Toward high-performance computation of surface approximation using a GPU

Recent progress in high-performance computing architectures enables performance enhancements in many fields. One of the most important applications of this enhancement is surface approximation from a set of points. In this research, we propose a technique for constructing a surface approximating an oriented set of samples that is fully supported on graphical processing units (GPUs). The proposed algorithm follows the implicit characterization framework. The algorithm transforms the input samples into an implicit surface that can be extracted using traditional marching cube techniques. Moreover, our approach benefits from the divide-and-conquer strategy in converting the global Poisson problem formulation into smaller independent subproblems. This division enables parallelization of the solutions of these independent sub-problems that can be run completely on a GPU. Additionally, we propose an enhanced mathematical formulation of the Poisson problem using a k-dimensional tree (kd-tree) and tetrahedral quadratic elements such that the input points have a greater contribution in solving the local Poisson problems. Finally, we present experiments that demonstrate the efficiency of our proposed approach.