Interpolation of 3D point data

Hello, I have a nx5 matrix where column 3, 4 and 5 are x,y,z 3D points respectively. I was wondering how I would interpolate (smooth) this 3D data. Many thanks

[Stephen23]

Do you want to interpolate, or to smooth the data? These are two quite different operations.

[shellmcg]

Hi Stephen, I mean interpolate, construct new data points to construct a smooth curve running through the already established 3D data points. Thanks

[Walter Roberson]

What properties does the curve need to have? Are you looking for a spline fit? A pchip fit?

[shellmcg]

Hi Walter, I was looking at a spline fit.

Answer 1

[John D'Errico]

You can use my interparc tool, as found on the file exchange. It is designed to solve exactly this problem, in 2 or more dimensions.

   xyz = interparc(1000,x,y,z,'spline');

xyz will be a 1000x3 array, where each row is an interpolated point on the curve.

Of course, you can do the interpolation in other ways. If you want to do the work in MATLAB yourself in much the same way as you tried to do it:

t = [0;cumsum(sqrt(diff(x).^2+diff(y).^2+diff(z).^2))];
t = t/t(end);

ti = linspace(0,1,1000);
xx = spline(t,x,ti);
yy = spline(t,y,ti);
zz = spline(t,z,ti);

The above solution, which uses a cumulative piecewise linear arclength as the parameter for interpolation, deals more properly with points that are not uniformly spaced.

Answer 2

[Walter Roberson]

See http://www.mathworks.com/help/matlab/scattered-data-interpolation.html

It looks to me as if you likely want a scattered interpolant.

[shellmcg]

No I am asked to do a spline fit. Any suggestions?

This is all I got with errors

xx=linspace(matrix(1,3),matrix(end,3),1000);
yy = spline(matrix(:,3),matrix(:,4),xx);
zz = spline(matrix(:,3),matrix(:,5),xx);

Thanks

[Adam Danz]

Updated link:

https://www.mathworks.com/help/matlab/math/interpolating-scattered-data.html

Answer 3

[shellmcg]

Figured this Question out

Inter_p= linspace(1,length(Data),1000); %create a array of points within the length of the data
xx=spline(1:length(Data),x,Inter_p); % use points created above to interpolate x,y,and z
yy=spline(1:length(Data),y,Inter_p);
zz=spline(1:length(Data),z,Inter_p);

[John D'Errico]

I'm sorry, but this answer is just a poor way of solving the problem, presuming the points are somehow equally spaced. Use of a spline as was done here can cause some strange artifacts.