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%% Copyright (c) 2011 Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
%%
%% This program is free software: you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program. If not, see <http://www.gnu.org/licenses/>.
%% -*- texinfo -*-
%% @deftypefn {Function File} {@var{nshape} = } shapetransform (@var{shape}, @var{T})
%% Applies transformation to a shape defined by piecewise smooth polynomials.
%%
%% @var{shape} is a cell where each elements is a 2-by-(poly_degree+1) matrix
%% containing a pair of polynomials.
%%
%% Format of @var{T} can be one of :
%% @example
%% @group
%% [c] , [a b] , [a b c] or [a b c]
%% [f] [d e] [d e f] [d e f]
%% [0 0 1]
%% @end group
%% @end example
%%
%% @seealso{shape2polygon, shapeplot}
%% @end deftypefn
function nshape = shapetransform (shape, Trans)
if size(Trans,1) < 2
error("geometry:shapetransform:InvalidArgument", ...
"Transformation can be 2x1, 2x2, 2x3 or 3x3. See help.");
end
if ~iscell(shape)
error("geometry:shapetransform:InvalidArgument", "Shape must be a cell of 2D polynomials.");
end
A =[];
v = [];
switch size(Trans,2)
case 1
% Just translation
v = Trans;
case 2
% Just linear transformation
A = Trans;
case 3
% Affine transform
A = Trans(1:2,1:2);
v = Trans(1:2,3);
end
nshape = cellfun (@(x)polytransform (x,A,v), shape, 'UniformOutput',false);
endfunction
function np = polytransform(p,A,v)
np = p;
if ~isempty (A)
np = A*np;
end
if ~isempty (v)
np(:,end) = np(:,end) + v;
end
endfunction
%!demo
%! shape = {[-93.172 606.368 -476.054 291.429; ...
%! -431.196 637.253 11.085 163.791]; ...
%! [-75.3626 -253.2337 457.1678 328.5714; ...
%! 438.7659 -653.6278 -7.9953 380.9336]; ...
%! [-89.5841 344.9716 -275.3876 457.1429; ...
%! -170.3613 237.8858 1.0469 158.0765];...
%! [32.900 -298.704 145.804 437.143; ...
%! -243.903 369.597 -34.265 226.648]; ...
%! [-99.081 409.127 -352.903 317.143; ...
%! 55.289 -114.223 -26.781 318.076]; ...
%! [-342.231 191.266 168.108 274.286; ...
%! 58.870 -38.083 -89.358 232.362]};
%!
%! A = shapearea (shape);
%! T = eye(2)/sqrt(A);
%! shape = shapetransform (shape,T);
%! T = shapecentroid (shape)(:);
%! shape = shapetransform (shape,-T + [2; 0]);
%!
%! close
%! shapeplot (shape,10,'-r','linewidth',2)
%! hold on
%! for i = 1:9
%! T = createRotation (i*pi/5)(1:2,1:2)/exp(0.3*i);
%! shapeplot (shapetransform(shape, T), 10, 'color',rand(1,3),'linewidth',2);
%! end
%! hold off
%! axis tight
%! axis square
%!shared shape
%! shape = {[-93.172 606.368 -476.054 291.429; ...
%! -431.196 637.253 11.085 163.791]; ...
%! [-75.3626 -253.2337 457.1678 328.5714; ...
%! 438.7659 -653.6278 -7.9953 380.9336]; ...
%! [-89.5841 344.9716 -275.3876 457.1429; ...
%! -170.3613 237.8858 1.0469 158.0765];...
%! [32.900 -298.704 145.804 437.143; ...
%! -243.903 369.597 -34.265 226.648]; ...
%! [-99.081 409.127 -352.903 317.143; ...
%! 55.289 -114.223 -26.781 318.076]; ...
%! [-342.231 191.266 168.108 274.286; ...
%! 58.870 -38.083 -89.358 232.362]};
%!test
%! v = shapecentroid (shape)(:);
%! nshape = shapetransform (shape, -v);
%! vn = shapecentroid (nshape)(:);
%! assert(vn,[0; 0],1e-2);
%!test
%! v = shapecentroid (shape)(:);
%! T = createLineReflection([0 0 1 0]);
%! nshape = shapetransform (shape, T);
%! vn = shapecentroid (nshape)(:);
%! assert(vn,T(1:2,1:2)*v);
%!test
%! v = shapecentroid (shape)(:);
%! T = createRotation(v.',pi/2);
%! nshape = shapetransform (shape, T);
%! vn = shapecentroid (nshape)(:);
%! assert(vn,v,1e-2);
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