Interpolation of 3D point data

Question

shellmcg 2016-4-19

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评论： Adam Danz 2019-12-19

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

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Walter Roberson 2016-4-20

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

shellmcg 2016-4-20

Hi Walter, I was looking at a spline fit.

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Answer 1

John D'Errico 2016-4-29

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编辑：John D'Errico 2016-4-29

在 MATLAB Online 中打开

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.

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Answer 2

Walter Roberson 2016-4-20

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

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

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shellmcg 2016-4-22

编辑：Walter Roberson 2016-4-22

在 MATLAB Online 中打开

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 2019-12-19

Updated link:

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

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Answer 3

shellmcg 2016-4-28

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在 MATLAB Online 中打开

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);

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John D'Errico 2016-4-28

编辑：John D'Errico 2016-4-29

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.

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