ComputeAreaOpt.m

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function area=ComputeAreaOpt(q,me)
% function area=ComputeAreaOpt(q,me)
%   Computation of areas of triangles in the mesh
%   - Optimized version
%
% Parameters:
%  q: Array of vertices coordinates, `2\times\nq` array. <br/>
%  `{\q}(\il,j)` is the
%  `\il`-th coordinate of the `j`-th vertex, `\il\in\{1,2\}` and
%  `j\in\ENS{1}{\nq}`
%  me: Connectivity array, `3\times\nme` array.<br/>
%  `\me(\jl,k)` is the storage index of the
%  `\jl`-th  vertex of the `k`-th triangle in the array `\q` of vertices coordinates, `\jl\in\{1,2,3\}` and
%       `k\in{\ENS{1}{\nme}}`.
%
% Return values:
%  area: Array of areas, `1\times\nme` array. area(k) is the area of the `k`-th triangle.
%
% OptFEM2DP1 [V1.2b1] -    Copyright (C) 2013  CJS (LAGA)
%
%   This file is part of OptFEM2DP1.
%   OptFEM2DP1 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.
%
%   OptFEM2DP1 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/>.
c1 = q(:,me(1,:));
d21 = q(:,me(2,:))-c1;
d31 = q(:,me(3,:))-c1;
area = 0.5*(d21(1,:).*d31(2,:)-d21(2,:).*d31(1,:));