interp1_ND

Below is a demonstration of the features of the interp1_ND function

Contents

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, [email protected]