2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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 %
13 % MagickCore Image Distortion Methods %
21 % Copyright 1999-2013 ImageMagick Studio LLC, a non-profit organization %
22 % dedicated to making software imaging solutions freely available. %
24 % You may not use this file except in compliance with the License. You may %
25 % obtain a copy of the License at %
27 % http://www.imagemagick.org/script/license.php %
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. %
35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
43 #include "MagickCore/studio.h"
44 #include "MagickCore/artifact.h"
45 #include "MagickCore/cache.h"
46 #include "MagickCore/cache-view.h"
47 #include "MagickCore/colorspace-private.h"
48 #include "MagickCore/composite-private.h"
49 #include "MagickCore/distort.h"
50 #include "MagickCore/exception.h"
51 #include "MagickCore/exception-private.h"
52 #include "MagickCore/gem.h"
53 #include "MagickCore/hashmap.h"
54 #include "MagickCore/image.h"
55 #include "MagickCore/list.h"
56 #include "MagickCore/matrix.h"
57 #include "MagickCore/matrix-private.h"
58 #include "MagickCore/memory_.h"
59 #include "MagickCore/monitor-private.h"
60 #include "MagickCore/option.h"
61 #include "MagickCore/pixel.h"
62 #include "MagickCore/pixel-accessor.h"
63 #include "MagickCore/pixel-private.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"
77 Numerous internal routines for image distortions.
79 static inline double MagickMin(const double x,const double y)
81 return( x < y ? x : y);
83 static inline double MagickMax(const double x,const double y)
85 return( x > y ? x : y);
88 static inline void AffineArgsToCoefficients(double *affine)
90 /* map external sx,ry,rx,sy,tx,ty to internal c0,c2,c4,c1,c3,c5 */
91 double tmp[4]; /* note indexes 0 and 5 remain unchanged */
92 tmp[0]=affine[1]; tmp[1]=affine[2]; tmp[2]=affine[3]; tmp[3]=affine[4];
93 affine[3]=tmp[0]; affine[1]=tmp[1]; affine[4]=tmp[2]; affine[2]=tmp[3];
96 static inline void CoefficientsToAffineArgs(double *coeff)
98 /* map internal c0,c1,c2,c3,c4,c5 to external sx,ry,rx,sy,tx,ty */
99 double tmp[4]; /* note indexes 0 and 5 remain unchanged */
100 tmp[0]=coeff[3]; tmp[1]=coeff[1]; tmp[2]=coeff[4]; tmp[3]=coeff[2];
101 coeff[1]=tmp[0]; coeff[2]=tmp[1]; coeff[3]=tmp[2]; coeff[4]=tmp[3];
103 static void InvertAffineCoefficients(const double *coeff,double *inverse)
105 /* From "Digital Image Warping" by George Wolberg, page 50 */
108 determinant=PerceptibleReciprocal(coeff[0]*coeff[4]-coeff[1]*coeff[3]);
109 inverse[0]=determinant*coeff[4];
110 inverse[1]=determinant*(-coeff[1]);
111 inverse[2]=determinant*(coeff[1]*coeff[5]-coeff[2]*coeff[4]);
112 inverse[3]=determinant*(-coeff[3]);
113 inverse[4]=determinant*coeff[0];
114 inverse[5]=determinant*(coeff[2]*coeff[3]-coeff[0]*coeff[5]);
117 static void InvertPerspectiveCoefficients(const double *coeff,
120 /* From "Digital Image Warping" by George Wolberg, page 53 */
123 determinant=PerceptibleReciprocal(coeff[0]*coeff[4]-coeff[3]*coeff[1]);
124 inverse[0]=determinant*(coeff[4]-coeff[7]*coeff[5]);
125 inverse[1]=determinant*(coeff[7]*coeff[2]-coeff[1]);
126 inverse[2]=determinant*(coeff[1]*coeff[5]-coeff[4]*coeff[2]);
127 inverse[3]=determinant*(coeff[6]*coeff[5]-coeff[3]);
128 inverse[4]=determinant*(coeff[0]-coeff[6]*coeff[2]);
129 inverse[5]=determinant*(coeff[3]*coeff[2]-coeff[0]*coeff[5]);
130 inverse[6]=determinant*(coeff[3]*coeff[7]-coeff[6]*coeff[4]);
131 inverse[7]=determinant*(coeff[6]*coeff[1]-coeff[0]*coeff[7]);
134 static inline double MagickRound(double x)
137 Round the fraction to nearest integer.
140 return((double) ((ssize_t) (x+0.5)));
141 return((double) ((ssize_t) (x-0.5)));
145 * Polynomial Term Defining Functions
147 * Order must either be an integer, or 1.5 to produce
148 * the 2 number_valuesal polynomial function...
149 * affine 1 (3) u = c0 + c1*x + c2*y
150 * bilinear 1.5 (4) u = '' + c3*x*y
151 * quadratic 2 (6) u = '' + c4*x*x + c5*y*y
152 * cubic 3 (10) u = '' + c6*x^3 + c7*x*x*y + c8*x*y*y + c9*y^3
153 * quartic 4 (15) u = '' + c10*x^4 + ... + c14*y^4
154 * quintic 5 (21) u = '' + c15*x^5 + ... + c20*y^5
155 * number in parenthesis minimum number of points needed.
156 * Anything beyond quintic, has not been implemented until
157 * a more automated way of determining terms is found.
159 * Note the slight re-ordering of the terms for a quadratic polynomial
160 * which is to allow the use of a bi-linear (order=1.5) polynomial.
161 * All the later polynomials are ordered simply from x^N to y^N
163 static size_t poly_number_terms(double order)
165 /* Return the number of terms for a 2d polynomial */
166 if ( order < 1 || order > 5 ||
167 ( order != floor(order) && (order-1.5) > MagickEpsilon) )
168 return 0; /* invalid polynomial order */
169 return((size_t) floor((order+1)*(order+2)/2));
172 static double poly_basis_fn(ssize_t n, double x, double y)
174 /* Return the result for this polynomial term */
176 case 0: return( 1.0 ); /* constant */
178 case 2: return( y ); /* affine order = 1 terms = 3 */
179 case 3: return( x*y ); /* bilinear order = 1.5 terms = 4 */
180 case 4: return( x*x );
181 case 5: return( y*y ); /* quadratic order = 2 terms = 6 */
182 case 6: return( x*x*x );
183 case 7: return( x*x*y );
184 case 8: return( x*y*y );
185 case 9: return( y*y*y ); /* cubic order = 3 terms = 10 */
186 case 10: return( x*x*x*x );
187 case 11: return( x*x*x*y );
188 case 12: return( x*x*y*y );
189 case 13: return( x*y*y*y );
190 case 14: return( y*y*y*y ); /* quartic order = 4 terms = 15 */
191 case 15: return( x*x*x*x*x );
192 case 16: return( x*x*x*x*y );
193 case 17: return( x*x*x*y*y );
194 case 18: return( x*x*y*y*y );
195 case 19: return( x*y*y*y*y );
196 case 20: return( y*y*y*y*y ); /* quintic order = 5 terms = 21 */
198 return( 0 ); /* should never happen */
200 static const char *poly_basis_str(ssize_t n)
202 /* return the result for this polynomial term */
204 case 0: return(""); /* constant */
205 case 1: return("*ii");
206 case 2: return("*jj"); /* affine order = 1 terms = 3 */
207 case 3: return("*ii*jj"); /* bilinear order = 1.5 terms = 4 */
208 case 4: return("*ii*ii");
209 case 5: return("*jj*jj"); /* quadratic order = 2 terms = 6 */
210 case 6: return("*ii*ii*ii");
211 case 7: return("*ii*ii*jj");
212 case 8: return("*ii*jj*jj");
213 case 9: return("*jj*jj*jj"); /* cubic order = 3 terms = 10 */
214 case 10: return("*ii*ii*ii*ii");
215 case 11: return("*ii*ii*ii*jj");
216 case 12: return("*ii*ii*jj*jj");
217 case 13: return("*ii*jj*jj*jj");
218 case 14: return("*jj*jj*jj*jj"); /* quartic order = 4 terms = 15 */
219 case 15: return("*ii*ii*ii*ii*ii");
220 case 16: return("*ii*ii*ii*ii*jj");
221 case 17: return("*ii*ii*ii*jj*jj");
222 case 18: return("*ii*ii*jj*jj*jj");
223 case 19: return("*ii*jj*jj*jj*jj");
224 case 20: return("*jj*jj*jj*jj*jj"); /* quintic order = 5 terms = 21 */
226 return( "UNKNOWN" ); /* should never happen */
228 static double poly_basis_dx(ssize_t n, double x, double y)
230 /* polynomial term for x derivative */
232 case 0: return( 0.0 ); /* constant */
233 case 1: return( 1.0 );
234 case 2: return( 0.0 ); /* affine order = 1 terms = 3 */
235 case 3: return( y ); /* bilinear order = 1.5 terms = 4 */
237 case 5: return( 0.0 ); /* quadratic order = 2 terms = 6 */
238 case 6: return( x*x );
239 case 7: return( x*y );
240 case 8: return( y*y );
241 case 9: return( 0.0 ); /* cubic order = 3 terms = 10 */
242 case 10: return( x*x*x );
243 case 11: return( x*x*y );
244 case 12: return( x*y*y );
245 case 13: return( y*y*y );
246 case 14: return( 0.0 ); /* quartic order = 4 terms = 15 */
247 case 15: return( x*x*x*x );
248 case 16: return( x*x*x*y );
249 case 17: return( x*x*y*y );
250 case 18: return( x*y*y*y );
251 case 19: return( y*y*y*y );
252 case 20: return( 0.0 ); /* quintic order = 5 terms = 21 */
254 return( 0.0 ); /* should never happen */
256 static double poly_basis_dy(ssize_t n, double x, double y)
258 /* polynomial term for y derivative */
260 case 0: return( 0.0 ); /* constant */
261 case 1: return( 0.0 );
262 case 2: return( 1.0 ); /* affine order = 1 terms = 3 */
263 case 3: return( x ); /* bilinear order = 1.5 terms = 4 */
264 case 4: return( 0.0 );
265 case 5: return( y ); /* quadratic order = 2 terms = 6 */
266 default: return( poly_basis_dx(n-1,x,y) ); /* weird but true */
268 /* NOTE: the only reason that last is not true for 'quadratic'
269 is due to the re-arrangement of terms to allow for 'bilinear'
274 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
278 % A f f i n e T r a n s f o r m I m a g e %
282 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
284 % AffineTransformImage() transforms an image as dictated by the affine matrix.
285 % It allocates the memory necessary for the new Image structure and returns
286 % a pointer to the new image.
288 % The format of the AffineTransformImage method is:
290 % Image *AffineTransformImage(const Image *image,
291 % AffineMatrix *affine_matrix,ExceptionInfo *exception)
293 % A description of each parameter follows:
295 % o image: the image.
297 % o affine_matrix: the affine matrix.
299 % o exception: return any errors or warnings in this structure.
302 MagickExport Image *AffineTransformImage(const Image *image,
303 const AffineMatrix *affine_matrix,ExceptionInfo *exception)
312 Affine transform image.
314 assert(image->signature == MagickSignature);
315 if (image->debug != MagickFalse)
316 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
317 assert(affine_matrix != (AffineMatrix *) NULL);
318 assert(exception != (ExceptionInfo *) NULL);
319 assert(exception->signature == MagickSignature);
320 distort[0]=affine_matrix->sx;
321 distort[1]=affine_matrix->rx;
322 distort[2]=affine_matrix->ry;
323 distort[3]=affine_matrix->sy;
324 distort[4]=affine_matrix->tx;
325 distort[5]=affine_matrix->ty;
326 deskew_image=DistortImage(image,AffineProjectionDistortion,6,distort,
327 MagickTrue,exception);
328 return(deskew_image);
332 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
336 + G e n e r a t e C o e f f i c i e n t s %
340 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
342 % GenerateCoefficients() takes user provided input arguments and generates
343 % the coefficients, needed to apply the specific distortion for either
344 % distorting images (generally using control points) or generating a color
345 % gradient from sparsely separated color points.
347 % The format of the GenerateCoefficients() method is:
349 % Image *GenerateCoefficients(const Image *image,DistortImageMethod method,
350 % const size_t number_arguments,const double *arguments,
351 % size_t number_values, ExceptionInfo *exception)
353 % A description of each parameter follows:
355 % o image: the image to be distorted.
357 % o method: the method of image distortion/ sparse gradient
359 % o number_arguments: the number of arguments given.
361 % o arguments: the arguments for this distortion method.
363 % o number_values: the style and format of given control points, (caller type)
364 % 0: 2 dimensional mapping of control points (Distort)
365 % Format: u,v,x,y where u,v is the 'source' of the
366 % the color to be plotted, for DistortImage()
367 % N: Interpolation of control points with N values (usally r,g,b)
368 % Format: x,y,r,g,b mapping x,y to color values r,g,b
369 % IN future, variable number of values may be given (1 to N)
371 % o exception: return any errors or warnings in this structure
373 % Note that the returned array of double values must be freed by the
374 % calling method using RelinquishMagickMemory(). This however may change in
375 % the future to require a more 'method' specific method.
377 % Because of this this method should not be classed as stable or used
378 % outside other MagickCore library methods.
381 static double *GenerateCoefficients(const Image *image,
382 DistortImageMethod *method,const size_t number_arguments,
383 const double *arguments,size_t number_values,ExceptionInfo *exception)
392 number_coeff, /* number of coefficients to return (array size) */
393 cp_size, /* number floating point numbers per control point */
394 cp_x,cp_y, /* the x,y indexes for control point */
395 cp_values; /* index of values for this control point */
396 /* number_values Number of values given per control point */
398 if ( number_values == 0 ) {
399 /* Image distortion using control points (or other distortion)
400 That is generate a mapping so that x,y->u,v given u,v,x,y
402 number_values = 2; /* special case: two values of u,v */
403 cp_values = 0; /* the values i,j are BEFORE the destination CP x,y */
404 cp_x = 2; /* location of x,y in input control values */
406 /* NOTE: cp_values, also used for later 'reverse map distort' tests */
409 cp_x = 0; /* location of x,y in input control values */
411 cp_values = 2; /* and the other values are after x,y */
412 /* Typically in this case the values are R,G,B color values */
414 cp_size = number_values+2; /* each CP defintion involves this many numbers */
416 /* If not enough control point pairs are found for specific distortions
417 fall back to Affine distortion (allowing 0 to 3 point pairs)
419 if ( number_arguments < 4*cp_size &&
420 ( *method == BilinearForwardDistortion
421 || *method == BilinearReverseDistortion
422 || *method == PerspectiveDistortion
424 *method = AffineDistortion;
428 case AffineDistortion:
429 /* also BarycentricColorInterpolate: */
430 number_coeff=3*number_values;
432 case PolynomialDistortion:
433 /* number of coefficents depend on the given polynomal 'order' */
434 if ( number_arguments <= 1 && (number_arguments-1)%cp_size != 0)
436 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
437 "InvalidArgument","%s : '%s'","Polynomial",
438 "Invalid number of args: order [CPs]...");
439 return((double *) NULL);
441 i = poly_number_terms(arguments[0]);
442 number_coeff = 2 + i*number_values;
444 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
445 "InvalidArgument","%s : '%s'","Polynomial",
446 "Invalid order, should be interger 1 to 5, or 1.5");
447 return((double *) NULL);
449 if ( number_arguments < 1+i*cp_size ) {
450 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
451 "InvalidArgument", "%s : 'require at least %.20g CPs'",
452 "Polynomial", (double) i);
453 return((double *) NULL);
456 case BilinearReverseDistortion:
457 number_coeff=4*number_values;
460 The rest are constants as they are only used for image distorts
462 case BilinearForwardDistortion:
463 number_coeff=10; /* 2*4 coeff plus 2 constants */
464 cp_x = 0; /* Reverse src/dest coords for forward mapping */
469 case QuadraterialDistortion:
470 number_coeff=19; /* BilinearForward + BilinearReverse */
473 case ShepardsDistortion:
474 number_coeff=1; /* The power factor to use */
479 case ScaleRotateTranslateDistortion:
480 case AffineProjectionDistortion:
481 case Plane2CylinderDistortion:
482 case Cylinder2PlaneDistortion:
485 case PolarDistortion:
486 case DePolarDistortion:
489 case PerspectiveDistortion:
490 case PerspectiveProjectionDistortion:
493 case BarrelDistortion:
494 case BarrelInverseDistortion:
498 perror("unknown method given"); /* just fail assertion */
501 /* allocate the array of coefficients needed */
502 coeff = (double *) AcquireQuantumMemory(number_coeff,sizeof(*coeff));
503 if (coeff == (double *) NULL) {
504 (void) ThrowMagickException(exception,GetMagickModule(),
505 ResourceLimitError,"MemoryAllocationFailed",
506 "%s", "GenerateCoefficients");
507 return((double *) NULL);
510 /* zero out coefficients array */
511 for (i=0; i < number_coeff; i++)
516 case AffineDistortion:
520 for each 'value' given
522 Input Arguments are sets of control points...
523 For Distort Images u,v, x,y ...
524 For Sparse Gradients x,y, r,g,b ...
526 if ( number_arguments%cp_size != 0 ||
527 number_arguments < cp_size ) {
528 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
529 "InvalidArgument", "%s : 'require at least %.20g CPs'",
531 coeff=(double *) RelinquishMagickMemory(coeff);
532 return((double *) NULL);
534 /* handle special cases of not enough arguments */
535 if ( number_arguments == cp_size ) {
536 /* Only 1 CP Set Given */
537 if ( cp_values == 0 ) {
538 /* image distortion - translate the image */
540 coeff[2] = arguments[0] - arguments[2];
542 coeff[5] = arguments[1] - arguments[3];
545 /* sparse gradient - use the values directly */
546 for (i=0; i<number_values; i++)
547 coeff[i*3+2] = arguments[cp_values+i];
551 /* 2 or more points (usally 3) given.
552 Solve a least squares simultaneous equation for coefficients.
562 /* create matrix, and a fake vectors matrix */
563 matrix = AcquireMagickMatrix(3UL,3UL);
564 vectors = (double **) AcquireQuantumMemory(number_values,sizeof(*vectors));
565 if (matrix == (double **) NULL || vectors == (double **) NULL)
567 matrix = RelinquishMagickMatrix(matrix, 3UL);
568 vectors = (double **) RelinquishMagickMemory(vectors);
569 coeff = (double *) RelinquishMagickMemory(coeff);
570 (void) ThrowMagickException(exception,GetMagickModule(),
571 ResourceLimitError,"MemoryAllocationFailed",
572 "%s", "DistortCoefficients");
573 return((double *) NULL);
575 /* fake a number_values x3 vectors matrix from coefficients array */
576 for (i=0; i < number_values; i++)
577 vectors[i] = &(coeff[i*3]);
578 /* Add given control point pairs for least squares solving */
579 for (i=0; i < number_arguments; i+=cp_size) {
580 terms[0] = arguments[i+cp_x]; /* x */
581 terms[1] = arguments[i+cp_y]; /* y */
582 terms[2] = 1; /* 1 */
583 LeastSquaresAddTerms(matrix,vectors,terms,
584 &(arguments[i+cp_values]),3UL,number_values);
586 if ( number_arguments == 2*cp_size ) {
587 /* Only two pairs were given, but we need 3 to solve the affine.
588 Fake extra coordinates by rotating p1 around p0 by 90 degrees.
589 x2 = x0 - (y1-y0) y2 = y0 + (x1-x0)
591 terms[0] = arguments[cp_x]
592 - ( arguments[cp_size+cp_y] - arguments[cp_y] ); /* x2 */
593 terms[1] = arguments[cp_y] +
594 + ( arguments[cp_size+cp_x] - arguments[cp_x] ); /* y2 */
595 terms[2] = 1; /* 1 */
596 if ( cp_values == 0 ) {
597 /* Image Distortion - rotate the u,v coordients too */
600 uv2[0] = arguments[0] - arguments[5] + arguments[1]; /* u2 */
601 uv2[1] = arguments[1] + arguments[4] - arguments[0]; /* v2 */
602 LeastSquaresAddTerms(matrix,vectors,terms,uv2,3UL,2UL);
605 /* Sparse Gradient - use values of p0 for linear gradient */
606 LeastSquaresAddTerms(matrix,vectors,terms,
607 &(arguments[cp_values]),3UL,number_values);
610 /* Solve for LeastSquares Coefficients */
611 status=GaussJordanElimination(matrix,vectors,3UL,number_values);
612 matrix = RelinquishMagickMatrix(matrix, 3UL);
613 vectors = (double **) RelinquishMagickMemory(vectors);
614 if ( status == MagickFalse ) {
615 coeff = (double *) RelinquishMagickMemory(coeff);
616 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
617 "InvalidArgument","%s : 'Unsolvable Matrix'",
618 CommandOptionToMnemonic(MagickDistortOptions, *method) );
619 return((double *) NULL);
624 case AffineProjectionDistortion:
627 Arguments: Affine Matrix (forward mapping)
628 Arguments sx, rx, ry, sy, tx, ty
629 Where u = sx*x + ry*y + tx
632 Returns coefficients (in there inverse form) ordered as...
635 AffineProjection Distortion Notes...
636 + Will only work with a 2 number_values for Image Distortion
637 + Can not be used for generating a sparse gradient (interpolation)
640 if (number_arguments != 6) {
641 coeff = (double *) RelinquishMagickMemory(coeff);
642 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
643 "InvalidArgument","%s : 'Needs 6 coeff values'",
644 CommandOptionToMnemonic(MagickDistortOptions, *method) );
645 return((double *) NULL);
647 /* FUTURE: trap test for sx*sy-rx*ry == 0 (determinant = 0, no inverse) */
648 for(i=0; i<6UL; i++ )
649 inverse[i] = arguments[i];
650 AffineArgsToCoefficients(inverse); /* map into coefficents */
651 InvertAffineCoefficients(inverse, coeff); /* invert */
652 *method = AffineDistortion;
656 case ScaleRotateTranslateDistortion:
658 /* Scale, Rotate and Translate Distortion
659 An alternative Affine Distortion
660 Argument options, by number of arguments given:
661 7: x,y, sx,sy, a, nx,ny
668 Where actions are (in order of application)
669 x,y 'center' of transforms (default = image center)
670 sx,sy scale image by this amount (default = 1)
671 a angle of rotation (argument required)
672 nx,ny move 'center' here (default = x,y or no movement)
673 And convert to affine mapping coefficients
675 ScaleRotateTranslate Distortion Notes...
676 + Does not use a set of CPs in any normal way
677 + Will only work with a 2 number_valuesal Image Distortion
678 + Cannot be used for generating a sparse gradient (interpolation)
684 /* set default center, and default scale */
685 x = nx = (double)(image->columns)/2.0 + (double)image->page.x;
686 y = ny = (double)(image->rows)/2.0 + (double)image->page.y;
688 switch ( number_arguments ) {
690 coeff = (double *) RelinquishMagickMemory(coeff);
691 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
692 "InvalidArgument","%s : 'Needs at least 1 argument'",
693 CommandOptionToMnemonic(MagickDistortOptions, *method) );
694 return((double *) NULL);
699 sx = sy = arguments[0];
703 x = nx = arguments[0];
704 y = ny = arguments[1];
705 switch ( number_arguments ) {
710 sx = sy = arguments[2];
719 sx = sy = arguments[2];
732 coeff = (double *) RelinquishMagickMemory(coeff);
733 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
734 "InvalidArgument","%s : 'Too Many Arguments (7 or less)'",
735 CommandOptionToMnemonic(MagickDistortOptions, *method) );
736 return((double *) NULL);
740 /* Trap if sx or sy == 0 -- image is scaled out of existance! */
741 if ( fabs(sx) < MagickEpsilon || fabs(sy) < MagickEpsilon ) {
742 coeff = (double *) RelinquishMagickMemory(coeff);
743 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
744 "InvalidArgument","%s : 'Zero Scale Given'",
745 CommandOptionToMnemonic(MagickDistortOptions, *method) );
746 return((double *) NULL);
748 /* Save the given arguments as an affine distortion */
749 a=DegreesToRadians(a); cosine=cos(a); sine=sin(a);
751 *method = AffineDistortion;
754 coeff[2]=x-nx*coeff[0]-ny*coeff[1];
757 coeff[5]=y-nx*coeff[3]-ny*coeff[4];
760 case PerspectiveDistortion:
762 Perspective Distortion (a ratio of affine distortions)
764 p(x,y) c0*x + c1*y + c2
765 u = ------ = ------------------
766 r(x,y) c6*x + c7*y + 1
768 q(x,y) c3*x + c4*y + c5
769 v = ------ = ------------------
770 r(x,y) c6*x + c7*y + 1
772 c8 = Sign of 'r', or the denominator affine, for the actual image.
773 This determines what part of the distorted image is 'ground'
774 side of the horizon, the other part is 'sky' or invalid.
775 Valid values are +1.0 or -1.0 only.
777 Input Arguments are sets of control points...
778 For Distort Images u,v, x,y ...
779 For Sparse Gradients x,y, r,g,b ...
781 Perspective Distortion Notes...
782 + Can be thought of as ratio of 3 affine transformations
783 + Not separatable: r() or c6 and c7 are used by both equations
784 + All 8 coefficients must be determined simultaniously
785 + Will only work with a 2 number_valuesal Image Distortion
786 + Can not be used for generating a sparse gradient (interpolation)
787 + It is not linear, but is simple to generate an inverse
788 + All lines within an image remain lines.
789 + but distances between points may vary.
803 if ( number_arguments%cp_size != 0 ||
804 number_arguments < cp_size*4 ) {
805 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
806 "InvalidArgument", "%s : 'require at least %.20g CPs'",
807 CommandOptionToMnemonic(MagickDistortOptions, *method), 4.0);
808 coeff=(double *) RelinquishMagickMemory(coeff);
809 return((double *) NULL);
811 /* fake 1x8 vectors matrix directly using the coefficients array */
812 vectors[0] = &(coeff[0]);
813 /* 8x8 least-squares matrix (zeroed) */
814 matrix = AcquireMagickMatrix(8UL,8UL);
815 if (matrix == (double **) NULL) {
816 (void) ThrowMagickException(exception,GetMagickModule(),
817 ResourceLimitError,"MemoryAllocationFailed",
818 "%s", "DistortCoefficients");
819 return((double *) NULL);
821 /* Add control points for least squares solving */
822 for (i=0; i < number_arguments; i+=4) {
823 terms[0]=arguments[i+cp_x]; /* c0*x */
824 terms[1]=arguments[i+cp_y]; /* c1*y */
825 terms[2]=1.0; /* c2*1 */
829 terms[6]=-terms[0]*arguments[i+cp_u]; /* 1/(c6*x) */
830 terms[7]=-terms[1]*arguments[i+cp_u]; /* 1/(c7*y) */
831 LeastSquaresAddTerms(matrix,vectors,terms,&(arguments[i+cp_u]),
837 terms[3]=arguments[i+cp_x]; /* c3*x */
838 terms[4]=arguments[i+cp_y]; /* c4*y */
839 terms[5]=1.0; /* c5*1 */
840 terms[6]=-terms[3]*arguments[i+cp_v]; /* 1/(c6*x) */
841 terms[7]=-terms[4]*arguments[i+cp_v]; /* 1/(c7*y) */
842 LeastSquaresAddTerms(matrix,vectors,terms,&(arguments[i+cp_v]),
845 /* Solve for LeastSquares Coefficients */
846 status=GaussJordanElimination(matrix,vectors,8UL,1UL);
847 matrix = RelinquishMagickMatrix(matrix, 8UL);
848 if ( status == MagickFalse ) {
849 coeff = (double *) RelinquishMagickMemory(coeff);
850 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
851 "InvalidArgument","%s : 'Unsolvable Matrix'",
852 CommandOptionToMnemonic(MagickDistortOptions, *method) );
853 return((double *) NULL);
856 Calculate 9'th coefficient! The ground-sky determination.
857 What is sign of the 'ground' in r() denominator affine function?
858 Just use any valid image coordinate (first control point) in
859 destination for determination of what part of view is 'ground'.
861 coeff[8] = coeff[6]*arguments[cp_x]
862 + coeff[7]*arguments[cp_y] + 1.0;
863 coeff[8] = (coeff[8] < 0.0) ? -1.0 : +1.0;
867 case PerspectiveProjectionDistortion:
870 Arguments: Perspective Coefficents (forward mapping)
872 if (number_arguments != 8) {
873 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
874 "InvalidArgument", "%s : 'Needs 8 coefficient values'",
875 CommandOptionToMnemonic(MagickDistortOptions, *method));
876 return((double *) NULL);
878 /* FUTURE: trap test c0*c4-c3*c1 == 0 (determinate = 0, no inverse) */
879 InvertPerspectiveCoefficients(arguments, coeff);
881 Calculate 9'th coefficient! The ground-sky determination.
882 What is sign of the 'ground' in r() denominator affine function?
883 Just use any valid image cocodinate in destination for determination.
884 For a forward mapped perspective the images 0,0 coord will map to
885 c2,c5 in the distorted image, so set the sign of denominator of that.
887 coeff[8] = coeff[6]*arguments[2]
888 + coeff[7]*arguments[5] + 1.0;
889 coeff[8] = (coeff[8] < 0.0) ? -1.0 : +1.0;
890 *method = PerspectiveDistortion;
894 case BilinearForwardDistortion:
895 case BilinearReverseDistortion:
897 /* Bilinear Distortion (Forward mapping)
898 v = c0*x + c1*y + c2*x*y + c3;
899 for each 'value' given
901 This is actually a simple polynomial Distortion! The difference
902 however is when we need to reverse the above equation to generate a
903 BilinearForwardDistortion (see below).
905 Input Arguments are sets of control points...
906 For Distort Images u,v, x,y ...
907 For Sparse Gradients x,y, r,g,b ...
918 /* check the number of arguments */
919 if ( number_arguments%cp_size != 0 ||
920 number_arguments < cp_size*4 ) {
921 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
922 "InvalidArgument", "%s : 'require at least %.20g CPs'",
923 CommandOptionToMnemonic(MagickDistortOptions, *method), 4.0);
924 coeff=(double *) RelinquishMagickMemory(coeff);
925 return((double *) NULL);
927 /* create matrix, and a fake vectors matrix */
928 matrix = AcquireMagickMatrix(4UL,4UL);
929 vectors = (double **) AcquireQuantumMemory(number_values,sizeof(*vectors));
930 if (matrix == (double **) NULL || vectors == (double **) NULL)
932 matrix = RelinquishMagickMatrix(matrix, 4UL);
933 vectors = (double **) RelinquishMagickMemory(vectors);
934 coeff = (double *) RelinquishMagickMemory(coeff);
935 (void) ThrowMagickException(exception,GetMagickModule(),
936 ResourceLimitError,"MemoryAllocationFailed",
937 "%s", "DistortCoefficients");
938 return((double *) NULL);
940 /* fake a number_values x4 vectors matrix from coefficients array */
941 for (i=0; i < number_values; i++)
942 vectors[i] = &(coeff[i*4]);
943 /* Add given control point pairs for least squares solving */
944 for (i=0; i < number_arguments; i+=cp_size) {
945 terms[0] = arguments[i+cp_x]; /* x */
946 terms[1] = arguments[i+cp_y]; /* y */
947 terms[2] = terms[0]*terms[1]; /* x*y */
948 terms[3] = 1; /* 1 */
949 LeastSquaresAddTerms(matrix,vectors,terms,
950 &(arguments[i+cp_values]),4UL,number_values);
952 /* Solve for LeastSquares Coefficients */
953 status=GaussJordanElimination(matrix,vectors,4UL,number_values);
954 matrix = RelinquishMagickMatrix(matrix, 4UL);
955 vectors = (double **) RelinquishMagickMemory(vectors);
956 if ( status == MagickFalse ) {
957 coeff = (double *) RelinquishMagickMemory(coeff);
958 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
959 "InvalidArgument","%s : 'Unsolvable Matrix'",
960 CommandOptionToMnemonic(MagickDistortOptions, *method) );
961 return((double *) NULL);
963 if ( *method == BilinearForwardDistortion ) {
964 /* Bilinear Forward Mapped Distortion
966 The above least-squares solved for coefficents but in the forward
967 direction, due to changes to indexing constants.
969 i = c0*x + c1*y + c2*x*y + c3;
970 j = c4*x + c5*y + c6*x*y + c7;
972 where i,j are in the destination image, NOT the source.
974 Reverse Pixel mapping however needs to use reverse of these
975 functions. It required a full page of algbra to work out the
976 reversed mapping formula, but resolves down to the following...
979 c9 = 2*(c2*c5-c1*c6); // '2*a' in the quadratic formula
981 i = i - c3; j = j - c7;
982 b = c6*i - c2*j + c8; // So that a*y^2 + b*y + c == 0
983 c = c4*i - c0*j; // y = ( -b +- sqrt(bb - 4ac) ) / (2*a)
987 y = ( -b + sqrt(r) ) / c9;
991 x = ( i - c1*y) / ( c1 - c2*y );
993 NB: if 'r' is negative there is no solution!
994 NB: the sign of the sqrt() should be negative if image becomes
995 flipped or flopped, or crosses over itself.
996 NB: techniqually coefficient c5 is not needed, anymore,
997 but kept for completness.
999 See Anthony Thyssen <A.Thyssen@griffith.edu.au>
1000 or Fred Weinhaus <fmw@alink.net> for more details.
1003 coeff[8] = coeff[0]*coeff[5] - coeff[1]*coeff[4];
1004 coeff[9] = 2*(coeff[2]*coeff[5] - coeff[1]*coeff[6]);
1009 case QuadrilateralDistortion:
1011 /* Map a Quadrilateral to a unit square using BilinearReverse
1012 Then map that unit square back to the final Quadrilateral
1013 using BilinearForward.
1015 Input Arguments are sets of control points...
1016 For Distort Images u,v, x,y ...
1017 For Sparse Gradients x,y, r,g,b ...
1020 /* UNDER CONSTRUCTION */
1025 case PolynomialDistortion:
1027 /* Polynomial Distortion
1029 First two coefficents are used to hole global polynomal information
1030 c0 = Order of the polynimial being created
1031 c1 = number_of_terms in one polynomial equation
1033 Rest of the coefficients map to the equations....
1034 v = c0 + c1*x + c2*y + c3*x*y + c4*x^2 + c5*y^2 + c6*x^3 + ...
1035 for each 'value' (number_values of them) given.
1036 As such total coefficients = 2 + number_terms * number_values
1038 Input Arguments are sets of control points...
1039 For Distort Images order [u,v, x,y] ...
1040 For Sparse Gradients order [x,y, r,g,b] ...
1042 Polynomial Distortion Notes...
1043 + UNDER DEVELOPMENT -- Do not expect this to remain as is.
1044 + Currently polynomial is a reversed mapped distortion.
1045 + Order 1.5 is fudged to map into a bilinear distortion.
1046 though it is not the same order as that distortion.
1054 nterms; /* number of polynomial terms per number_values */
1062 /* first two coefficients hold polynomial order information */
1063 coeff[0] = arguments[0];
1064 coeff[1] = (double) poly_number_terms(arguments[0]);
1065 nterms = (size_t) coeff[1];
1067 /* create matrix, a fake vectors matrix, and least sqs terms */
1068 matrix = AcquireMagickMatrix(nterms,nterms);
1069 vectors = (double **) AcquireQuantumMemory(number_values,sizeof(*vectors));
1070 terms = (double *) AcquireQuantumMemory(nterms, sizeof(*terms));
1071 if (matrix == (double **) NULL ||
1072 vectors == (double **) NULL ||
1073 terms == (double *) NULL )
1075 matrix = RelinquishMagickMatrix(matrix, nterms);
1076 vectors = (double **) RelinquishMagickMemory(vectors);
1077 terms = (double *) RelinquishMagickMemory(terms);
1078 coeff = (double *) RelinquishMagickMemory(coeff);
1079 (void) ThrowMagickException(exception,GetMagickModule(),
1080 ResourceLimitError,"MemoryAllocationFailed",
1081 "%s", "DistortCoefficients");
1082 return((double *) NULL);
1084 /* fake a number_values x3 vectors matrix from coefficients array */
1085 for (i=0; i < number_values; i++)
1086 vectors[i] = &(coeff[2+i*nterms]);
1087 /* Add given control point pairs for least squares solving */
1088 for (i=1; i < number_arguments; i+=cp_size) { /* NB: start = 1 not 0 */
1089 for (j=0; j < (ssize_t) nterms; j++)
1090 terms[j] = poly_basis_fn(j,arguments[i+cp_x],arguments[i+cp_y]);
1091 LeastSquaresAddTerms(matrix,vectors,terms,
1092 &(arguments[i+cp_values]),nterms,number_values);
1094 terms = (double *) RelinquishMagickMemory(terms);
1095 /* Solve for LeastSquares Coefficients */
1096 status=GaussJordanElimination(matrix,vectors,nterms,number_values);
1097 matrix = RelinquishMagickMatrix(matrix, nterms);
1098 vectors = (double **) RelinquishMagickMemory(vectors);
1099 if ( status == MagickFalse ) {
1100 coeff = (double *) RelinquishMagickMemory(coeff);
1101 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1102 "InvalidArgument","%s : 'Unsolvable Matrix'",
1103 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1104 return((double *) NULL);
1111 Args: arc_width rotate top_edge_radius bottom_edge_radius
1112 All but first argument are optional
1113 arc_width The angle over which to arc the image side-to-side
1114 rotate Angle to rotate image from vertical center
1115 top_radius Set top edge of source image at this radius
1116 bottom_radius Set bootom edge to this radius (radial scaling)
1118 By default, if the radii arguments are nor provided the image radius
1119 is calculated so the horizontal center-line is fits the given arc
1122 The output image size is ALWAYS adjusted to contain the whole image,
1123 and an offset is given to position image relative to the 0,0 point of
1124 the origin, allowing users to use relative positioning onto larger
1125 background (via -flatten).
1127 The arguments are converted to these coefficients
1128 c0: angle for center of source image
1129 c1: angle scale for mapping to source image
1130 c2: radius for top of source image
1131 c3: radius scale for mapping source image
1132 c4: centerline of arc within source image
1134 Note the coefficients use a center angle, so asymptotic join is
1135 furthest from both sides of the source image. This also means that
1136 for arc angles greater than 360 the sides of the image will be
1139 Arc Distortion Notes...
1140 + Does not use a set of CPs
1141 + Will only work with Image Distortion
1142 + Can not be used for generating a sparse gradient (interpolation)
1144 if ( number_arguments >= 1 && arguments[0] < MagickEpsilon ) {
1145 coeff = (double *) RelinquishMagickMemory(coeff);
1146 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1147 "InvalidArgument","%s : 'Arc Angle Too Small'",
1148 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1149 return((double *) NULL);
1151 if ( number_arguments >= 3 && arguments[2] < MagickEpsilon ) {
1152 coeff = (double *) RelinquishMagickMemory(coeff);
1153 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1154 "InvalidArgument","%s : 'Outer Radius Too Small'",
1155 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1156 return((double *) NULL);
1158 coeff[0] = -MagickPI2; /* -90, place at top! */
1159 if ( number_arguments >= 1 )
1160 coeff[1] = DegreesToRadians(arguments[0]);
1162 coeff[1] = MagickPI2; /* zero arguments - center is at top */
1163 if ( number_arguments >= 2 )
1164 coeff[0] += DegreesToRadians(arguments[1]);
1165 coeff[0] /= Magick2PI; /* normalize radians */
1166 coeff[0] -= MagickRound(coeff[0]);
1167 coeff[0] *= Magick2PI; /* de-normalize back to radians */
1168 coeff[3] = (double)image->rows-1;
1169 coeff[2] = (double)image->columns/coeff[1] + coeff[3]/2.0;
1170 if ( number_arguments >= 3 ) {
1171 if ( number_arguments >= 4 )
1172 coeff[3] = arguments[2] - arguments[3];
1174 coeff[3] *= arguments[2]/coeff[2];
1175 coeff[2] = arguments[2];
1177 coeff[4] = ((double)image->columns-1.0)/2.0;
1181 case PolarDistortion:
1182 case DePolarDistortion:
1184 /* (De)Polar Distortion (same set of arguments)
1185 Args: Rmax, Rmin, Xcenter,Ycenter, Afrom,Ato
1186 DePolar can also have the extra arguments of Width, Height
1188 Coefficients 0 to 5 is the sanatized version first 6 input args
1189 Coefficient 6 is the angle to coord ratio and visa-versa
1190 Coefficient 7 is the radius to coord ratio and visa-versa
1192 WARNING: It is possible for Radius max<min and/or Angle from>to
1194 if ( number_arguments == 3
1195 || ( number_arguments > 6 && *method == PolarDistortion )
1196 || number_arguments > 8 ) {
1197 (void) ThrowMagickException(exception,GetMagickModule(),
1198 OptionError,"InvalidArgument", "%s : number of arguments",
1199 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1200 coeff=(double *) RelinquishMagickMemory(coeff);
1201 return((double *) NULL);
1203 /* Rmax - if 0 calculate appropriate value */
1204 if ( number_arguments >= 1 )
1205 coeff[0] = arguments[0];
1208 /* Rmin - usally 0 */
1209 coeff[1] = number_arguments >= 2 ? arguments[1] : 0.0;
1211 if ( number_arguments >= 4 ) {
1212 coeff[2] = arguments[2];
1213 coeff[3] = arguments[3];
1215 else { /* center of actual image */
1216 coeff[2] = (double)(image->columns)/2.0+image->page.x;
1217 coeff[3] = (double)(image->rows)/2.0+image->page.y;
1219 /* Angle from,to - about polar center 0 is downward */
1220 coeff[4] = -MagickPI;
1221 if ( number_arguments >= 5 )
1222 coeff[4] = DegreesToRadians(arguments[4]);
1223 coeff[5] = coeff[4];
1224 if ( number_arguments >= 6 )
1225 coeff[5] = DegreesToRadians(arguments[5]);
1226 if ( fabs(coeff[4]-coeff[5]) < MagickEpsilon )
1227 coeff[5] += Magick2PI; /* same angle is a full circle */
1228 /* if radius 0 or negative, its a special value... */
1229 if ( coeff[0] < MagickEpsilon ) {
1230 /* Use closest edge if radius == 0 */
1231 if ( fabs(coeff[0]) < MagickEpsilon ) {
1232 coeff[0]=MagickMin(fabs(coeff[2]-image->page.x),
1233 fabs(coeff[3]-image->page.y));
1234 coeff[0]=MagickMin(coeff[0],
1235 fabs(coeff[2]-image->page.x-image->columns));
1236 coeff[0]=MagickMin(coeff[0],
1237 fabs(coeff[3]-image->page.y-image->rows));
1239 /* furthest diagonal if radius == -1 */
1240 if ( fabs(-1.0-coeff[0]) < MagickEpsilon ) {
1242 rx = coeff[2]-image->page.x;
1243 ry = coeff[3]-image->page.y;
1244 coeff[0] = rx*rx+ry*ry;
1245 ry = coeff[3]-image->page.y-image->rows;
1246 coeff[0] = MagickMax(coeff[0],rx*rx+ry*ry);
1247 rx = coeff[2]-image->page.x-image->columns;
1248 coeff[0] = MagickMax(coeff[0],rx*rx+ry*ry);
1249 ry = coeff[3]-image->page.y;
1250 coeff[0] = MagickMax(coeff[0],rx*rx+ry*ry);
1251 coeff[0] = sqrt(coeff[0]);
1254 /* IF Rmax <= 0 or Rmin < 0 OR Rmax < Rmin, THEN error */
1255 if ( coeff[0] < MagickEpsilon || coeff[1] < -MagickEpsilon
1256 || (coeff[0]-coeff[1]) < MagickEpsilon ) {
1257 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1258 "InvalidArgument", "%s : Invalid Radius",
1259 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1260 coeff=(double *) RelinquishMagickMemory(coeff);
1261 return((double *) NULL);
1263 /* converstion ratios */
1264 if ( *method == PolarDistortion ) {
1265 coeff[6]=(double) image->columns/(coeff[5]-coeff[4]);
1266 coeff[7]=(double) image->rows/(coeff[0]-coeff[1]);
1268 else { /* *method == DePolarDistortion */
1269 coeff[6]=(coeff[5]-coeff[4])/image->columns;
1270 coeff[7]=(coeff[0]-coeff[1])/image->rows;
1274 case Cylinder2PlaneDistortion:
1275 case Plane2CylinderDistortion:
1277 /* 3D Cylinder to/from a Tangential Plane
1279 Projection between a clinder and flat plain from a point on the
1280 center line of the cylinder.
1282 The two surfaces coincide in 3D space at the given centers of
1283 distortion (perpendicular to projection point) on both images.
1286 Coefficents: FOV(radians), Radius, center_x,y, dest_center_x,y
1288 FOV (Field Of View) the angular field of view of the distortion,
1289 across the width of the image, in degrees. The centers are the
1290 points of least distortion in the input and resulting images.
1292 These centers are however determined later.
1294 Coeff 0 is the FOV angle of view of image width in radians
1295 Coeff 1 is calculated radius of cylinder.
1296 Coeff 2,3 center of distortion of input image
1297 Coefficents 4,5 Center of Distortion of dest (determined later)
1299 if ( arguments[0] < MagickEpsilon || arguments[0] > 160.0 ) {
1300 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1301 "InvalidArgument", "%s : Invalid FOV Angle",
1302 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1303 coeff=(double *) RelinquishMagickMemory(coeff);
1304 return((double *) NULL);
1306 coeff[0] = DegreesToRadians(arguments[0]);
1307 if ( *method == Cylinder2PlaneDistortion )
1308 /* image is curved around cylinder, so FOV angle (in radians)
1309 * scales directly to image X coordinate, according to its radius.
1311 coeff[1] = (double) image->columns/coeff[0];
1313 /* radius is distance away from an image with this angular FOV */
1314 coeff[1] = (double) image->columns / ( 2 * tan(coeff[0]/2) );
1316 coeff[2] = (double)(image->columns)/2.0+image->page.x;
1317 coeff[3] = (double)(image->rows)/2.0+image->page.y;
1318 coeff[4] = coeff[2];
1319 coeff[5] = coeff[3]; /* assuming image size is the same */
1322 case BarrelDistortion:
1323 case BarrelInverseDistortion:
1325 /* Barrel Distortion
1326 Rs=(A*Rd^3 + B*Rd^2 + C*Rd + D)*Rd
1327 BarrelInv Distortion
1328 Rs=Rd/(A*Rd^3 + B*Rd^2 + C*Rd + D)
1330 Where Rd is the normalized radius from corner to middle of image
1331 Input Arguments are one of the following forms (number of arguments)...
1336 8: Ax,Bx,Cx,Dx Ay,By,Cy,Dy
1337 10: Ax,Bx,Cx,Dx Ay,By,Cy,Dy X,Y
1339 Returns 10 coefficent values, which are de-normalized (pixel scale)
1340 Ax, Bx, Cx, Dx, Ay, By, Cy, Dy, Xc, Yc
1342 /* Radius de-normalization scaling factor */
1344 rscale = 2.0/MagickMin((double) image->columns,(double) image->rows);
1346 /* sanity check number of args must = 3,4,5,6,8,10 or error */
1347 if ( (number_arguments < 3) || (number_arguments == 7) ||
1348 (number_arguments == 9) || (number_arguments > 10) )
1350 coeff=(double *) RelinquishMagickMemory(coeff);
1351 (void) ThrowMagickException(exception,GetMagickModule(),
1352 OptionError,"InvalidArgument", "%s : number of arguments",
1353 CommandOptionToMnemonic(MagickDistortOptions, *method) );
1354 return((double *) NULL);
1356 /* A,B,C,D coefficients */
1357 coeff[0] = arguments[0];
1358 coeff[1] = arguments[1];
1359 coeff[2] = arguments[2];
1360 if ((number_arguments == 3) || (number_arguments == 5) )
1361 coeff[3] = 1.0 - coeff[0] - coeff[1] - coeff[2];
1363 coeff[3] = arguments[3];
1364 /* de-normalize the coefficients */
1365 coeff[0] *= pow(rscale,3.0);
1366 coeff[1] *= rscale*rscale;
1368 /* Y coefficients: as given OR same as X coefficients */
1369 if ( number_arguments >= 8 ) {
1370 coeff[4] = arguments[4] * pow(rscale,3.0);
1371 coeff[5] = arguments[5] * rscale*rscale;
1372 coeff[6] = arguments[6] * rscale;
1373 coeff[7] = arguments[7];
1376 coeff[4] = coeff[0];
1377 coeff[5] = coeff[1];
1378 coeff[6] = coeff[2];
1379 coeff[7] = coeff[3];
1381 /* X,Y Center of Distortion (image coodinates) */
1382 if ( number_arguments == 5 ) {
1383 coeff[8] = arguments[3];
1384 coeff[9] = arguments[4];
1386 else if ( number_arguments == 6 ) {
1387 coeff[8] = arguments[4];
1388 coeff[9] = arguments[5];
1390 else if ( number_arguments == 10 ) {
1391 coeff[8] = arguments[8];
1392 coeff[9] = arguments[9];
1395 /* center of the image provided (image coodinates) */
1396 coeff[8] = (double)image->columns/2.0 + image->page.x;
1397 coeff[9] = (double)image->rows/2.0 + image->page.y;
1401 case ShepardsDistortion:
1403 /* Shepards Distortion input arguments are the coefficents!
1404 Just check the number of arguments is valid!
1405 Args: u1,v1, x1,y1, ...
1406 OR : u1,v1, r1,g1,c1, ...
1408 if ( number_arguments%cp_size != 0 ||
1409 number_arguments < cp_size ) {
1410 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1411 "InvalidArgument", "%s : 'requires CP's (4 numbers each)'",
1412 CommandOptionToMnemonic(MagickDistortOptions, *method));
1413 coeff=(double *) RelinquishMagickMemory(coeff);
1414 return((double *) NULL);
1416 /* User defined weighting power for Shepard's Method */
1417 { const char *artifact=GetImageArtifact(image,"shepards:power");
1418 if ( artifact != (const char *) NULL ) {
1419 coeff[0]=StringToDouble(artifact,(char **) NULL) / 2.0;
1420 if ( coeff[0] < MagickEpsilon ) {
1421 (void) ThrowMagickException(exception,GetMagickModule(),
1422 OptionError,"InvalidArgument","%s", "-define shepards:power" );
1423 coeff=(double *) RelinquishMagickMemory(coeff);
1424 return((double *) NULL);
1428 coeff[0]=1.0; /* Default power of 2 (Inverse Squared) */
1435 /* you should never reach this point */
1436 perror("no method handler"); /* just fail assertion */
1437 return((double *) NULL);
1441 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1445 + D i s t o r t R e s i z e I m a g e %
1449 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1451 % DistortResizeImage() resize image using the equivalent but slower image
1452 % distortion operator. The filter is applied using a EWA cylindrical
1453 % resampling. But like resize the final image size is limited to whole pixels
1454 % with no effects by virtual-pixels on the result.
1456 % Note that images containing a transparency channel will be twice as slow to
1457 % resize as images one without transparency.
1459 % The format of the DistortResizeImage method is:
1461 % Image *AdaptiveResizeImage(const Image *image,const size_t columns,
1462 % const size_t rows,ExceptionInfo *exception)
1464 % A description of each parameter follows:
1466 % o image: the image.
1468 % o columns: the number of columns in the resized image.
1470 % o rows: the number of rows in the resized image.
1472 % o exception: return any errors or warnings in this structure.
1475 MagickExport Image *DistortResizeImage(const Image *image,
1476 const size_t columns,const size_t rows,ExceptionInfo *exception)
1478 #define DistortResizeImageTag "Distort/Image"
1494 Distort resize image.
1496 assert(image != (const Image *) NULL);
1497 assert(image->signature == MagickSignature);
1498 if (image->debug != MagickFalse)
1499 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1500 assert(exception != (ExceptionInfo *) NULL);
1501 assert(exception->signature == MagickSignature);
1502 if ((columns == 0) || (rows == 0))
1503 return((Image *) NULL);
1504 /* Do not short-circuit this resize if final image size is unchanged */
1506 (void) ResetMagickMemory(distort_args,0,12*sizeof(double));
1507 distort_args[4]=(double) image->columns;
1508 distort_args[6]=(double) columns;
1509 distort_args[9]=(double) image->rows;
1510 distort_args[11]=(double) rows;
1512 vp_save=GetImageVirtualPixelMethod(image);
1514 tmp_image=CloneImage(image,0,0,MagickTrue,exception);
1515 if ( tmp_image == (Image *) NULL )
1516 return((Image *) NULL);
1517 (void) SetImageVirtualPixelMethod(tmp_image,TransparentVirtualPixelMethod,
1520 if (image->alpha_trait != BlendPixelTrait)
1523 Image has not transparency channel, so we free to use it
1525 (void) SetImageAlphaChannel(tmp_image,SetAlphaChannel,exception);
1526 resize_image=DistortImage(tmp_image,AffineDistortion,12,distort_args,
1527 MagickTrue,exception),
1529 tmp_image=DestroyImage(tmp_image);
1530 if ( resize_image == (Image *) NULL )
1531 return((Image *) NULL);
1533 (void) SetImageAlphaChannel(resize_image,DeactivateAlphaChannel,exception);
1538 Image has transparency so handle colors and alpha separatly.
1539 Basically we need to separate Virtual-Pixel alpha in the resized
1540 image, so only the actual original images alpha channel is used.
1542 distort alpha channel separately
1547 (void) SetImageAlphaChannel(tmp_image,ExtractAlphaChannel,exception);
1548 (void) SetImageAlphaChannel(tmp_image,OpaqueAlphaChannel,exception);
1549 resize_alpha=DistortImage(tmp_image,AffineDistortion,12,distort_args,
1550 MagickTrue,exception),
1551 tmp_image=DestroyImage(tmp_image);
1552 if (resize_alpha == (Image *) NULL)
1553 return((Image *) NULL);
1555 /* distort the actual image containing alpha + VP alpha */
1556 tmp_image=CloneImage(image,0,0,MagickTrue,exception);
1557 if ( tmp_image == (Image *) NULL )
1558 return((Image *) NULL);
1559 (void) SetImageVirtualPixelMethod(tmp_image,
1560 TransparentVirtualPixelMethod,exception);
1561 resize_image=DistortImage(tmp_image,AffineDistortion,12,distort_args,
1562 MagickTrue,exception),
1563 tmp_image=DestroyImage(tmp_image);
1564 if ( resize_image == (Image *) NULL)
1566 resize_alpha=DestroyImage(resize_alpha);
1567 return((Image *) NULL);
1569 /* replace resize images alpha with the separally distorted alpha */
1570 (void) SetImageAlphaChannel(resize_image,DeactivateAlphaChannel,
1572 (void) SetImageAlphaChannel(resize_alpha,DeactivateAlphaChannel,
1574 (void) CompositeImage(resize_image,resize_alpha,CopyAlphaCompositeOp,
1575 MagickTrue,0,0,exception);
1576 resize_alpha=DestroyImage(resize_alpha);
1578 (void) SetImageVirtualPixelMethod(resize_image,vp_save,exception);
1581 Clean up the results of the Distortion
1583 crop_area.width=columns;
1584 crop_area.height=rows;
1588 tmp_image=resize_image;
1589 resize_image=CropImage(tmp_image,&crop_area,exception);
1590 tmp_image=DestroyImage(tmp_image);
1591 return(resize_image);
1595 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1599 % D i s t o r t I m a g e %
1603 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1605 % DistortImage() distorts an image using various distortion methods, by
1606 % mapping color lookups of the source image to a new destination image
1607 % usally of the same size as the source image, unless 'bestfit' is set to
1610 % If 'bestfit' is enabled, and distortion allows it, the destination image is
1611 % adjusted to ensure the whole source 'image' will just fit within the final
1612 % destination image, which will be sized and offset accordingly. Also in
1613 % many cases the virtual offset of the source image will be taken into
1614 % account in the mapping.
1616 % If the '-verbose' control option has been set print to standard error the
1617 % equicelent '-fx' formula with coefficients for the function, if practical.
1619 % The format of the DistortImage() method is:
1621 % Image *DistortImage(const Image *image,const DistortImageMethod method,
1622 % const size_t number_arguments,const double *arguments,
1623 % MagickBooleanType bestfit, ExceptionInfo *exception)
1625 % A description of each parameter follows:
1627 % o image: the image to be distorted.
1629 % o method: the method of image distortion.
1631 % ArcDistortion always ignores source image offset, and always
1632 % 'bestfit' the destination image with the top left corner offset
1633 % relative to the polar mapping center.
1635 % Affine, Perspective, and Bilinear, do least squares fitting of the
1636 % distrotion when more than the minimum number of control point pairs
1639 % Perspective, and Bilinear, fall back to a Affine distortion when less
1640 % than 4 control point pairs are provided. While Affine distortions
1641 % let you use any number of control point pairs, that is Zero pairs is
1642 % a No-Op (viewport only) distortion, one pair is a translation and
1643 % two pairs of control points do a scale-rotate-translate, without any
1646 % o number_arguments: the number of arguments given.
1648 % o arguments: an array of floating point arguments for this method.
1650 % o bestfit: Attempt to 'bestfit' the size of the resulting image.
1651 % This also forces the resulting image to be a 'layered' virtual
1652 % canvas image. Can be overridden using 'distort:viewport' setting.
1654 % o exception: return any errors or warnings in this structure
1656 % Extra Controls from Image meta-data (artifacts)...
1659 % Output to stderr alternatives, internal coefficents, and FX
1660 % equivalents for the distortion operation (if feasible).
1661 % This forms an extra check of the distortion method, and allows users
1662 % access to the internal constants IM calculates for the distortion.
1664 % o "distort:viewport"
1665 % Directly set the output image canvas area and offest to use for the
1666 % resulting image, rather than use the original images canvas, or a
1667 % calculated 'bestfit' canvas.
1670 % Scale the size of the output canvas by this amount to provide a
1671 % method of Zooming, and for super-sampling the results.
1673 % Other settings that can effect results include
1675 % o 'interpolate' For source image lookups (scale enlargements)
1677 % o 'filter' Set filter to use for area-resampling (scale shrinking).
1678 % Set to 'point' to turn off and use 'interpolate' lookup
1682 MagickExport Image *DistortImage(const Image *image,DistortImageMethod method,
1683 const size_t number_arguments,const double *arguments,
1684 MagickBooleanType bestfit,ExceptionInfo *exception)
1686 #define DistortImageTag "Distort/Image"
1696 geometry; /* geometry of the distorted space viewport */
1701 assert(image != (Image *) NULL);
1702 assert(image->signature == MagickSignature);
1703 if (image->debug != MagickFalse)
1704 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1705 assert(exception != (ExceptionInfo *) NULL);
1706 assert(exception->signature == MagickSignature);
1710 Handle Special Compound Distortions
1712 if ( method == ResizeDistortion )
1714 if ( number_arguments != 2 )
1716 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
1717 "InvalidArgument","%s : '%s'","Resize",
1718 "Invalid number of args: 2 only");
1719 return((Image *) NULL);
1721 distort_image=DistortResizeImage(image,(size_t)arguments[0],
1722 (size_t)arguments[1], exception);
1723 return(distort_image);
1727 Convert input arguments (usually as control points for reverse mapping)
1728 into mapping coefficients to apply the distortion.
1730 Note that some distortions are mapped to other distortions,
1731 and as such do not require specific code after this point.
1733 coeff = GenerateCoefficients(image, &method, number_arguments,
1734 arguments, 0, exception);
1735 if ( coeff == (double *) NULL )
1736 return((Image *) NULL);
1739 Determine the size and offset for a 'bestfit' destination.
1740 Usally the four corners of the source image is enough.
1743 /* default output image bounds, when no 'bestfit' is requested */
1744 geometry.width=image->columns;
1745 geometry.height=image->rows;
1749 if ( method == ArcDistortion ) {
1750 bestfit = MagickTrue; /* always calculate a 'best fit' viewport */
1753 /* Work out the 'best fit', (required for ArcDistortion) */
1756 s,d,min,max; /* source, dest coords --mapping--> min, max coords */
1759 fix_bounds = MagickTrue; /* enlarge bounds for VP handling */
1761 s.x=s.y=min.x=max.x=min.y=max.y=0.0; /* keep compiler happy */
1763 /* defines to figure out the bounds of the distorted image */
1764 #define InitalBounds(p) \
1766 /* printf("%lg,%lg -> %lg,%lg\n", s.x,s.y, d.x,d.y); */ \
1767 min.x = max.x = p.x; \
1768 min.y = max.y = p.y; \
1770 #define ExpandBounds(p) \
1772 /* printf("%lg,%lg -> %lg,%lg\n", s.x,s.y, d.x,d.y); */ \
1773 min.x = MagickMin(min.x,p.x); \
1774 max.x = MagickMax(max.x,p.x); \
1775 min.y = MagickMin(min.y,p.y); \
1776 max.y = MagickMax(max.y,p.y); \
1781 case AffineDistortion:
1782 { double inverse[6];
1783 InvertAffineCoefficients(coeff, inverse);
1784 s.x = (double) image->page.x;
1785 s.y = (double) image->page.y;
1786 d.x = inverse[0]*s.x+inverse[1]*s.y+inverse[2];
1787 d.y = inverse[3]*s.x+inverse[4]*s.y+inverse[5];
1789 s.x = (double) image->page.x+image->columns;
1790 s.y = (double) image->page.y;
1791 d.x = inverse[0]*s.x+inverse[1]*s.y+inverse[2];
1792 d.y = inverse[3]*s.x+inverse[4]*s.y+inverse[5];
1794 s.x = (double) image->page.x;
1795 s.y = (double) image->page.y+image->rows;
1796 d.x = inverse[0]*s.x+inverse[1]*s.y+inverse[2];
1797 d.y = inverse[3]*s.x+inverse[4]*s.y+inverse[5];
1799 s.x = (double) image->page.x+image->columns;
1800 s.y = (double) image->page.y+image->rows;
1801 d.x = inverse[0]*s.x+inverse[1]*s.y+inverse[2];
1802 d.y = inverse[3]*s.x+inverse[4]*s.y+inverse[5];
1806 case PerspectiveDistortion:
1807 { double inverse[8], scale;
1808 InvertPerspectiveCoefficients(coeff, inverse);
1809 s.x = (double) image->page.x;
1810 s.y = (double) image->page.y;
1811 scale=inverse[6]*s.x+inverse[7]*s.y+1.0;
1812 scale=PerceptibleReciprocal(scale);
1813 d.x = scale*(inverse[0]*s.x+inverse[1]*s.y+inverse[2]);
1814 d.y = scale*(inverse[3]*s.x+inverse[4]*s.y+inverse[5]);
1816 s.x = (double) image->page.x+image->columns;
1817 s.y = (double) image->page.y;
1818 scale=inverse[6]*s.x+inverse[7]*s.y+1.0;
1819 scale=PerceptibleReciprocal(scale);
1820 d.x = scale*(inverse[0]*s.x+inverse[1]*s.y+inverse[2]);
1821 d.y = scale*(inverse[3]*s.x+inverse[4]*s.y+inverse[5]);
1823 s.x = (double) image->page.x;
1824 s.y = (double) image->page.y+image->rows;
1825 scale=inverse[6]*s.x+inverse[7]*s.y+1.0;
1826 scale=PerceptibleReciprocal(scale);
1827 d.x = scale*(inverse[0]*s.x+inverse[1]*s.y+inverse[2]);
1828 d.y = scale*(inverse[3]*s.x+inverse[4]*s.y+inverse[5]);
1830 s.x = (double) image->page.x+image->columns;
1831 s.y = (double) image->page.y+image->rows;
1832 scale=inverse[6]*s.x+inverse[7]*s.y+1.0;
1833 scale=PerceptibleReciprocal(scale);
1834 d.x = scale*(inverse[0]*s.x+inverse[1]*s.y+inverse[2]);
1835 d.y = scale*(inverse[3]*s.x+inverse[4]*s.y+inverse[5]);
1841 /* Forward Map Corners */
1842 a = coeff[0]-coeff[1]/2; ca = cos(a); sa = sin(a);
1846 d.x = (coeff[2]-coeff[3])*ca;
1847 d.y = (coeff[2]-coeff[3])*sa;
1849 a = coeff[0]+coeff[1]/2; ca = cos(a); sa = sin(a);
1853 d.x = (coeff[2]-coeff[3])*ca;
1854 d.y = (coeff[2]-coeff[3])*sa;
1856 /* Orthogonal points along top of arc */
1857 for( a=(double) (ceil((double) ((coeff[0]-coeff[1]/2.0)/MagickPI2))*MagickPI2);
1858 a<(coeff[0]+coeff[1]/2.0); a+=MagickPI2 ) {
1859 ca = cos(a); sa = sin(a);
1865 Convert the angle_to_width and radius_to_height
1866 to appropriate scaling factors, to allow faster processing
1867 in the mapping function.
1869 coeff[1] = (double) (Magick2PI*image->columns/coeff[1]);
1870 coeff[3] = (double)image->rows/coeff[3];
1873 case PolarDistortion:
1875 if (number_arguments < 2)
1876 coeff[2] = coeff[3] = 0.0;
1877 min.x = coeff[2]-coeff[0];
1878 max.x = coeff[2]+coeff[0];
1879 min.y = coeff[3]-coeff[0];
1880 max.y = coeff[3]+coeff[0];
1881 /* should be about 1.0 if Rmin = 0 */
1882 coeff[7]=(double) geometry.height/(coeff[0]-coeff[1]);
1885 case DePolarDistortion:
1887 /* direct calculation as it needs to tile correctly
1888 * for reversibility in a DePolar-Polar cycle */
1889 fix_bounds = MagickFalse;
1890 geometry.x = geometry.y = 0;
1891 geometry.height = (size_t) ceil(coeff[0]-coeff[1]);
1892 geometry.width = (size_t)
1893 ceil((coeff[0]-coeff[1])*(coeff[5]-coeff[4])*0.5);
1894 /* correct scaling factors relative to new size */
1895 coeff[6]=(coeff[5]-coeff[4])/geometry.width; /* changed width */
1896 coeff[7]=(coeff[0]-coeff[1])/geometry.height; /* should be about 1.0 */
1899 case Cylinder2PlaneDistortion:
1901 /* direct calculation so center of distortion is either a pixel
1902 * center, or pixel edge. This allows for reversibility of the
1904 geometry.x = geometry.y = 0;
1905 geometry.width = (size_t) ceil( 2.0*coeff[1]*tan(coeff[0]/2.0) );
1906 geometry.height = (size_t) ceil( 2.0*coeff[3]/cos(coeff[0]/2.0) );
1907 /* correct center of distortion relative to new size */
1908 coeff[4] = (double) geometry.width/2.0;
1909 coeff[5] = (double) geometry.height/2.0;
1910 fix_bounds = MagickFalse;
1913 case Plane2CylinderDistortion:
1915 /* direct calculation center is either pixel center, or pixel edge
1916 * so as to allow reversibility of the image distortion */
1917 geometry.x = geometry.y = 0;
1918 geometry.width = (size_t) ceil(coeff[0]*coeff[1]); /* FOV * radius */
1919 geometry.height = (size_t) (2*coeff[3]); /* input image height */
1920 /* correct center of distortion relative to new size */
1921 coeff[4] = (double) geometry.width/2.0;
1922 coeff[5] = (double) geometry.height/2.0;
1923 fix_bounds = MagickFalse;
1926 case ShepardsDistortion:
1927 case BilinearForwardDistortion:
1928 case BilinearReverseDistortion:
1930 case QuadrilateralDistortion:
1932 case PolynomialDistortion:
1933 case BarrelDistortion:
1934 case BarrelInverseDistortion:
1936 /* no calculated bestfit available for these distortions */
1937 bestfit = MagickFalse;
1938 fix_bounds = MagickFalse;
1942 /* Set the output image geometry to calculated 'bestfit'.
1943 Yes this tends to 'over do' the file image size, ON PURPOSE!
1944 Do not do this for DePolar which needs to be exact for virtual tiling.
1947 geometry.x = (ssize_t) floor(min.x-0.5);
1948 geometry.y = (ssize_t) floor(min.y-0.5);
1949 geometry.width=(size_t) ceil(max.x-geometry.x+0.5);
1950 geometry.height=(size_t) ceil(max.y-geometry.y+0.5);
1953 } /* end bestfit destination image calculations */
1955 /* The user provided a 'viewport' expert option which may
1956 overrides some parts of the current output image geometry.
1957 This also overrides its default 'bestfit' setting.
1959 { const char *artifact=GetImageArtifact(image,"distort:viewport");
1960 viewport_given = MagickFalse;
1961 if ( artifact != (const char *) NULL ) {
1962 MagickStatusType flags=ParseAbsoluteGeometry(artifact,&geometry);
1964 (void) ThrowMagickException(exception,GetMagickModule(),
1965 OptionWarning,"InvalidSetting","'%s' '%s'",
1966 "distort:viewport",artifact);
1968 viewport_given = MagickTrue;
1972 /* Verbose output */
1973 if ( IfStringTrue(GetImageArtifact(image,"verbose")) ) {
1976 char image_gen[MaxTextExtent];
1979 /* Set destination image size and virtual offset */
1980 if ( bestfit || viewport_given ) {
1981 (void) FormatLocaleString(image_gen, MaxTextExtent," -size %.20gx%.20g "
1982 "-page %+.20g%+.20g xc: +insert \\\n",(double) geometry.width,
1983 (double) geometry.height,(double) geometry.x,(double) geometry.y);
1984 lookup="v.p{ xx-v.page.x-.5, yy-v.page.y-.5 }";
1987 image_gen[0] = '\0'; /* no destination to generate */
1988 lookup = "p{ xx-page.x-.5, yy-page.y-.5 }"; /* simplify lookup */
1992 case AffineDistortion:
1996 inverse = (double *) AcquireQuantumMemory(6,sizeof(*inverse));
1997 if (inverse == (double *) NULL) {
1998 coeff = (double *) RelinquishMagickMemory(coeff);
1999 (void) ThrowMagickException(exception,GetMagickModule(),
2000 ResourceLimitError,"MemoryAllocationFailed",
2001 "%s", "DistortImages");
2002 return((Image *) NULL);
2004 InvertAffineCoefficients(coeff, inverse);
2005 CoefficientsToAffineArgs(inverse);
2006 (void) FormatLocaleFile(stderr, "Affine Projection:\n");
2007 (void) FormatLocaleFile(stderr, " -distort AffineProjection \\\n '");
2008 for (i=0; i < 5; i++)
2009 (void) FormatLocaleFile(stderr, "%lf,", inverse[i]);
2010 (void) FormatLocaleFile(stderr, "%lf'\n", inverse[5]);
2011 inverse = (double *) RelinquishMagickMemory(inverse);
2013 (void) FormatLocaleFile(stderr, "Affine Distort, FX Equivelent:\n");
2014 (void) FormatLocaleFile(stderr, "%s", image_gen);
2015 (void) FormatLocaleFile(stderr, " -fx 'ii=i+page.x+0.5; jj=j+page.y+0.5;\n");
2016 (void) FormatLocaleFile(stderr, " xx=%+lf*ii %+lf*jj %+lf;\n",
2017 coeff[0], coeff[1], coeff[2]);
2018 (void) FormatLocaleFile(stderr, " yy=%+lf*ii %+lf*jj %+lf;\n",
2019 coeff[3], coeff[4], coeff[5]);
2020 (void) FormatLocaleFile(stderr, " %s' \\\n", lookup);
2025 case PerspectiveDistortion:
2029 inverse = (double *) AcquireQuantumMemory(8,sizeof(*inverse));
2030 if (inverse == (double *) NULL) {
2031 coeff = (double *) RelinquishMagickMemory(coeff);
2032 (void) ThrowMagickException(exception,GetMagickModule(),
2033 ResourceLimitError,"MemoryAllocationFailed",
2034 "%s", "DistortCoefficients");
2035 return((Image *) NULL);
2037 InvertPerspectiveCoefficients(coeff, inverse);
2038 (void) FormatLocaleFile(stderr, "Perspective Projection:\n");
2039 (void) FormatLocaleFile(stderr, " -distort PerspectiveProjection \\\n '");
2041 (void) FormatLocaleFile(stderr, "%lf, ", inverse[i]);
2042 (void) FormatLocaleFile(stderr, "\n ");
2044 (void) FormatLocaleFile(stderr, "%lf, ", inverse[i]);
2045 (void) FormatLocaleFile(stderr, "%lf'\n", inverse[7]);
2046 inverse = (double *) RelinquishMagickMemory(inverse);
2048 (void) FormatLocaleFile(stderr, "Perspective Distort, FX Equivelent:\n");
2049 (void) FormatLocaleFile(stderr, "%s", image_gen);
2050 (void) FormatLocaleFile(stderr, " -fx 'ii=i+page.x+0.5; jj=j+page.y+0.5;\n");
2051 (void) FormatLocaleFile(stderr, " rr=%+lf*ii %+lf*jj + 1;\n",
2052 coeff[6], coeff[7]);
2053 (void) FormatLocaleFile(stderr, " xx=(%+lf*ii %+lf*jj %+lf)/rr;\n",
2054 coeff[0], coeff[1], coeff[2]);
2055 (void) FormatLocaleFile(stderr, " yy=(%+lf*ii %+lf*jj %+lf)/rr;\n",
2056 coeff[3], coeff[4], coeff[5]);
2057 (void) FormatLocaleFile(stderr, " rr%s0 ? %s : blue' \\\n",
2058 coeff[8] < 0 ? "<" : ">", lookup);
2062 case BilinearForwardDistortion:
2063 (void) FormatLocaleFile(stderr, "BilinearForward Mapping Equations:\n");
2064 (void) FormatLocaleFile(stderr, "%s", image_gen);
2065 (void) FormatLocaleFile(stderr, " i = %+lf*x %+lf*y %+lf*x*y %+lf;\n",
2066 coeff[0], coeff[1], coeff[2], coeff[3]);
2067 (void) FormatLocaleFile(stderr, " j = %+lf*x %+lf*y %+lf*x*y %+lf;\n",
2068 coeff[4], coeff[5], coeff[6], coeff[7]);
2071 (void) FormatLocaleFile(stderr, " c8 = %+lf c9 = 2*a = %+lf;\n",
2072 coeff[8], coeff[9]);
2074 (void) FormatLocaleFile(stderr, "BilinearForward Distort, FX Equivelent:\n");
2075 (void) FormatLocaleFile(stderr, "%s", image_gen);
2076 (void) FormatLocaleFile(stderr, " -fx 'ii=i+page.x%+lf; jj=j+page.y%+lf;\n",
2077 0.5-coeff[3], 0.5-coeff[7]);
2078 (void) FormatLocaleFile(stderr, " bb=%lf*ii %+lf*jj %+lf;\n",
2079 coeff[6], -coeff[2], coeff[8]);
2080 /* Handle Special degenerate (non-quadratic) or trapezoidal case */
2081 if ( coeff[9] != 0 ) {
2082 (void) FormatLocaleFile(stderr, " rt=bb*bb %+lf*(%lf*ii%+lf*jj);\n",
2083 -2*coeff[9], coeff[4], -coeff[0]);
2084 (void) FormatLocaleFile(stderr, " yy=( -bb + sqrt(rt) ) / %lf;\n",
2087 (void) FormatLocaleFile(stderr, " yy=(%lf*ii%+lf*jj)/bb;\n",
2088 -coeff[4], coeff[0]);
2089 (void) FormatLocaleFile(stderr, " xx=(ii %+lf*yy)/(%lf %+lf*yy);\n",
2090 -coeff[1], coeff[0], coeff[2]);
2091 if ( coeff[9] != 0 )
2092 (void) FormatLocaleFile(stderr, " (rt < 0 ) ? red : %s'\n", lookup);
2094 (void) FormatLocaleFile(stderr, " %s' \\\n", lookup);
2097 case BilinearReverseDistortion:
2099 (void) FormatLocaleFile(stderr, "Polynomial Projection Distort:\n");
2100 (void) FormatLocaleFile(stderr, " -distort PolynomialProjection \\\n");
2101 (void) FormatLocaleFile(stderr, " '1.5, %lf, %lf, %lf, %lf,\n",
2102 coeff[3], coeff[0], coeff[1], coeff[2]);
2103 (void) FormatLocaleFile(stderr, " %lf, %lf, %lf, %lf'\n",
2104 coeff[7], coeff[4], coeff[5], coeff[6]);
2106 (void) FormatLocaleFile(stderr, "BilinearReverse Distort, FX Equivelent:\n");
2107 (void) FormatLocaleFile(stderr, "%s", image_gen);
2108 (void) FormatLocaleFile(stderr, " -fx 'ii=i+page.x+0.5; jj=j+page.y+0.5;\n");
2109 (void) FormatLocaleFile(stderr, " xx=%+lf*ii %+lf*jj %+lf*ii*jj %+lf;\n",
2110 coeff[0], coeff[1], coeff[2], coeff[3]);
2111 (void) FormatLocaleFile(stderr, " yy=%+lf*ii %+lf*jj %+lf*ii*jj %+lf;\n",
2112 coeff[4], coeff[5], coeff[6], coeff[7]);
2113 (void) FormatLocaleFile(stderr, " %s' \\\n", lookup);
2116 case PolynomialDistortion:
2118 size_t nterms = (size_t) coeff[1];
2119 (void) FormatLocaleFile(stderr, "Polynomial (order %lg, terms %lu), FX Equivelent\n",
2120 coeff[0],(unsigned long) nterms);
2121 (void) FormatLocaleFile(stderr, "%s", image_gen);
2122 (void) FormatLocaleFile(stderr, " -fx 'ii=i+page.x+0.5; jj=j+page.y+0.5;\n");
2123 (void) FormatLocaleFile(stderr, " xx =");
2124 for (i=0; i<(ssize_t) nterms; i++) {
2125 if ( i != 0 && i%4 == 0 ) (void) FormatLocaleFile(stderr, "\n ");
2126 (void) FormatLocaleFile(stderr, " %+lf%s", coeff[2+i],
2129 (void) FormatLocaleFile(stderr, ";\n yy =");
2130 for (i=0; i<(ssize_t) nterms; i++) {
2131 if ( i != 0 && i%4 == 0 ) (void) FormatLocaleFile(stderr, "\n ");
2132 (void) FormatLocaleFile(stderr, " %+lf%s", coeff[2+i+nterms],
2135 (void) FormatLocaleFile(stderr, ";\n %s' \\\n", lookup);
2140 (void) FormatLocaleFile(stderr, "Arc Distort, Internal Coefficients:\n");
2141 for ( i=0; i<5; i++ )
2142 (void) FormatLocaleFile(stderr, " c%.20g = %+lf\n", (double) i, coeff[i]);
2143 (void) FormatLocaleFile(stderr, "Arc Distort, FX Equivelent:\n");
2144 (void) FormatLocaleFile(stderr, "%s", image_gen);
2145 (void) FormatLocaleFile(stderr, " -fx 'ii=i+page.x; jj=j+page.y;\n");
2146 (void) FormatLocaleFile(stderr, " xx=(atan2(jj,ii)%+lf)/(2*pi);\n",
2148 (void) FormatLocaleFile(stderr, " xx=xx-round(xx);\n");
2149 (void) FormatLocaleFile(stderr, " xx=xx*%lf %+lf;\n",
2150 coeff[1], coeff[4]);
2151 (void) FormatLocaleFile(stderr, " yy=(%lf - hypot(ii,jj)) * %lf;\n",
2152 coeff[2], coeff[3]);
2153 (void) FormatLocaleFile(stderr, " v.p{xx-.5,yy-.5}' \\\n");
2156 case PolarDistortion:
2158 (void) FormatLocaleFile(stderr, "Polar Distort, Internal Coefficents\n");
2159 for ( i=0; i<8; i++ )
2160 (void) FormatLocaleFile(stderr, " c%.20g = %+lf\n", (double) i, coeff[i]);
2161 (void) FormatLocaleFile(stderr, "Polar Distort, FX Equivelent:\n");
2162 (void) FormatLocaleFile(stderr, "%s", image_gen);
2163 (void) FormatLocaleFile(stderr, " -fx 'ii=i+page.x%+lf; jj=j+page.y%+lf;\n",
2164 -coeff[2], -coeff[3]);
2165 (void) FormatLocaleFile(stderr, " xx=(atan2(ii,jj)%+lf)/(2*pi);\n",
2166 -(coeff[4]+coeff[5])/2 );
2167 (void) FormatLocaleFile(stderr, " xx=xx-round(xx);\n");
2168 (void) FormatLocaleFile(stderr, " xx=xx*2*pi*%lf + v.w/2;\n",
2170 (void) FormatLocaleFile(stderr, " yy=(hypot(ii,jj)%+lf)*%lf;\n",
2171 -coeff[1], coeff[7] );
2172 (void) FormatLocaleFile(stderr, " v.p{xx-.5,yy-.5}' \\\n");
2175 case DePolarDistortion:
2177 (void) FormatLocaleFile(stderr, "DePolar Distort, Internal Coefficents\n");
2178 for ( i=0; i<8; i++ )
2179 (void) FormatLocaleFile(stderr, " c%.20g = %+lf\n", (double) i, coeff[i]);
2180 (void) FormatLocaleFile(stderr, "DePolar Distort, FX Equivelent:\n");
2181 (void) FormatLocaleFile(stderr, "%s", image_gen);
2182 (void) FormatLocaleFile(stderr, " -fx 'aa=(i+.5)*%lf %+lf;\n", coeff[6], -coeff[4] );
2183 (void) FormatLocaleFile(stderr, " rr=(j+.5)*%lf %+lf;\n", coeff[7], +coeff[1] );
2184 (void) FormatLocaleFile(stderr, " xx=rr*sin(aa) %+lf;\n", coeff[2] );
2185 (void) FormatLocaleFile(stderr, " yy=rr*cos(aa) %+lf;\n", coeff[3] );
2186 (void) FormatLocaleFile(stderr, " v.p{xx-.5,yy-.5}' \\\n");
2189 case Cylinder2PlaneDistortion:
2191 (void) FormatLocaleFile(stderr, "Cylinder to Plane Distort, Internal Coefficents\n");
2192 (void) FormatLocaleFile(stderr, " cylinder_radius = %+lf\n", coeff[1]);
2193 (void) FormatLocaleFile(stderr, "Cylinder to Plane Distort, FX Equivelent:\n");
2194 (void) FormatLocaleFile(stderr, "%s", image_gen);
2195 (void) FormatLocaleFile(stderr, " -fx 'ii=i+page.x%+lf+0.5; jj=j+page.y%+lf+0.5;\n",
2196 -coeff[4], -coeff[5]);
2197 (void) FormatLocaleFile(stderr, " aa=atan(ii/%+lf);\n", coeff[1] );
2198 (void) FormatLocaleFile(stderr, " xx=%lf*aa%+lf;\n",
2199 coeff[1], coeff[2] );
2200 (void) FormatLocaleFile(stderr, " yy=jj*cos(aa)%+lf;\n", coeff[3] );
2201 (void) FormatLocaleFile(stderr, " %s' \\\n", lookup);
2204 case Plane2CylinderDistortion:
2206 (void) FormatLocaleFile(stderr, "Plane to Cylinder Distort, Internal Coefficents\n");
2207 (void) FormatLocaleFile(stderr, " cylinder_radius = %+lf\n", coeff[1]);
2208 (void) FormatLocaleFile(stderr, "Plane to Cylinder Distort, FX Equivelent:\n");
2209 (void) FormatLocaleFile(stderr, "%s", image_gen);
2210 (void) FormatLocaleFile(stderr, " -fx 'ii=i+page.x%+lf+0.5; jj=j+page.y%+lf+0.5;\n",
2211 -coeff[4], -coeff[5]);
2212 (void) FormatLocaleFile(stderr, " ii=ii/%+lf;\n", coeff[1] );
2213 (void) FormatLocaleFile(stderr, " xx=%lf*tan(ii)%+lf;\n",
2214 coeff[1], coeff[2] );
2215 (void) FormatLocaleFile(stderr, " yy=jj/cos(ii)%+lf;\n",
2217 (void) FormatLocaleFile(stderr, " %s' \\\n", lookup);
2220 case BarrelDistortion:
2221 case BarrelInverseDistortion:
2223 /* NOTE: This does the barrel roll in pixel coords not image coords
2224 ** The internal distortion must do it in image coordinates,
2225 ** so that is what the center coeff (8,9) is given in.
2227 xc = ((double)image->columns-1.0)/2.0 + image->page.x;
2228 yc = ((double)image->rows-1.0)/2.0 + image->page.y;
2229 (void) FormatLocaleFile(stderr, "Barrel%s Distort, FX Equivelent:\n",
2230 method == BarrelDistortion ? "" : "Inv");
2231 (void) FormatLocaleFile(stderr, "%s", image_gen);
2232 if ( fabs(coeff[8]-xc-0.5) < 0.1 && fabs(coeff[9]-yc-0.5) < 0.1 )
2233 (void) FormatLocaleFile(stderr, " -fx 'xc=(w-1)/2; yc=(h-1)/2;\n");
2235 (void) FormatLocaleFile(stderr, " -fx 'xc=%lf; yc=%lf;\n",
2236 coeff[8]-0.5, coeff[9]-0.5);
2237 (void) FormatLocaleFile(stderr,
2238 " ii=i-xc; jj=j-yc; rr=hypot(ii,jj);\n");
2239 (void) FormatLocaleFile(stderr, " ii=ii%s(%lf*rr*rr*rr %+lf*rr*rr %+lf*rr %+lf);\n",
2240 method == BarrelDistortion ? "*" : "/",
2241 coeff[0],coeff[1],coeff[2],coeff[3]);
2242 (void) FormatLocaleFile(stderr, " jj=jj%s(%lf*rr*rr*rr %+lf*rr*rr %+lf*rr %+lf);\n",
2243 method == BarrelDistortion ? "*" : "/",
2244 coeff[4],coeff[5],coeff[6],coeff[7]);
2245 (void) FormatLocaleFile(stderr, " v.p{fx*ii+xc,fy*jj+yc}' \\\n");
2252 /* The user provided a 'scale' expert option will scale the
2253 output image size, by the factor given allowing for super-sampling
2254 of the distorted image space. Any scaling factors must naturally
2255 be halved as a result.
2257 { const char *artifact;
2258 artifact=GetImageArtifact(image,"distort:scale");
2259 output_scaling = 1.0;
2260 if (artifact != (const char *) NULL) {
2261 output_scaling = fabs(StringToDouble(artifact,(char **) NULL));
2262 geometry.width=(size_t) (output_scaling*geometry.width+0.5);
2263 geometry.height=(size_t) (output_scaling*geometry.height+0.5);
2264 geometry.x=(ssize_t) (output_scaling*geometry.x+0.5);
2265 geometry.y=(ssize_t) (output_scaling*geometry.y+0.5);
2266 if ( output_scaling < 0.1 ) {
2267 coeff = (double *) RelinquishMagickMemory(coeff);
2268 (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
2269 "InvalidArgument","%s", "-set option:distort:scale" );
2270 return((Image *) NULL);
2272 output_scaling = 1/output_scaling;
2275 #define ScaleFilter(F,A,B,C,D) \
2276 ScaleResampleFilter( (F), \
2277 output_scaling*(A), output_scaling*(B), \
2278 output_scaling*(C), output_scaling*(D) )
2281 Initialize the distort image attributes.
2283 distort_image=CloneImage(image,geometry.width,geometry.height,MagickTrue,
2285 if (distort_image == (Image *) NULL)
2286 return((Image *) NULL);
2287 /* if image is ColorMapped - change it to DirectClass */
2288 if (SetImageStorageClass(distort_image,DirectClass,exception) == MagickFalse)
2290 distort_image=DestroyImage(distort_image);
2291 return((Image *) NULL);
2293 if ((IsPixelInfoGray(&distort_image->background_color) == MagickFalse) &&
2294 (IsGrayColorspace(distort_image->colorspace) != MagickFalse))
2295 (void) TransformImageColorspace(distort_image,sRGBColorspace,exception);
2296 if (distort_image->background_color.alpha_trait == BlendPixelTrait)
2297 distort_image->alpha_trait=BlendPixelTrait;
2298 distort_image->page.x=geometry.x;
2299 distort_image->page.y=geometry.y;
2301 { /* ----- MAIN CODE -----
2302 Sample the source image to each pixel in the distort image.
2317 **restrict resample_filter;
2324 GetPixelInfo(distort_image,&zero);
2325 resample_filter=AcquireResampleFilterThreadSet(image,
2326 UndefinedVirtualPixelMethod,MagickFalse,exception);
2327 distort_view=AcquireAuthenticCacheView(distort_image,exception);
2328 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2329 #pragma omp parallel for schedule(static,4) shared(progress,status) \
2330 magick_threads(image,distort_image,distort_image->rows,1)
2332 for (j=0; j < (ssize_t) distort_image->rows; j++)
2335 id = GetOpenMPThreadId();
2338 validity; /* how mathematically valid is this the mapping */
2344 pixel, /* pixel color to assign to distorted image */
2345 invalid; /* the color to assign when distort result is invalid */
2349 s; /* transform destination image x,y to source image x,y */
2357 q=QueueCacheViewAuthenticPixels(distort_view,0,j,distort_image->columns,1,
2359 if (q == (Quantum *) NULL)
2366 /* Define constant scaling vectors for Affine Distortions
2367 Other methods are either variable, or use interpolated lookup
2371 case AffineDistortion:
2372 ScaleFilter( resample_filter[id],
2374 coeff[3], coeff[4] );
2380 /* Initialize default pixel validity
2381 * negative: pixel is invalid output 'matte_color'
2382 * 0.0 to 1.0: antialiased, mix with resample output
2383 * 1.0 or greater: use resampled output.
2387 invalid=distort_image->matte_color;
2388 if (distort_image->colorspace == CMYKColorspace)
2389 ConvertRGBToCMYK(&invalid); /* what about other color spaces? */
2390 for (i=0; i < (ssize_t) distort_image->columns; i++)
2392 /* map pixel coordinate to distortion space coordinate */
2393 d.x = (double) (geometry.x+i+0.5)*output_scaling;
2394 d.y = (double) (geometry.y+j+0.5)*output_scaling;
2395 s = d; /* default is a no-op mapping */
2398 case AffineDistortion:
2400 s.x=coeff[0]*d.x+coeff[1]*d.y+coeff[2];
2401 s.y=coeff[3]*d.x+coeff[4]*d.y+coeff[5];
2402 /* Affine partial derivitives are constant -- set above */
2405 case PerspectiveDistortion:
2408 p,q,r,abs_r,abs_c6,abs_c7,scale;
2409 /* perspective is a ratio of affines */
2410 p=coeff[0]*d.x+coeff[1]*d.y+coeff[2];
2411 q=coeff[3]*d.x+coeff[4]*d.y+coeff[5];
2412 r=coeff[6]*d.x+coeff[7]*d.y+1.0;
2413 /* Pixel Validity -- is it a 'sky' or 'ground' pixel */
2414 validity = (r*coeff[8] < 0.0) ? 0.0 : 1.0;
2415 /* Determine horizon anti-alias blending */
2417 abs_c6 = fabs(coeff[6]);
2418 abs_c7 = fabs(coeff[7]);
2419 if ( abs_c6 > abs_c7 ) {
2420 if ( abs_r < abs_c6*output_scaling )
2421 validity = 0.5 - coeff[8]*r/(coeff[6]*output_scaling);
2423 else if ( abs_r < abs_c7*output_scaling )
2424 validity = 0.5 - coeff[8]*r/(coeff[7]*output_scaling);
2425 /* Perspective Sampling Point (if valid) */
2426 if ( validity > 0.0 ) {
2427 /* divide by r affine, for perspective scaling */
2431 /* Perspective Partial Derivatives or Scaling Vectors */
2433 ScaleFilter( resample_filter[id],
2434 (r*coeff[0] - p*coeff[6])*scale,
2435 (r*coeff[1] - p*coeff[7])*scale,
2436 (r*coeff[3] - q*coeff[6])*scale,
2437 (r*coeff[4] - q*coeff[7])*scale );
2441 case BilinearReverseDistortion:
2443 /* Reversed Mapped is just a simple polynomial */
2444 s.x=coeff[0]*d.x+coeff[1]*d.y+coeff[2]*d.x*d.y+coeff[3];
2445 s.y=coeff[4]*d.x+coeff[5]*d.y
2446 +coeff[6]*d.x*d.y+coeff[7];
2447 /* Bilinear partial derivitives of scaling vectors */
2448 ScaleFilter( resample_filter[id],
2449 coeff[0] + coeff[2]*d.y,
2450 coeff[1] + coeff[2]*d.x,
2451 coeff[4] + coeff[6]*d.y,
2452 coeff[5] + coeff[6]*d.x );
2455 case BilinearForwardDistortion:
2457 /* Forward mapped needs reversed polynomial equations
2458 * which unfortunatally requires a square root! */
2460 d.x -= coeff[3]; d.y -= coeff[7];
2461 b = coeff[6]*d.x - coeff[2]*d.y + coeff[8];
2462 c = coeff[4]*d.x - coeff[0]*d.y;
2465 /* Handle Special degenerate (non-quadratic) case
2466 * Currently without horizon anti-alising */
2467 if ( fabs(coeff[9]) < MagickEpsilon )
2470 c = b*b - 2*coeff[9]*c;
2474 s.y = ( -b + sqrt(c) )/coeff[9];
2476 if ( validity > 0.0 )
2477 s.x = ( d.x - coeff[1]*s.y) / ( coeff[0] + coeff[2]*s.y );
2479 /* NOTE: the sign of the square root should be -ve for parts
2480 where the source image becomes 'flipped' or 'mirrored'.
2481 FUTURE: Horizon handling
2482 FUTURE: Scaling factors or Deritives (how?)
2487 case BilinearDistortion:
2488 /* Bilinear mapping of any Quadrilateral to any Quadrilateral */
2489 /* UNDER DEVELOPMENT */
2492 case PolynomialDistortion:
2494 /* multi-ordered polynomial */
2499 nterms=(ssize_t)coeff[1];
2502 du,dv; /* the du,dv vectors from unit dx,dy -- derivatives */
2504 s.x=s.y=du.x=du.y=dv.x=dv.y=0.0;
2505 for(k=0; k < nterms; k++) {
2506 s.x += poly_basis_fn(k,d.x,d.y)*coeff[2+k];
2507 du.x += poly_basis_dx(k,d.x,d.y)*coeff[2+k];
2508 du.y += poly_basis_dy(k,d.x,d.y)*coeff[2+k];
2509 s.y += poly_basis_fn(k,d.x,d.y)*coeff[2+k+nterms];
2510 dv.x += poly_basis_dx(k,d.x,d.y)*coeff[2+k+nterms];
2511 dv.y += poly_basis_dy(k,d.x,d.y)*coeff[2+k+nterms];
2513 ScaleFilter( resample_filter[id], du.x,du.y,dv.x,dv.y );
2518 /* what is the angle and radius in the destination image */
2519 s.x = (double) ((atan2(d.y,d.x) - coeff[0])/Magick2PI);
2520 s.x -= MagickRound(s.x); /* angle */
2521 s.y = hypot(d.x,d.y); /* radius */
2523 /* Arc Distortion Partial Scaling Vectors
2524 Are derived by mapping the perpendicular unit vectors
2525 dR and dA*R*2PI rather than trying to map dx and dy
2526 The results is a very simple orthogonal aligned ellipse.
2528 if ( s.y > MagickEpsilon )
2529 ScaleFilter( resample_filter[id],
2530 (double) (coeff[1]/(Magick2PI*s.y)), 0, 0, coeff[3] );
2532 ScaleFilter( resample_filter[id],
2533 distort_image->columns*2, 0, 0, coeff[3] );
2535 /* now scale the angle and radius for source image lookup point */
2536 s.x = s.x*coeff[1] + coeff[4] + image->page.x +0.5;
2537 s.y = (coeff[2] - s.y) * coeff[3] + image->page.y;
2540 case PolarDistortion:
2541 { /* 2D Cartesain to Polar View */
2544 s.x = atan2(d.x,d.y) - (coeff[4]+coeff[5])/2;
2546 s.x -= MagickRound(s.x);
2547 s.x *= Magick2PI; /* angle - relative to centerline */
2548 s.y = hypot(d.x,d.y); /* radius */
2550 /* Polar Scaling vectors are based on mapping dR and dA vectors
2551 This results in very simple orthogonal scaling vectors
2553 if ( s.y > MagickEpsilon )
2554 ScaleFilter( resample_filter[id],
2555 (double) (coeff[6]/(Magick2PI*s.y)), 0, 0, coeff[7] );
2557 ScaleFilter( resample_filter[id],
2558 distort_image->columns*2, 0, 0, coeff[7] );
2560 /* now finish mapping radius/angle to source x,y coords */
2561 s.x = s.x*coeff[6] + (double)image->columns/2.0 + image->page.x;
2562 s.y = (s.y-coeff[1])*coeff[7] + image->page.y;
2565 case DePolarDistortion:
2566 { /* @D Polar to Carteasain */
2567 /* ignore all destination virtual offsets */
2568 d.x = ((double)i+0.5)*output_scaling*coeff[6]-coeff[4];
2569 d.y = ((double)j+0.5)*output_scaling*coeff[7]+coeff[1];
2570 s.x = d.y*sin(d.x) + coeff[2];
2571 s.y = d.y*cos(d.x) + coeff[3];
2572 /* derivatives are usless - better to use SuperSampling */
2575 case Cylinder2PlaneDistortion:
2576 { /* 3D Cylinder to Tangential Plane */
2578 /* relative to center of distortion */
2579 d.x -= coeff[4]; d.y -= coeff[5];
2580 d.x /= coeff[1]; /* x' = x/r */
2581 ax=atan(d.x); /* aa = atan(x/r) = u/r */
2582 cx=cos(ax); /* cx = cos(atan(x/r)) = 1/sqrt(x^2+u^2) */
2583 s.x = coeff[1]*ax; /* u = r*atan(x/r) */
2584 s.y = d.y*cx; /* v = y*cos(u/r) */
2585 /* derivatives... (see personnal notes) */
2586 ScaleFilter( resample_filter[id],
2587 1.0/(1.0+d.x*d.x), 0.0, -d.x*s.y*cx*cx/coeff[1], s.y/d.y );
2589 if ( i == 0 && j == 0 ) {
2590 fprintf(stderr, "x=%lf y=%lf u=%lf v=%lf\n", d.x*coeff[1], d.y, s.x, s.y);
2591 fprintf(stderr, "phi = %lf\n", (double)(ax * 180.0/MagickPI) );
2592 fprintf(stderr, "du/dx=%lf du/dx=%lf dv/dx=%lf dv/dy=%lf\n",
2593 1.0/(1.0+d.x*d.x), 0.0, -d.x*s.y*cx*cx/coeff[1], s.y/d.y );
2596 /* add center of distortion in source */
2597 s.x += coeff[2]; s.y += coeff[3];
2600 case Plane2CylinderDistortion:
2601 { /* 3D Cylinder to Tangential Plane */
2602 /* relative to center of distortion */
2603 d.x -= coeff[4]; d.y -= coeff[5];
2605 /* is pixel valid - horizon of a infinite Virtual-Pixel Plane
2606 * (see Anthony Thyssen's personal note) */
2607 validity = (double) (coeff[1]*MagickPI2 - fabs(d.x))/output_scaling + 0.5;
2609 if ( validity > 0.0 ) {
2611 d.x /= coeff[1]; /* x'= x/r */
2612 cx = 1/cos(d.x); /* cx = 1/cos(x/r) */
2613 tx = tan(d.x); /* tx = tan(x/r) */
2614 s.x = coeff[1]*tx; /* u = r * tan(x/r) */
2615 s.y = d.y*cx; /* v = y / cos(x/r) */
2616 /* derivatives... (see Anthony Thyssen's personal notes) */
2617 ScaleFilter( resample_filter[id],
2618 cx*cx, 0.0, s.y*cx/coeff[1], cx );
2620 /*if ( i == 0 && j == 0 )*/
2621 if ( d.x == 0.5 && d.y == 0.5 ) {
2622 fprintf(stderr, "x=%lf y=%lf u=%lf v=%lf\n", d.x*coeff[1], d.y, s.x, s.y);
2623 fprintf(stderr, "radius = %lf phi = %lf validity = %lf\n",
2624 coeff[1], (double)(d.x * 180.0/MagickPI), validity );
2625 fprintf(stderr, "du/dx=%lf du/dx=%lf dv/dx=%lf dv/dy=%lf\n",
2626 cx*cx, 0.0, s.y*cx/coeff[1], cx);
2630 /* add center of distortion in source */
2631 s.x += coeff[2]; s.y += coeff[3];
2634 case BarrelDistortion:
2635 case BarrelInverseDistortion:
2636 { /* Lens Barrel Distionion Correction */
2637 double r,fx,fy,gx,gy;
2638 /* Radial Polynomial Distortion (de-normalized) */
2641 r = sqrt(d.x*d.x+d.y*d.y);
2642 if ( r > MagickEpsilon ) {
2643 fx = ((coeff[0]*r + coeff[1])*r + coeff[2])*r + coeff[3];
2644 fy = ((coeff[4]*r + coeff[5])*r + coeff[6])*r + coeff[7];
2645 gx = ((3*coeff[0]*r + 2*coeff[1])*r + coeff[2])/r;
2646 gy = ((3*coeff[4]*r + 2*coeff[5])*r + coeff[6])/r;
2647 /* adjust functions and scaling for 'inverse' form */
2648 if ( method == BarrelInverseDistortion ) {
2649 fx = 1/fx; fy = 1/fy;
2650 gx *= -fx*fx; gy *= -fy*fy;
2652 /* Set the source pixel to lookup and EWA derivative vectors */
2653 s.x = d.x*fx + coeff[8];
2654 s.y = d.y*fy + coeff[9];
2655 ScaleFilter( resample_filter[id],
2656 gx*d.x*d.x + fx, gx*d.x*d.y,
2657 gy*d.x*d.y, gy*d.y*d.y + fy );
2660 /* Special handling to avoid divide by zero when r==0
2662 ** The source and destination pixels match in this case
2663 ** which was set at the top of the loop using s = d;
2664 ** otherwise... s.x=coeff[8]; s.y=coeff[9];
2666 if ( method == BarrelDistortion )
2667 ScaleFilter( resample_filter[id],
2668 coeff[3], 0, 0, coeff[7] );
2669 else /* method == BarrelInverseDistortion */
2670 /* FUTURE, trap for D==0 causing division by zero */
2671 ScaleFilter( resample_filter[id],
2672 1.0/coeff[3], 0, 0, 1.0/coeff[7] );
2676 case ShepardsDistortion:
2677 { /* Shepards Method, or Inverse Weighted Distance for
2678 displacement around the destination image control points
2679 The input arguments are the coefficents to the function.
2680 This is more of a 'displacement' function rather than an
2681 absolute distortion function.
2683 Note: We can not determine derivatives using shepards method
2684 so only a point sample interpolatation can be used.
2691 denominator = s.x = s.y = 0;
2692 for(i=0; i<number_arguments; i+=4) {
2694 ((double)d.x-arguments[i+2])*((double)d.x-arguments[i+2])
2695 + ((double)d.y-arguments[i+3])*((double)d.y-arguments[i+3]);
2696 weight = pow(weight,coeff[0]); /* shepards power factor */
2697 weight = ( weight < 1.0 ) ? 1.0 : 1.0/weight;
2699 s.x += (arguments[ i ]-arguments[i+2])*weight;
2700 s.y += (arguments[i+1]-arguments[i+3])*weight;
2701 denominator += weight;
2705 s.x += d.x; /* make it as relative displacement */
2710 break; /* use the default no-op given above */
2712 /* map virtual canvas location back to real image coordinate */
2713 if ( bestfit && method != ArcDistortion ) {
2714 s.x -= image->page.x;
2715 s.y -= image->page.y;
2720 if ( validity <= 0.0 ) {
2721 /* result of distortion is an invalid pixel - don't resample */
2722 SetPixelInfoPixel(distort_image,&invalid,q);
2725 /* resample the source image to find its correct color */
2726 (void) ResamplePixelColor(resample_filter[id],s.x,s.y,&pixel,
2728 /* if validity between 0.0 and 1.0 mix result with invalid pixel */
2729 if ( validity < 1.0 ) {
2730 /* Do a blend of sample color and invalid pixel */
2731 /* should this be a 'Blend', or an 'Over' compose */
2732 CompositePixelInfoBlend(&pixel,validity,&invalid,(1.0-validity),
2735 SetPixelInfoPixel(distort_image,&pixel,q);
2737 q+=GetPixelChannels(distort_image);
2739 sync=SyncCacheViewAuthenticPixels(distort_view,exception);
2740 if (sync == MagickFalse)
2742 if (image->progress_monitor != (MagickProgressMonitor) NULL)
2747 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2748 #pragma omp critical (MagickCore_DistortImage)
2750 proceed=SetImageProgress(image,DistortImageTag,progress++,
2752 if (proceed == MagickFalse)
2756 distort_view=DestroyCacheView(distort_view);
2757 resample_filter=DestroyResampleFilterThreadSet(resample_filter);
2759 if (status == MagickFalse)
2760 distort_image=DestroyImage(distort_image);
2763 /* Arc does not return an offset unless 'bestfit' is in effect
2764 And the user has not provided an overriding 'viewport'.
2766 if ( method == ArcDistortion && !bestfit && !viewport_given ) {
2767 distort_image->page.x = 0;
2768 distort_image->page.y = 0;
2770 coeff = (double *) RelinquishMagickMemory(coeff);
2771 return(distort_image);
2775 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2779 % R o t a t e I m a g e %
2783 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2785 % RotateImage() creates a new image that is a rotated copy of an existing
2786 % one. Positive angles rotate counter-clockwise (right-hand rule), while
2787 % negative angles rotate clockwise. Rotated images are usually larger than
2788 % the originals and have 'empty' triangular corners. X axis. Empty
2789 % triangles left over from shearing the image are filled with the background
2790 % color defined by member 'background_color' of the image. RotateImage
2791 % allocates the memory necessary for the new Image structure and returns a
2792 % pointer to the new image.
2794 % The format of the RotateImage method is:
2796 % Image *RotateImage(const Image *image,const double degrees,
2797 % ExceptionInfo *exception)
2799 % A description of each parameter follows.
2801 % o image: the image.
2803 % o degrees: Specifies the number of degrees to rotate the image.
2805 % o exception: return any errors or warnings in this structure.
2808 MagickExport Image *RotateImage(const Image *image,const double degrees,
2809 ExceptionInfo *exception)
2825 Adjust rotation angle.
2827 assert(image != (Image *) NULL);
2828 assert(image->signature == MagickSignature);
2829 if (image->debug != MagickFalse)
2830 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2831 assert(exception != (ExceptionInfo *) NULL);
2832 assert(exception->signature == MagickSignature);
2834 while (angle < -45.0)
2836 for (rotations=0; angle > 45.0; rotations++)
2839 shear.x=(-tan((double) DegreesToRadians(angle)/2.0));
2840 shear.y=sin((double) DegreesToRadians(angle));
2841 if ((fabs(shear.x) < MagickEpsilon) && (fabs(shear.y) < MagickEpsilon))
2842 return(IntegralRotateImage(image,rotations,exception));
2843 distort_image=CloneImage(image,0,0,MagickTrue,exception);
2844 if (distort_image == (Image *) NULL)
2845 return((Image *) NULL);
2846 (void) SetImageVirtualPixelMethod(distort_image,BackgroundVirtualPixelMethod,
2848 rotate_image=DistortImage(distort_image,ScaleRotateTranslateDistortion,1,
2849 °rees,MagickTrue,exception);
2850 distort_image=DestroyImage(distort_image);
2851 return(rotate_image);
2855 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2859 % S p a r s e C o l o r I m a g e %
2863 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2865 % SparseColorImage(), given a set of coordinates, interpolates the colors
2866 % found at those coordinates, across the whole image, using various methods.
2868 % The format of the SparseColorImage() method is:
2870 % Image *SparseColorImage(const Image *image,
2871 % const SparseColorMethod method,const size_t number_arguments,
2872 % const double *arguments,ExceptionInfo *exception)
2874 % A description of each parameter follows:
2876 % o image: the image to be filled in.
2878 % o method: the method to fill in the gradient between the control points.
2880 % The methods used for SparseColor() are often simular to methods
2881 % used for DistortImage(), and even share the same code for determination
2882 % of the function coefficents, though with more dimensions (or resulting
2885 % o number_arguments: the number of arguments given.
2887 % o arguments: array of floating point arguments for this method--
2888 % x,y,color_values-- with color_values given as normalized values.
2890 % o exception: return any errors or warnings in this structure
2893 MagickExport Image *SparseColorImage(const Image *image,
2894 const SparseColorMethod method,const size_t number_arguments,
2895 const double *arguments,ExceptionInfo *exception)
2897 #define SparseColorTag "Distort/SparseColor"
2911 assert(image != (Image *) NULL);
2912 assert(image->signature == MagickSignature);
2913 if (image->debug != MagickFalse)
2914 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2915 assert(exception != (ExceptionInfo *) NULL);
2916 assert(exception->signature == MagickSignature);
2918 /* Determine number of color values needed per control point */
2920 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
2922 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
2924 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
2926 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
2927 (image->colorspace == CMYKColorspace))
2929 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
2930 (image->alpha_trait == BlendPixelTrait))
2934 Convert input arguments into mapping coefficients, this this case
2935 we are mapping (distorting) colors, rather than coordinates.
2937 { DistortImageMethod
2940 distort_method=(DistortImageMethod) method;
2941 if ( distort_method >= SentinelDistortion )
2942 distort_method = ShepardsDistortion; /* Pretend to be Shepards */
2943 coeff = GenerateCoefficients(image, &distort_method, number_arguments,
2944 arguments, number_colors, exception);
2945 if ( coeff == (double *) NULL )
2946 return((Image *) NULL);
2948 Note some Distort Methods may fall back to other simpler methods,
2949 Currently the only fallback of concern is Bilinear to Affine
2950 (Barycentric), which is alaso sparse_colr method. This also ensures
2951 correct two and one color Barycentric handling.
2953 sparse_method = (SparseColorMethod) distort_method;
2954 if ( distort_method == ShepardsDistortion )
2955 sparse_method = method; /* return non-distort methods to normal */
2956 if ( sparse_method == InverseColorInterpolate )
2957 coeff[0]=0.5; /* sqrt() the squared distance for inverse */
2960 /* Verbose output */
2961 if ( IfStringTrue(GetImageArtifact(image,"verbose")) ) {
2963 switch (sparse_method) {
2964 case BarycentricColorInterpolate:
2966 register ssize_t x=0;
2967 (void) FormatLocaleFile(stderr, "Barycentric Sparse Color:\n");
2968 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
2969 (void) FormatLocaleFile(stderr, " -channel R -fx '%+lf*i %+lf*j %+lf' \\\n",
2970 coeff[x], coeff[x+1], coeff[x+2]),x+=3;
2971 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
2972 (void) FormatLocaleFile(stderr, " -channel G -fx '%+lf*i %+lf*j %+lf' \\\n",
2973 coeff[x], coeff[x+1], coeff[x+2]),x+=3;
2974 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
2975 (void) FormatLocaleFile(stderr, " -channel B -fx '%+lf*i %+lf*j %+lf' \\\n",
2976 coeff[x], coeff[x+1], coeff[x+2]),x+=3;
2977 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
2978 (image->colorspace == CMYKColorspace))
2979 (void) FormatLocaleFile(stderr, " -channel K -fx '%+lf*i %+lf*j %+lf' \\\n",
2980 coeff[x], coeff[x+1], coeff[x+2]),x+=3;
2981 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
2982 (image->alpha_trait == BlendPixelTrait))
2983 (void) FormatLocaleFile(stderr, " -channel A -fx '%+lf*i %+lf*j %+lf' \\\n",
2984 coeff[x], coeff[x+1], coeff[x+2]),x+=3;
2987 case BilinearColorInterpolate:
2989 register ssize_t x=0;
2990 (void) FormatLocaleFile(stderr, "Bilinear Sparse Color\n");
2991 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
2992 (void) FormatLocaleFile(stderr, " -channel R -fx '%+lf*i %+lf*j %+lf*i*j %+lf;\n",
2993 coeff[ x ], coeff[x+1],
2994 coeff[x+2], coeff[x+3]),x+=4;
2995 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
2996 (void) FormatLocaleFile(stderr, " -channel G -fx '%+lf*i %+lf*j %+lf*i*j %+lf;\n",
2997 coeff[ x ], coeff[x+1],
2998 coeff[x+2], coeff[x+3]),x+=4;
2999 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
3000 (void) FormatLocaleFile(stderr, " -channel B -fx '%+lf*i %+lf*j %+lf*i*j %+lf;\n",
3001 coeff[ x ], coeff[x+1],
3002 coeff[x+2], coeff[x+3]),x+=4;
3003 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
3004 (image->colorspace == CMYKColorspace))
3005 (void) FormatLocaleFile(stderr, " -channel K -fx '%+lf*i %+lf*j %+lf*i*j %+lf;\n",
3006 coeff[ x ], coeff[x+1],
3007 coeff[x+2], coeff[x+3]),x+=4;
3008 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
3009 (image->alpha_trait == BlendPixelTrait))
3010 (void) FormatLocaleFile(stderr, " -channel A -fx '%+lf*i %+lf*j %+lf*i*j %+lf;\n",
3011 coeff[ x ], coeff[x+1],
3012 coeff[x+2], coeff[x+3]),x+=4;
3016 /* sparse color method is too complex for FX emulation */
3021 /* Generate new image for generated interpolated gradient.
3022 * ASIDE: Actually we could have just replaced the colors of the original
3023 * image, but IM Core policy, is if storage class could change then clone
3027 sparse_image=CloneImage(image,0,0,MagickTrue,exception);
3028 if (sparse_image == (Image *) NULL)
3029 return((Image *) NULL);
3030 if (SetImageStorageClass(sparse_image,DirectClass,exception) == MagickFalse)
3031 { /* if image is ColorMapped - change it to DirectClass */
3032 sparse_image=DestroyImage(sparse_image);
3033 return((Image *) NULL);
3035 { /* ----- MAIN CODE ----- */
3050 sparse_view=AcquireAuthenticCacheView(sparse_image,exception);
3051 #if defined(MAGICKCORE_OPENMP_SUPPORT)
3052 #pragma omp parallel for schedule(static,4) shared(progress,status) \
3053 magick_threads(image,sparse_image,sparse_image->rows,1)
3055 for (j=0; j < (ssize_t) sparse_image->rows; j++)
3061 pixel; /* pixel to assign to distorted image */
3069 q=GetCacheViewAuthenticPixels(sparse_view,0,j,sparse_image->columns,
3071 if (q == (Quantum *) NULL)
3076 GetPixelInfo(sparse_image,&pixel);
3077 for (i=0; i < (ssize_t) image->columns; i++)
3079 GetPixelInfoPixel(image,q,&pixel);
3080 switch (sparse_method)
3082 case BarycentricColorInterpolate:
3084 register ssize_t x=0;
3085 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
3086 pixel.red = coeff[x]*i +coeff[x+1]*j
3088 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
3089 pixel.green = coeff[x]*i +coeff[x+1]*j
3091 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
3092 pixel.blue = coeff[x]*i +coeff[x+1]*j
3094 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
3095 (image->colorspace == CMYKColorspace))
3096 pixel.black = coeff[x]*i +coeff[x+1]*j
3098 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
3099 (image->alpha_trait == BlendPixelTrait))
3100 pixel.alpha = coeff[x]*i +coeff[x+1]*j
3104 case BilinearColorInterpolate:
3106 register ssize_t x=0;
3107 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
3108 pixel.red = coeff[x]*i + coeff[x+1]*j +
3109 coeff[x+2]*i*j + coeff[x+3], x+=4;
3110 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
3111 pixel.green = coeff[x]*i + coeff[x+1]*j +
3112 coeff[x+2]*i*j + coeff[x+3], x+=4;
3113 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
3114 pixel.blue = coeff[x]*i + coeff[x+1]*j +
3115 coeff[x+2]*i*j + coeff[x+3], x+=4;
3116 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
3117 (image->colorspace == CMYKColorspace))
3118 pixel.black = coeff[x]*i + coeff[x+1]*j +
3119 coeff[x+2]*i*j + coeff[x+3], x+=4;
3120 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
3121 (image->alpha_trait == BlendPixelTrait))
3122 pixel.alpha = coeff[x]*i + coeff[x+1]*j +
3123 coeff[x+2]*i*j + coeff[x+3], x+=4;
3126 case InverseColorInterpolate:
3127 case ShepardsColorInterpolate:
3128 { /* Inverse (Squared) Distance weights average (IDW) */
3134 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
3136 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
3138 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
3140 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
3141 (image->colorspace == CMYKColorspace))
3143 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
3144 (image->alpha_trait == BlendPixelTrait))
3147 for(k=0; k<number_arguments; k+=2+number_colors) {
3148 register ssize_t x=(ssize_t) k+2;
3150 ((double)i-arguments[ k ])*((double)i-arguments[ k ])
3151 + ((double)j-arguments[k+1])*((double)j-arguments[k+1]);
3152 weight = pow(weight,coeff[0]); /* inverse of power factor */
3153 weight = ( weight < 1.0 ) ? 1.0 : 1.0/weight;
3154 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
3155 pixel.red += arguments[x++]*weight;
3156 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
3157 pixel.green += arguments[x++]*weight;
3158 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
3159 pixel.blue += arguments[x++]*weight;
3160 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
3161 (image->colorspace == CMYKColorspace))
3162 pixel.black += arguments[x++]*weight;
3163 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
3164 (image->alpha_trait == BlendPixelTrait))
3165 pixel.alpha += arguments[x++]*weight;
3166 denominator += weight;
3168 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
3169 pixel.red/=denominator;
3170 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
3171 pixel.green/=denominator;
3172 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
3173 pixel.blue/=denominator;
3174 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
3175 (image->colorspace == CMYKColorspace))
3176 pixel.black/=denominator;
3177 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
3178 (image->alpha_trait == BlendPixelTrait))
3179 pixel.alpha/=denominator;
3182 case VoronoiColorInterpolate:
3184 { /* Just use the closest control point you can find! */
3188 minimum = MagickHuge;
3190 for(k=0; k<number_arguments; k+=2+number_colors) {
3192 ((double)i-arguments[ k ])*((double)i-arguments[ k ])
3193 + ((double)j-arguments[k+1])*((double)j-arguments[k+1]);
3194 if ( distance < minimum ) {
3195 register ssize_t x=(ssize_t) k+2;
3196 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
3197 pixel.red=arguments[x++];
3198 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
3199 pixel.green=arguments[x++];
3200 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
3201 pixel.blue=arguments[x++];
3202 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
3203 (image->colorspace == CMYKColorspace))
3204 pixel.black=arguments[x++];
3205 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
3206 (image->alpha_trait == BlendPixelTrait))
3207 pixel.alpha=arguments[x++];
3214 /* set the color directly back into the source image */
3215 if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
3216 pixel.red*=QuantumRange;
3217 if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
3218 pixel.green*=QuantumRange;
3219 if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
3220 pixel.blue*=QuantumRange;
3221 if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
3222 (image->colorspace == CMYKColorspace))
3223 pixel.black*=QuantumRange;
3224 if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
3225 (image->alpha_trait == BlendPixelTrait))
3226 pixel.alpha*=QuantumRange;
3227 SetPixelInfoPixel(sparse_image,&pixel,q);
3228 q+=GetPixelChannels(sparse_image);
3230 sync=SyncCacheViewAuthenticPixels(sparse_view,exception);
3231 if (sync == MagickFalse)
3233 if (image->progress_monitor != (MagickProgressMonitor) NULL)
3238 #if defined(MAGICKCORE_OPENMP_SUPPORT)
3239 #pragma omp critical (MagickCore_SparseColorImage)
3241 proceed=SetImageProgress(image,SparseColorTag,progress++,image->rows);
3242 if (proceed == MagickFalse)
3246 sparse_view=DestroyCacheView(sparse_view);
3247 if (status == MagickFalse)
3248 sparse_image=DestroyImage(sparse_image);
3250 coeff = (double *) RelinquishMagickMemory(coeff);
3251 return(sparse_image);