Multi-level hermite variational interpolation and quasi-interpolation

Abstract

Based on the Hermite variational implicit surface reconstruction presented in Pan et al. (Science in China Series F: Information Sciences 52(2):308---315, 2009), we propose a multi-level interpolation method to overcome the problems resulted from using compactly supported radial basis functions (CSRBFs). In addition, we present a multi-level quasi-interpolation method which directly uses normal vectors to construct non-zero constraints and avoids solving any linear system, a common step of variational surface reconstruction, and leads to a fast and stable surface reconstruction from scattered points. With adaptive support size, our approach is robust and can successfully reconstruct surfaces on non-uniform and noisy point sets. Moreover, as the computation of quasi-interpolation is independent for each point, it can be easily parallelized on multi-core CPUs.