/* %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % % % % % DDDD IIIII SSSSS TTTTT OOO RRRR TTTTT % % D D I SS T O O R R T % % D D I SSS T O O RRRR T % % D D I SS T O O R R T % % DDDD IIIII SSSSS T OOO R R T % % % % % % ImageMagick Image Distortion Methods. % % % % Software Design % % John Cristy % % Anthony Thyssen % % June 2007 % % % % % % Copyright 1999-2007 ImageMagick Studio LLC, a non-profit organization % % dedicated to making software imaging solutions freely available. % % % % You may not use this file except in compliance with the License. You may % % obtain a copy of the License at % % % % http://www.imagemagick.org/script/license.php % % % % Unless required by applicable law or agreed to in writing, software % % distributed under the License is distributed on an "AS IS" BASIS, % % WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. % % See the License for the specific language governing permissions and % % limitations under the License. % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % */ /* Include declarations. */ #include "magick/studio.h" #include "magick/artifact.h" #include "magick/cache-view.h" #include "magick/colorspace-private.h" #include "magick/composite-private.h" #include "magick/distort.h" #include "magick/exception.h" #include "magick/exception-private.h" #include "magick/gem.h" #include "magick/hashmap.h" #include "magick/image.h" #include "magick/list.h" #include "magick/matrix.h" #include "magick/memory_.h" #include "magick/pixel.h" #include "magick/pixel-private.h" #include "magick/resample.h" #include "magick/registry.h" #include "magick/semaphore.h" #include "magick/splay-tree.h" #include "magick/string_.h" /* %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % % % % % D i s t o r t I m a g e % % % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % DistortImage() distorts an image using various distortion methods, by % mapping color lookups of the source image to a new destination image % usally of the same size as the source image, unless 'bestfit' is set to % true. % % If 'bestfit' is enabled, and distortion allows it, the destination image is % adjusted to ensure the whole source 'image' will just fit within the final % destination image, which will be sized and offset accordingly. Also in % many cases the virtual offset of the source image will be taken into % account in the mapping. % % ArcDistortion will always ignore source image offset, and always 'bestfit' % the destination image with the top left corner offset relative to the polar % mapping center. % % Bilinear has no simple inverse mapping so will not allow 'bestfit' style % of image distortion. % % The format of the DistortImage() method is: % % Image *DistortImage(const Image *image,const DistortImageMethod method, % const unsigned long number_arguments,const double *arguments, % const MagickBooleanType bestfit, ExceptionInfo *exception) % % A description of each parameter follows: % % o image: The image to be distorted. % % o method: The method of image distortion. % % o number_arguments: The number of arguments given. % % o arguments: The arguments for this distortion method. % % o bestfit: Attempt to resize destination to fit distorted source. % % o exception: Return any errors or warnings in this structure % */ #if 0 /* This function is no longer requires -- to be removed */ static MagickBooleanType SolveAffineDistortion( const unsigned long number_points,const PointInfo *points,double **matrix, double *vector) { /* Given the transformations of the coordinates for two triangles u0,v0, x0,y0, u1,v1, x1,y1, u2,v2, x2,y2, ... Solve for the 6 cofficients c0..c6 for a affine distortion: u = c0*x + c2*y + c4 v = c1*x + c3*y + c5 */ register int i; double x,y,u,v; if (number_points < 6) return(MagickFalse); for( i = 0; i < 6; ) { u = points[i].x; v = points[i].y; x = points[i+1].x; y = points[i+1].y; vector[i]=u; matrix[i][0]=x; matrix[i][2]=y; matrix[i][4]=1.0; i++; vector[i]=v; matrix[i][1]=x; matrix[i][3]=y; matrix[i][5]=1.0; i++; } return(GaussJordanElimination(matrix,&vector,6UL,1UL)); } #endif static void InvertAffineCoefficients(const double *coefficients,double *inverse) { double determinant; determinant=1.0/(coefficients[0]*coefficients[3]-coefficients[1]*coefficients[2]); inverse[0]=determinant*coefficients[3]; inverse[1]=determinant*(-coefficients[1]); inverse[2]=determinant*(-coefficients[2]); inverse[3]=determinant*coefficients[0]; inverse[4]=(-coefficients[4])*inverse[0]-coefficients[5]*inverse[2]; inverse[5]=(-coefficients[4])*inverse[1]-coefficients[5]*inverse[3]; } #if 0 /* This function is no longer requires -- to be removed */ static MagickBooleanType SolveBilinearDistortion( const unsigned long number_points,const PointInfo *points,double **matrix, double *vector) { /* Given the transformations of the coordinates of two quadrilaterals: u0,v0, x0,y0, u1,v1, x1,y1, u2,v2, x2,y2, ... Solve for the 8 coeffecients c0..c7 for a bilinear distortion: u = c0*x + c1*y + c2*x*y + c3 v = c4*x + c5*y + c6*x*y + c7 */ register int i; double x,y,u,v; if (number_points < 8) return(MagickFalse); for( i = 0; i < 8; ) { u = points[i].x; v = points[i].y; x = points[i+1].x; y = points[i+1].y; vector[i]=u; matrix[i][0]=x; matrix[i][1]=y; matrix[i][2]=x*y; matrix[i][3]=1.0; i++; vector[i]=v; matrix[i][4]=x; matrix[i][5]=y; matrix[i][6]=x*y; matrix[i][7]=1.0; i++; } return(GaussJordanElimination(matrix,&vector,8UL,1UL)); } static MagickBooleanType SolvePerspectiveDistortion( const unsigned long number_points,const PointInfo *points,double **matrix, double *vector) { /* Given the coordinates of two quadrilaterals: u0,v0, x0,y0, u1,v1, x1,y1, u2,v2, x2,y2, ... Solve for the 8 coefficients c0..c7 for a perspective distortion: u = ( c0*x + c1*y + c2 ) / ( c6*x + c7*y + 1 ) v = ( c3*x + c4*y + c5 ) / ( c6*x + c7*y + 1 ) */ register int i; double x,y,u,v; if (number_points < 8) return(MagickFalse); for( i = 0; i < 8; ) { u = points[i].x; v = points[i].y; x = points[i+1].x; y = points[i+1].y; vector[i]=u; matrix[i][0]=x; matrix[i][1]=y; matrix[i][2]=1.0; matrix[i][6]=-x*u; matrix[i][7]=-y*u; i++; vector[i]=v; matrix[i][3]=x; matrix[i][4]=y; matrix[i][5]=1.0; matrix[i][6]=-x*v; matrix[i][7]=-y*v; i++; } return(GaussJordanElimination(matrix,&vector,8UL,1UL)); } #endif static void InvertPerspectiveCoefficients(const double *coefficients, double *inverse) { double determinant; /* From "Digital Image Warping" by George Wolberg, page 53 */ determinant=1.0/(coefficients[0]*coefficients[4]-coefficients[3]*coefficients[1]); inverse[0]=determinant*(coefficients[4]-coefficients[7]*coefficients[5]); inverse[1]=determinant*(coefficients[7]*coefficients[2]-coefficients[1]); inverse[2]=determinant*(coefficients[1]*coefficients[5]-coefficients[4]*coefficients[2]); inverse[3]=determinant*(coefficients[6]*coefficients[5]-coefficients[3]); inverse[4]=determinant*(coefficients[0]-coefficients[6]*coefficients[2]); inverse[5]=determinant*(coefficients[3]*coefficients[2]-coefficients[0]*coefficients[5]); inverse[6]=determinant*(coefficients[3]*coefficients[7]-coefficients[6]*coefficients[4]); inverse[7]=determinant*(coefficients[6]*coefficients[1]-coefficients[0]*coefficients[7]); } static inline double MagickRound(double x) { assert(x >= (1.0*LONG_MIN-0.5)); assert(x <= (1.0*LONG_MAX+0.5)); if (x >= 0.0) return((double) ((long) (x+0.5))); return((double) ((long) (x-0.5))); } MagickExport Image *DistortImage(Image *image,const DistortImageMethod method, const unsigned long number_arguments,const double *arguments, MagickBooleanType bestfit, ExceptionInfo *exception) { #define DistortImageTag "Distort/Image" const char *artifact; double coefficients[9], validity; Image *distort_image; register long i, x; long j, y; PointInfo point; /* point to sample (center of filtered resample of area) */ MagickPixelPacket pixel, /* pixel to assign to distorted image */ invalid; /* the color to assign when distort result is invalid */ register IndexPacket *indexes; register PixelPacket *q; ResampleFilter *resample_filter; ViewInfo *distort_view; MagickBooleanType status; RectangleInfo geometry; assert(image != (Image *) NULL); assert(image->signature == MagickSignature); if (image->debug != MagickFalse) (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename); assert(exception != (ExceptionInfo *) NULL); assert(exception->signature == MagickSignature); (void) ResetMagickMemory(coefficients,0,sizeof(coefficients)); /* Convert input arguments into mapping coefficents for distortion */ switch (method) { case AffineDistortion: { double **matrix, **vectors, terms[3]; /* Affine Distortion u = c0*x + c2*y + c4 v = c1*x + c3*y + c5 Input Arguments are pairs of distorted coodinates (minimum 3 sets) Which will be used to generate the coefficients of the above. u1,v1, x1,y1, u2,v2, x2,y2, u3,v3, x3,y3, ... */ if (number_arguments < 12) { (void) ThrowMagickException(exception,GetMagickModule(),OptionError, "InvalidArgument","%s : '%s'","distort Affine", "Minimum of 3 pairs of coords needed (12 numbers)"); return((Image *) NULL); } if (number_arguments%4 != 0) { (void) ThrowMagickException(exception,GetMagickModule(),OptionError, "InvalidArgument","%s : '%s'","distort Affine", "Requires pairs of coords (sX,sY,dX,dY)"); return((Image *) NULL); } matrix = AcquireMagickMatrix(3UL,3UL); vectors = AcquireMagickMatrix(2UL,3UL); if (matrix == (double **) NULL || vectors == (double **) NULL) { matrix = RelinquishMagickMatrix(matrix, 3UL); vectors = RelinquishMagickMatrix(vectors, 2UL); ThrowImageException(ResourceLimitError,"MemoryAllocationFailed"); return((Image *) NULL); } /* Add control points for least squares solving */ for (i=0; i < (long) number_arguments; i+=4) { terms[0] = arguments[i+2]; /* x */ terms[1] = arguments[i+3]; /* y */ terms[2] = 1; /* 1 */ LeastSquaresAddTerms(matrix,vectors,terms,&(arguments[i]),3UL,2UL); } status=GaussJordanElimination(matrix,vectors,3UL,2UL); matrix = RelinquishMagickMatrix(matrix, 3UL); if ( status == MagickTrue ) { /* Affine has a bit of a weird ordering of coefficents. This ordering is for backward compatibility with the older affine functions of IM. */ coefficients[0] = vectors[0][0]; /* u = ... */ coefficients[2] = vectors[0][1]; coefficients[4] = vectors[0][2]; coefficients[1] = vectors[1][0]; /* v = ... */ coefficients[3] = vectors[1][1]; coefficients[5] = vectors[1][2]; } vectors = RelinquishMagickMatrix(vectors, 2UL); if ( status == MagickFalse ) { (void) ThrowMagickException(exception,GetMagickModule(),OptionError, "InvalidArgument","%s : '%s'","distort Affine", "Unsolvable Matrix"); return((Image *) NULL); } break; } case AffineProjectionDistortion: { /* Arguments: Affine Matrix (forward mapping) sx, rx, ry, sy, tx, ty */ if (number_arguments != 6) { (void) ThrowMagickException(exception,GetMagickModule(),OptionError, "InvalidArgument","%s : '%s'","distort AffineProjection", "Needs 6 numbers"); return((Image *) NULL); } InvertAffineCoefficients(arguments, coefficients); break; } case BilinearDistortion: { double **matrix, *vectors[2], terms[4]; /* Bilinear Distortion (reversed) u = c0*x + c1*y + c2*x*y + c3; v = c4*x + c5*y + c6*x*y + c7; Input Arguments are pairs of distorted coodinates (minimum 4 pairs) Which will be used to generate the coefficients of the above. u1,v1, x1,y1, u2,v2, x2,y2, u3,v3, x3,y3, u4,v4, x4,y4 ... */ if (number_arguments < 16) { (void) ThrowMagickException(exception,GetMagickModule(),OptionError, "InvalidArgument","%s : '%s'","distort Bilinear", "Minimum of 4 pairs of coords needed (16 numbers)"); return((Image *) NULL); } if (number_arguments%4 != 0) { (void) ThrowMagickException(exception,GetMagickModule(),OptionError, "InvalidArgument","%s : '%s'","distort Bilinear", "Requires pairs of coords (sX,sY,dX,dY)"); return((Image *) NULL); } matrix = AcquireMagickMatrix(4UL,4UL); if (matrix == (double **) NULL) { matrix = RelinquishMagickMatrix(matrix, 4UL); ThrowImageException(ResourceLimitError,"MemoryAllocationFailed"); return((Image *) NULL); } /* fake a 2x3 vectors matrix from coefficients array */ for (i=0; i < 8L; i++) coefficients[i] = 0.0; vectors[0] = &(coefficients[0]); vectors[1] = &(coefficients[4]); /* Add control points for least squares solving */ for (i=0; i < (long) number_arguments; i+=4) { terms[0] = arguments[i+2]; /* x */ terms[1] = arguments[i+3]; /* y */ terms[2] = terms[0]*terms[1]; /* x*y */ terms[3] = 1; /* 1 */ LeastSquaresAddTerms(matrix,vectors,terms,&(arguments[i]),4UL,2UL); } status=GaussJordanElimination(matrix,vectors,4UL,2UL); matrix = RelinquishMagickMatrix(matrix, 4UL); if ( status == MagickFalse ) { (void) ThrowMagickException(exception,GetMagickModule(),OptionError, "InvalidArgument","%s : '%s'","distort Bilinear", "Unsolvable Matrix"); return((Image *) NULL); } break; } case PerspectiveDistortion: { double **matrix, *vectors[1], terms[8]; /* Perspective Distortion (a ratio of affine distortions) p() c0*x + c1*y + c2 u = ----- = ------------------ r() c6*x + c7*y + 1 q() c3*x + c4*y + c5 v = ----- = ------------------ r() c6*x + c7*y + 1 c8 = Sign of 'r', or the denominator affine, for the actual image. This determines what part of the distorted image is 'ground' side of the horizon, the other part is 'sky' or invalid. WARNING: Equations are linked, and not separable. Input Arguments are pairs of distorted coodinates (minimum 4 pairs) Which will be used to generate the coefficients of the above. u1,v1, x1,y1, u2,v2, x2,y2, u3,v3, x3,y3, u4,v4, x4,y4 ... */ if (number_arguments < 16) { (void) ThrowMagickException(exception,GetMagickModule(),OptionError, "InvalidArgument","%s : '%s'","distort Bilinear", "Minimum of 4 pairs of coords needed (16 numbers)"); return((Image *) NULL); } if (number_arguments%4 != 0) { (void) ThrowMagickException(exception,GetMagickModule(),OptionError, "InvalidArgument","%s : '%s'","distort Bilinear", "Requires pairs of coords (sX,sY,dX,dY)"); return((Image *) NULL); } matrix = AcquireMagickMatrix(8UL,8UL); if (matrix == (double **) NULL) { matrix = RelinquishMagickMatrix(matrix, 8UL); ThrowImageException(ResourceLimitError,"MemoryAllocationFailed"); return((Image *) NULL); } /* fake a 1x8 vectors matrix from coefficients array */ for (i=0; i < 8L; i++) coefficients[i] = 0.0; vectors[0] = &(coefficients[0]); /* Add control points for least squares solving */ for (i=0; i < (long) number_arguments; i+=4) { terms[0] = arguments[i+2]; /* c0*x */ terms[1] = arguments[i+3]; /* c1*y */ terms[2]=1.0; /* c2*1 */ terms[3]=0.0; terms[4]=0.0; terms[5]=0.0; terms[6]=-terms[0]*arguments[i]; /* 1/(c6*x) */ terms[7]=-terms[1]*arguments[i]; /* 1/(c7*y) */ LeastSquaresAddTerms(matrix,vectors,terms,&(arguments[i]), 8UL,1UL); terms[0]=0.0; terms[1]=0.0; terms[2]=0.0; terms[3] = arguments[i+2]; /* c3*x */ terms[4] = arguments[i+3]; /* c4*y */ terms[5]=1.0; /* c5*1 */ terms[6]=-terms[3]*arguments[i+1]; /* 1/(c6*x) */ terms[7]=-terms[4]*arguments[i+1]; /* 1/(c7*y) */ LeastSquaresAddTerms(matrix,vectors,terms,&(arguments[i+1]), 8UL,1UL); } status=GaussJordanElimination(matrix,vectors,8UL,1UL); matrix = RelinquishMagickMatrix(matrix, 8UL); if ( status == MagickFalse ) { (void) ThrowMagickException(exception,GetMagickModule(),OptionError, "InvalidArgument","%s : '%s'","distort Prespective", "Unsolvable Matrix"); return((Image *) NULL); } /* Calculate 9'th coefficient! The ground-sky determination. What is sign of the 'ground' in r() denominator affine function? Just use any valid image cocodinate in destination for determination. Picking destination coordinate from first coordinet pair. */ coefficients[8] = coefficients[6]*arguments[2] + coefficients[7]*arguments[3] + 1.0; coefficients[8] = (coefficients[8] < 0.0) ? -1.0 : +1.0; break; } case PerspectiveProjectionDistortion: { /* Arguments: Perspective Coefficents (forward mapping) */ if (number_arguments != 8) { (void) ThrowMagickException(exception,GetMagickModule(),OptionError, "InvalidArgument","%s : '%s'", "distort PerspectiveProjection", "Needs 8 numbers"); return((Image *) NULL); } InvertPerspectiveCoefficients(arguments, coefficients); /* Calculate 9'th coefficient! The ground-sky determination. What is sign of the 'ground' in r() denominator affine function? Just use any valid image cocodinate in destination for determination. For a forward mapped perspective the images 0,0 coord will map to c2,c5 in the distorted image, so get the sign of denominator of that. */ coefficients[8] = coefficients[6]*arguments[2] + coefficients[7]*arguments[5] + 1.0; coefficients[8] = (coefficients[8] < 0.0) ? -1.0 : +1.0; break; } case ScaleRotateTranslateDistortion: { double cosine, sine, x,y,sx,sy,a,nx,ny; /* Argument options, by number of arguments given: 7: x,y, sx,sy, a, nx,ny 6: x,y, s, a, nx,ny 5: x,y, sx,sy, a 4: x,y, s, a 3: x,y, a 2: s, a 1: a Where actions are (in order of application) x,y 'center' of transforms (default = image center) sx,sy scale image by this amount (default = 1) a angle of rotation (argument required) nx,ny move 'center' here (default = no movement) And convert to affine mapping coefficients */ x = nx = (double)image->columns/2.0; y = ny = (double)image->rows/2.0; if ( bestfit ) { x = nx += (double)image->page.x; y = ny += (double)image->page.y; } sx = sy = 1.0; switch ( number_arguments ) { case 0: (void) ThrowMagickException(exception,GetMagickModule(),OptionError, "InvalidArgument","%s : '%s'", "distort ScaleTranslateRotate", "Needs at least 1 argument"); return((Image *) NULL); case 1: a = arguments[0]; break; case 2: sx = sy = arguments[0]; a = arguments[1]; break; default: x = nx = arguments[0]; y = ny = arguments[1]; switch ( number_arguments ) { case 3: a = arguments[2]; break; case 4: sx = sy = arguments[2]; a = arguments[3]; break; case 5: sx = arguments[2]; sy = arguments[3]; a = arguments[4]; break; case 6: sx = sy = arguments[2]; a = arguments[3]; nx = arguments[4]; ny = arguments[5]; break; case 7: sx = arguments[2]; sy = arguments[3]; a = arguments[4]; nx = arguments[5]; ny = arguments[6]; break; default: (void) ThrowMagickException(exception,GetMagickModule(),OptionError, "InvalidArgument","%s : '%s'", "distort ScaleTranslateRotate", "Too Many Arguments (7 or less)"); return((Image *) NULL); } break; } a=DegreesToRadians(a); cosine=cos(a); sine=sin(a); coefficients[0]=cosine/sx; coefficients[1]=(-sine)/sy; coefficients[2]=sine/sx; coefficients[3]=cosine/sy; coefficients[4]=x-nx*coefficients[0]-ny*coefficients[2]; coefficients[5]=y-nx*coefficients[1]-ny*coefficients[3]; break; } case ArcDistortion: { /* Arc Distortion Args: arc_width rotate top_edge_radius bottom_edge_radius All but first argument are optional arc_width The angle over which to arc the image side-to-side rotate Angle to rotate image from vertical center top_radius Set top edge of source image at this radius bottom_radius Set bootom edge to this radius (radial scaling) By default, if the radii arguments are nor provided the image radius is calculated so the horizontal center-line is fits the given arc without scaling. The output image size is ALWAYS adjusted to contain the whole image, and an offset is given to position image relative to the 0,0 point of the origin, allowing users to use relative positioning onto larger background (via -flatten). The arguments are converted to these coefficents c0: angle for center of source image c1: angle scale for mapping to source image c2: radius for top of source image c3: radius scale for mapping source image c4: centerline of arc within source image Note the coefficents use a center angle, so asymptotic join is furthest from both sides of the source image. This also means that for arc angles greater than 360 the sides of the image will be trimmed equally. */ if ( number_arguments >= 1 && arguments[0] < MagickEpsilon ) { (void) ThrowMagickException(exception,GetMagickModule(),OptionError, "InvalidArgument","%s : '%s'", "distort Arc", "Arc Angle Too Small"); return((Image *) NULL); } if ( number_arguments >= 3 && arguments[2] < MagickEpsilon ) { (void) ThrowMagickException(exception,GetMagickModule(),OptionError, "InvalidArgument","%s : '%s'", "distort Arc", "Outer Radius Too Small"); return((Image *) NULL); } coefficients[0] = -MagickPI/2.0; if ( number_arguments >= 1 ) coefficients[1] = DegreesToRadians(arguments[0]); else coefficients[1] = MagickPI/2.0; if ( number_arguments >= 2 ) coefficients[0] += DegreesToRadians(arguments[1]); coefficients[0] -= MagickRound(coefficients[0]/(2.0*MagickPI)) *2.0*MagickPI; coefficients[3] = 1.0*image->rows-1; coefficients[2] = 1.0*image->columns/coefficients[1] + coefficients[3]/2.0; if ( number_arguments >= 3 ) { if ( number_arguments >= 4 ) coefficients[3] = arguments[2] - arguments[3]; else coefficients[3] *= arguments[2]/coefficients[2]; coefficients[2] = arguments[2]; } coefficients[4] = (1.0*image->columns-1.0)/2.0; /* Always work out the 'best fit' for Arc Distort (required) */ bestfit = MagickTrue; break; } default: break; } /* Determine the size and offset for a 'bestfit' destination. Usally the four corners of the source image is enough. */ /* default output image bounds, when no 'bestfit' is requested */ geometry.width=image->columns; geometry.height=image->rows; geometry.x=0; geometry.y=0; point.x=0.0; point.y=0.0; if ( bestfit ) { double min_x,max_x,min_y,max_y; /* defines to figure out the bounds of the distorted image */ #define InitalBounds(px,py) \ { \ min_x = max_x = (px); \ min_y = max_y = (py); \ } #define ExpandBounds(px,py) \ { \ if ( (px) < min_x ) min_x = (px); \ if ( (px) > max_x ) max_x = (px); \ if ( (py) < min_y ) min_y = (py); \ if ( (py) > max_y ) max_y = (py); \ } switch (method) { case AffineDistortion: case AffineProjectionDistortion: case ScaleRotateTranslateDistortion: { double inverse[6]; InvertAffineCoefficients(coefficients, inverse); x = image->page.x; y = image->page.y; point.x=inverse[0]*x+inverse[2]*y+inverse[4]; point.y=inverse[1]*x+inverse[3]*y+inverse[5]; InitalBounds( point.x, point.y ); x = image->page.x+image->columns-1; y = image->page.y; point.x=inverse[0]*x+inverse[2]*y+inverse[4]; point.y=inverse[1]*x+inverse[3]*y+inverse[5]; ExpandBounds( point.x, point.y ); x = image->page.x; y = image->page.y+image->rows-1; point.x=inverse[0]*x+inverse[2]*y+inverse[4]; point.y=inverse[1]*x+inverse[3]*y+inverse[5]; ExpandBounds( point.x, point.y ); x = image->page.x+image->columns-1; y = image->page.y+image->rows-1; point.x=inverse[0]*x+inverse[2]*y+inverse[4]; point.y=inverse[1]*x+inverse[3]*y+inverse[5]; ExpandBounds( point.x, point.y ); break; } case PerspectiveDistortion: case PerspectiveProjectionDistortion: { double inverse[8], scale; InvertPerspectiveCoefficients(coefficients, inverse); x = image->page.x; y = image->page.y; scale=inverse[6]*x+inverse[7]*y+1.0; scale=1.0/( (fabs(scale) <= MagickEpsilon) ? 1.0 : scale ); point.x=scale*(inverse[0]*x+inverse[1]*y+inverse[2]); point.y=scale*(inverse[3]*x+inverse[4]*y+inverse[5]); InitalBounds( point.x, point.y ); x = image->page.x+image->columns-1; y = image->page.y; scale=inverse[6]*x+inverse[7]*y+1.0; scale=1.0/( (fabs(scale) <= MagickEpsilon) ? 1.0 : scale ); point.x=scale*(inverse[0]*x+inverse[1]*y+inverse[2]); point.y=scale*(inverse[3]*x+inverse[4]*y+inverse[5]); ExpandBounds( point.x, point.y ); x = image->page.x; y = image->page.y+image->rows-1; scale=inverse[6]*x+inverse[7]*y+1.0; scale=1.0/( (fabs(scale) <= MagickEpsilon) ? 1.0 : scale ); point.x=scale*(inverse[0]*x+inverse[1]*y+inverse[2]); point.y=scale*(inverse[3]*x+inverse[4]*y+inverse[5]); ExpandBounds( point.x, point.y ); x = image->page.x+image->columns-1; y = image->page.y+image->rows-1; scale=inverse[6]*x+inverse[7]*y+1.0; scale=1.0/( (fabs(scale) <= MagickEpsilon) ? 1.0 : scale ); point.x=scale*(inverse[0]*x+inverse[1]*y+inverse[2]); point.y=scale*(inverse[3]*x+inverse[4]*y+inverse[5]); ExpandBounds( point.x, point.y ); break; } case ArcDistortion: { double a, ca, sa; /* Forward Map Corners */ a = coefficients[0]-coefficients[1]/2; ca = cos(a); sa = sin(a); point.x = coefficients[2]*ca; point.y = coefficients[2]*sa; InitalBounds( point.x, point.y ); point.x = (coefficients[2]-coefficients[3])*ca; point.y = (coefficients[2]-coefficients[3])*sa; ExpandBounds( point.x, point.y ); a = coefficients[0]+coefficients[1]/2; ca = cos(a); sa = sin(a); point.x = coefficients[2]*ca; point.y = coefficients[2]*sa; ExpandBounds( point.x, point.y ); point.x = (coefficients[2]-coefficients[3])*ca; point.y = (coefficients[2]-coefficients[3])*sa; ExpandBounds( point.x, point.y ); /* orthogonal points along top of arc */ for( a=ceil((coefficients[0]-coefficients[1]/2.0)*2.0/MagickPI) *MagickPI/2.0; a<(coefficients[0]+coefficients[1]/2.0); a+=MagickPI/2.0 ) { ca = cos(a); sa = sin(a); point.x = coefficients[2]*ca; point.y = coefficients[2]*sa; ExpandBounds( point.x, point.y ); } /* Convert the angle_to_width and radius_to_height to appropriate scaling factors, to allow faster processing in the mapping function. */ coefficients[1] = 2.0*MagickPI*image->columns/coefficients[1]; coefficients[3] = 1.0*image->rows/coefficients[3]; break; } case BilinearDistortion: default: /* no bestfit available for this distortion YET */ bestfit = MagickFalse; } /* Set the output image geometry to the 'bestfit' of the image */ if ( bestfit ) { geometry.x=(long) floor(min_x-MagickEpsilon); geometry.y=(long) floor(min_y-MagickEpsilon); geometry.width=(unsigned long) ceil(max_x-geometry.x+1+MagickEpsilon); geometry.height=(unsigned long) ceil(max_y-geometry.y+1+MagickEpsilon); } } /* User provided override of the output geometry */ artifact=GetImageArtifact(image,"distort:viewport"); if (artifact != (const char *) NULL) (void) ParseAbsoluteGeometry(artifact,&geometry); /* Initialize the distort image attributes. */ distort_image=CloneImage(image,geometry.width,geometry.height,MagickTrue, exception); if (distort_image == (Image *) NULL) return((Image *) NULL); if (SetImageStorageClass(distort_image,DirectClass) == MagickFalse) { InheritException(exception,&distort_image->exception); distort_image=DestroyImage(distort_image); return((Image *) NULL); } distort_image->page.x=geometry.x; distort_image->page.y=geometry.y; if (distort_image->background_color.opacity != OpaqueOpacity) distort_image->matte=MagickTrue; /* Open Image views as needed. */ resample_filter=AcquireResampleFilter(image,exception); GetMagickPixelPacket(distort_image,&pixel); distort_view=OpenCacheView(distort_image); /* Define constant scaling vectors for Affine Distortions */ switch (method) { case AffineDistortion: case AffineProjectionDistortion: case ScaleRotateTranslateDistortion: ScaleResampleFilter( resample_filter, coefficients[0], coefficients[2], coefficients[1], coefficients[3] ); break; default: break; } /* Initialize default pixel validity * negative: pixel is invalid output 'matte_color' * 0.0 to 1.0: antialiased, mix with resample output * 1.0 or greater: use resampled output. */ validity = 1.0; GetMagickPixelPacket(distort_image,&invalid); SetMagickPixelPacket(distort_image, &distort_image->matte_color, (IndexPacket *) NULL, &invalid); if (distort_image->colorspace == CMYKColorspace) ConvertRGBToCMYK(&invalid); /* what about other color spaces? */ /* Sample the source image to each pixel in the distort image. */ for (j=0; j < (long) distort_image->rows; j++) { q=SetCacheView(distort_view,0,j,distort_image->columns,1); if (q == (PixelPacket *) NULL) break; indexes=GetCacheViewIndexes(distort_view); y = j+geometry.y; for (i=0; i < (long) distort_image->columns; i++) { x = i+geometry.x; switch (method) { case AffineDistortion: case AffineProjectionDistortion: case ScaleRotateTranslateDistortion: { point.x=coefficients[0]*x+coefficients[2]*y+coefficients[4]; point.y=coefficients[1]*x+coefficients[3]*y+coefficients[5]; /* Affine partical derivitives are constant -- set above */ break; } case BilinearDistortion: { point.x=coefficients[0]*x+coefficients[1]*y+coefficients[2]*x*y+ coefficients[3]; point.y=coefficients[4]*x+coefficients[5]*y+coefficients[6]*x*y+ coefficients[7]; /* Bilinear partical derivitives of scaling vectors */ ScaleResampleFilter( resample_filter, coefficients[0] + coefficients[2]*y, coefficients[1] + coefficients[2]*x, coefficients[4] + coefficients[6]*y, coefficients[5] + coefficients[6]*x ); break; } case PerspectiveDistortion: case PerspectiveProjectionDistortion: { double p,q,r,abs_r,abs_c6,abs_c7,scale; /* perspective is a ratio of affines */ p=coefficients[0]*x+coefficients[1]*y+coefficients[2]; q=coefficients[3]*x+coefficients[4]*y+coefficients[5]; r=coefficients[6]*x+coefficients[7]*y+1.0; /* Pixel Validity -- is it a 'sky' or 'ground' pixel */ validity = (r*coefficients[8] < 0.0) ? 0.0 : 1.0; /* Determine horizon anti-aliase blending */ abs_r = fabs(r)*2; abs_c6 = fabs(coefficients[6]); abs_c7 = fabs(coefficients[7]); if ( abs_c6 > abs_c7 ) { if ( abs_r < abs_c6 ) validity = 0.5 - coefficients[8]*r/coefficients[6]; } else if ( abs_r < abs_c7 ) validity = .5 - coefficients[8]*r/coefficients[7]; /* Perspective Sampling Point (if valid) */ if ( validity > 0.0 ) { scale = 1.0/r; point.x = p*scale; point.y = q*scale; /* Perspective Partial Derivatives or Scaling Vectors */ scale *= scale; ScaleResampleFilter( resample_filter, (r*coefficients[0] - p*coefficients[6])*scale, (r*coefficients[1] - p*coefficients[7])*scale, (r*coefficients[3] - q*coefficients[6])*scale, (r*coefficients[4] - q*coefficients[7])*scale ); } break; } case ArcDistortion: { double radius = sqrt((double) x*x+y*y); point.x = (atan2((double)y,(double)x) - coefficients[0])/(2*MagickPI); point.x -= MagickRound(point.x); point.x = point.x*coefficients[1] + coefficients[4]; point.y = (coefficients[2] - radius) * coefficients[3]; /* Polar Distortion Partial Derivatives or Scaling Vectors We give the deritives of du/dr, dv/dr and du/da, dv/da rather than provide the complex du/dx,dv/dx and du/dy,dv/dy. The result will be the same, but it is simplier to calculate. */ if ( radius > MagickEpsilon ) ScaleResampleFilter( resample_filter, coefficients[1]/(2*MagickPI) / radius, 0, 0, coefficients[3] ); else ScaleResampleFilter( resample_filter, MagickHuge, 0, 0, coefficients[3] ); break; } default: { /* Noop distortion (failsafe). */ point.x=(double) i; point.y=(double) j; break; } } if ( bestfit && method != ArcDistortion ) { point.x -= image->page.x; point.y -= image->page.y; } if ( validity <= 0.0 ) { /* result of distortion is an invalid pixel - don't resample */ SetPixelPacket(distort_image,&invalid,q,indexes); } else { /* resample the source image to find its correct color */ pixel=ResamplePixelColor(resample_filter,point.x,point.y); /* if validity between 0.0 and 1.0 mix result with invalid pixel */ if ( validity < 1.0 ) { /* Do a blend of sample color and invalid pixel */ /* should this be a 'Blend', or an 'Over' compose */ MagickPixelCompositeBlend(&pixel, validity, &invalid, (1.0-validity), &pixel); } SetPixelPacket(distort_image,&pixel,q,indexes); } q++; indexes++; } if (SyncImagePixels(distort_image) == MagickFalse) break; if ((image->progress_monitor != (MagickProgressMonitor) NULL) && (QuantumTick(y,image->rows) != MagickFalse)) { status=image->progress_monitor(DistortImageTag,y,image->rows, image->client_data); if (status == MagickFalse) break; } } distort_view=CloseCacheView(distort_view); resample_filter=DestroyResampleFilter(resample_filter); /* Arc does not return an offset unless 'bestfit' is in effect */ if ( method == ArcDistortion && !bestfit && artifact==(const char *)NULL ) { distort_image->page.x = 0; distort_image->page.y = 0; } return(distort_image); }