CGAL 3D Function Interpolation

Question

In the CGAL manual, it says here:

Scattered data interpolation solves the following problem: given measures of a function on a set of data points, the task is to interpolate this function on an arbitrary query point. More formally, let P={p1,…,pn} be a set of n points in R2 or R3 and Φ be a scalar function defined on the convex hull of P. We assume that the function values are known at the points of P, i.e. to each pi∈P, we associate zi=Φ(pi).

Then it proceeds to show examples, but the closest example to interpolation in 3D that I find is the example, Interpolation/surface_neighbor_coordinates_3.cpp. As far as I can tell, this only finds the neighbor vertices of a point.

Is there a subsequent step that I can take to find the interpolated function value at an arbitrary query point in 3D? (Specifically, over a sphere?)

Answer 1

In the same page you quote, at the section "3 Interpolation Methods", there is the description of interpolation methods, with two examples. It is probably what you are looking for. You would have to adapt those examples to 3D, though.