Surface reconstruction using bivariate simplex splines on Delaunay configurations
Recently, a new bivariate simplex spline scheme based on Delaunay configuration has been introduced into the geometric computing community, and it defines a complete spline space that retains many attractive theoretic and computational properties. In this paper, we develop a novel shape modeling framework to reconstruct a closed surface of arbitrary topology based on this new spline scheme. Our framework takes a triangulated set of points, and by solving a linear least-square problem and iteratively refining parameter domains with newly added knots, we can finally obtain a continuous spline surface satisfying the requirement of a user-specified error tolerance. Unlike existing surface reconstruction methods based on triangular B-splines (or DMS splines), in which auxiliary knots must be explicitly added in advance to form a knot sequence for construction of each basis function, our new algorithm completely avoids this less-intuitive and labor-intensive knot generating procedure. We demonstrate the efficacy and effectiveness of our algorithm on real-world, scattered datasets for shape representation and computing. © 2009 Elsevier Ltd. All rights reserved.
Publication Source (Journal or Book title)
Computers and Graphics (Pergamon)
Cao, J., Li, X., Wang, G., & Qin, H. (2009). Surface reconstruction using bivariate simplex splines on Delaunay configurations. Computers and Graphics (Pergamon), 33 (3), 341-350. https://doi.org/10.1016/j.cag.2009.03.013