  We introduce a geometric stencil selection algorithm for Laplacian in 3D that
significantly improves octant-based selection considered earlier. The goal of
the algorithm is to choose a small subset from a set of irregular points
surrounding a given point that admits an accurate numerical differentiation
formula. The subset serves as an influence set for the numerical approximation
of the Laplacian in meshless finite difference methods using either polynomial
or kernel-based techniques. Numerical experiments demonstrate a competitive
performance of this method in comparison to the finite element method and to
other selection methods for solving the Dirichlet problems for the Poisson
equation on several STL models. Discretization nodes for these domains are
obtained either by 3D triangulations or from Cartesian grids or Halton
quasi-random sequences.
