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## Copyright (C) 2004-2011 David Legland <david.legland@grignon.inra.fr>
## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## All rights reserved.
##
## 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 AUTHOR 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.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{h} = } suppportFunction (@var{polygon})
## @deftypefnx {Function File} {@var{h} = } suppportFunction (@var{polygon}, @var{n})
## @deftypefnx {Function File} {@var{h} = } suppportFunction (@var{polygon}, @var{v})
## Compute support function of a polygon
##
## H = supportFunction(POLYGON, N)
## uses N points for suport function approximation
##
## H = supportFunction(POLYGON)
## assume 24 points for approximation
##
## H = supportFunction(POLYGON, V)
## where V is a vector, uses vector V of angles to compute support
## function.
##
## @seealso{convexification}
## @end deftypefn
function h = supportFunction(polygon, varargin)
N = 24;
u = (0:2*pi/N:2*pi*(1-1/N)).';
if length(varargin)==1
var = varargin{1};
if length(var)==1
N = var;
u = (0:2*pi/N:2*pi*(1-1/N)).';
else
u = var(:);
end
end
h = zeros(size(u));
for i=1:length(u)
v = repmat([cos(u(i)) sin(u(i))], [size(polygon, 1), 1]);
h(i) = max(dot(polygon, v, 2));
end
endfunction
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