Interpolation of 3D surface

Hi!

I have a data set in 3D, say x, y and z. I need to use these data points and fit/interpolate a 3D surface, I have used griddata, triscatteredinterp and interp2 but no method seems to work (as I would like). When I plot the data points and the constructed surface they don't fit, the data points seems to be ignored.

Is there another, a better way to do this? Please, let me know if you need more information or the data set.

Thanks in advance, Catarina

[Matt Tearle]

The functions you mentioned are the right ones for fitting in 3-D. Can you show the code you've tried?

[Catarina]

Hi Matt,

I think the problem is within my data and use of function rather than code problem. The code is working but is not producing what I need.

//Catarina

Answer 1

[John D'Errico]

Often this is really a problem of misuse. Those tools are designed for direct functional relationships, which could in theory be written as z = f(x,y), but where the function f is unknown. However, usually when I see this type of comment, that the interpolant failed to work, the person was trying to represent some multi-valued surface as a function. Thus, you cannot fit the surface of a sphere as a function, f(x,y).

At other times, the user tries to fit a surface to data that does not support a full surface. For example can you fit a surface to the data

x = 1:10; y = x; y = x + y;

NO!!!!!!!! This data lives on a line. It is insufficient to define a complete surface.

Next, if the data REALLY does represent a valid surface to be modeled, then the problem may be an issue of a surface that a triangulation deals poorly with. Perhaps the data represents a non-convex domain, or the user wants to extrapolate, or any of a variety of problems.

In order to know what is your problem, we need to see the data, to see what you tried. We cannot know what you would like without more help from you.

[Catarina]

Hi John,

Thanks for your reply. I might be misusing the functions.

I have a set of pareto optimal solutions from a multi objective optimization and I need to fit a 3D surface to this data, which should belong to a convex domain. If you have the time I would definitely appreciate if you could have a look at it. The data set is rather small (might be a problem) so I can email it to you, ok?

Thanks, Catarina

[John D'Errico]

Yes, you may send me the data to look at. It is best if you send me the actual data, rather than just a plot of it anyway, as then I may be able to offer several choices of how you might build a surface.

[Nelson Ribeiro]

Hello. I have the same problem. I have a set of pareto optimal solutions obtained from solving a multi objective optimization problem and I want to fit a 3D surface to the points. Catarina could you tell me any hints on how did you solved this problem?

Answer 2

[Swathi Chandrasekar]

I may have had a similar problem.If x,y and z are arrays then plot them using plot3 to see what they look like.If it looks like they lie on a surface then interpolate using fit function.