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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 newFaces = minConvexHull(points, varargin)
%MINCONVEXHULL Return the unique minimal convex hull of a set of 3D points.
%
% FACES = minConvexHull(PTS)
% NODES is a set of 3D points (as a Nx3 array). The function computes
% the convex hull, and merge contiguous coplanar faces. The result is a
% set of polygonal faces, such that there are no coplanar faces.
% FACES is a cell array, each cell containing the vector of indices of
% nodes given in NODES for the corresponding face.
%
% FACES = minConvexHull(PTS, PRECISION)
% Adjust the threshold for deciding if two faces are coplanar or
% parallel. Default value is 1e-14.
%
% Example
% % extract square faces from a cube
% [n, e, f] = createCube;
% f2 = minConvexHull(n);
% drawMesh(n, f2);
%
% % Subdivides and smooths a mesh rpresenting a cube
% [n, e, f] = createCube;
% [n2, f2] = subdivideMesh(n, triangulateFaces(f), 4);
% [n3, f3] = smoothMesh(n2, f2);
% figure; drawMesh(n3, f3);
% axis equal; view(3);
% % merge coplanar faces, making apparent the faces of the original cube
% f4 = minConvexHull(n3);
% figure; drawMesh(n3, f4);
% axis equal; view(3);
%
%
% See also
% meshes3d, mergeCoplanarFaces, drawMesh, convhull, convhulln
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2006-07-05
% Copyright 2006-2023 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
% set up precision
acc = 1e-14;
if ~isempty(varargin)
acc = varargin{1};
end
% triangulated convex hull. It is not uniquely defined.
faces = convhulln(points);
% compute centroid of the nodes
pointsCentroid = centroid(points);
% number of base triangular faces
N = size(faces, 1);
% compute normals of given faces
normals = planeNormal(createPlane(...
points(faces(:,1),:), points(faces(:,2),:), points(faces(:,3),:)));
% initialize empty faces
newFaces = {};
% Processing flag for each triangle
% 1 : triangle to process, 0 : already processed
% in the beginning, every triangle face need to be processed
flag = ones(N, 1);
% iterate on each triangular face of the convex hull
for iFace = 1:N
% check if face was already performed
if ~flag(iFace)
continue;
end
% indices of faces with same normal
ind = find(abs(vectorNorm3d(cross(repmat(normals(iFace, :), [N 1]), normals)))<acc);
ind = ind(ind~=iFace);
% keep only coplanar faces (test coplanarity of points in both face)
ind2 = iFace;
for j = 1:length(ind)
if isCoplanar(points([faces(iFace,:) faces(ind(j),:)], :), acc)
ind2 = [ind2 ind(j)]; %#ok<AGROW>
end
end
% compute order of the vertices in current face
faceVertices = unique(faces(ind2, :));
[tmp, I] = angleSort3d(points(faceVertices, :)); %#ok<ASGLU>
% create the new face, ensuring it is a row vector
face = faceVertices(I);
face = face(:)';
% ensure face has normal pointing outwards
outerNormal = meshFaceCentroids(points, face) - pointsCentroid;
if dot(meshFaceNormals(points, face), outerNormal, 2) < 0
face = face([1 end:-1:2]);
end
% add a new face to the list
newFaces = [newFaces {face}]; %#ok<AGROW>
% mark processed faces
flag(ind2) = 0;
end
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