A new Projection Method for Point Set Surfaces

Abstract

A successful approach in triangulating point set surfaces is to apply operations, like a projection operator for advancing front algorithms, directly to Moving-Least Squares (MLS) surfaces. The MLS method naturally handles noisy input data and is especially useful for point clouds derived from real-world solids. Unfortunately, MLS is computationally extensive and complex. We present a novel projection method that does not require solving a nonlinear optimization problem as MLS does. We create a polynomial approximation of the surface similar to MLS but our method adapts the degree of the polynomial with respect to the points to be approximated. The approximated points are iteratively collected compromising connectivity information. We enhance the orientation of the local coordinate system to further improve the method. The results confirm that our method is more robust and also accelerates triangulation due to a preprocessing step that needs to be done only once per data set.