patchConnectivity

Below is a demonstration of the features of the patchConnectivity function

Contents

Syntax

[C]=patchConnectivity(F,V,conType);

Description

This functions creates connectivity matrices for the input patch data defined by the faces F and the vertices V. The output is a structure containing the connectivity matrices:

C.vertex.vertex C.vertex.face C.vertex.edge

C.edge.face C.edge.vertex C.edge.edge

C.face.vertex C.face.face C.face.edge

If the 3rd optional input conType is not provided its default value is 'all' and all connectivity matrices are output in the structure. If not all types are desired the user may request only particular types by setting conType. The following conTypes can be specified: conType (v stands for vertex, f for face, e for edge): 'all','vv','vf','ve','ev','ef','ee','fv','ff','fe'

Examples

clear; close all; clc;

Plot settings

markerSize=50;

Example 1: Demonstrating patchConnectivity for different patch types

for testCase=1:3

    switch testCase
        case 1
            [F,V]=geoSphere(1,1);
        case 2
            [F,V]=quadSphere(2,1);
        case 3
            r=1; %Sphere radius
            rc=1.5; %Central radius
            nr=12;
            nc=18;
            patchType='honey';
            [F,V]=patchTorus(r,nr,rc,nc,patchType);
    end

Using patchConnectivity to compute connectivity arrays

    [C]=patchConnectivity(F,V);

    E=C.edge.vertex;
    Z=V(:,3);
    [~,indPlotVertex]=max(Z);
    [~,indPlotFace]=max(mean(Z(F),2));
    [~,indPlotEdge]=max(mean(Z(E),2));

Visualize vertex connectivity

    indVertexVertex=C.vertex.vertex(indPlotVertex,:);
    indVertexVertex=indVertexVertex(indVertexVertex>0);
    indVertexFace=C.vertex.face(indPlotVertex,:);
    indVertexEdge=C.vertex.edge(indPlotVertex,:);

    cFigure;
    subplot(1,3,1); hold on;
    title('Vertex-vertex connectivity');
    gpatch(F,V,'kw','k',0.5)

    hl(1)=plotV(V(indPlotVertex,:),'g.','MarkerSize',markerSize);
    hl(2)=plotV(V(indVertexVertex,:),'r.','MarkerSize',markerSize);

    legend(hl,{'Example point','Connected points'},'Location','SouthOutside');

    axisGeom;
    view(2);
    camlight headlight;
    axis off;
    clear hl;

    subplot(1,3,2); hold on;
    title('Vertex-face connectivity');
    gpatch(F,V,'kw','k',0.5)

    hl(1)=plotV(V(indPlotVertex,:),'g.','MarkerSize',markerSize);
    hl(2)=gpatch(F(indVertexFace,:),V,'r','r',1);

    legend(hl,{'Example point','Connected faces'},'Location','SouthOutside');

    axisGeom;
    view(2);
    camlight headlight;
    axis off;
    clear hl;

    subplot(1,3,3); hold on;
    title('Vertex-edge connectivity');
    gpatch(F,V,'kw','k',0.5)

    hl(1)=plotV(V(indPlotVertex,:),'g.','MarkerSize',markerSize);
    hl(2)=gpatch(E(indVertexEdge,:),V,'none','r',1);
    hl(2).LineWidth=3;
    legend(hl,{'Example point','Connected Edges'},'Location','SouthOutside');

    axisGeom;
    view(2);
    camlight headlight;
    axis off;
    clear hl;

    drawnow;

Visualize face connectivity

    indFaceVertex=C.face.vertex(indPlotFace,:);
    indFaceVertex=indFaceVertex(indFaceVertex>0);
    indFaceFace=C.face.face(indPlotFace,:);
    indFaceFace=indFaceFace(indFaceFace>0);
    indFaceEdge=C.face.edge(indPlotFace,:);

    cFigure;
    subplot(1,3,1); hold on;
    title('Face-vertex connectivity');
    gpatch(F,V,'kw','k',0.5)

    hl(1)=gpatch(F(indPlotFace,:),V,'g','g',1);
    hl(2)=plotV(V(indFaceVertex,:),'r.','MarkerSize',markerSize);

    legend(hl,{'Example face','Connected points'},'Location','SouthOutside');

    axisGeom;
    view(2);
    camlight headlight;
    axis off;
    clear hl;

    subplot(1,3,2); hold on;
    title('Face-face connectivity');
    gpatch(F,V,'kw','k',0.5)

    hl(1)=gpatch(F(indPlotFace,:),V,'g','g',1);
    hl(2)=gpatch(F(indFaceFace,:),V,'r','r',1);

    legend(hl,{'Example face','Connected faces'},'Location','SouthOutside');

    axisGeom;
    view(2);
    camlight headlight;
    axis off;
    clear hl;

    subplot(1,3,3); hold on;
    title('Face-edge connectivity');
    gpatch(F,V,'kw','k',0.5)

    hl(1)=gpatch(F(indPlotFace,:),V,'g','g',1);
    hl(2)=gpatch(E(indFaceEdge,:),V,'none','r',1);
    hl(2).LineWidth=3;
    legend(hl,{'Example face','Connected Edges'},'Location','SouthOutside');

    axisGeom;
    view(2);
    camlight headlight;
    axis off;
    clear hl;

    drawnow;

Visualize edge connectivity

    indEdgeVertex=C.edge.vertex(indPlotEdge,:);
    indEdgeVertex=indEdgeVertex(indEdgeVertex>0);
    indEdgeFace=C.edge.face(indPlotEdge,:);
    indEdgeFace=indEdgeFace(indEdgeFace>0);
    indEdgeEdge=C.edge.edge(indPlotEdge,:);
    indEdgeEdge=indEdgeEdge(indEdgeEdge>0);

    cFigure;
    subplot(1,3,1); hold on;
    title('Edge-vertex connectivity');
    gpatch(F,V,'kw','k',0.5)

    hl(1)=gpatch(E(indPlotEdge,:),V,'g','g',1); hl(1).LineWidth=3;
    hl(2)=plotV(V(indEdgeVertex,:),'r.','MarkerSize',markerSize);

    legend(hl,{'Example edge','Connected points'},'Location','SouthOutside');

    axisGeom;
    view(2);
    camlight headlight;
    axis off;
    clear hl;

    subplot(1,3,2); hold on;
    title('Edge-face connectivity');
    gpatch(F,V,'kw','k',0.5)

    hl(1)=gpatch(E(indPlotEdge,:),V,'g','g',1); hl(1).LineWidth=3;
    hl(2)=gpatch(F(indEdgeFace,:),V,'r','r',1);

    legend(hl,{'Example edge','Connected faces'},'Location','SouthOutside');

    axisGeom;
    view(2);
    camlight headlight;
    axis off;
    clear hl;

    subplot(1,3,3); hold on;
    title('Edge-edge connectivity');
    gpatch(F,V,'kw','k',0.5)

    hl(1)=gpatch(E(indPlotEdge,:),V,'g','g',1); hl(1).LineWidth=3;
    hl(2)=gpatch(E(indEdgeEdge,:),V,'none','r',1); hl(2).LineWidth=3;
    legend(hl,{'Example edge','Connected Edges'},'Location','SouthOutside');

    axisGeom;
    view(2);
    camlight headlight;
    axis off;
    clear hl;

    drawnow;

end

Example 2: Using the conTypes input to control output request

Request only the edge-edge connectivity

C=patchConnectivity(F,V,'ee')

C = 

  struct with fields:

    edge: [1×1 struct]

Request both the edge-edge connectivity and the face-face connectivity

C=patchConnectivity(F,V,{'ee','ff'})

C = 

  struct with fields:

    edge: [1×1 struct]
    face: [1×1 struct]

Loop over all types and compare computation speed

conTypeSet={'all','vv','vf','ve','ev','ef','ee','fv','ff','fe'};
for q=1:1:numel(conTypeSet)
    tic
    C=patchConnectivity(F,V,conTypeSet{q});
    t=toc;
    disp([conTypeSet{q},': ',num2str(t),' seconds'])
end

all: 0.00651 seconds
vv: 0.00128 seconds
vf: 0.000399 seconds
ve: 0.000795 seconds
ev: 0.000872 seconds
ef: 0.00066 seconds
ee: 0.001145 seconds
fv: 0.000348 seconds
ff: 0.001461 seconds
fe: 0.00111 seconds

GIBBON www.gibboncode.org

Kevin Mattheus Moerman, [email protected]

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License: https://github.com/gibbonCode/GIBBON/blob/master/LICENSE

GIBBON: The Geometry and Image-based Bioengineering add-On. A toolbox for image segmentation, image-based modeling, meshing, and finite element analysis.

Copyright (C) 2019 Kevin Mattheus Moerman

This program 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.

This program 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/.

Published with MATLAB® R2019a