# regionTriMesh2D

Below is a basic demonstration of the features of the regionTriMesh2D function.

## Contents

```clear; close all; clc;
```

## CREATING A REGION MESH

Creating boundary curves

```V1=[-1 -1; -1 1; 1 1; 1 -1];
```

Meshing the region

```% The input variable regionCell is a cell array containing all the boundary
% curves, e.g. for a two curve region 1 we would have something like
% regionSpec{1}={V1,V2} where V1 and V2 are the boundary curves. Multiple
% curves may be given here. The first curve should form the outer boundary
% of the entire region, the curves that follow should define holes inside
% this boundary and the space inside them is therefore not meshed.

%Defining a region
regionCell={V1}; %A region between V1 and V2 (V2 forms a hole inside V1)

plotOn=1; %This turns on/off plotting

%Desired point spacing
pointSpacing=0.1;

[F,V]=regionTriMesh2D(regionCell,pointSpacing,1,plotOn);
plotV(V1,'b-','LineWidth',2);
axis tight;
drawnow;
``` ## CREATING A REGION MESH WITH HOLES

Creating boundary curves

```%Boundary 1
ns=150;
t=linspace(0,2*pi,ns);
t=t(1:end-1);
r=6+2.*sin(5*t);
[x,y] = pol2cart(t,r);
V1=[x(:) y(:)];

%Boundary 2
[x,y] = pol2cart(t,ones(size(t)));
V2=[x(:) y(:)+4];

%Boundary 3
[x,y] = pol2cart(t,2*ones(size(t)));
V3=[x(:) y(:)-0.5];
```

Meshing the region

```% The input variable regionCell is a cell array containing all the boundary
% curves, e.g. for a two curve region 1 we would have something like
% regionSpec{1}={V1,V2} where V1 and V2 are the boundary curves. Multiple
% curves may be given here. The first curve should form the outer boundary
% of the entire region, the curves that follow should define holes inside
% this boundary and the space inside them is therefore not meshed.

%Defining a region
regionCell={V1,V2,V3}; %A region between V1 and V2 (V2 forms a hole inside V1)

plotOn=1; %This turns on/off plotting

%Desired point spacing
pointSpacing=0.5;

[F,V]=regionTriMesh2D(regionCell,pointSpacing,1,plotOn);
plotV(V1,'b-','LineWidth',2);
plotV(V2,'b-','LineWidth',2);
plotV(V3,'b-','LineWidth',2);
axis tight;
drawnow;
``` ## CREATING A REGION MESH WITH HOLES

Creating boundary curves

```%Boundary 1
ns=10000;
t=linspace(0,2*pi,ns);
t=t(1:end-1);
r=5;
a=2;
R=r-(a.*cos(7*(t-pi).^2)-a);
[x,y] = pol2cart(t,R);
V1=[x(:) y(:)];

%Boundary 2
[x,y] = pol2cart(t,(0.75*r)*ones(size(t)));
V2=[x(:) y(:)];
```

Meshing the region

```% The input variable regionCell is a cell array containing all the boundary
% curves, e.g. for a two curve region 1 we would have something like
% regionSpec{1}={V1,V2} where V1 and V2 are the boundary curves. Multiple
% curves may be given here. The first curve should form the outer boundary
% of the entire region, the curves that follow should define holes inside
% this boundary and the space inside them is therefore not meshed.

%Defining a region
regionCell={V1,V2}; %A region between V1 and V2 (V2 forms a hole inside V1)

plotOn=1; %This turns on/off plotting

%Desired point spacing
pointSpacing=0.25;

[F,V]=regionTriMesh2D(regionCell,pointSpacing,1,plotOn);
plotV(V1,'b-','LineWidth',2);
plotV(V2,'b-','LineWidth',2);
axis tight;
drawnow;
``` ```[F,V,boundaryInd]=regionTriMesh2D(regionCell,pointSpacing,1,plotOn);

cFigure; hold on;
gpatch(F,V,'gw');
plotV(V(boundaryInd,:),'b.','markerSize',25);
axisGeom;
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.

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You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.