Ecien t Triangulation of Point Clouds Using Floater Parameterization

A method for constructing 3D triangulations of scanned 3D point data has been introduced by Floater et al.. First, a 2D parameteriz- ation of the points is computed and triangulated. The 3D triangu- lation is obtained directly from the 2D triangulation. This method requires an ordered boundary of the point cloud, and the computa- tion of the 2D parameterization requires the solution of a large linear system. In this paper we present an ecien t boundary estimation algorithm, and we compare various approaches to solve the linear system. We show that, after an appropriate reordering of the mat- rix, the system can be solved very ecien tly using a direct sparse solver.