Efficient Reconstruction From Scattered Points

Abstract

Most algorithms that reconstruct surface from sample points rely on computationally demanding operations to derive the reconstruction, beside this, most of the classical algorithm use a kind of three-dimensional structure to derive a two-dimensional one. In this paper we introduce an innovative approach for generating two-dimensional piecewise linear approximations from sample points in R3 that simplify significantly the numerical calculation and the memory usage in the reconstruction process. The approach proposed here is an advancing front approach that uses rigid movements in the three-dimensional space and a bidimensional Delaunay triangulation as the main tools for the algorithm. The principal idea is to use a combination of rotations and translations in order to simplify the calculations and avoid the three-dimensional structure used by the most of the algorithms. Avoiding those structures, this approach can reduce the computational cost and numerical instabilities typically associated with the classical algorithm reconstructions.