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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 meshes = splitMesh(vertices, faces, varargin)
%SPLITMESH Return the connected components of a mesh.
%
% MESHES = splitMesh(VERTICES, FACES) returns the connected components of
% the mesh defined by vertices and faces as a struct array with the
% fields vertices and faces sorted by increasing vertex number
%
% MESHES = splitMesh(MESH) with the vertices-faces-struct MESH is also
% possible
%
% ... = splitMesh(..., 'mostVertices') returns only the component with
% the most vertices. Other options are 'all' (default),
% 'maxBoundingBox' that returns the component with the largest bounding
% box, and 'maxVolume' returns the component with the largest volume.
%
%
% Example
% [v1, f1] = boxToMesh([1 0 -1 0 -1 0]);
% [v2, f2] = boxToMesh([-1 0 1 0 -1 0]);
% [v3, f3] = createSoccerBall;
% f1 = triangulateFaces(f1);
% f2 = triangulateFaces(f2);
% f3 = triangulateFaces(f3);
% [vertices, faces] = concatenateMeshes(v1, f1, v3, f3, v2, f2);
% meshes = splitMesh(vertices, faces);
% figure('color','w'); view(3); axis equal
% cmap=hsv(length(meshes));
% for m=1:length(meshes)
% drawMesh(meshes(m), cmap(m,:))
% end
%
% See also
% concatenateMeshes
%
% Source
% Local functions are part of the gptoolbox of Alec Jacobson
% https://github.com/alecjacobson/gptoolbox
% ------
% Author: oqilipo
% E-mail: N/A
% Created: 2017-09-17
% Copyright 2017-2023
% input parsing
if isstruct(vertices)
if nargin > 1; varargin = [faces, varargin]; end
[vertices, faces]=parseMeshData(vertices);
end
parser = inputParser;
validStrings = {'all','mostVertices','maxBoundingBox','maxVolume'};
addOptional(parser,'components','all',@(x) any(validatestring(x, validStrings)));
parse(parser,varargin{:});
outputComp = validatestring(parser.Results.components, validStrings);
% algorithm
CC = connected_components(faces);
[a,~]=hist(CC,unique(CC));
[~,b] = sort(a);
meshes=repmat(struct('vertices',[],'faces',[]),length(b),1);
for cc=b
meshes(cc)=removeMeshVertices(vertices, faces, ~(CC'==b(cc)));
end
% output parsing
switch outputComp
case 'mostVertices'
meshes=meshes(end);
case 'maxBoundingBox'
[~,sortingIndices] = sort(arrayfun(@(x) box3dVolume(boundingBox3d(x.vertices)), meshes));
meshes = meshes(sortingIndices(end));
case 'maxVolume'
[~,sortingIndices] = sort(arrayfun(@(x) meshVolume(x.vertices, x.faces), meshes));
meshes = meshes(sortingIndices(end));
end
end
%% Local functions are part of the gptoolbox by Alec Jacobson
function C = connected_components(F)
% CONNECTED_COMPONENTS Determine the connected components of a mesh
% described by the simplex list F. Components are determined with respect
% to the edges of the mesh. That is, a single component may contain
% non-manifold edges and vertices.
%
% C = connected_components(F)
%
% Inputs:
% F #F by simplex-size list of simplices
% Outputs:
% C #V list of ids for each CC
%
% Examples:
% trisurf(F,V(:,1),V(:,2),V(:,3), ...
% connected_components([F;repmat(size(V,1),1,3)]));
% build adjacency list
A = adjacency_matrix(F);
[~,C] = conncomp(A);
end
function [A] = adjacency_matrix(E)
% ADJACENCY_MATRIX Build sparse adjacency matrix from edge list or face list
%
% [A] = adjacency_matrix(E)
% [A] = adjacency_matrix(F)
% [A] = adjacency_matrix(T)
%
% Inputs:
% E #E by 2 edges list
% or
% F #F by 3 triangle list
% or
% T #F by 4 tet list
% Outputs:
% A #V by #V adjacency matrix (#V = max(E(:)))
%
if size(E,2)>2
F = E;
E = meshEdges(F);
end
A = sparse([E(:,1) E(:,2)],[E(:,2) E(:,1)],1);
end
function [S,C] = conncomp(G)
% CONNCOMP Drop in replacement for graphconncomp.m from the bioinformatics
% toobox. G is an n by n adjacency matrix, then this identifies the S
% connected components C. This is also an order of magnitude faster.
%
% [S,C] = conncomp(G)
%
% Inputs:
% G n by n adjacency matrix
% Outputs:
% S scalar number of connected components
% C
% Transpose to match graphconncomp
G = G';
[p,~,r] = dmperm(G+speye(size(G)));
S = numel(r)-1;
C = cumsum(full(sparse(1,r(1:end-1),1,1,size(G,1))));
C(p) = C;
end
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