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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 energy = meshEnergy(vertices, faces)
%MESHENERGY Computes the energy of a tesselation, as the sum of second area moments.
%
% This function can be used to check that the total energy of Centroidal
% Voronoi Tesselation (CVT) decreases with the iterations of the Lloyd
% algorithm.
%
% E = meshEnergy(V, F)
% V is the list of mesh vertices, and F are faces, as a cell array of
% vertex indices.
%
% Example
% meshEnergy
%
% See also
% centroidalVoronoi2d, cvtUpdate, polygonSecondAreaMoments
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2017-09-01, using Matlab 9.1.0.441655 (R2016b)
% Copyright 2017-2023 INRA - Cepia Software Platform
nFaces = meshFaceNumber(vertices, faces);
energyList = zeros(nFaces, 1);
polygons = meshFacePolygons(vertices, faces);
for i = 1:nFaces
[Ix, Iy, Ixy] = polygonSecondAreaMoments(polygons{i}); %#ok<ASGLU>
energyList(i) = hypot(Ix, Iy);
end
energy = sum(energyList);
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