# tri2rhombi

Below is a demonstration of the features of the tri2rhombi function

## Contents

clear; close all; clc;

## Syntax

[Ft,Vt,Ct]=tri2rhombi(F,V,C);

## Description

This function refines the surface region defined by the logic logicFaces, belonging to the surface given by the faces F and vertices V. The region is refined by: 1) taking the dual tesselation, 2) retriangulating the dual mesh to include the original points.

The input consists of: F: the faces V: the vertices logicFaces: A logic for the faces requiring refinement C: color data on either the faces or the vertices

The ouput can consist of: FT: Faces VT: Vertices C_type: Color/label for triangle type, i.e. original (1), refined (2), or boundary (3) indIni: Indices for original points C_new: New color data for faces or vertices

## Examples

Plot settings

fontSize=15;
cMap=gjet(4);
faceAlpha=0.5;
plotColor1=cMap(1,:);
plotColor2=cMap(2,:);
plotColor3=cMap(4,:);
faceColor1=0.5*ones(1,3);
edgeWidth=1;
markerSize=25;

## Example: Converting triangles to rhombi (quads)

Building example geometry

[F,V]=graphicsModels(9);

Refine surface region using tri2rhombi

[Ft,Vt]=tri2rhombi(F,V);
%Plotting results
cFigure;
subplot(1,2,1); hold on;
title('Original','FontSize',fontSize);
gpatch(F,V,'rw','k',1,edgeWidth);
axisGeom(gca,fontSize);
view(0,0); zoom(2);
axis off;

subplot(1,2,2); hold on;
title('Rhombi','FontSize',fontSize);
gpatch(Ft,Vt,'gw','k',1,edgeWidth);
axisGeom(gca,fontSize);
view(0,0); zoom(2);
axis off;
drawnow;

## Example: Converting triangles to rhombi on a non-closed surface

Building example geometry

%Defining geodesic dome
n=1; %Refinements
[F,V,~]=hemiSphereMesh(n,r,0);

Refine surface region using tri2rhombi

[Ft,Vt]=tri2rhombi(F,V);
%Plotting results
cFigure;
subplot(1,2,1); hold on;
title('Original','FontSize',fontSize);
gpatch(F,V,'rw','k',1,edgeWidth);
axisGeom(gca,fontSize);
axis off;

subplot(1,2,2); hold on;
title('Rhombi','FontSize',fontSize);
gpatch(Ft,Vt,'gw','k',1,edgeWidth);
axisGeom(gca,fontSize);
axis off;
drawnow;

GIBBON www.gibboncode.org

Kevin Mattheus Moerman, [email protected]

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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/.