How can I interpolate points in 3D space?

Question

I have 3D space. And I know for example N points in this space (x1,y1,z1), (x2,y2,z2)..., (xn,yn,zn). I want to interplolate points, that is different from this. How can I do this in Matlab?

Answer 1

As always, there are questions left unanswered by your one line query.

If the data is of the form where there is a functional relationship z(x,y), (or y(x,z) or x(y,z)) then you might potentially be able to use one of the interpolation tools. Thus, suppose you have data that lies on a lattice in the (x,y) plane, thus some value of z at each point in that lattice. In this case, you can use interp2.

Alternatively, if the data is scattered, but there is some single valued functional relationship z(x,y) that you don't have, but it is some continuous function. Infinite first derivatives are a problem too here. In this case, assuming that you have data that at least fills some convex domain in the (x,y) plane, you can still interpolate a value of z. For this, use griddata, or TriScatteredInterp. Or you might use my own gridfit tool, as found on the file exchange.

Next, the way you describe the data, I'm not at all positive that you have something in one of the above forms. For example, if your data lies along some curved path in this 3D domain, and you wish to interpolate points along that curved arc can be done using my interparc tool, also found on the file exchange.

One last case that people often seem to have when they talk about interpolation of a spatial set like this, is just a general surface, that they wish to build a neatly interpolated, smooth surface. It might be something as simple as the surface of a sphere, or something wildly more complex. (These things are never simple.) For this, you might be able to use a convex hull to approximate something, if it is a closed convex surface. More complex surfaces might require a tool like CRUST, although I have no implementation of it I can offer to you. Google will help you there, if that is what you need.

The point of all this is, how you interpolate your data depends on what form the data is in, what it represents, and the shape of the relationship you will be interpolating.

Answer 2

interp3 may help you. Here is the documentation.