# grid2patch

Below is a demonstration of the features of the grid2patch function

## Contents

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

## Syntax

[F,V,C]=grid2patch(X,Y,Z,C,perdiocOpt);

## Description

This function generates patch data for gridded surface coordinates defined by X,Y,Z (e.g. as produced by functions like meshgrid or ndgrid). Optional inputs include the color data C (a color for each vertex), perdiocOpt (a 1x2 logic) which sets periodicity of the surface in the first or second direction. Similar to MATLAB's surf2patch function (which does not include periodic connectivity).

## Examples

Plot settings

```cMap=gjet(250);
fontSize=15;
```

## Example: Converting gridded surface data to patch data

```[X,Y]=ndgrid(linspace(0,2*pi,25));
Z=sin(X)+sin(Y);
```

Creating patch data for the cylinger

```[F,V,C]=grid2patch(X,Y,Z,Z);
```

Visualizing outputs

```cFigure; hold on;
gpatch(F,V,C,'k');
drawnow;
```

## Example: periodicity in direction 1

```n=12;
t=linspace(-pi,pi,n+1);
t=t(1:end-1);
v1=[cos(t(:)) sin(t(:)) zeros(size(t(:))) ];
v2=3*v1;

%Get coordinate matrices
m=5;
X=linspacen(v1(:,1),v2(:,1),m);
Y=linspacen(v1(:,2),v2(:,2),m);
Z=linspacen(v1(:,3),v2(:,3),m);

%Collect node set
VN=[X(:) Y(:) Z(:)];
numSteps=n-1;
```

Creating patch data for the cylinger

```[F1,V1]=grid2patch(X,Y,Z,[],[0 0]); %Not periodic
[F2,V2]=grid2patch(X,Y,Z,[],[1 0]); %Periodic in first direction
```

Visualizing outputs

```cFigure;
subplot(1,2,1); hold on;
title('Not periodic')
gpatch(F1,V1,'bw','k');
gpatch(patchBoundary(F1,V1),V1,'none','r',1,3);

subplot(1,2,2); hold on;
title('Periodic in 1st direction')
gpatch(F2,V2,'bw','k');
gpatch(patchBoundary(F2,V2),V2,'none','r',1,3);
drawnow;
```

## Example: periodicity in direction 2

Creating an example of a cylinder

```t=linspace(-pi,pi,25);
t=t(1:end-1);
[T,Z]=meshgrid(t,linspace(0,1,5));

[X,Y]=pol2cart(T,ones(size(T)));
```

Creating patch data for the cylinger

```[F1,V1,C1]=grid2patch(X,Y,Z,T,[0 0]); %Not periodic
[F2,V2,C2]=grid2patch(X,Y,Z,T,[0 1]); %Periodic in first direction
```

Visualizing outputs

```cFigure;
subplot(1,2,1); hold on;
title('Not periodic')
gpatch(F1,V1,C1,'k');
gpatch(patchBoundary(F1,V1),V1,'none','r',1,3);

subplot(1,2,2); hold on;
title('Periodic in 2nd direction')
gpatch(F2,V2,C2,'k');
gpatch(patchBoundary(F2,V2),V2,'none','r',1,3);
drawnow;
```

## Example: periodicity in both directions

Creating an example of a cylinder

```n=12; m=25;
t=linspace(-pi,pi,n+1);
t=t(1:end-1);
v=[cos(t(:)) zeros(size(t(:))) sin(t(:))];
v(:,1)=v(:,1)+3;

a=linspace(0,2*pi,m+1); a=a(1:end-1);
X=zeros(n,m);
Y=zeros(n,m);
Z=zeros(n,m);

for q=1:1:m
R=euler2DCM([0 0 a(q)]);
vr=v*R;
X(:,q)=vr(:,1);
Y(:,q)=vr(:,2);
Z(:,q)=vr(:,3);
end
```

Creating patch data for the cylinger

```[F1,V1,C1]=grid2patch(X,Y,Z,Z,[0 0]); %Not periodic
[F2,V2,C2]=grid2patch(X,Y,Z,Z,[0 1]); %Periodic in first direction
[F3,V3,C3]=grid2patch(X,Y,Z,Z,[1 0]); %Periodic in second direction
[F4,V4,C4]=grid2patch(X,Y,Z,Z,[1 1]); %Periodic both directions
```

Visualizing outputs

```cFigure;
subplot(2,2,1); hold on;
title('Not periodic')
gpatch(F1,V1,C1,'k');
gpatch(patchBoundary(F1,V1),V1,'none','r',1,3);

subplot(2,2,2); hold on;
title('Periodic in 1st direction')
gpatch(F2,V2,C2,'k');
gpatch(patchBoundary(F2,V2),V2,'none','r',1,3);

subplot(2,2,3); hold on;
title('Periodic in 2nd direction')
gpatch(F3,V3,C3,'k');
gpatch(patchBoundary(F3,V3),V3,'none','r',1,3);

subplot(2,2,4); hold on;
title('Periodic in 1st and 2nd direction')
gpatch(F4,V4,C4,'k');
gpatch(patchBoundary(F4,V4),V4,'none','r',1,3);

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

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