Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
441202 | Computer Aided Geometric Design | 2012 | 13 Pages |
Radial Basis Function (RBF) has been used in surface reconstruction methods to interpolate or approximate scattered data points, which involves solving a large linear system. The linear systems for determining coefficients of RBF may be ill-conditioned when processing a large point set, which leads to unstable numerical results. We introduce a quasi-interpolation framework based on compactly supported RBF to solve this problem. In this framework, implicit surfaces can be reconstructed without solving a large linear system. With the help of an adaptive space partitioning technique, our approach is robust and can successfully reconstruct surfaces on non-uniform and noisy point sets. Moreover, as the computation of quasi-interpolation is localized, it can be easily parallelized on multi-core CPUs.
► This research introduces a quasi-interpolation method for fitting Radial Basis Functions (RBFs) onto scattered points. ► This method avoids solving large linear systems which may be ill-conditioned.