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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 theta = polyhedronNormalAngle(varargin)
%POLYHEDRONNORMALANGLE Compute normal angle at a vertex of a 3D polyhedron.
%
% THETA = polyhedraNormalAngle(NODES, EDGES, FACES, IND);
% THETA = polyhedraNormalAngle(NODES, FACES, IND);
% where NODES is a set of 3D points, and FACES a set of faces, whose
% elements are indices to NODES array, compute the normal angle at the
% vertex whose index is given by IND.
%
% THETA = polyhedraNormalAngle(GRAPH, IND);
% Uses a graph structure for definineg polyhedron. GRAPH structure should
% contain at least two fields : 'nodes' and 'faces'.
%
% Example :
% % create a simple (irregular) tetrahedra
% nodes = [0 0 0;1 0 0;0 1 0;0 0 1];
% faces = [1 2 3;1 2 4;1 3 4;2 3 4];
% % compute normal angle at each vertex
% theta = polyhedronNormalAngle(nodes, faces, 1:size(nodes, 1));
% % sum of normal angles should be equal to 4*pi :
% sum(theta)
%
% Note: works only for polyhedra with convex faces!
%
% See also
% polyhedra, polygon3dNormalAngle
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-11-30
% Copyright 2005-2023 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
if length(varargin)==4
nodes = varargin{1};
faces = varargin{3};
ind = varargin{4};
elseif length(varargin)==3
nodes = varargin{1};
faces = varargin{2};
ind = varargin{3};
elseif length(varargin)==2
graph = varargin{1};
nodes = graph.nodes;
faces = graph.faces;
ind = varargin{2};
else
error('wrong number of arguments');
end
% number of angles to compute
na = length(ind);
theta = zeros(na, 1);
for i = 1:na
thetaf = [];
% find faces containing given vertex,
% and compute normal angle at each face containing vertex
if iscell(faces)
for j = 1:length(faces)
if ismember(ind(i), faces{j})
% create 3D polygon
face = nodes(faces{j}, :);
% index of point in polygon
indp = find(faces{j}==i);
% compute normal angle of vertex
thetaf = [thetaf polygon3dNormalAngle(face, indp)]; %#ok<AGROW>
end
end
else
indf = find(sum(ismember(faces, ind(i)), 2));
thetaf = zeros(length(indf), 1);
for j = 1:length(indf)
ind2 = faces(indf(j), :);
face = nodes(ind2, :);
indp = find(ind2==ind(i));
thetaf(j) = pi - polygon3dNormalAngle(face, indp);
end
end
% compute normal angle of polyhedron, by use of angle defect formula
theta(i) = 2*pi - sum(thetaf);
end
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