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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 normals = meshFaceNormals(varargin)
%MESHFACENORMALS Compute normal vector of faces in a 3D mesh.
%
% NORMALS = meshFaceNormals(VERTICES, FACES)
% VERTICES is a set of 3D points (as a N-by-3 array), and FACES is either
% a N-by-3 index array or a cell array of indices. The function computes
% the normal vector of each face.
% The orientation of the normal is defined by the sign of cross product
% between vectors joining vertices 1 to 2 and 1 to 3.
%
%
% Example
% [v e f] = createIcosahedron;
% normals1 = meshFaceNormals(v, f);
% centros1 = meshFaceCentroids(v, f);
% figure; drawMesh(v, f);
% hold on; axis equal; view(3);
% drawVector3d(centros1, normals1);
%
% pts = rand(50, 3);
% hull = minConvexHull(pts);
% normals2 = meshFaceNormals(pts, hull);
%
% See also
% meshes3d, meshFaceCentroids, meshVertexNormals, drawFaceNormals
% drawMesh
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2006-07-05
% Copyright 2006-2023 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
% parse input data
[vertices, faces] = parseMeshData(varargin{:});
if isnumeric(faces)
% compute vector of first edges
v1 = vertices(faces(:,2),1:3) - vertices(faces(:,1),1:3);
v2 = vertices(faces(:,3),1:3) - vertices(faces(:,1),1:3);
% compute normals using cross product (nodes have same size)
normals = cross(v1, v2, 2);
else
% initialize empty array
normals = zeros(length(faces), 3);
for i = 1:length(faces)
face = faces{i};
% compute vector of first edges
v1 = vertices(face(2),1:3) - vertices(face(1),1:3);
v2 = vertices(face(3),1:3) - vertices(face(1),1:3);
% compute normals using cross product
normals(i, :) = cross(v1, v2, 2);
end
end
normals = normalizeVector3d(normals);
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