function supportValue = computeSupportValueVrep(vrep, pointMatrix)
% calculates the support values for a polytope in V-representation 
%
% Syntax: supportValue = computeSupportValueVrep(vrep, pointMatrix)
%
% The support function of a polytope P is defined as:
%     h(P, x) = [max over all points y in P] y * x'
%   where this function might contain multiple points x simultanously. They
%   are given in each row of pointMatrix.
%
% Given an H-representation with the facet normals a(i) and the 
%   corresponding distances h(i), it holds:
%     h(P, a(i)) = h(i)
%
% See also: computeFeretVrep, computeProjectionAreaVrep, computeVolumeVrep,
%   computeFacetAreaVrep, computeSupportValueHrep

% The elk-library: convex geometry applied to crystallization modeling.
%   Copyright (C) 2012 Alexander Reinhold
%
% 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/>.

if size(pointMatrix, 2) ~= size(vrep.V, 2)
    error('elk:polytope:wrongType', ...
        ['Specify the points in a matrix 1 point per row. Dimension with'...
        'V-representation polytope must match.']);
end

supportValue = -inf(size(pointMatrix, 1), 1);
for iVertex = 1:size(vrep.V, 1)
    supportValue(:) = max(supportValue, pointMatrix * vrep.V(iVertex, :)');
end