# interp1_ND

Below is a demonstration of the features of the interp1_ND function

## Syntax

[Yi]=interp1_ND(X,Y,Xi,interpDim,interpMethod);

## Description

The interp1_ND function is similar to interp1. However it can perform 1D interpolation for multidimensional arrays. E.g. Time interpolation for 3D image data varying in time. The direction of interpolation is specified by interpDim, and the method by interpMethod ('nearest','linear','cubic','pchip').

## Examples

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

PLOT SETTINGS

```fontSize=15;
markerSize=30;
lineWidth=2;
```

## Example: Using interp1_ND for 1D arrays (similar to interp1 function)

Creating a basic example curve

```n=15;
f=3;
x=linspace(0,2*pi,n);
y=sin(f*x);
y(x>=1.5*pi)=-2;
y(x<=0.5*pi)=-2;
```

Interpolate Using interp1_ND_ND

```ni=n*10;
xi=linspace(min(x(:)),max(x(:)),ni);
interpDim=2;
yi_1 = interp1_ND(x,y,xi,interpDim,'nearest');
yi_2 = interp1_ND(x,y,xi,interpDim,'linear');
yi_3 = interp1_ND(x,y,xi,interpDim,'cubic');
yi_4 = interp1_ND(x,y,xi,interpDim,'pchip');
```
```cFigure;
subplot(2,2,1); hold on;
title('nearest','FontSize',fontSize);
xlabel('X','FontSize',fontSize);ylabel('Y','FontSize',fontSize);
plot(x,y,'k.','markerSize',markerSize);
plot(xi,yi_1,'r-','lineWidth',lineWidth);
axis tight; axis equal; box on; grid on;

subplot(2,2,2); hold on;
title('linear','FontSize',fontSize);
xlabel('X','FontSize',fontSize);ylabel('Y','FontSize',fontSize);
plot(x,y,'k.','markerSize',markerSize);
plot(xi,yi_2,'g-','lineWidth',lineWidth);
axis tight; axis equal; box on; grid on;

subplot(2,2,3); hold on;
title('cubic','FontSize',fontSize);
xlabel('X','FontSize',fontSize);ylabel('Y','FontSize',fontSize);
plot(x,y,'k.','markerSize',markerSize);
plot(xi,yi_3,'b-','lineWidth',lineWidth);
axis tight; axis equal; box on; grid on;

subplot(2,2,4); hold on;
title('pchip','FontSize',fontSize);
xlabel('X','FontSize',fontSize);ylabel('Y','FontSize',fontSize);
plot(x,y,'k.','markerSize',markerSize);
plot(xi,yi_4,'y-','lineWidth',lineWidth);
axis tight; axis equal; box on; grid on;

drawnow;
```

## Example: Using interp1_ND for 2D arrays

Creating a basic 2D array example set

```siz1=10;
xRange=linspace(0,2*pi,n);
X=xRange(ones(1,siz1),:);

Y=sin(f*X);
Y(X>=1.5*pi)=-2;
Y(X<=0.5*pi)=-2;
```

Interpolate using interp1_ND

```xRange=linspace(0,2*pi,ni);
Xi=xRange(ones(1,size(X,1)),:);

interpMethod='cubic';
interpDim=2;
Yi = interp1_ND(X,Y,Xi,interpDim,interpMethod);
```
```x=X(1,:);
y=Y(1,:);
xi=Xi(1,:);
yi=Yi(1,:);
cFigure; hold on;
title('Using interp1_ND for 2D arrays','FontSize',fontSize,'Interpreter','none');
xlabel('X','FontSize',fontSize);ylabel('Y','FontSize',fontSize);

plot(x,y,'k.','markerSize',markerSize);
plot(xi,yi,'b.-','markerSize',markerSize/3);
axis tight; axis equal; box on; grid on;
drawnow;
```

## Example: Using interp1_ND for 3D arrays

```interpDim=1;
siz=50*ones(1,3);%.*ones(1,nDim);
siz(interpDim)=n;

xRange=linspace(0,2*pi,n);
switch interpDim
case 1
[X,~,~]=ndgrid(xRange,1:siz(2),1:siz(3));
case 2
[~,X,~]=ndgrid(1:siz(1),xRange,1:siz(3));
case 3
[~,~,X]=ndgrid(1:siz(1),1:siz(2),xRange);
end

Y=sin(f*X);
Y(X>=1.5*pi)=-2;
Y(X<=0.5*pi)=-2;
```

Interpolate using interp1_ND

```xRange=linspace(0,2*pi,ni);
switch interpDim
case 1
[Xi,~,~]=ndgrid(xRange,1:size(X,2),1:size(X,3));
case 2
[~,Xi,~]=ndgrid(1:size(X,1),xRange,1:size(X,3));
case 3
[~,~,Xi]=ndgrid(1:size(X,1),1:size(X,2),xRange);
end

interpMethod='cubic';
Yi = interp1_ND(X,Y,Xi,interpDim,interpMethod);
```
```switch interpDim
case 1
xi=squeeze(Xi(:,1,1));
yi=squeeze(Yi(:,1,1));
case 2
xi=squeeze(Xi(1,:,1));
yi=squeeze(Yi(1,:,1));
case 3
xi=squeeze(Xi(1,1,:));
yi=squeeze(Yi(1,1,:));
end

cFigure; hold on;
title('Using interp1_ND for 3D arrays','FontSize',fontSize,'Interpreter','none');
xlabel('X','FontSize',fontSize);ylabel('Y','FontSize',fontSize);

plot(x,y,'k.','markerSize',markerSize);
plot(xi,yi,'b.-','markerSize',markerSize/3);
axis tight; axis equal; box on; grid on;
drawnow;
```

## The above generalizes for higher dimensions

GIBBON www.gibboncode.org

Kevin Mattheus Moerman, gibbon.toolbox@gmail.com

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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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