Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / geometry-1.5.0 / polygons2d / polygon2shape.m

diff --git a/octave_packages/geometry-1.5.0/polygons2d/polygon2shape.m b/octave_packages/geometry-1.5.0/polygons2d/polygon2shape.m
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+++ b/octave_packages/geometry-1.5.0/polygons2d/polygon2shape.m
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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
+## (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);
+