We consider a surface reconstruction problem from geometrical points (i.e., points given without any order) distributed on a series of smooth parallel cross sections in ${mathbb{R}}^3$. To solve the problem, we utilize the natural points ordering method in ${mathbb{R}}^2$, described in [18], which is a method of reconstructing a curve from a set of sample points and is based on the concept of diffusion motions of a small object from one point to the other point. With only the information of the positions of these geometrical points, we construct an acceptable surface consisting of triangular facets using a heuristic algorithm to link a pair of parallel cross-sections constructed via the natural points ordering method. We show numerical simulations for the proposed algorithm with some sets of sample points.