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## Copyright (C) 2024 David Legland
## 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.
##
## 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 the copyright holders.
function h = supportFunction(polygon, varargin)
%SUPPORTFUNCTION 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.
%
% See also
% polygons2d, convexification
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2004-12-20
% Copyright 2004-2023 INRA - TPV URPOI - BIA IMASTE
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
% ensure u vertical vector
if size(u, 1)==1
u=u';
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
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