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[Octave-cvsupdate] SF.net SVN: octave:[8931] trunk/octave-forge/main/geometry
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From: <jpi...@us...> - 2011-11-02 15:47:13
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Revision: 8931
http://octave.svn.sourceforge.net/octave/?rev=8931&view=rev
Author: jpicarbajal
Date: 2011-11-02 15:47:06 +0000 (Wed, 02 Nov 2011)
Log Message:
-----------
geometry. Adding some functions to manipulate piecewise smooth polygons
Modified Paths:
--------------
trunk/octave-forge/main/geometry/DESCRIPTION
trunk/octave-forge/main/geometry/PKG_ADD
trunk/octave-forge/main/geometry/PKG_DEL
trunk/octave-forge/main/geometry/inst/shapearea.m
Added Paths:
-----------
trunk/octave-forge/main/geometry/inst/polygon2shape.m
trunk/octave-forge/main/geometry/inst/polygons2d/
trunk/octave-forge/main/geometry/inst/polygons2d/drawPolygon.m
trunk/octave-forge/main/geometry/inst/polygons2d/polygons2d.m
trunk/octave-forge/main/geometry/inst/shape2polygon.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
Modified: trunk/octave-forge/main/geometry/DESCRIPTION
===================================================================
--- trunk/octave-forge/main/geometry/DESCRIPTION 2011-11-02 15:01:46 UTC (rev 8930)
+++ trunk/octave-forge/main/geometry/DESCRIPTION 2011-11-02 15:47:06 UTC (rev 8931)
@@ -1,6 +1,6 @@
Name: Geometry
-Version: 1.2.1
-Date: 2011-11-2
+Version: 1.2.2
+Date: 2011-11-9
Author: David Legland <dav...@gr...>, Juan Pablo Carbajal <car...@if...>
Maintainer: Juan Pablo Carbajal <car...@if...>
Title: Computational Geometry
Modified: trunk/octave-forge/main/geometry/PKG_ADD
===================================================================
--- trunk/octave-forge/main/geometry/PKG_ADD 2011-11-02 15:01:46 UTC (rev 8930)
+++ trunk/octave-forge/main/geometry/PKG_ADD 2011-11-02 15:47:06 UTC (rev 8931)
@@ -1,5 +1,5 @@
%1
-dirlist = {"geom2d","io"};
+dirlist = {"geom2d","io","polygons2d"};
dirname = fileparts (canonicalize_file_name (mfilename ("fullpath")));
if (! exist (fullfile (dirname, "inst"), "dir"))
Modified: trunk/octave-forge/main/geometry/PKG_DEL
===================================================================
--- trunk/octave-forge/main/geometry/PKG_DEL 2011-11-02 15:01:46 UTC (rev 8930)
+++ trunk/octave-forge/main/geometry/PKG_DEL 2011-11-02 15:47:06 UTC (rev 8931)
@@ -1,5 +1,5 @@
%1
-dirlist = {"geom2d","io"};
+dirlist = {"geom2d","io","polygons2d"};
dirname = fileparts (canonicalize_file_name (mfilename ("fullpath")));
if (! exist (fullfile (dirname, "inst"), "dir"))
Copied: trunk/octave-forge/main/geometry/inst/polygon2shape.m (from rev 8918, trunk/octave-forge/main/mechanics/inst/private/polygon2shape.m)
===================================================================
--- trunk/octave-forge/main/geometry/inst/polygon2shape.m (rev 0)
+++ trunk/octave-forge/main/geometry/inst/polygon2shape.m 2011-11-02 15:47:06 UTC (rev 8931)
@@ -0,0 +1,34 @@
+## 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/drawPolygon.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/polygons2d/drawPolygon.m (rev 0)
+++ trunk/octave-forge/main/geometry/inst/polygons2d/drawPolygon.m 2011-11-02 15:47:06 UTC (rev 8931)
@@ -0,0 +1,144 @@
+%% Copyright (c) 2011, INRA
+%% 2005-2011, David Legland <dav...@gr...>
+%% 2011 Adapted to Octave by Juan Pablo Carbajal <car...@if...>
+%%
+%% All rights reserved.
+%% (simplified BSD License)
+%%
+%% Redistribution and use in source and binary forms, with or without
+%% modification, are permitted provided that the following conditions are met:
+%%
+%% 1. Redistributions of source code must retain the above copyright notice, this
+%% list of conditions and the following disclaimer.
+%%
+%% 2. Redistributions in binary form must reproduce the above copyright notice,
+%% this list of conditions and the following disclaimer in the documentation
+%% and/or other materials provided with the distribution.
+%%
+%% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+%% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+%% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+%% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
+%% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+%% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+%% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+%% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+%% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+%% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+%% POSSIBILITY OF SUCH DAMAGE.
+%%
+%% The views and conclusions contained in the software and documentation are
+%% those of the authors and should not be interpreted as representing official
+%% policies, either expressed or implied, of copyright holder.
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} {@var{h} = } drawPolygon (@var{coord})
+%% @deftypefnx {Function File} {@var{h} = } drawPolygon (@var{px}, @var{py})
+%% @deftypefnx {Function File} {@var{h} = } drawPolygon (@var{polys})
+%% Draw a polygon specified by a list of points.
+%%
+%% drawPolygon(COORD);
+%% Packs coordinates in a single [N*2] array.
+%%
+%% drawPolygon(PX, PY);
+%% Specifies coordinates in separate arrays.
+%%
+%% drawPolygon(POLYS)
+%% Packs coordinate of several polygons in a cell array. Each element of
+%% the array is a Ni*2 double array.
+%%
+%% H = drawPolygon(...);
+%% Also return a handle to the list of line objects.
+%%
+%%
+%% @seealso{polygons2d, drawCurve}
+%% @end deftypefn
+
+function varargout = drawPolygon(varargin)
+
+ % check input
+ if isempty(varargin)
+ error('need to specify a polygon');
+ end
+
+ var = varargin{1};
+
+ %% Manage cell arrays of polygons
+
+ % case of a set of polygons stored in a cell array
+ if iscell(var)
+ N = length(var);
+ h = zeros(N, 1);
+ for i = 1:N
+ state = ishold(gca);
+ hold on;
+ % check for empty polygons
+ if ~isempty(var{i})
+ h(i) = drawPolygon(var{i}, varargin{2:end});
+ end
+ if ~state
+ hold off
+ end
+ end
+
+ if nargout > 0
+ varargout = {h};
+ end
+
+ return;
+ end
+
+
+ %% Parse coordinates and options
+
+ % Extract coordinates of polygon vertices
+ if size(var, 2) > 1
+ % first argument is a polygon array
+ px = var(:, 1);
+ py = var(:, 2);
+ varargin(1) = [];
+ else
+ % arguments 1 and 2 correspond to x and y coordinate respectively
+ if length(varargin) < 2
+ error('Should specify either a N-by-2 array, or 2 N-by-1 vectors');
+ end
+
+ px = varargin{1};
+ py = varargin{2};
+ varargin(1:2) = [];
+ end
+
+ % set default line format
+ if isempty(varargin)
+ varargin = {'b-'};
+ end
+
+ % check case of polygons with holes
+ if sum(isnan(px(:))) > 0
+ polygons = splitPolygons([px py]);
+ h = drawPolygon(polygons);
+
+ if nargout > 0
+ varargout = {h};
+ end
+
+ return;
+ end
+
+
+ %% Draw the polygon
+
+ % ensure last point is the same as the first one
+ px(size(px, 1)+1, :) = px(1,:);
+ py(size(py, 1)+1, :) = py(1,:);
+
+ % draw the polygon outline
+ h = plot(px, py, varargin{:});
+
+ % format output arg
+ if nargout > 0
+ varargout = {h};
+ end
+
+endfunction
+
Added: trunk/octave-forge/main/geometry/inst/polygons2d/polygons2d.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/polygons2d/polygons2d.m (rev 0)
+++ trunk/octave-forge/main/geometry/inst/polygons2d/polygons2d.m 2011-11-02 15:47:06 UTC (rev 8931)
@@ -0,0 +1,180 @@
+%% Copyright (c) 2011, INRA
+%% 2005-2011, David Legland <dav...@gr...>
+%% 2011 Adapted to Octave by Juan Pablo Carbajal <car...@if...>
+%%
+%% All rights reserved.
+%% (simplified BSD License)
+%%
+%% Redistribution and use in source and binary forms, with or without
+%% modification, are permitted provided that the following conditions are met:
+%%
+%% 1. Redistributions of source code must retain the above copyright notice, this
+%% list of conditions and the following disclaimer.
+%%
+%% 2. Redistributions in binary form must reproduce the above copyright notice,
+%% this list of conditions and the following disclaimer in the documentation
+%% and/or other materials provided with the distribution.
+%%
+%% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+%% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+%% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+%% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
+%% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+%% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+%% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+%% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+%% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+%% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+%% POSSIBILITY OF SUCH DAMAGE.
+%%
+%% The views and conclusions contained in the software and documentation are
+%% those of the authors and should not be interpreted as representing official
+%% policies, either expressed or implied, of copyright holder.
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} {} polygons2d ()
+%% MATGEOM-POLYGONS
+%%
+%% The 'polygons' module contains functions operating on shapes composed
+%% of a vertex list, like polygons or polylines.
+%%
+%% We call 'polyline' the curve defined by a series of vertices.
+%% A polyline can be either closed or open, depending on whether the last
+%% vertex is connected to the first one or not. This can be given as an
+%% option is some functions in the module.
+%% A 'polygon' is the planar domain delimited by a closed polyline. We
+%% sometimes want to consider 'complex polygons', whose boundary is
+%% composed of several disjoint domains. The domain defined by a single
+%% closed polyline is called 'simple polygon'.
+%% We call 'curve' a polyline with many vertices, such that the polyline
+%% can be considered as a discrete approximation of a "real" curve.
+%%
+%% A simple polygon or polyline is represented by a N-by-2 array, each row
+%% of the array representing the coordinates of a vertex.
+%% Simple polygons are assumed to be closed, so there is no need to repeat
+%% the first vertex at the end.
+%% As both polygons and polylines can be represented by a list of vertex
+%% coordinates, some functions also consider the vertex list itself. Such
+%% functions are prefixed by 'pointSet'. Also, many functions prefixed by
+%% 'polygon' or 'polyline' works also on the other type of shape.
+%%
+%% For multiple-connected polygons, the different connected boundaries are
+%% separated by a row [NaN NaN].
+%%
+%% For some functions, the orientation of the polygon can be relevant: CCW
+%% stands for 'Conter-Clockwise' (positive orientation), CW stands for
+%% 'Clockwise'.
+%%
+%% Polylines are parametrized in the following way:
+%% * the i-th vertex is located at position i-1
+%% * points of the i-th edge have positions ranging linearly from i-1 to i
+%% The parametrization domain for an open polyline is from 0 to Nv-1, and
+%% from 0 to Nv for a closed polyline (positions 0 and Nv correspond to
+%% the same point).
+%%
+%% Example:
+%% % Simple polygon:
+%% P1 = [1 1;2 1;2 2;1 2];
+%% drawPolygon(P1);
+%% axis([0 5 0 5]);
+%% % Multiple polygon:
+%% P2 = [10 10;40 10;40 40;10 40;NaN NaN;20 20;20 30;30 30;30 20];
+%% figure;drawPolygon(P2); axis([0 50 0 50]);
+%%
+%%
+%% Point Sets
+%% pointSetBounds - Bounding box of a set of points
+%% pointSetsAverage - Compute the average of several point sets
+%% minimumCaliperDiameter - Minimum caliper diameter of a set of points
+%% findPoint - Find index of a point in an set from its coordinates
+%%
+%% Polylines
+%% polylinePoint - Extract a point from a polyline
+%% polylineLength - Return length of a polyline given as a list of points
+%% polylineCentroid - Compute centroid of a curve defined by a series of points
+%% polylineSubcurve - Extract a portion of a polyline
+%% reversePolyline - Reverse a polyline, by iterating vertices from the end
+%% isPointOnPolyline - Test if a point belongs to a polyline
+%% projPointOnPolyline - Compute position of a point projected on a polyline
+%% distancePointPolyline - Compute shortest distance between a point and a polyline
+%% distancePolylines - Compute the shortest distance between 2 polylines
+%% intersectPolylines - Find the common points between 2 polylines
+%% polylineSelfIntersections - Find self-intersections points of a polyline
+%%
+%% Curves (polylines with lot of vertices)
+%% parametrize - Parametrization of a curve, based on edges length
+%% curvature - Estimate curvature of a polyline defined by points
+%% cart2geod - Convert cartesian coordinates to geodesic coord.
+%% geod2cart - Convert geodesic coordinates to cartesian coord.
+%% curveMoment - Compute inertia moment of a 2D curve
+%% curveCMoment - Compute centered inertia moment of a 2D curve
+%% curveCSMoment - Compute centered scaled moment of a 2D curve
+%%
+%% Polygons
+%% polygonPoint - Extract a point from a polygon
+%% polygonSubcurve - Extract a portion of a polygon
+%% reversePolygon - Reverse a polygon, by iterating vertices from the end
+%% projPointOnPolygon - Compute position of a point projected on a polygon
+%% splitPolygons - Convert a NaN separated polygon list to a cell array of polygons
+%% clipPolygon - Clip a polygon with a rectangular box
+%% clipPolygonHP - Clip a polygon with a Half-plane defined by a directed line
+%% intersectLinePolygon - Intersection points between a line and a polygon
+%% intersectRayPolygon - Intersection points between a ray and a polygon
+%% polygonSelfIntersections - Find-self intersection points of a polygon
+%% convexHull - Convex hull of a set of points
+%% polygonLoops - Divide a possibly self-intersecting polygon into a set of simple loops
+%% expandPolygon - Expand a polygon by a given (signed) distance
+%% medialAxisConvex - Compute medial axis of a convex polygon
+%%
+%% Measures on Polygons
+%% isPointInPolygon - Test if a point is located inside a polygon
+%% polygonContains - Test if a point is contained in a multiply connected polygon
+%% polygonCentroid - Compute the centroid (center of mass) of a polygon
+%% polygonArea - Compute the signed area of a polygon
+%% polygonLength - Perimeter of a polygon
+%% polygonNormalAngle - Compute the normal angle at a vertex of the polygon
+%% polygonBounds - Compute the bounding box of a polygon
+%% distancePointPolygon - Compute shortest distance between a point and a polygon
+%% distancePolygons - Compute the shortest distance between 2 polygons
+%%
+%% Triangles
+%% isPointInTriangle - Test if a point is located inside a triangle
+%% triangleArea - Area of a triangle
+%%
+%% Functions from stochastic geometry
+%% steinerPoint - Compute steiner point (weighted centroid) of a polygon
+%% steinerPolygon - Create a Steiner polygon from a set of vectors
+%% supportFunction - Compute support function of a polygon
+%% convexification - Compute the convexification of a polygon
+%%
+%% Input, Output and conversions
+%% readPolygon - Read a polygon stored in a file
+%% polygonToRow - Convert polygon coordinates to a row vector
+%% rowToPolygon - Create a polygon from a row vector
+%% rectAsPolygon - Convert a (centered) rectangle into a series of points
+%%
+%% Drawing functions
+%% drawPolyline - Draw a polyline specified by a list of points
+%% drawPolygon - Draw a polygon specified by a list of points
+%% fillPolygon - Fill a polygon specified by a list of points
+%%
+%%
+%% Credits:
+%% * function intersectPolylines uses the 'interX' contribution from "NS"
+%% (file exchange 22441, called 'curve-intersections')
+%%
+%% -----
+%% Author: David Legland
+%% e-mail: dav...@gr...
+%% created the 07/11/2005.
+%% Homepage: http://matgeom.sourceforge.net/
+%% http://www.pfl-cepia.inra.fr/index.php?page=geom2d
+%% Copyright INRA - Cepia Software Platform.
+%%
+%% @end deftypefn%
+
+function polygons2d ()
+
+help('polygons2d');
+
+endfunction
Copied: trunk/octave-forge/main/geometry/inst/shape2polygon.m (from rev 8918, trunk/octave-forge/main/mechanics/inst/private/shape2polygon.m)
===================================================================
--- trunk/octave-forge/main/geometry/inst/shape2polygon.m (rev 0)
+++ trunk/octave-forge/main/geometry/inst/shape2polygon.m 2011-11-02 15:47:06 UTC (rev 8931)
@@ -0,0 +1,46 @@
+## 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
+
Modified: trunk/octave-forge/main/geometry/inst/shapearea.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/shapearea.m 2011-11-02 15:01:46 UTC (rev 8930)
+++ trunk/octave-forge/main/geometry/inst/shapearea.m 2011-11-02 15:47:06 UTC (rev 8931)
@@ -24,7 +24,10 @@
function A = shapearea (shape)
A = sum(cellfun (@Aint, shape));
-
+ if A < 0
+ A = -A;
+ end
+
endfunction
function dA = Aint (x)
Added: trunk/octave-forge/main/geometry/inst/shapecentroid.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/shapecentroid.m (rev 0)
+++ trunk/octave-forge/main/geometry/inst/shapecentroid.m 2011-11-02 15:47:06 UTC (rev 8931)
@@ -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.
+%%
+%% 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);
+
Added: trunk/octave-forge/main/geometry/inst/shapeplot.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/shapeplot.m (rev 0)
+++ trunk/octave-forge/main/geometry/inst/shapeplot.m 2011-11-02 15:47:06 UTC (rev 8931)
@@ -0,0 +1,28 @@
+%% 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
Added: trunk/octave-forge/main/geometry/inst/shapetransform.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/shapetransform.m (rev 0)
+++ trunk/octave-forge/main/geometry/inst/shapetransform.m 2011-11-02 15:47:06 UTC (rev 8931)
@@ -0,0 +1,137 @@
+%% 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);
+
Copied: trunk/octave-forge/main/geometry/inst/simplifypolygon.m (from rev 8918, trunk/octave-forge/main/mechanics/inst/private/simplifypolygon.m)
===================================================================
--- trunk/octave-forge/main/geometry/inst/simplifypolygon.m (rev 0)
+++ trunk/octave-forge/main/geometry/inst/simplifypolygon.m 2011-11-02 15:47:06 UTC (rev 8931)
@@ -0,0 +1,29 @@
+## 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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