scale enlargements)
1749%
1750% o 'filter' Set filter to use for area-resampling (scale shrinking).
1751% Set to 'point' to turn off and use 'interpolate' lookup
1752% instead
1753%
1754*/
1755MagickExport Image *DistortImage(const Image *image, DistortMethod method,
1756 const size_t number_arguments,const double *arguments,
1757 MagickBooleanType bestfit,ExceptionInfo *exception)
1758{
1759#define DistortImageTag "Distort/Image"
1760
1761 double
1762 *coeff,
1763 output_scaling;
1764
1765 Image
1766 *distort_image;
1767
1768 RectangleInfo
1769 geometry; /* geometry of the distorted space viewport */
1770
1771 MagickBooleanType
1772 viewport_given;
1773
1774 PixelInfo
1775 invalid; /* the color to assign when distort result is invalid */
1776
1777 assert(image != (Image *) NULL);
1778 assert(image->signature == MagickCoreSignature);
1779 assert(exception != (ExceptionInfo *) NULL);
1780 assert(exception->signature == MagickCoreSignature);
1781 if (IsEventLogging() != MagickFalse)
1782 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1783 /*
1784 Handle Special Compound Distortions
1785 */
1786 if ( method == ResizeDistortion )
1787 {
1788 if ( number_arguments != 2 )
1789 {
1790 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1791 "InvalidArgument","%s : '%s'","Resize",
1792 "Invalid number of args: 2 only");
1793 return((Image *) NULL);
1794 }
1795 distort_image=DistortResizeImage(image,CastDoubleToSizeT(arguments[0]),
1796 CastDoubleToSizeT(arguments[1]),exception);
1797 return(distort_image);
1798 }
1799
1800 /*
1801 Convert input arguments (usually as control points for reverse mapping)
1802 into mapping coefficients to apply the distortion.
1803
1804 Note that some distortions are mapped to other distortions,
1805 and as such do not require specific code after this point.
1806 */
1807 coeff = GenerateCoefficients(image, &method, number_arguments,
1808 arguments, 0, exception);
1809 if ( coeff == (double *) NULL )
1810 return((Image *) NULL);
1811
1812 /*
1813 Determine the size and offset for a 'bestfit' destination.
1814 Usually the four corners of the source image is enough.
1815 */
1816
1817 /* default output image bounds, when no 'bestfit' is requested */
1818 geometry.width=image->columns;
1819 geometry.height=image->rows;
1820 geometry.x=0;
1821 geometry.y=0;
1822
1823 if ( method == ArcDistortion ) {
1824 bestfit = MagickTrue; /* always calculate a 'best fit' viewport */
1825 }
1826
1827 /* Work out the 'best fit', (required for ArcDistortion) */
1828 if ( bestfit ) {
1829 PointInfo
1830 s,d,min,max; /* source, dest coords --mapping--> min, max coords */
1831
1832 MagickBooleanType
1833 fix_bounds = MagickTrue; /* enlarge bounds for VP handling */
1834
1835 s.x=s.y=min.x=max.x=min.y=max.y=0.0; /* keep compiler happy */
1836
1837/* defines to figure out the bounds of the distorted image */
1838#define InitalBounds(p) \
1839{ \
1840 /* printf("%lg,%lg -> %lg,%lg\n", s.x,s.y, d.x,d.y); */ \
1841 min.x = max.x = p.x; \
1842 min.y = max.y = p.y; \
1843}
1844#define ExpandBounds(p) \
1845{ \
1846 /* printf("%lg,%lg -> %lg,%lg\n", s.x,s.y, d.x,d.y); */ \
1847 min.x = MagickMin(min.x,p.x); \
1848 max.x = MagickMax(max.x,p.x); \
1849 min.y = MagickMin(min.y,p.y); \
1850 max.y = MagickMax(max.y,p.y); \
1851}
1852
1853 switch (method)
1854 {
1855 case AffineDistortion:
1856 case RigidAffineDistortion:
1857 { double inverse[6];
1858 InvertAffineCoefficients(coeff, inverse);
1859 s.x = (double) image->page.x;
1860 s.y = (double) image->page.y;
1861 d.x = inverse[0]*s.x+inverse[1]*s.y+inverse[2];
1862 d.y = inverse[3]*s.x+inverse[4]*s.y+inverse[5];
1863 InitalBounds(d);
1864 s.x = (double) image->page.x+image->columns;
1865 s.y = (double) image->page.y;
1866 d.x = inverse[0]*s.x+inverse[1]*s.y+inverse[2];
1867 d.y = inverse[3]*s.x+inverse[4]*s.y+inverse[5];
1868 ExpandBounds(d);
1869 s.x = (double) image->page.x;
1870 s.y = (double) image->page.y+image->rows;
1871 d.x = inverse[0]*s.x+inverse[1]*s.y+inverse[2];
1872 d.y = inverse[3]*s.x+inverse[4]*s.y+inverse[5];
1873 ExpandBounds(d);
1874 s.x = (double) image->page.x+image->columns;
1875 s.y = (double) image->page.y+image->rows;
1876 d.x = inverse[0]*s.x+inverse[1]*s.y+inverse[2];
1877 d.y = inverse[3]*s.x+inverse[4]*s.y+inverse[5];
1878 ExpandBounds(d);
1879 break;
1880 }
1881 case PerspectiveDistortion:
1882 { double inverse[8], scale;
1883 InvertPerspectiveCoefficients(coeff, inverse);
1884 s.x = (double) image->page.x;
1885 s.y = (double) image->page.y;
1886 scale=inverse[6]*s.x+inverse[7]*s.y+1.0;
1887 scale=MagickSafeReciprocal(scale);
1888 d.x = scale*(inverse[0]*s.x+inverse[1]*s.y+inverse[2]);
1889 d.y = scale*(inverse[3]*s.x+inverse[4]*s.y+inverse[5]);
1890 InitalBounds(d);
1891 s.x = (double) image->page.x+image->columns;
1892 s.y = (double) image->page.y;
1893 scale=inverse[6]*s.x+inverse[7]*s.y+1.0;
1894 scale=MagickSafeReciprocal(scale);
1895 d.x = scale*(inverse[0]*s.x+inverse[1]*s.y+inverse[2]);
1896 d.y = scale*(inverse[3]*s.x+inverse[4]*s.y+inverse[5]);
1897 ExpandBounds(d);
1898 s.x = (double) image->page.x;
1899 s.y = (double) image->page.y+image->rows;
1900 scale=inverse[6]*s.x+inverse[7]*s.y+1.0;
1901 scale=MagickSafeReciprocal(scale);
1902 d.x = scale*(inverse[0]*s.x+inverse[1]*s.y+inverse[2]);
1903 d.y = scale*(inverse[3]*s.x+inverse[4]*s.y+inverse[5]);
1904 ExpandBounds(d);
1905 s.x = (double) image->page.x+image->columns;
1906 s.y = (double) image->page.y+image->rows;
1907 scale=inverse[6]*s.x+inverse[7]*s.y+1.0;
1908 scale=MagickSafeReciprocal(scale);
1909 d.x = scale*(inverse[0]*s.x+inverse[1]*s.y+inverse[2]);
1910 d.y = scale*(inverse[3]*s.x+inverse[4]*s.y+inverse[5]);
1911 ExpandBounds(d);
1912 break;
1913 }
1914 case ArcDistortion:
1915 { double a, ca, sa;
1916 /* Forward Map Corners */
1917 a = coeff[0]-coeff[1]/2; ca = cos(a); sa = sin(a);
1918 d.x = coeff[2]*ca;
1919 d.y = coeff[2]*sa;
1920 InitalBounds(d);
1921 d.x = (coeff[2]-coeff[3])*ca;
1922 d.y = (coeff[2]-coeff[3])*sa;
1923 ExpandBounds(d);
1924 a = coeff[0]+coeff[1]/2; ca = cos(a); sa = sin(a);
1925 d.x = coeff[2]*ca;
1926 d.y = coeff[2]*sa;
1927 ExpandBounds(d);
1928 d.x = (coeff[2]-coeff[3])*ca;
1929 d.y = (coeff[2]-coeff[3])*sa;
1930 ExpandBounds(d);
1931 /* Orthogonal points along top of arc */
1932 for( a=(double) (ceil((double) ((coeff[0]-coeff[1]/2.0)/MagickPI2))*MagickPI2);
1933 a<(coeff[0]+coeff[1]/2.0); a+=MagickPI2 ) {
1934 ca = cos(a); sa = sin(a);
1935 d.x = coeff[2]*ca;
1936 d.y = coeff[2]*sa;
1937 ExpandBounds(d);
1938 }
1939 /*
1940 Convert the angle_to_width and radius_to_height
1941 to appropriate scaling factors, to allow faster processing
1942 in the mapping function.
1943 */
1944 coeff[1] = (double) (Magick2PI*image->columns/coeff[1]);
1945 coeff[3] = (double)image->rows/coeff[3];
1946 break;
1947 }
1948 case PolarDistortion:
1949 {
1950 if (number_arguments < 2)
1951 coeff[2] = coeff[3] = 0.0;
1952 min.x = coeff[2]-coeff[0];
1953 max.x = coeff[2]+coeff[0];
1954 min.y = coeff[3]-coeff[0];
1955 max.y = coeff[3]+coeff[0];
1956 /* should be about 1.0 if Rmin = 0 */
1957 coeff[7]=(double) geometry.height/(coeff[0]-coeff[1]);
1958 break;
1959 }
1960 case DePolarDistortion:
1961 {
1962 /* direct calculation as it needs to tile correctly
1963 * for reversibility in a DePolar-Polar cycle */
1964 fix_bounds = MagickFalse;
1965 geometry.x = geometry.y = 0;
1966 geometry.height = CastDoubleToSizeT(ceil(coeff[0]-coeff[1]));
1967 geometry.width = CastDoubleToSizeT(ceil((coeff[0]-coeff[1])*
1968 (coeff[5]-coeff[4])*0.5));
1969 /* correct scaling factors relative to new size */
1970 coeff[6]=(coeff[5]-coeff[4]) * MagickSafeReciprocal(
1971 (double) geometry.width); /* changed width */
1972 coeff[7]=(coeff[0]-coeff[1]) * MagickSafeReciprocal(
1973 (double) geometry.height); /* should be about 1.0 */
1974 break;
1975 }
1976 case Cylinder2PlaneDistortion:
1977 {
1978 /* direct calculation so center of distortion is either a pixel
1979 * center, or pixel edge. This allows for reversibility of the
1980 * distortion */
1981 geometry.x = geometry.y = 0;
1982 geometry.width = CastDoubleToSizeT(ceil( 2.0*coeff[1]*tan(coeff[0]/2.0) ));
1983 geometry.height = CastDoubleToSizeT(ceil( 2.0*coeff[3]/cos(coeff[0]/2.0) ));
1984 /* correct center of distortion relative to new size */
1985 coeff[4] = (double) geometry.width/2.0;
1986 coeff[5] = (double) geometry.height/2.0;
1987 fix_bounds = MagickFalse;
1988 break;
1989 }
1990 case Plane2CylinderDistortion:
1991 {
1992 /* direct calculation center is either pixel center, or pixel edge
1993 * so as to allow reversibility of the image distortion */
1994 geometry.x = geometry.y = 0;
1995 geometry.width = CastDoubleToSizeT(ceil(coeff[0]*coeff[1])); /* FOV * radius */
1996 geometry.height = CastDoubleToSizeT(2.0*coeff[3]); /* input image height */
1997 /* correct center of distortion relative to new size */
1998 coeff[4] = (double) geometry.width/2.0;
1999 coeff[5] = (double) geometry.height/2.0;
2000 fix_bounds = MagickFalse;
2001 break;
2002 }
2003 case ShepardsDistortion:
2004 case BilinearForwardDistortion:
2005 case BilinearReverseDistortion:
2006#if 0
2007 case QuadrilateralDistortion:
2008#endif
2009 case PolynomialDistortion:
2010 case BarrelDistortion:
2011 case BarrelInverseDistortion:
2012 default:
2013 /* no calculated bestfit available for these distortions */
2014 bestfit = MagickFalse;
2015 fix_bounds = MagickFalse;
2016 break;
2017 }
2018
2019 /* Set the output image geometry to calculated 'bestfit'.
2020 Yes this tends to 'over do' the file image size, ON PURPOSE!
2021 Do not do this for DePolar which needs to be exact for virtual tiling.
2022 */
2023 if ( fix_bounds ) {
2024 geometry.x = CastDoubleToSsizeT(floor(min.x-0.5));
2025 geometry.y = CastDoubleToSsizeT(floor(min.y-0.5));
2026 geometry.width=CastDoubleToSizeT(ceil(max.x-geometry.x+0.5));
2027 geometry.height=CastDoubleToSizeT(ceil(max.y-geometry.y+0.5));
2028 }
2029
2030 } /* end bestfit destination image calculations */
2031
2032 /* The user provided a 'viewport' expert option which may
2033 overrides some parts of the current output image geometry.
2034 This also overrides its default 'bestfit' setting.
2035 */
2036 { const char *artifact=GetImageArtifact(image,"distort:viewport");
2037 viewport_given = MagickFalse;
2038 if ( artifact != (const char *) NULL ) {
2039 MagickStatusType flags=ParseAbsoluteGeometry(artifact,&geometry);
2040 if (flags==NoValue)
2041 (void) ThrowMagickException(exception,GetMagickModule(),
2042 OptionWarning,"InvalidSetting","'%s' '%s'",
2043 "distort:viewport",artifact);
2044 else
2045 viewport_given = MagickTrue;
2046 }
2047 }
2048
2049 /* Verbose output */
2050 if (IsStringTrue(GetImageArtifact(image,"verbose")) != MagickFalse) {
2051 ssize_t
2052 i;
2053 char image_gen[MagickPathExtent];
2054 const char *lookup;
2055
2056 /* Set destination image size and virtual offset */
2057 if ( bestfit || viewport_given ) {
2058 (void) FormatLocaleString(image_gen,MagickPathExtent,
2059 " -size %.20gx%.20g -page %+.20g%+.20g xc: +insert \\\n",
2060 (double) geometry.width,(double) geometry.height,(double) geometry.x,
2061 (double) geometry.y);
2062 lookup="v.p{xx-v.page.x-0.5,yy-v.page.y-0.5}";
2063 }
2064 else {
2065 image_gen[0] = '\0'; /* no destination to generate */
2066 lookup = "p{xx-page.x-0.5,yy-page.y-0.5}"; /* simplify lookup */
2067 }
2068
2069 switch (method)
2070 {
2071 case AffineDistortion:
2072 case RigidAffineDistortion:
2073 {
2074 double
2075 *inverse;
2076
2077 inverse=(double *) AcquireQuantumMemory(6,sizeof(*inverse));
2078 if (inverse == (double *) NULL)
2079 {
2080 coeff=(double *) RelinquishMagickMemory(coeff);
2081 (void) ThrowMagickException(exception,GetMagickModule(),
2082 ResourceLimitError,"MemoryAllocationFailed","%s","DistortImages");
2083 return((Image *) NULL);
2084 }
2085 InvertAffineCoefficients(coeff, inverse);
2086 CoefficientsToAffineArgs(inverse);
2087 (void) FormatLocaleFile(stderr, "Affine projection:\n");
2088 (void) FormatLocaleFile(stderr,
2089 " -distort AffineProjection \\\n '");
2090 for (i=0; i < 5; i++)
2091 (void) FormatLocaleFile(stderr, "%.*g,",GetMagickPrecision(),
2092 inverse[i]);
2093 (void) FormatLocaleFile(stderr, "%.*g'\n",GetMagickPrecision(),
2094 inverse[5]);
2095 (void) FormatLocaleFile(stderr,
2096 "Equivalent scale, rotation(deg), translation:\n");
2097 (void) FormatLocaleFile(stderr," %.*g,%.*g,%.*g,%.*g\n",
2098 GetMagickPrecision(),sqrt(inverse[0]*inverse[0]+
2099 inverse[1]*inverse[1]),GetMagickPrecision(),
2100 RadiansToDegrees(atan2(inverse[1],inverse[0])),
2101 GetMagickPrecision(),inverse[4],GetMagickPrecision(),inverse[5]);
2102 inverse=(double *) RelinquishMagickMemory(inverse);
2103 (void) FormatLocaleFile(stderr,"Affine distort, FX equivalent:\n");
2104 (void) FormatLocaleFile(stderr, "%s", image_gen);
2105 (void) FormatLocaleFile(stderr,
2106 " -fx 'ii=i+page.x+0.5; jj=j+page.y+0.5;\n");
2107 (void) FormatLocaleFile(stderr," xx=%+.*g*ii %+.*g*jj %+.*g;\n",
2108 GetMagickPrecision(),coeff[0],GetMagickPrecision(),coeff[1],
2109 GetMagickPrecision(),coeff[2]);
2110 (void) FormatLocaleFile(stderr," yy=%+.*g*ii %+.*g*jj %+.*g;\n",
2111 GetMagickPrecision(),coeff[3],GetMagickPrecision(),coeff[4],
2112 GetMagickPrecision(),coeff[5]);
2113 (void) FormatLocaleFile(stderr," %s' \\\n",lookup);
2114 break;
2115 }
2116 case PerspectiveDistortion:
2117 {
2118 double
2119 *inverse;
2120
2121 inverse=(double *) AcquireQuantumMemory(8,sizeof(*inverse));
2122 if (inverse == (double *) NULL)
2123 {
2124 coeff=(double *) RelinquishMagickMemory(coeff);
2125 (void) ThrowMagickException(exception,GetMagickModule(),
2126 ResourceLimitError,"MemoryAllocationFailed","%s",
2127 "DistortCoefficients");
2128 return((Image *) NULL);
2129 }
2130 InvertPerspectiveCoefficients(coeff, inverse);
2131 (void) FormatLocaleFile(stderr,"Perspective Projection:\n");
2132 (void) FormatLocaleFile(stderr,
2133 " -distort PerspectiveProjection \\\n '");
2134 for (i=0; i < 4; i++)
2135 (void) FormatLocaleFile(stderr, "%.*g, ",GetMagickPrecision(),
2136 inverse[i]);
2137 (void) FormatLocaleFile(stderr, "\n ");
2138 for ( ; i < 7; i++)
2139 (void) FormatLocaleFile(stderr, "%.*g, ",GetMagickPrecision(),
2140 inverse[i]);
2141 (void) FormatLocaleFile(stderr, "%.*g'\n",GetMagickPrecision(),
2142 inverse[7]);
2143 inverse=(double *) RelinquishMagickMemory(inverse);
2144 (void) FormatLocaleFile(stderr,"Perspective Distort, FX Equivalent:\n");
2145 (void) FormatLocaleFile(stderr,"%.1024s",image_gen);
2146 (void) FormatLocaleFile(stderr,
2147 " -fx 'ii=i+page.x+0.5; jj=j+page.y+0.5;\n");
2148 (void) FormatLocaleFile(stderr," rr=%+.*g*ii %+.*g*jj + 1;\n",
2149 GetMagickPrecision(),coeff[6],GetMagickPrecision(),coeff[7]);
2150 (void) FormatLocaleFile(stderr,
2151 " xx=(%+.*g*ii %+.*g*jj %+.*g)/rr;\n",
2152 GetMagickPrecision(),coeff[0],GetMagickPrecision(),coeff[1],
2153 GetMagickPrecision(),coeff[2]);
2154 (void) FormatLocaleFile(stderr,
2155 " yy=(%+.*g*ii %+.*g*jj %+.*g)/rr;\n",
2156 GetMagickPrecision(),coeff[3],GetMagickPrecision(),coeff[4],
2157 GetMagickPrecision(),coeff[5]);
2158 (void) FormatLocaleFile(stderr," rr%s0 ? %s : blue' \\\n",
2159 coeff[8] < 0.0 ? "<" : ">", lookup);
2160 break;
2161 }
2162 case BilinearForwardDistortion:
2163 {
2164 (void) FormatLocaleFile(stderr,"BilinearForward Mapping Equations:\n");
2165 (void) FormatLocaleFile(stderr,"%s", image_gen);
2166 (void) FormatLocaleFile(stderr," i = %+lf*x %+lf*y %+lf*x*y %+lf;\n",
2167 coeff[0],coeff[1],coeff[2],coeff[3]);
2168 (void) FormatLocaleFile(stderr," j = %+lf*x %+lf*y %+lf*x*y %+lf;\n",
2169 coeff[4],coeff[5],coeff[6],coeff[7]);
2170#if 0
2171 /* for debugging */
2172 (void) FormatLocaleFile(stderr, " c8 = %+lf c9 = 2*a = %+lf;\n",
2173 coeff[8], coeff[9]);
2174#endif
2175 (void) FormatLocaleFile(stderr,
2176 "BilinearForward Distort, FX Equivalent:\n");
2177 (void) FormatLocaleFile(stderr,"%s", image_gen);
2178 (void) FormatLocaleFile(stderr,
2179 " -fx 'ii=i+page.x%+lf; jj=j+page.y%+lf;\n",0.5-coeff[3],0.5-
2180 coeff[7]);
2181 (void) FormatLocaleFile(stderr," bb=%lf*ii %+lf*jj %+lf;\n",
2182 coeff[6], -coeff[2], coeff[8]);
2183 /* Handle Special degenerate (non-quadratic) or trapezoidal case */
2184 if (coeff[9] != 0)
2185 {
2186 (void) FormatLocaleFile(stderr,
2187 " rt=bb*bb %+lf*(%lf*ii%+lf*jj);\n",-2*coeff[9],coeff[4],
2188 -coeff[0]);
2189 (void) FormatLocaleFile(stderr,
2190 " yy=( -bb + sqrt(rt) ) / %lf;\n",coeff[9]);
2191 }
2192 else
2193 (void) FormatLocaleFile(stderr," yy=(%lf*ii%+lf*jj)/bb;\n",
2194 -coeff[4],coeff[0]);
2195 (void) FormatLocaleFile(stderr,
2196 " xx=(ii %+lf*yy)/(%lf %+lf*yy);\n",-coeff[1],coeff[0],
2197 coeff[2]);
2198 if ( coeff[9] != 0 )
2199 (void) FormatLocaleFile(stderr," (rt < 0 ) ? red : %s'\n",
2200 lookup);
2201 else
2202 (void) FormatLocaleFile(stderr," %s' \\\n", lookup);
2203 break;
2204 }
2205 case BilinearReverseDistortion:
2206 {
2207#if 0
2208 (void) FormatLocaleFile(stderr, "Polynomial Projection Distort:\n");
2209 (void) FormatLocaleFile(stderr, " -distort PolynomialProjection \\\n");
2210 (void) FormatLocaleFile(stderr, " '1.5, %lf, %lf, %lf, %lf,\n",
2211 coeff[3], coeff[0], coeff[1], coeff[2]);
2212 (void) FormatLocaleFile(stderr, " %lf, %lf, %lf, %lf'\n",
2213 coeff[7], coeff[4], coeff[5], coeff[6]);
2214#endif
2215 (void) FormatLocaleFile(stderr,
2216 "BilinearReverse Distort, FX Equivalent:\n");
2217 (void) FormatLocaleFile(stderr,"%s", image_gen);
2218 (void) FormatLocaleFile(stderr,
2219 " -fx 'ii=i+page.x+0.5; jj=j+page.y+0.5;\n");
2220 (void) FormatLocaleFile(stderr,
2221 " xx=%+lf*ii %+lf*jj %+lf*ii*jj %+lf;\n",coeff[0],coeff[1],
2222 coeff[2], coeff[3]);
2223 (void) FormatLocaleFile(stderr,
2224 " yy=%+lf*ii %+lf*jj %+lf*ii*jj %+lf;\n",coeff[4],coeff[5],
2225 coeff[6], coeff[7]);
2226 (void) FormatLocaleFile(stderr," %s' \\\n", lookup);
2227 break;
2228 }
2229 case PolynomialDistortion:
2230 {
2231 size_t nterms = CastDoubleToSizeT(coeff[1]);
2232 (void) FormatLocaleFile(stderr,
2233 "Polynomial (order %lg, terms %lu), FX Equivalent\n",coeff[0],
2234 (unsigned long) nterms);
2235 (void) FormatLocaleFile(stderr,"%s", image_gen);
2236 (void) FormatLocaleFile(stderr,
2237 " -fx 'ii=i+page.x+0.5; jj=j+page.y+0.5;\n");
2238 (void) FormatLocaleFile(stderr, " xx =");
2239 for (i=0; i < (ssize_t) nterms; i++)
2240 {
2241 if ((i != 0) && (i%4 == 0))
2242 (void) FormatLocaleFile(stderr, "\n ");
2243 (void) FormatLocaleFile(stderr," %+lf%s",coeff[2+i],
2244 poly_basis_str(i));
2245 }
2246 (void) FormatLocaleFile(stderr,";\n yy =");
2247 for (i=0; i < (ssize_t) nterms; i++)
2248 {
2249 if ((i != 0) && (i%4 == 0))
2250 (void) FormatLocaleFile(stderr,"\n ");
2251 (void) FormatLocaleFile(stderr," %+lf%s",coeff[2+i+(int) nterms],
2252 poly_basis_str(i));
2253 }
2254 (void) FormatLocaleFile(stderr,";\n %s' \\\n", lookup);
2255 break;
2256 }
2257 case ArcDistortion:
2258 {
2259 (void) FormatLocaleFile(stderr,"Arc Distort, Internal Coefficients:\n");
2260 for (i=0; i < 5; i++)
2261 (void) FormatLocaleFile(stderr,
2262 " c%.20g = %+lf\n",(double) i,coeff[i]);
2263 (void) FormatLocaleFile(stderr,"Arc Distort, FX Equivalent:\n");
2264 (void) FormatLocaleFile(stderr,"%s", image_gen);
2265 (void) FormatLocaleFile(stderr," -fx 'ii=i+page.x; jj=j+page.y;\n");
2266 (void) FormatLocaleFile(stderr," xx=(atan2(jj,ii)%+lf)/(2*pi);\n",
2267 -coeff[0]);
2268 (void) FormatLocaleFile(stderr," xx=xx-round(xx);\n");
2269 (void) FormatLocaleFile(stderr," xx=xx*%lf %+lf;\n",coeff[1],
2270 coeff[4]);
2271 (void) FormatLocaleFile(stderr,
2272 " yy=(%lf - hypot(ii,jj)) * %lf;\n",coeff[2],coeff[3]);
2273 (void) FormatLocaleFile(stderr," v.p{xx-.5,yy-.5}' \\\n");
2274 break;
2275 }
2276 case PolarDistortion:
2277 {
2278 (void) FormatLocaleFile(stderr,"Polar Distort, Internal Coefficients\n");
2279 for (i=0; i < 8; i++)
2280 (void) FormatLocaleFile(stderr," c%.20g = %+lf\n",(double) i,
2281 coeff[i]);
2282 (void) FormatLocaleFile(stderr,"Polar Distort, FX Equivalent:\n");
2283 (void) FormatLocaleFile(stderr,"%s", image_gen);
2284 (void) FormatLocaleFile(stderr,
2285 " -fx 'ii=i+page.x%+lf; jj=j+page.y%+lf;\n",-coeff[2],-coeff[3]);
2286 (void) FormatLocaleFile(stderr," xx=(atan2(ii,jj)%+lf)/(2*pi);\n",
2287 -(coeff[4]+coeff[5])/2 );
2288 (void) FormatLocaleFile(stderr," xx=xx-round(xx);\n");
2289 (void) FormatLocaleFile(stderr," xx=xx*2*pi*%lf + v.w/2;\n",
2290 coeff[6] );
2291 (void) FormatLocaleFile(stderr," yy=(hypot(ii,jj)%+lf)*%lf;\n",
2292 -coeff[1],coeff[7] );
2293 (void) FormatLocaleFile(stderr," v.p{xx-.5,yy-.5}' \\\n");
2294 break;
2295 }
2296 case DePolarDistortion:
2297 {
2298 (void) FormatLocaleFile(stderr,
2299 "DePolar Distort, Internal Coefficients\n");
2300 for (i=0; i < 8; i++)
2301 (void) FormatLocaleFile(stderr," c%.20g = %+lf\n",(double) i,
2302 coeff[i]);
2303 (void) FormatLocaleFile(stderr,"DePolar Distort, FX Equivalent:\n");
2304 (void) FormatLocaleFile(stderr,"%s", image_gen);
2305 (void) FormatLocaleFile(stderr," -fx 'aa=(i+.5)*%lf %+lf;\n",
2306 coeff[6],+coeff[4]);
2307 (void) FormatLocaleFile(stderr," rr=(j+.5)*%lf %+lf;\n",
2308 coeff[7],+coeff[1]);
2309 (void) FormatLocaleFile(stderr," xx=rr*sin(aa) %+lf;\n",
2310 coeff[2]);
2311 (void) FormatLocaleFile(stderr," yy=rr*cos(aa) %+lf;\n",
2312 coeff[3]);
2313 (void) FormatLocaleFile(stderr," v.p{xx-.5,yy-.5}' \\\n");
2314 break;
2315 }
2316 case Cylinder2PlaneDistortion:
2317 {
2318 (void) FormatLocaleFile(stderr,
2319 "Cylinder to Plane Distort, Internal Coefficients\n");
2320 (void) FormatLocaleFile(stderr," cylinder_radius = %+lf\n",coeff[1]);
2321 (void) FormatLocaleFile(stderr,
2322 "Cylinder to Plane Distort, FX Equivalent:\n");
2323 (void) FormatLocaleFile(stderr, "%s", image_gen);
2324 (void) FormatLocaleFile(stderr,
2325 " -fx 'ii=i+page.x%+lf+0.5; jj=j+page.y%+lf+0.5;\n",-coeff[4],
2326 -coeff[5]);
2327 (void) FormatLocaleFile(stderr," aa=atan(ii/%+lf);\n",coeff[1]);
2328 (void) FormatLocaleFile(stderr," xx=%lf*aa%+lf;\n",
2329 coeff[1],coeff[2]);
2330 (void) FormatLocaleFile(stderr," yy=jj*cos(aa)%+lf;\n",coeff[3]);
2331 (void) FormatLocaleFile(stderr," %s' \\\n", lookup);
2332 break;
2333 }
2334 case Plane2CylinderDistortion:
2335 {
2336 (void) FormatLocaleFile(stderr,
2337 "Plane to Cylinder Distort, Internal Coefficients\n");
2338 (void) FormatLocaleFile(stderr," cylinder_radius = %+lf\n",coeff[1]);
2339 (void) FormatLocaleFile(stderr,
2340 "Plane to Cylinder Distort, FX Equivalent:\n");
2341 (void) FormatLocaleFile(stderr,"%s", image_gen);
2342 (void) FormatLocaleFile(stderr,
2343 " -fx 'ii=i+page.x%+lf+0.5; jj=j+page.y%+lf+0.5;\n",-coeff[4],
2344 -coeff[5]);
2345 (void) FormatLocaleFile(stderr," ii=ii/%+lf;\n",coeff[1]);
2346 (void) FormatLocaleFile(stderr," xx=%lf*tan(ii)%+lf;\n",coeff[1],
2347 coeff[2] );
2348 (void) FormatLocaleFile(stderr," yy=jj/cos(ii)%+lf;\n",coeff[3]);
2349 (void) FormatLocaleFile(stderr," %s' \\\n", lookup);
2350 break;
2351 }
2352 case BarrelDistortion:
2353 case BarrelInverseDistortion:
2354 {
2355 double
2356 xc,
2357 yc;
2358
2359 /*
2360 NOTE: This does the barrel roll in pixel coords not image coords
2361 The internal distortion must do it in image coordinates,
2362 so that is what the center coeff (8,9) is given in.
2363 */
2364 xc=((double)image->columns-1.0)/2.0+image->page.x;
2365 yc=((double)image->rows-1.0)/2.0+image->page.y;
2366 (void) FormatLocaleFile(stderr, "Barrel%s Distort, FX Equivalent:\n",
2367 method == BarrelDistortion ? "" : "Inv");
2368 (void) FormatLocaleFile(stderr, "%s", image_gen);
2369 if ( fabs(coeff[8]-xc-0.5) < 0.1 && fabs(coeff[9]-yc-0.5) < 0.1 )
2370 (void) FormatLocaleFile(stderr," -fx 'xc=(w-1)/2; yc=(h-1)/2;\n");
2371 else
2372 (void) FormatLocaleFile(stderr," -fx 'xc=%lf; yc=%lf;\n",coeff[8]-
2373 0.5,coeff[9]-0.5);
2374 (void) FormatLocaleFile(stderr,
2375 " ii=i-xc; jj=j-yc; rr=hypot(ii,jj);\n");
2376 (void) FormatLocaleFile(stderr,
2377 " ii=ii%s(%lf*rr*rr*rr %+lf*rr*rr %+lf*rr %+lf);\n",
2378 method == BarrelDistortion ? "*" : "/",coeff[0],coeff[1],coeff[2],
2379 coeff[3]);
2380 (void) FormatLocaleFile(stderr,
2381 " jj=jj%s(%lf*rr*rr*rr %+lf*rr*rr %+lf*rr %+lf);\n",
2382 method == BarrelDistortion ? "*" : "/",coeff[4],coeff[5],coeff[6],
2383 coeff[7]);
2384 (void) FormatLocaleFile(stderr," p{ii+xc,jj+yc}' \\\n");
2385 break;
2386 }
2387 default:
2388 break;
2389 }
2390 }
2391 /*
2392 The user provided a 'scale' expert option will scale the output image size,
2393 by the factor given allowing for super-sampling of the distorted image
2394 space. Any scaling factors must naturally be halved as a result.
2395 */
2396 { const char *artifact;
2397 artifact=GetImageArtifact(image,"distort:scale");
2398 output_scaling = 1.0;
2399 if (artifact != (const char *) NULL) {
2400 output_scaling = fabs(StringToDouble(artifact,(char **) NULL));
2401 geometry.width=CastDoubleToSizeT(output_scaling*geometry.width+0.5);
2402 geometry.height=CastDoubleToSizeT(output_scaling*geometry.height+0.5);
2403 geometry.x=(ssize_t) (output_scaling*geometry.x+0.5);
2404 geometry.y=(ssize_t) (output_scaling*geometry.y+0.5);
2405 if ( output_scaling < 0.1 ) {
2406 coeff = (double *) RelinquishMagickMemory(coeff);
2407 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
2408 "InvalidArgument","%s", "-set option:distort:scale" );
2409 return((Image *) NULL);
2410 }
2411 output_scaling = 1/output_scaling;
2412 }
2413 }
2414#define ScaleFilter(F,A,B,C,D) \
2415 ScaleResampleFilter( (F), \
2416 output_scaling*(A), output_scaling*(B), \
2417 output_scaling*(C), output_scaling*(D) )
2418
2419 /*
2420 Initialize the distort image attributes.
2421 */
2422 distort_image=CloneImage(image,geometry.width,geometry.height,MagickTrue,
2423 exception);
2424 if (distort_image == (Image *) NULL)
2425 {
2426 coeff=(double *) RelinquishMagickMemory(coeff);
2427 return((Image *) NULL);
2428 }
2429 /* if image is ColorMapped - change it to DirectClass */
2430 if (SetImageStorageClass(distort_image,DirectClass,exception) == MagickFalse)
2431 {
2432 coeff=(double *) RelinquishMagickMemory(coeff);
2433 distort_image=DestroyImage(distort_image);
2434 return((Image *) NULL);
2435 }
2436 if ((IsPixelInfoGray(&distort_image->background_color) == MagickFalse) &&
2437 (IsGrayColorspace(distort_image->colorspace) != MagickFalse))
2438 (void) SetImageColorspace(distort_image,sRGBColorspace,exception);
2439 if (distort_image->background_color.alpha_trait != UndefinedPixelTrait)
2440 distort_image->alpha_trait=BlendPixelTrait;
2441 distort_image->page.x=geometry.x;
2442 distort_image->page.y=geometry.y;
2443 ConformPixelInfo(distort_image,&distort_image->matte_color,&invalid,
2444 exception);
2445
2446 { /* ----- MAIN CODE -----
2447 Sample the source image to each pixel in the distort image.
2448 */
2449 CacheView
2450 *distort_view;
2451
2452 MagickBooleanType
2453 status;
2454
2455 MagickOffsetType
2456 progress;
2457
2458 PixelInfo
2459 zero;
2460
2461 ResampleFilter
2462 **magick_restrict resample_filter;
2463
2464 ssize_t
2465 j;
2466
2467 status=MagickTrue;
2468 progress=0;
2469 GetPixelInfo(distort_image,&zero);
2470 resample_filter=AcquireResampleFilterTLS(image,UndefinedVirtualPixelMethod,
2471 MagickFalse,exception);
2472 distort_view=AcquireAuthenticCacheView(distort_image,exception);
2473#if defined(MAGICKCORE_OPENMP_SUPPORT)
2474 #pragma omp parallel for schedule(static) shared(progress,status) \
2475 magick_number_threads(image,distort_image,distort_image->rows,1)
2476#endif
2477 for (j=0; j < (ssize_t) distort_image->rows; j++)
2478 {
2479 const int
2480 id = GetOpenMPThreadId();
2481
2482 double
2483 validity; /* how mathematically valid is this the mapping */
2484
2485 MagickBooleanType
2486 sync;
2487
2488 PixelInfo
2489 pixel; /* pixel color to assign to distorted image */
2490
2491 PointInfo
2492 d,
2493 s; /* transform destination image x,y to source image x,y */
2494
2495 ssize_t
2496 i;
2497
2498 Quantum
2499 *magick_restrict q;
2500
2501 q=QueueCacheViewAuthenticPixels(distort_view,0,j,distort_image->columns,1,
2502 exception);
2503 if (q == (Quantum *) NULL)
2504 {
2505 status=MagickFalse;
2506 continue;
2507 }
2508 pixel=zero;
2509
2510 /* Define constant scaling vectors for Affine Distortions
2511 Other methods are either variable, or use interpolated lookup
2512 */
2513 switch (method)
2514 {
2515 case AffineDistortion:
2516 case RigidAffineDistortion:
2517 ScaleFilter( resample_filter[id],
2518 coeff[0], coeff[1],
2519 coeff[3], coeff[4] );
2520 break;
2521 default:
2522 break;
2523 }
2524
2525 /* Initialize default pixel validity
2526 * negative: pixel is invalid output 'matte_color'
2527 * 0.0 to 1.0: antialiased, mix with resample output
2528 * 1.0 or greater: use resampled output.
2529 */
2530 validity = 1.0;
2531
2532 for (i=0; i < (ssize_t) distort_image->columns; i++)
2533 {
2534 /* map pixel coordinate to distortion space coordinate */
2535 d.x = (double) (geometry.x+i+0.5)*output_scaling;
2536 d.y = (double) (geometry.y+j+0.5)*output_scaling;
2537 s = d; /* default is a no-op mapping */
2538 switch (method)
2539 {
2540 case AffineDistortion:
2541 case RigidAffineDistortion:
2542 {
2543 s.x=coeff[0]*d.x+coeff[1]*d.y+coeff[2];
2544 s.y=coeff[3]*d.x+coeff[4]*d.y+coeff[5];
2545 /* Affine partial derivatives are constant -- set above */
2546 break;
2547 }
2548 case PerspectiveDistortion:
2549 {
2550 double
2551 p,n,r,abs_r,abs_c6,abs_c7,scale;
2552 /* perspective is a ratio of affines */
2553 p=coeff[0]*d.x+coeff[1]*d.y+coeff[2];
2554 n=coeff[3]*d.x+coeff[4]*d.y+coeff[5];
2555 r=coeff[6]*d.x+coeff[7]*d.y+1.0;
2556 /* Pixel Validity -- is it a 'sky' or 'ground' pixel */
2557 validity = (r*coeff[8] < 0.0) ? 0.0 : 1.0;
2558 /* Determine horizon anti-alias blending */
2559 abs_r = fabs(r)*2;
2560 abs_c6 = fabs(coeff[6]);
2561 abs_c7 = fabs(coeff[7]);
2562 if ( abs_c6 > abs_c7 ) {
2563 if ( abs_r < abs_c6*output_scaling )
2564 validity = 0.5 - coeff[8]*r/(coeff[6]*output_scaling);
2565 }
2566 else if ( abs_r < abs_c7*output_scaling )
2567 validity = 0.5 - coeff[8]*r/(coeff[7]*output_scaling);
2568 /* Perspective Sampling Point (if valid) */
2569 if ( validity > 0.0 ) {
2570 /* divide by r affine, for perspective scaling */
2571 scale = 1.0/r;
2572 s.x = p*scale;
2573 s.y = n*scale;
2574 /* Perspective Partial Derivatives or Scaling Vectors */
2575 scale *= scale;
2576 ScaleFilter( resample_filter[id],
2577 (r*coeff[0] - p*coeff[6])*scale,
2578 (r*coeff[1] - p*coeff[7])*scale,
2579 (r*coeff[3] - n*coeff[6])*scale,
2580 (r*coeff[4] - n*coeff[7])*scale );
2581 }
2582 break;
2583 }
2584 case BilinearReverseDistortion:
2585 {
2586 /* Reversed Mapped is just a simple polynomial */
2587 s.x=coeff[0]*d.x+coeff[1]*d.y+coeff[2]*d.x*d.y+coeff[3];
2588 s.y=coeff[4]*d.x+coeff[5]*d.y
2589 +coeff[6]*d.x*d.y+coeff[7];
2590 /* Bilinear partial derivatives of scaling vectors */
2591 ScaleFilter( resample_filter[id],
2592 coeff[0] + coeff[2]*d.y,
2593 coeff[1] + coeff[2]*d.x,
2594 coeff[4] + coeff[6]*d.y,
2595 coeff[5] + coeff[6]*d.x );
2596 break;
2597 }
2598 case BilinearForwardDistortion:
2599 {
2600 /* Forward mapped needs reversed polynomial equations
2601 * which unfortunately requires a square root! */
2602 double b,c;
2603 d.x -= coeff[3]; d.y -= coeff[7];
2604 b = coeff[6]*d.x - coeff[2]*d.y + coeff[8];
2605 c = coeff[4]*d.x - coeff[0]*d.y;
2606
2607 validity = 1.0;
2608 /* Handle Special degenerate (non-quadratic) case
2609 * Currently without horizon anti-aliasing */
2610 if ( fabs(coeff[9]) < MagickEpsilon )
2611 s.y = -c/b;
2612 else {
2613 c = b*b - 2*coeff[9]*c;
2614 if ( c < 0.0 )
2615 validity = 0.0;
2616 else
2617 s.y = ( -b + sqrt(c) )/coeff[9];
2618 }
2619 if ( validity > 0.0 )
2620 s.x = ( d.x - coeff[1]*s.y) / ( coeff[0] + coeff[2]*s.y );
2621
2622 /* NOTE: the sign of the square root should be -ve for parts
2623 where the source image becomes 'flipped' or 'mirrored'.
2624 FUTURE: Horizon handling
2625 FUTURE: Scaling factors or Derivatives (how?)
2626 */
2627 break;
2628 }
2629#if 0
2630 case BilinearDistortion:
2631 /* Bilinear mapping of any Quadrilateral to any Quadrilateral */
2632 /* UNDER DEVELOPMENT */
2633 break;
2634#endif
2635 case PolynomialDistortion:
2636 {
2637 /* multi-ordered polynomial */
2638 ssize_t
2639 k;
2640
2641 ssize_t
2642 nterms=(ssize_t)coeff[1];
2643
2644 PointInfo
2645 du,dv; /* the du,dv vectors from unit dx,dy -- derivatives */
2646
2647 s.x=s.y=du.x=du.y=dv.x=dv.y=0.0;
2648 for(k=0; k < nterms; k++) {
2649 s.x += poly_basis_fn(k,d.x,d.y)*coeff[2+k];
2650 du.x += poly_basis_dx(k,d.x,d.y)*coeff[2+k];
2651 du.y += poly_basis_dy(k,d.x,d.y)*coeff[2+k];
2652 s.y += poly_basis_fn(k,d.x,d.y)*coeff[2+k+nterms];
2653 dv.x += poly_basis_dx(k,d.x,d.y)*coeff[2+k+nterms];
2654 dv.y += poly_basis_dy(k,d.x,d.y)*coeff[2+k+nterms];
2655 }
2656 ScaleFilter( resample_filter[id], du.x,du.y,dv.x,dv.y );
2657 break;
2658 }
2659 case ArcDistortion:
2660 {
2661 /* what is the angle and radius in the destination image */
2662 s.x = (double) ((atan2(d.y,d.x) - coeff[0])/Magick2PI);
2663 s.x -= MagickRound(s.x); /* angle */
2664 s.y = hypot(d.x,d.y); /* radius */
2665
2666 /* Arc Distortion Partial Scaling Vectors
2667 Are derived by mapping the perpendicular unit vectors
2668 dR and dA*R*2PI rather than trying to map dx and dy
2669 The results is a very simple orthogonal aligned ellipse.
2670 */
2671 if ( s.y > MagickEpsilon )
2672 ScaleFilter( resample_filter[id],
2673 (double) (coeff[1]/(Magick2PI*s.y)), 0, 0, coeff[3] );
2674 else
2675 ScaleFilter( resample_filter[id],
2676 distort_image->columns*2, 0, 0, coeff[3] );
2677
2678 /* now scale the angle and radius for source image lookup point */
2679 s.x = s.x*coeff[1] + coeff[4] + image->page.x +0.5;
2680 s.y = (coeff[2] - s.y) * coeff[3] + image->page.y;
2681 break;
2682 }
2683 case PolarDistortion:
2684 { /* 2D Cartesian to Polar View */
2685 d.x -= coeff[2];
2686 d.y -= coeff[3];
2687 s.x = atan2(d.x,d.y) - (coeff[4]+coeff[5])/2;
2688 s.x /= Magick2PI;
2689 s.x -= MagickRound(s.x);
2690 s.x *= Magick2PI; /* angle - relative to centerline */
2691 s.y = hypot(d.x,d.y); /* radius */
2692
2693 /* Polar Scaling vectors are based on mapping dR and dA vectors
2694 This results in very simple orthogonal scaling vectors
2695 */
2696 if ( s.y > MagickEpsilon )
2697 ScaleFilter( resample_filter[id],
2698 (double) (coeff[6]/(Magick2PI*s.y)), 0, 0, coeff[7] );
2699 else
2700 ScaleFilter( resample_filter[id],
2701 distort_image->columns*2, 0, 0, coeff[7] );
2702
2703 /* now finish mapping radius/angle to source x,y coords */
2704 s.x = s.x*coeff[6] + (double)image->columns/2.0 + image->page.x;
2705 s.y = (s.y-coeff[1])*coeff[7] + image->page.y;
2706 break;
2707 }
2708 case DePolarDistortion:
2709 { /* @D Polar to Cartesian */
2710 /* ignore all destination virtual offsets */
2711 d.x = ((double)i+0.5)*output_scaling*coeff[6]+coeff[4];
2712 d.y = ((double)j+0.5)*output_scaling*coeff[7]+coeff[1];
2713 s.x = d.y*sin(d.x) + coeff[2];
2714 s.y = d.y*cos(d.x) + coeff[3];
2715 /* derivatives are useless - better to use SuperSampling */
2716 break;
2717 }
2718 case Cylinder2PlaneDistortion:
2719 { /* 3D Cylinder to Tangential Plane */
2720 double ax, cx;
2721 /* relative to center of distortion */
2722 d.x -= coeff[4]; d.y -= coeff[5];
2723 d.x /= coeff[1]; /* x' = x/r */
2724 ax=atan(d.x); /* aa = atan(x/r) = u/r */
2725 cx=cos(ax); /* cx = cos(atan(x/r)) = 1/sqrt(x^2+u^2) */
2726 s.x = coeff[1]*ax; /* u = r*atan(x/r) */
2727 s.y = d.y*cx; /* v = y*cos(u/r) */
2728 /* derivatives... (see personal notes) */
2729 ScaleFilter( resample_filter[id],
2730 1.0/(1.0+d.x*d.x), 0.0, -d.x*s.y*cx*cx/coeff[1], s.y/d.y );
2731#if 0
2732if ( i == 0 && j == 0 ) {
2733 fprintf(stderr, "x=%lf y=%lf u=%lf v=%lf\n", d.x*coeff[1], d.y, s.x, s.y);
2734 fprintf(stderr, "phi = %lf\n", (double)(ax * 180.0/MagickPI) );
2735 fprintf(stderr, "du/dx=%lf du/dx=%lf dv/dx=%lf dv/dy=%lf\n",
2736 1.0/(1.0+d.x*d.x), 0.0, -d.x*s.y*cx*cx/coeff[1], s.y/d.y );
2737 fflush(stderr); }
2738#endif
2739 /* add center of distortion in source */
2740 s.x += coeff[2]; s.y += coeff[3];
2741 break;
2742 }
2743 case Plane2CylinderDistortion:
2744 { /* 3D Cylinder to Tangential Plane */
2745 /* relative to center of distortion */
2746 d.x -= coeff[4]; d.y -= coeff[5];
2747
2748 /* is pixel valid - horizon of a infinite Virtual-Pixel Plane
2749 * (see Anthony Thyssen's personal note) */
2750 validity = (double) (coeff[1]*MagickPI2 - fabs(d.x))/output_scaling + 0.5;
2751
2752 if ( validity > 0.0 ) {
2753 double cx,tx;
2754 d.x /= coeff[1]; /* x'= x/r */
2755 cx = 1/cos(d.x); /* cx = 1/cos(x/r) */
2756 tx = tan(d.x); /* tx = tan(x/r) */
2757 s.x = coeff[1]*tx; /* u = r * tan(x/r) */
2758 s.y = d.y*cx; /* v = y / cos(x/r) */
2759 /* derivatives... (see Anthony Thyssen's personal notes) */
2760 ScaleFilter( resample_filter[id],
2761 cx*cx, 0.0, s.y*cx/coeff[1], cx );
2762#if 0
2763/*if ( i == 0 && j == 0 )*/
2764if ( d.x == 0.5 && d.y == 0.5 ) {
2765 fprintf(stderr, "x=%lf y=%lf u=%lf v=%lf\n", d.x*coeff[1], d.y, s.x, s.y);
2766 fprintf(stderr, "radius = %lf phi = %lf validity = %lf\n",
2767 coeff[1], (double)(d.x * 180.0/MagickPI), validity );
2768 fprintf(stderr, "du/dx=%lf du/dx=%lf dv/dx=%lf dv/dy=%lf\n",
2769 cx*cx, 0.0, s.y*cx/coeff[1], cx);
2770 fflush(stderr); }
2771#endif
2772 }
2773 /* add center of distortion in source */
2774 s.x += coeff[2]; s.y += coeff[3];
2775 break;
2776 }
2777 case BarrelDistortion:
2778 case BarrelInverseDistortion:
2779 { /* Lens Barrel Distortion Correction */
2780 double r,fx,fy,gx,gy;
2781 /* Radial Polynomial Distortion (de-normalized) */
2782 d.x -= coeff[8];
2783 d.y -= coeff[9];
2784 r = sqrt(d.x*d.x+d.y*d.y);
2785 if ( r > MagickEpsilon ) {
2786 fx = ((coeff[0]*r + coeff[1])*r + coeff[2])*r + coeff[3];
2787 fy = ((coeff[4]*r + coeff[5])*r + coeff[6])*r + coeff[7];
2788 gx = ((3*coeff[0]*r + 2*coeff[1])*r + coeff[2])/r;
2789 gy = ((3*coeff[4]*r + 2*coeff[5])*r + coeff[6])/r;
2790 /* adjust functions and scaling for 'inverse' form */
2791 if ( method == BarrelInverseDistortion ) {
2792 fx = 1/fx; fy = 1/fy;
2793 gx *= -fx*fx; gy *= -fy*fy;
2794 }
2795 /* Set the source pixel to lookup and EWA derivative vectors */
2796 s.x = d.x*fx + coeff[8];
2797 s.y = d.y*fy + coeff[9];
2798 ScaleFilter( resample_filter[id],
2799 gx*d.x*d.x + fx, gx*d.x*d.y,
2800 gy*d.x*d.y, gy*d.y*d.y + fy );
2801 }
2802 else {
2803 /* Special handling to avoid divide by zero when r==0
2804 **
2805 ** The source and destination pixels match in this case
2806 ** which was set at the top of the loop using s = d;
2807 ** otherwise... s.x=coeff[8]; s.y=coeff[9];
2808 */
2809 if ( method == BarrelDistortion )
2810 ScaleFilter( resample_filter[id],
2811 coeff[3], 0, 0, coeff[7] );
2812 else /* method == BarrelInverseDistortion */
2813 /* FUTURE, trap for D==0 causing division by zero */
2814 ScaleFilter( resample_filter[id],
2815 1.0/coeff[3], 0, 0, 1.0/coeff[7] );
2816 }
2817 break;
2818 }
2819 case ShepardsDistortion:
2820 { /* Shepards Method, or Inverse Weighted Distance for
2821 displacement around the destination image control points
2822 The input arguments are the coefficients to the function.
2823 This is more of a 'displacement' function rather than an
2824 absolute distortion function.
2825
2826 Note: We can not determine derivatives using shepards method
2827 so only a point sample interpolation can be used.
2828 */
2829 double
2830 denominator;
2831
2832 size_t
2833 k;
2834
2835 denominator = s.x = s.y = 0;
2836 for(k=0; k<number_arguments; k+=4) {
2837 double weight =
2838 ((double)d.x-arguments[k+2])*((double)d.x-arguments[k+2])
2839 + ((double)d.y-arguments[k+3])*((double)d.y-arguments[k+3]);
2840 weight = pow(weight,coeff[0]); /* shepards power factor */
2841 weight = ( weight < 1.0 ) ? 1.0 : 1.0/weight;
2842
2843 s.x += (arguments[ k ]-arguments[k+2])*weight;
2844 s.y += (arguments[k+1]-arguments[k+3])*weight;
2845 denominator += weight;
2846 }
2847 s.x /= denominator;
2848 s.y /= denominator;
2849 s.x += d.x; /* make it as relative displacement */
2850 s.y += d.y;
2851 break;
2852 }
2853 default:
2854 break; /* use the default no-op given above */
2855 }
2856 /* map virtual canvas location back to real image coordinate */
2857 if ( bestfit && method != ArcDistortion ) {
2858 s.x -= image->page.x;
2859 s.y -= image->page.y;
2860 }
2861 s.x -= 0.5;
2862 s.y -= 0.5;
2863
2864 if ( validity <= 0.0 ) {
2865 /* result of distortion is an invalid pixel - don't resample */
2866 SetPixelViaPixelInfo(distort_image,&invalid,q);
2867 }
2868 else {
2869 /* resample the source image to find its correct color */
2870 status=ResamplePixelColor(resample_filter[id],s.x,s.y,&pixel,
2871 exception);
2872 if (status == MagickFalse)
2873 SetPixelViaPixelInfo(distort_image,&invalid,q);
2874 else
2875 {
2876 /* if validity between 0.0 & 1.0 mix result with invalid pixel */
2877 if ( validity < 1.0 ) {
2878 /* Do a blend of sample color and invalid pixel */
2879 /* should this be a 'Blend', or an 'Over' compose */
2880 CompositePixelInfoBlend(&pixel,validity,&invalid,(1.0-validity),
2881 &pixel);
2882 }
2883 SetPixelViaPixelInfo(distort_image,&pixel,q);
2884 }
2885 }
2886 q+=(ptrdiff_t) GetPixelChannels(distort_image);
2887 }
2888 sync=SyncCacheViewAuthenticPixels(distort_view,exception);
2889 if (sync == MagickFalse)
2890 status=MagickFalse;
2891 if (image->progress_monitor != (MagickProgressMonitor) NULL)
2892 {
2893 MagickBooleanType
2894 proceed;
2895
2896#if defined(MAGICKCORE_OPENMP_SUPPORT)
2897 #pragma omp atomic
2898#endif
2899 progress++;
2900 proceed=SetImageProgress(image,DistortImageTag,progress,image->rows);
2901 if (proceed == MagickFalse)
2902 status=MagickFalse;
2903 }
2904 }
2905 distort_view=DestroyCacheView(distort_view);
2906 resample_filter=DestroyResampleFilterTLS(resample_filter);
2907
2908 if (status == MagickFalse)
2909 distort_image=DestroyImage(distort_image);
2910 }
2911
2912 /* Arc does not return an offset unless 'bestfit' is in effect
2913 And the user has not provided an overriding 'viewport'.
2914 */
2915 if ( method == ArcDistortion && !bestfit && !viewport_given ) {
2916 distort_image->page.x = 0;
2917 distort_image->page.y = 0;
2918 }
2919 coeff=(double *) RelinquishMagickMemory(coeff);
2920 return(distort_image);
2921}
2922␌
2923/*
2924%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2925% %
2926% %
2927% %
2928% R o t a t e I m a g e %
2929% %
2930% %
2931% %
2932%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2933%
2934% RotateImage() creates a new image that is a rotated copy of an existing
2935% one. Positive angles rotate counter-clockwise (right-hand rule), while
2936% negative angles rotate clockwise. Rotated images are usually larger than
2937% the originals and have 'empty' triangular corners. X axis. Empty
2938% triangles left over from shearing the image are filled with the background
2939% color defined by member 'background_color' of the image. RotateImage
2940% allocates the memory necessary for the new Image structure and returns a
2941% pointer to the new image.
2942%
2943% The format of the RotateImage method is:
2944%
2945% Image *RotateImage(const Image *image,const double degrees,
2946% ExceptionInfo *exception)
2947%
2948% A description of each parameter follows.
2949%
2950% o image: the image.
2951%
2952% o degrees: Specifies the number of degrees to rotate the image.
2953%
2954% o exception: return any errors or warnings in this structure.
2955%
2956*/
2957MagickExport Image *RotateImage(const Image *image,const double degrees,
2958 ExceptionInfo *exception)
2959{
2960 Image
2961 *distort_image,
2962 *rotate_image;
2963
2964 double
2965 angle;
2966
2967 PointInfo
2968 shear;
2969
2970 size_t
2971 rotations;
2972
2973 /*
2974 Adjust rotation angle.
2975 */
2976 assert(image != (Image *) NULL);
2977 assert(image->signature == MagickCoreSignature);
2978 if (IsEventLogging() != MagickFalse)
2979 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2980 assert(exception != (ExceptionInfo *) NULL);
2981 assert(exception->signature == MagickCoreSignature);
2982 angle=fmod(degrees,360.0);
2983 while (angle < -45.0)
2984 angle+=360.0;
2985 for (rotations=0; angle > 45.0; rotations++)
2986 angle-=90.0;
2987 rotations%=4;
2988 shear.x=(-tan((double) DegreesToRadians(angle)/2.0));
2989 shear.y=sin((double) DegreesToRadians(angle));
2990 if ((fabs(shear.x) < MagickEpsilon) && (fabs(shear.y) < MagickEpsilon))
2991 return(IntegralRotateImage(image,rotations,exception));
2992 distort_image=CloneImage(image,0,0,MagickTrue,exception);
2993 if (distort_image == (Image *) NULL)
2994 return((Image *) NULL);
2995 (void) SetImageVirtualPixelMethod(distort_image,BackgroundVirtualPixelMethod,
2996 exception);
2997 rotate_image=DistortImage(distort_image,ScaleRotateTranslateDistortion,1,
2998 &degrees,MagickTrue,exception);
2999 distort_image=DestroyImage(distort_image);
3000 return(rotate_image);
3001}
3002␌
3003/*
3004%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3005% %
3006% %
3007% %
3008% S p a r s e C o l o r I m a g e %
3009% %
3010% %
3011% %
3012%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3013%
3014% SparseColorImage(), given a set of coordinates, interpolates the colors
3015% found at those coordinates, across the whole image, using various methods.
3016%
3017% The format of the SparseColorImage() method is:
3018%
3019% Image *SparseColorImage(const Image *image,
3020% const SparseColorMethod method,const size_t number_arguments,
3021% const double *arguments,ExceptionInfo *exception)
3022%
3023% A description of each parameter follows:
3024%
3025% o image: the image to be filled in.
3026%
3027% o method: the method to fill in the gradient between the control points.
3028%
3029% The methods used for SparseColor() are often simular to methods
3030% used for DistortImage(), and even share the same code for determination
3031% of the function coefficients, though with more dimensions (or resulting
3032% values).
3033%
3034% o number_arguments: the number of arguments given.
3035%
3036% o arguments: array of floating point arguments for this method--
3037% x,y,color_values-- with color_values given as normalized values.
3038%
3039% o exception: return any errors or warnings in this structure
3040%
3041*/
3042MagickExport Image *SparseColorImage(const Image *image,
3043 const SparseColorMethod method,const size_t number_arguments,
3044 const double *arguments,ExceptionInfo *exception)
3045{
3046#define SparseColorTag "Distort/SparseColor"
3047
3048 double
3049 *coeff;
3050
3051 Image
3052 *sparse_image;
3053
3054 size_t
3055 number_colors;
3056
3057 SparseColorMethod
3058 sparse_method;
3059
3060 assert(image != (Image *) NULL);
3061 assert(image->signature == MagickCoreSignature);
3062 assert(exception != (ExceptionInfo *) NULL);
3063 assert(exception->signature == MagickCoreSignature);
3064 if (IsEventLogging() != MagickFalse)
3065 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
3066
3067 /* Determine number of color values needed per control point */
3068 number_colors=0;
3069 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
3070 number_colors++;
3071 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
3072 number_colors++;
3073 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
3074 number_colors++;
3075 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
3076 (image->colorspace == CMYKColorspace))
3077 number_colors++;
3078 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
3079 (image->alpha_trait != UndefinedPixelTrait))
3080 number_colors++;
3081
3082 /*
3083 Convert input arguments into mapping coefficients, in this case
3084 we are mapping (distorting) colors, rather than coordinates.
3085 */
3086 { DistortMethod
3087 distort_method;
3088
3089 distort_method=(DistortMethod) method;
3090 if ( distort_method >= SentinelDistortion )
3091 distort_method = ShepardsDistortion; /* Pretend to be Shepards */
3092 coeff = GenerateCoefficients(image, &distort_method, number_arguments,
3093 arguments, number_colors, exception);
3094 if ( coeff == (double *) NULL )
3095 return((Image *) NULL);
3096 /*
3097 Note some Distort Methods may fall back to other simpler methods,
3098 Currently the only fallback of concern is Bilinear to Affine
3099 (Barycentric), which is also sparse_colr method. This also ensures
3100 correct two and one color Barycentric handling.
3101 */
3102 sparse_method = (SparseColorMethod) distort_method;
3103 if ( distort_method == ShepardsDistortion )
3104 sparse_method = method; /* return non-distort methods to normal */
3105 if ( sparse_method == InverseColorInterpolate )
3106 coeff[0]=0.5; /* sqrt() the squared distance for inverse */
3107 }
3108
3109 /* Verbose output */
3110 if (IsStringTrue(GetImageArtifact(image,"verbose")) != MagickFalse) {
3111
3112 switch (sparse_method) {
3113 case BarycentricColorInterpolate:
3114 {
3115 ssize_t x=0;
3116 (void) FormatLocaleFile(stderr, "Barycentric Sparse Color:\n");
3117 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
3118 (void) FormatLocaleFile(stderr, " -channel R -fx '%+lf*i %+lf*j %+lf' \\\n",
3119 coeff[x], coeff[x+1], coeff[x+2]),x+=3;
3120 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
3121 (void) FormatLocaleFile(stderr, " -channel G -fx '%+lf*i %+lf*j %+lf' \\\n",
3122 coeff[x], coeff[x+1], coeff[x+2]),x+=3;
3123 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
3124 (void) FormatLocaleFile(stderr, " -channel B -fx '%+lf*i %+lf*j %+lf' \\\n",
3125 coeff[x], coeff[x+1], coeff[x+2]),x+=3;
3126 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
3127 (image->colorspace == CMYKColorspace))
3128 (void) FormatLocaleFile(stderr, " -channel K -fx '%+lf*i %+lf*j %+lf' \\\n",
3129 coeff[x], coeff[x+1], coeff[x+2]),x+=3;
3130 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
3131 (image->alpha_trait != UndefinedPixelTrait))
3132 (void) FormatLocaleFile(stderr, " -channel A -fx '%+lf*i %+lf*j %+lf' \\\n",
3133 coeff[x], coeff[x+1], coeff[x+2]),x+=3;
3134 break;
3135 }
3136 case BilinearColorInterpolate:
3137 {
3138 ssize_t x=0;
3139 (void) FormatLocaleFile(stderr, "Bilinear Sparse Color\n");
3140 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
3141 (void) FormatLocaleFile(stderr, " -channel R -fx '%+lf*i %+lf*j %+lf*i*j %+lf;\n",
3142 coeff[ x ], coeff[x+1],
3143 coeff[x+2], coeff[x+3]),x+=4;
3144 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
3145 (void) FormatLocaleFile(stderr, " -channel G -fx '%+lf*i %+lf*j %+lf*i*j %+lf;\n",
3146 coeff[ x ], coeff[x+1],
3147 coeff[x+2], coeff[x+3]),x+=4;
3148 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
3149 (void) FormatLocaleFile(stderr, " -channel B -fx '%+lf*i %+lf*j %+lf*i*j %+lf;\n",
3150 coeff[ x ], coeff[x+1],
3151 coeff[x+2], coeff[x+3]),x+=4;
3152 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
3153 (image->colorspace == CMYKColorspace))
3154 (void) FormatLocaleFile(stderr, " -channel K -fx '%+lf*i %+lf*j %+lf*i*j %+lf;\n",
3155 coeff[ x ], coeff[x+1],
3156 coeff[x+2], coeff[x+3]),x+=4;
3157 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
3158 (image->alpha_trait != UndefinedPixelTrait))
3159 (void) FormatLocaleFile(stderr, " -channel A -fx '%+lf*i %+lf*j %+lf*i*j %+lf;\n",
3160 coeff[ x ], coeff[x+1],
3161 coeff[x+2], coeff[x+3]),x+=4;
3162 break;
3163 }
3164 default:
3165 /* sparse color method is too complex for FX emulation */
3166 break;
3167 }
3168 }
3169
3170 /* Generate new image for generated interpolated gradient.
3171 * ASIDE: Actually we could have just replaced the colors of the original
3172 * image, but IM Core policy, is if storage class could change then clone
3173 * the image.
3174 */
3175
3176 sparse_image=CloneImage(image,0,0,MagickTrue,exception);
3177 if (sparse_image == (Image *) NULL)
3178 return((Image *) NULL);
3179 if (SetImageStorageClass(sparse_image,DirectClass,exception) == MagickFalse)
3180 { /* if image is ColorMapped - change it to DirectClass */
3181 sparse_image=DestroyImage(sparse_image);
3182 return((Image *) NULL);
3183 }
3184 if (IsGrayColorspace(sparse_image->colorspace) != MagickFalse)
3185 (void) SetImageColorspace(sparse_image,sRGBColorspace,exception);
3186 { /* ----- MAIN CODE ----- */
3187 CacheView
3188 *sparse_view;
3189
3190 MagickBooleanType
3191 status;
3192
3193 MagickOffsetType
3194 progress;
3195
3196 ssize_t
3197 j;
3198
3199 status=MagickTrue;
3200 progress=0;
3201 sparse_view=AcquireAuthenticCacheView(sparse_image,exception);
3202#if defined(MAGICKCORE_OPENMP_SUPPORT)
3203 #pragma omp parallel for schedule(static) shared(progress,status) \
3204 magick_number_threads(image,sparse_image,sparse_image->rows,1)
3205#endif
3206 for (j=0; j < (ssize_t) sparse_image->rows; j++)
3207 {
3208 MagickBooleanType
3209 sync;
3210
3211 PixelInfo
3212 pixel; /* pixel to assign to distorted image */
3213
3214 Quantum
3215 *magick_restrict q;
3216
3217 ssize_t
3218 i;
3219
3220 q=GetCacheViewAuthenticPixels(sparse_view,0,j,sparse_image->columns,1,
3221 exception);
3222 if (q == (Quantum *) NULL)
3223 {
3224 status=MagickFalse;
3225 continue;
3226 }
3227 GetPixelInfo(sparse_image,&pixel);
3228 for (i=0; i < (ssize_t) sparse_image->columns; i++)
3229 {
3230 GetPixelInfoPixel(sparse_image,q,&pixel);
3231 switch (sparse_method)
3232 {
3233 case BarycentricColorInterpolate:
3234 {
3235 ssize_t x=0;
3236 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3237 pixel.red = coeff[x]*i +coeff[x+1]*j
3238 +coeff[x+2], x+=3;
3239 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3240 pixel.green = coeff[x]*i +coeff[x+1]*j
3241 +coeff[x+2], x+=3;
3242 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3243 pixel.blue = coeff[x]*i +coeff[x+1]*j
3244 +coeff[x+2], x+=3;
3245 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3246 (sparse_image->colorspace == CMYKColorspace))
3247 pixel.black = coeff[x]*i +coeff[x+1]*j
3248 +coeff[x+2], x+=3;
3249 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3250 (sparse_image->alpha_trait != UndefinedPixelTrait))
3251 pixel.alpha = coeff[x]*i +coeff[x+1]*j
3252 +coeff[x+2], x+=3;
3253 break;
3254 }
3255 case BilinearColorInterpolate:
3256 {
3257 ssize_t x=0;
3258 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3259 pixel.red = coeff[x]*i + coeff[x+1]*j +
3260 coeff[x+2]*i*j + coeff[x+3], x+=4;
3261 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3262 pixel.green = coeff[x]*i + coeff[x+1]*j +
3263 coeff[x+2]*i*j + coeff[x+3], x+=4;
3264 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3265 pixel.blue = coeff[x]*i + coeff[x+1]*j +
3266 coeff[x+2]*i*j + coeff[x+3], x+=4;
3267 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3268 (image->colorspace == CMYKColorspace))
3269 pixel.black = coeff[x]*i + coeff[x+1]*j +
3270 coeff[x+2]*i*j + coeff[x+3], x+=4;
3271 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3272 (sparse_image->alpha_trait != UndefinedPixelTrait))
3273 pixel.alpha = coeff[x]*i + coeff[x+1]*j +
3274 coeff[x+2]*i*j + coeff[x+3], x+=4;
3275 break;
3276 }
3277 case InverseColorInterpolate:
3278 case ShepardsColorInterpolate:
3279 { /* Inverse (Squared) Distance weights average (IDW) */
3280 double
3281 denominator;
3282
3283 size_t
3284 k;
3285
3286 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3287 pixel.red=0.0;
3288 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3289 pixel.green=0.0;
3290 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3291 pixel.blue=0.0;
3292 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3293 (image->colorspace == CMYKColorspace))
3294 pixel.black=0.0;
3295 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3296 (sparse_image->alpha_trait != UndefinedPixelTrait))
3297 pixel.alpha=0.0;
3298 denominator = 0.0;
3299 for (k=0; k<number_arguments; k+=2+number_colors)
3300 {
3301 double weight =
3302 ((double) i-arguments[ k ])*((double) i-arguments[ k ])
3303 + ((double) j-arguments[k+1])*((double) j-arguments[k+1]);
3304 ssize_t x = (ssize_t) k+2;
3305
3306 weight = pow(weight,coeff[0]); /* inverse of power factor */
3307 weight = ( weight < 1.0 ) ? 1.0 : 1.0/weight;
3308 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3309 pixel.red += arguments[x++]*weight;
3310 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3311 pixel.green += arguments[x++]*weight;
3312 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3313 pixel.blue += arguments[x++]*weight;
3314 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3315 (image->colorspace == CMYKColorspace))
3316 pixel.black += arguments[x++]*weight;
3317 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3318 (sparse_image->alpha_trait != UndefinedPixelTrait))
3319 pixel.alpha += arguments[x++]*weight;
3320 denominator += weight;
3321 }
3322 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3323 pixel.red/=denominator;
3324 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3325 pixel.green/=denominator;
3326 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3327 pixel.blue/=denominator;
3328 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3329 (image->colorspace == CMYKColorspace))
3330 pixel.black/=denominator;
3331 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3332 (sparse_image->alpha_trait != UndefinedPixelTrait))
3333 pixel.alpha/=denominator;
3334 break;
3335 }
3336 case ManhattanColorInterpolate:
3337 {
3338 double
3339 minimum = MagickMaximumValue;
3340
3341 size_t
3342 k;
3343
3344 /*
3345 Just use the closest control point you can find!
3346 */
3347 for (k=0; k<number_arguments; k+=2+number_colors)
3348 {
3349 double distance = fabs((double)i-arguments[ k ])+
3350 fabs((double)j-arguments[k+1]);
3351 if ( distance < minimum ) {
3352 ssize_t x=(ssize_t) k+2;
3353 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3354 pixel.red=arguments[x++];
3355 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3356 pixel.green=arguments[x++];
3357 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3358 pixel.blue=arguments[x++];
3359 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3360 (image->colorspace == CMYKColorspace))
3361 pixel.black=arguments[x++];
3362 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3363 (sparse_image->alpha_trait != UndefinedPixelTrait))
3364 pixel.alpha=arguments[x++];
3365 minimum = distance;
3366 }
3367 }
3368 break;
3369 }
3370 case VoronoiColorInterpolate:
3371 default:
3372 {
3373 double
3374 minimum = MagickMaximumValue;
3375
3376 size_t
3377 k;
3378
3379 /*
3380 Just use the closest control point you can find!
3381 */
3382 for (k=0; k<number_arguments; k+=2+number_colors) {
3383 double distance =
3384 ((double) i-arguments[ k ])*((double) i-arguments[ k ])
3385 + ((double) j-arguments[k+1])*((double) j-arguments[k+1]);
3386 if ( distance < minimum ) {
3387 ssize_t x = (ssize_t) k+2;
3388 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3389 pixel.red=arguments[x++];
3390 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3391 pixel.green=arguments[x++];
3392 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3393 pixel.blue=arguments[x++];
3394 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3395 (image->colorspace == CMYKColorspace))
3396 pixel.black=arguments[x++];
3397 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3398 (sparse_image->alpha_trait != UndefinedPixelTrait))
3399 pixel.alpha=arguments[x++];
3400 minimum = distance;
3401 }
3402 }
3403 break;
3404 }
3405 }
3406 /* set the color directly back into the source image */
3407 if ((GetPixelRedTraits(sparse_image) & UpdatePixelTrait) != 0)
3408 pixel.red=(MagickRealType) ClampPixel((double) QuantumRange*
3409 pixel.red);
3410 if ((GetPixelGreenTraits(sparse_image) & UpdatePixelTrait) != 0)
3411 pixel.green=(MagickRealType) ClampPixel((double) QuantumRange*
3412 pixel.green);
3413 if ((GetPixelBlueTraits(sparse_image) & UpdatePixelTrait) != 0)
3414 pixel.blue=(MagickRealType) ClampPixel((double) QuantumRange*
3415 pixel.blue);
3416 if (((GetPixelBlackTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3417 (image->colorspace == CMYKColorspace))
3418 pixel.black=(MagickRealType) ClampPixel((double) QuantumRange*
3419 pixel.black);
3420 if (((GetPixelAlphaTraits(sparse_image) & UpdatePixelTrait) != 0) &&
3421 (image->alpha_trait != UndefinedPixelTrait))
3422 pixel.alpha=(MagickRealType) ClampPixel((double) QuantumRange*
3423 pixel.alpha);
3424 SetPixelViaPixelInfo(sparse_image,&pixel,q);
3425 q+=(ptrdiff_t) GetPixelChannels(sparse_image);
3426 }
3427 sync=SyncCacheViewAuthenticPixels(sparse_view,exception);
3428 if (sync == MagickFalse)
3429 status=MagickFalse;
3430 if (image->progress_monitor != (MagickProgressMonitor) NULL)
3431 {
3432 MagickBooleanType
3433 proceed;
3434
3435#if defined(MAGICKCORE_OPENMP_SUPPORT)
3436 #pragma omp atomic
3437#endif
3438 progress++;
3439 proceed=SetImageProgress(image,SparseColorTag,progress,image->rows);
3440 if (proceed == MagickFalse)
3441 status=MagickFalse;
3442 }
3443 }
3444 sparse_view=DestroyCacheView(sparse_view);
3445 if (status == MagickFalse)
3446 sparse_image=DestroyImage(sparse_image);
3447 }
3448 coeff = (double *) RelinquishMagickMemory(coeff);
3449 return(sparse_image);
3450}