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[Octave-cvsupdate] SF.net SVN: octave:[8971] trunk/octave-forge/main/geometry/inst
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From: <jpi...@us...> - 2011-11-03 23:40:33
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Revision: 8971
http://octave.svn.sourceforge.net/octave/?rev=8971&view=rev
Author: jpicarbajal
Date: 2011-11-03 23:40:25 +0000 (Thu, 03 Nov 2011)
Log Message:
-----------
geometry. Adding new functions, improving docstring
Added Paths:
-----------
trunk/octave-forge/main/geometry/inst/polygons2d/polygon2shape.m
trunk/octave-forge/main/geometry/inst/polygons2d/simplifypolygon.m
trunk/octave-forge/main/geometry/inst/shape2d/
trunk/octave-forge/main/geometry/inst/shape2d/shape2polygon.m
trunk/octave-forge/main/geometry/inst/shape2d/shapearea.m
trunk/octave-forge/main/geometry/inst/shape2d/shapecentroid.m
trunk/octave-forge/main/geometry/inst/shape2d/shapeplot.m
trunk/octave-forge/main/geometry/inst/shape2d/shapetransform.m
Removed Paths:
-------------
trunk/octave-forge/main/geometry/inst/polygon2shape.m
trunk/octave-forge/main/geometry/inst/shape2polygon.m
trunk/octave-forge/main/geometry/inst/shapearea.m
trunk/octave-forge/main/geometry/inst/shapecentroid.m
trunk/octave-forge/main/geometry/inst/shapeplot.m
trunk/octave-forge/main/geometry/inst/shapetransform.m
trunk/octave-forge/main/geometry/inst/simplifypolygon.m
Deleted: trunk/octave-forge/main/geometry/inst/polygon2shape.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/polygon2shape.m 2011-11-03 22:45:47 UTC (rev 8970)
+++ trunk/octave-forge/main/geometry/inst/polygon2shape.m 2011-11-03 23:40:25 UTC (rev 8971)
@@ -1,34 +0,0 @@
-## Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
-##
-## 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
-## (at your option) 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/>.
-
-function shape = polygon2shape (polygon)
-
- # Filter colinear points
- polygon = simplifypolygon (polygon);
-
- np = size(polygon,1);
- # polygonal shapes are memory inefficient!!
- # TODO filter the regions where edge angles are canging slowly and fit
- # polynomial of degree 3;
- pp = nan (2*np,2);
-
- # Transform edges into polynomials of degree 1;
- # pp = [(p1-p0) p0];
- pp(:,1) = diff(polygon([1:end 1],:)).'(:);
- pp(:,2) = polygon.'(:);
-
- shape = mat2cell(pp, 2*ones (1,np), 2);
-
-endfunction
Added: trunk/octave-forge/main/geometry/inst/polygons2d/polygon2shape.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/polygons2d/polygon2shape.m (rev 0)
+++ trunk/octave-forge/main/geometry/inst/polygons2d/polygon2shape.m 2011-11-03 23:40:25 UTC (rev 8971)
@@ -0,0 +1,54 @@
+## Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
+##
+## 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
+## (at your option) 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{shape} = } polygon2shape (@var{polygon})
+%% Converts a polygon to a shape with edges defined by smooth polynomials.
+%%
+%% @var{polygon} is a N-by-2 matrix, each row representing a vertex.
+%% @var{shape} is a N-by-1 cell, where each element is a pair of polynomials
+%% compatible with polyval.
+%%
+%% In its current state, the shape is formed by polynomials of degree 1. Therefore
+%% the shape representation costs more memory except for colinear points in the
+%% polygon.
+%%
+%% @seealso{shape2polygon, simplifypolygon, polyval}
+%% @end deftypefn
+
+function shape = polygon2shape (polygon)
+
+ # Filter colinear points
+ polygon = simplifypolygon (polygon);
+
+ np = size(polygon,1);
+ # polygonal shapes are memory inefficient!!
+ # TODO filter the regions where edge angles are canging slowly and fit
+ # polynomial of degree 3;
+ pp = nan (2*np,2);
+
+ # Transform edges into polynomials of degree 1;
+ # pp = [(p1-p0) p0];
+ pp(:,1) = diff(polygon([1:end 1],:)).'(:);
+ pp(:,2) = polygon.'(:);
+
+ shape = mat2cell(pp, 2*ones (1,np), 2);
+
+endfunction
+
+%!test
+%! pp = [0 0; 1 0; 1 1; 0 1];
+%! s = polygon2shape (pp);
+
Added: trunk/octave-forge/main/geometry/inst/polygons2d/simplifypolygon.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/polygons2d/simplifypolygon.m (rev 0)
+++ trunk/octave-forge/main/geometry/inst/polygons2d/simplifypolygon.m 2011-11-03 23:40:25 UTC (rev 8971)
@@ -0,0 +1,59 @@
+## Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
+##
+## 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
+## (at your option) 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{spoly} = } simplifypolygon (@var{poly})
+%% Filter colinear vertex from a 2D polygon.
+%%
+%% @var{poly} is a N-by-2 matrix, each row representing a vertex.
+%%
+%% @seealso{shape2polygon}
+%% @end deftypefn
+function polygonsimp = simplifypolygon (polygon)
+
+ # Filter colinear points
+ edges = diff(polygon([1:end 1],:));
+ ned = size(edges,1);
+ nxt = [2:ned 1];
+
+ # check if consecutive edges are parallel
+ para = edges(:,1).*edges(nxt,2) - edges(:,2).*edges(nxt,1);
+ ind = abs(para) > sqrt(eps);
+
+ polygonsimp = polygon(circshift (ind,1),:);
+
+endfunction
+
+%!test
+%! P = [0 0; 1 0; 0 1];
+%! P2 = [0 0; 0.1 0; 0.2 0; 0.25 0; 1 0; 0 1; 0 0.7; 0 0.6; 0 0.3; 0 0.1];
+%! assert(P,simplifypolygon (P2))
+
+%!demo
+%!
+%! P = [0 0; 1 0; 0 1];
+%! P2 = [0 0; 0.1 0; 0.2 0; 0.25 0; 1 0; 0 1; 0 0.7; 0 0.6; 0 0.3; 0 0.1];
+%! Pr = simplifypolygon (P2);
+%!
+%! cla
+%! drawPolygon(P,'or;Reference;');
+%! hold on
+%! drawPolygon(P2,'x-b;Redundant;');
+%! drawPolygon(Pr,'*g;Simplified;');
+%! hold off
+%!
+%! % --------------------------------------------------------------------------
+%! % The two polygons describe the same figure, a triangle. Extra points are
+%! % removed form the redundant one.
Added: trunk/octave-forge/main/geometry/inst/shape2d/shape2polygon.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/shape2d/shape2polygon.m (rev 0)
+++ trunk/octave-forge/main/geometry/inst/shape2d/shape2polygon.m 2011-11-03 23:40:25 UTC (rev 8971)
@@ -0,0 +1,51 @@
+## Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
+##
+## 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
+## (at your option) 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{polygon} = } shape2polygon (@var{shape})
+%% @deftypefnx {Function File} {@var{polygon} = } shape2polygon (@var{shape},@var{N})
+%% Transforms a 2D shape described by piecewise smooth polynomials into a polygon.
+%%
+%% @var{shape} is a n-by-1 cell where each element is a pair of polynomials
+%% compatible with polyval.
+%% @var{polygon} is a k-by-2 matrix, where each row represents a vertex.
+%% @var{N} defines the number of points to be used in non-straigth edges.
+%%
+%% @seealso{polygon2shape, drawPolygon}
+%% @end deftypefn
+
+function polygon = shape2polygon (shape, N=16)
+
+ polygon = cell2mat ( ...
+ cellfun(@(x) func (x,N), shape,'UniformOutput',false) );
+
+ if size(polygon, 1) == 1
+ polygon(2,1) = polyval(shape{1}(1,:),1);
+ polygon(2,2) = polyval(shape{1}(2,:),1);
+ end
+
+endfunction
+
+function y = func(x,N)
+
+ if size(x,2) > 2
+ t = linspace(0,1-1/N,N).';
+ y(:,1) = polyval(x(1,:),t);
+ y(:,2) = polyval(x(2,:),t);
+ else
+ y = x(:,2).';
+ end
+
+endfunction
Added: trunk/octave-forge/main/geometry/inst/shape2d/shapearea.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/shape2d/shapearea.m (rev 0)
+++ trunk/octave-forge/main/geometry/inst/shape2d/shapearea.m 2011-11-03 23:40:25 UTC (rev 8971)
@@ -0,0 +1,71 @@
+%% Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
+%%
+%% 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
+%% (at your option) 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{a} =} shapearea (@var{pp})
+%% Calculate the area of a 2D shape defined with piecewise smooth polynomials.
+%%
+%% Shape is defined with piecewise smooth polynomials. @var{pp} is a
+%% cell where each elements is a 2-by-(poly_degree+1) array containing a pair of
+%% polynomials.
+%%
+%% @code{px(i,:) = pp@{i@}(1,:)} and @code{py(i,:) = pp@{i@}(2,:)}.
+%%
+%% @seealso{shapecentroid, shape2polygon, shapeplot}
+%% @end deftypefn
+
+function A = shapearea (shape)
+
+ A = sum(cellfun (@Aint, shape));
+ if A < 0
+ A = -A;
+ end
+
+endfunction
+
+function dA = Aint (x)
+
+ px = x(1,:);
+ py = x(2,:);
+
+ P = polyint (conv (px, polyderiv(py)));
+
+ dA = diff(polyval(P,[0 1]));
+
+end
+
+%!demo % non-convex bezier shape
+%! weirdhearth ={[-17.6816 -34.3989 7.8580 3.7971; ...
+%! 15.4585 -28.3820 -18.7645 9.8519]; ...
+%! [-27.7359 18.1039 -34.5718 3.7878; ...
+%! -40.7440 49.7999 -25.5011 2.2304]};
+%! A = shapearea (weirdhearth)
+
+%!test
+%! triangle = {[1 0; 0 0]; [-0.5 1; 1 0]; [-0.5 0.5; -1 1]};
+%! A = shapearea (triangle);
+%! assert (0.5, A);
+
+%!test
+%! circle = {[1.715729 -6.715729 0 5; ...
+%! -1.715729 -1.568542 8.284271 0]; ...
+%! [1.715729 1.568542 -8.284271 0; ...
+%! 1.715729 -6.715729 0 5]; ...
+%! [-1.715729 6.715729 0 -5; ...
+%! 1.715729 1.568542 -8.284271 0]; ...
+%! [-1.715729 -1.568542 8.284271 0; ...
+%! -1.715729 6.715729 0 -5]};
+%! A = shapearea (circle);
+%! assert (pi*5^2, A, 5e-2);
Added: trunk/octave-forge/main/geometry/inst/shape2d/shapecentroid.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/shape2d/shapecentroid.m (rev 0)
+++ trunk/octave-forge/main/geometry/inst/shape2d/shapecentroid.m 2011-11-03 23:40:25 UTC (rev 8971)
@@ -0,0 +1,71 @@
+%% Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
+%%
+%% 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
+%% (at your option) 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{cm} =} shapecentroid (@var{pp})
+%% Centroid of a plane shape defined with piecewise smooth polynomials.
+%%
+%% The shape is defined with piecewise smooth polynomials. @var{pp} is a
+%% cell where each elements is a 2-by-(poly_degree+1) matrix containing a pair
+%% of polynomials.
+%% @code{px(i,:) = pp@{i@}(1,:)} and @code{py(i,:) = pp@{i@}(2,:)}.
+%%
+%% @seealso{shapearea, shape2polygon}
+%% @end deftypefn
+
+function cm = shapecentroid (shape)
+
+ cm = sum( cell2mat ( cellfun (@CMint, shape, 'UniformOutput', false)));
+ A = shapearea(shape);
+ cm = cm / A;
+
+endfunction
+
+function dcm = CMint (x)
+
+ px = x(1,:);
+ py = x(2,:);
+ Px = polyint (conv(conv (px , px)/2 , polyderiv (py)));
+ Py = polyint (conv(-conv (py , py)/2 , polyderiv (px)));
+
+ dcm = zeros (1,2);
+ dcm(1) = diff(polyval(Px,[0 1]));
+ dcm(2) = diff(polyval(Py,[0 1]));
+
+endfunction
+
+%!demo % non-convex bezier shape
+%! weirdhearth ={[-17.6816 -34.3989 7.8580 3.7971; ...
+%! 15.4585 -28.3820 -18.7645 9.8519]; ...
+%! [-27.7359 18.1039 -34.5718 3.7878; ...
+%! -40.7440 49.7999 -25.5011 2.2304]};
+%! CoM = shapecentroid (weirdhearth)
+
+%!test
+%! square = {[1 -0.5; 0 -0.5]; [0 0.5; 1 -0.5]; [-1 0.5; 0 0.5]; [0 -0.5; -1 0.5]};
+%! CoM = shapecentroid (square);
+%! assert (CoM, [0 0], sqrt(eps));
+
+%!test
+%! circle = {[1.715729 -6.715729 0 5; ...
+%! -1.715729 -1.568542 8.284271 0]; ...
+%! [1.715729 1.568542 -8.284271 0; ...
+%! 1.715729 -6.715729 0 5]; ...
+%! [-1.715729 6.715729 0 -5; ...
+%! 1.715729 1.568542 -8.284271 0]; ...
+%! [-1.715729 -1.568542 8.284271 0; ...
+%! -1.715729 6.715729 0 -5]};
+%! CoM = shapecentroid (circle);
+%! assert (CoM , [0 0], 5e-3);
Added: trunk/octave-forge/main/geometry/inst/shape2d/shapeplot.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/shape2d/shapeplot.m (rev 0)
+++ trunk/octave-forge/main/geometry/inst/shape2d/shapeplot.m 2011-11-03 23:40:25 UTC (rev 8971)
@@ -0,0 +1,35 @@
+%% Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
+%%
+%% 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{h} = } shapeplot (@var{shape})
+%% @deftypefnx {Function File} {@var{h} = } shapeplot (@var{shape}, @var{N})
+%% @deftypefnx {Function File} {@var{h} = } shapeplot (@dots{}, @var{param}, @var{value})
+%% Pots a 2D shape defined by piecewise smooth polynomials.
+%%
+%% @var{pp} is a cell where each elements is a 2-by-(poly_degree+1) matrix
+%% containing a pair of polynomials.
+%% @var{N} is the number of points to be used in non-straight edges.
+%% Additional parameter value pairs are passed to @code{drawPolygon}.
+%%
+%% @seealso{drawPolygon, shape2polygon}
+%% @end deftypefn
+
+function h = shapeplot(shape, N = 16, varargin)
+
+ p = shape2polygon(shape, N);
+ h = drawPolygon(p,varargin{:});
+
+endfunction
Added: trunk/octave-forge/main/geometry/inst/shape2d/shapetransform.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/shape2d/shapetransform.m (rev 0)
+++ trunk/octave-forge/main/geometry/inst/shape2d/shapetransform.m 2011-11-03 23:40:25 UTC (rev 8971)
@@ -0,0 +1,142 @@
+%% Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
+%%
+%% 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 :
+%% @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
+%%
+%% @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]);
+%!
+%! cla
+%! 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);
Deleted: trunk/octave-forge/main/geometry/inst/shape2polygon.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/shape2polygon.m 2011-11-03 22:45:47 UTC (rev 8970)
+++ trunk/octave-forge/main/geometry/inst/shape2polygon.m 2011-11-03 23:40:25 UTC (rev 8971)
@@ -1,46 +0,0 @@
-## Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
-##
-## 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
-## (at your option) 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{polygon} = } shape2polygon (@var{shape})
-%% @deftypefnx {Function File} {@var{polygon} = } shape2polygon (@var{shape},@var{N})
-%% Transforms a 2D shape described by piecewise smooth polynomials into a polygon.
-%%
-%% @seealso{drawPolygon}
-%% @end deftypefn
-function polygon = shape2polygon (shape, N=16)
-
- polygon = cell2mat ( ...
- cellfun(@(x) func (x,N), shape,'UniformOutput',false) );
-
- if size(polygon, 1) == 1
- polygon(2,1) = polyval(shape{1}(1,:),1);
- polygon(2,2) = polyval(shape{1}(2,:),1);
- end
-
-endfunction
-
-function y = func(x,N)
-
- if size(x,2) > 2
- t = linspace(0,1-1/N,N).';
- y(:,1) = polyval(x(1,:),t);
- y(:,2) = polyval(x(2,:),t);
- else
- y = x(:,2).';
- end
-
-endfunction
-
Deleted: trunk/octave-forge/main/geometry/inst/shapearea.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/shapearea.m 2011-11-03 22:45:47 UTC (rev 8970)
+++ trunk/octave-forge/main/geometry/inst/shapearea.m 2011-11-03 23:40:25 UTC (rev 8971)
@@ -1,67 +0,0 @@
-%% Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
-%%
-%% 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
-%% (at your option) 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{a} =} shapearea (@var{pp})
-%% Shape is defined with piecewise smooth polynomials. @var{pp} is a
-%% cell where each elements is a 2-by-(poly_degree+1) array containing
-%% @code{px(i,:) = pp@{i@}(1,:)} and @code{py(i,:) = pp@{i@}(2,:)}.
-%%
-%% @end deftypefn
-
-function A = shapearea (shape)
-
- A = sum(cellfun (@Aint, shape));
- if A < 0
- A = -A;
- end
-
-endfunction
-
-function dA = Aint (x)
-
- px = x(1,:);
- py = x(2,:);
-
- P = polyint (conv (px, polyderiv(py)));
-
- dA = diff(polyval(P,[0 1]));
-
-end
-
-%!demo % non-convex bezier shape
-%! weirdhearth ={[-17.6816 -34.3989 7.8580 3.7971; ...
-%! 15.4585 -28.3820 -18.7645 9.8519]; ...
-%! [-27.7359 18.1039 -34.5718 3.7878; ...
-%! -40.7440 49.7999 -25.5011 2.2304]};
-%! A = shapearea (weirdhearth)
-
-%!test
-%! triangle = {[1 0; 0 0]; [-0.5 1; 1 0]; [-0.5 0.5; -1 1]};
-%! A = shapearea (triangle);
-%! assert (0.5, A);
-
-%!test
-%! circle = {[1.715729 -6.715729 0 5; ...
-%! -1.715729 -1.568542 8.284271 0]; ...
-%! [1.715729 1.568542 -8.284271 0; ...
-%! 1.715729 -6.715729 0 5]; ...
-%! [-1.715729 6.715729 0 -5; ...
-%! 1.715729 1.568542 -8.284271 0]; ...
-%! [-1.715729 -1.568542 8.284271 0; ...
-%! -1.715729 6.715729 0 -5]};
-%! A = shapearea (circle);
-%! assert (pi*5^2, A, 5e-2);
-
Deleted: trunk/octave-forge/main/geometry/inst/shapecentroid.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/shapecentroid.m 2011-11-03 22:45:47 UTC (rev 8970)
+++ trunk/octave-forge/main/geometry/inst/shapecentroid.m 2011-11-03 23:40:25 UTC (rev 8971)
@@ -1,71 +0,0 @@
-%% Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
-%%
-%% 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
-%% (at your option) 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{cm} =} shapecentroid (@var{pp})
-%% Centroid of a plane shape.
-%%
-%% The shape is defined with piecewise smooth polynomials. @var{pp} is a
-%% cell where each elements is a 2-by-(poly_degree+1) matrix containing
-%% @code{px(i,:) = pp@{i@}(1,:)} and @code{py(i,:) = pp@{i@}(2,:)}.
-%%
-%% @seealso{shapearea}
-%% @end deftypefn
-
-function cm = shapecentroid (shape)
-
- cm = sum( cell2mat ( cellfun (@CMint, shape, 'UniformOutput', false)));
- A = shapearea(shape);
- cm = cm / A;
-
-endfunction
-
-function dcm = CMint (x)
-
- px = x(1,:);
- py = x(2,:);
- Px = polyint (conv(conv (px , px)/2 , polyderiv (py)));
- Py = polyint (conv(-conv (py , py)/2 , polyderiv (px)));
-
- dcm = zeros (1,2);
- dcm(1) = diff(polyval(Px,[0 1]));
- dcm(2) = diff(polyval(Py,[0 1]));
-
-endfunction
-
-%!demo % non-convex bezier shape
-%! weirdhearth ={[-17.6816 -34.3989 7.8580 3.7971; ...
-%! 15.4585 -28.3820 -18.7645 9.8519]; ...
-%! [-27.7359 18.1039 -34.5718 3.7878; ...
-%! -40.7440 49.7999 -25.5011 2.2304]};
-%! CoM = shapecentroid (weirdhearth)
-
-%!test
-%! square = {[1 -0.5; 0 -0.5]; [0 0.5; 1 -0.5]; [-1 0.5; 0 0.5]; [0 -0.5; -1 0.5]};
-%! CoM = shapecentroid (square);
-%! assert (CoM, [0 0], sqrt(eps));
-
-%!test
-%! circle = {[1.715729 -6.715729 0 5; ...
-%! -1.715729 -1.568542 8.284271 0]; ...
-%! [1.715729 1.568542 -8.284271 0; ...
-%! 1.715729 -6.715729 0 5]; ...
-%! [-1.715729 6.715729 0 -5; ...
-%! 1.715729 1.568542 -8.284271 0]; ...
-%! [-1.715729 -1.568542 8.284271 0; ...
-%! -1.715729 6.715729 0 -5]};
-%! CoM = shapecentroid (circle);
-%! assert (CoM , [0 0], 5e-3);
-
Deleted: trunk/octave-forge/main/geometry/inst/shapeplot.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/shapeplot.m 2011-11-03 22:45:47 UTC (rev 8970)
+++ trunk/octave-forge/main/geometry/inst/shapeplot.m 2011-11-03 23:40:25 UTC (rev 8971)
@@ -1,28 +0,0 @@
-%% Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
-%%
-%% 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{h} = } shapeplot (@var{shape})
-%% @deftypefnx {Function File} {@var{h} = } shapeplot (@var{shape}, @var{N})
-%% Pots a 2D shape defined by piecewise smooth polynomials.
-%%
-%% @end deftypefn
-
-function h = shapeplot(shape, N = 16, varargin)
-
- p = shape2polygon(shape, N);
- h = drawPolygon(p,varargin{:});
-
-endfunction
Deleted: trunk/octave-forge/main/geometry/inst/shapetransform.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/shapetransform.m 2011-11-03 22:45:47 UTC (rev 8970)
+++ trunk/octave-forge/main/geometry/inst/shapetransform.m 2011-11-03 23:40:25 UTC (rev 8971)
@@ -1,137 +0,0 @@
-%% Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
-%%
-%% 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.
-%%
-%% Format of @var{T} can be one of :
-%% [c] , [a b] , [a b c] or [a b c]
-%% [f] [d e] [d e f] [d e f]
-%% [0 0 1]
-%%
-%% @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]);
-%!
-%! cla
-%! 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);
-
Deleted: trunk/octave-forge/main/geometry/inst/simplifypolygon.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/simplifypolygon.m 2011-11-03 22:45:47 UTC (rev 8970)
+++ trunk/octave-forge/main/geometry/inst/simplifypolygon.m 2011-11-03 23:40:25 UTC (rev 8971)
@@ -1,29 +0,0 @@
-## Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
-##
-## 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
-## (at your option) 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/>.
-
-function polygonsimp = simplifypolygon (polygon)
-
- # Filter colinear points
- edges = diff(polygon([1:end 1],:));
- ned = size(edges,1);
- nxt = [2:ned 1];
-
- # check if consecutive edges are parallel
- para = edges(:,1).*edges(nxt,2) - edges(:,2).*edges(nxt,1);
- ind = abs(para) > sqrt(eps);
-
- polygonsimp = polygon(circshift (ind,1),:);
-
-endfunction
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