# insphere

Below is a demonstration of the features of the `insphere` function

## Contents

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

## Syntax

`[R,Vc]=insphere(E,V);`

## Description

Computes the incentres Vc, and inraddi R of the inspheres for the tetrahedral input mesh defined by the element array E and the vertices V.

## Examples

Plot settings

fontSize=20; faceAlpha1=0.1;

% A tetrahedral mesh

```
boxDim=[2 2 1]; % Box dimenstions
pointSpacing=1;
[meshStruct]=tetMeshBox(boxDim,pointSpacing);
```

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- TETGEN Tetrahedral meshing --- 09-Jun-2023 16:35:48 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Writing SMESH file --- 09-Jun-2023 16:35:48 ----> Adding node field ----> Adding facet field ----> Adding holes specification ----> Adding region specification --- Done --- 09-Jun-2023 16:35:48 --- Running TetGen to mesh input boundary--- 09-Jun-2023 16:35:48 Opening /home/kevin/DATA/Code/matlab/GIBBON/data/temp/temp.smesh. --- Done --- 09-Jun-2023 16:35:48 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Importing TetGen files --- 09-Jun-2023 16:35:48 --- Done --- 09-Jun-2023 16:35:48

Acces output fields

E=meshStruct.elements; V=meshStruct.nodes; F=meshStruct.faces; Fb=meshStruct.facesBoundary; faceBoundaryMarker=meshStruct.boundaryMarker;

Compute incentres and inradii for the set of tetrahedra

[R,Vc]=insphere(E,V);

Visualise inspheres

cFigure; hold on; title('A tetrahedral mesh showing inspheres','FontSize',fontSize); hp1=gpatch(F,V,'w','k',faceAlpha1,2); [Fs,Vs]=geoSphere(2,1); for q=1:1:size(E,1) hp2=gpatch(Fs,Vs.*R(q)+Vc(q,:),'rw','none'); end legend([hp1,hp2],{'Tetrahedral mesh','inspheres'},'Location','northeastoutside'); axisGeom(gca,fontSize); camlight headlight; drawnow;

* 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) 2006-2023 Kevin Mattheus Moerman and the GIBBON contributors

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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