Restricted Trivariate Polycube Splines for Volumetric Data Modeling

—This paper presents a volumetric modeling framework to construct a novel spline scheme called restricted trivariate polycube splines (RTP-splines). The RTP-spline aims to generalize both trivariate T-splines and tensor-product B-splines; it uses solid polycube structure as underlying parametric domains and strictly bounds blending functions within such domains. We construct volumetric RTP-splines in a top-down fashion in four steps: 1) Extending the polycube domain to its bounding volume via space filling; 2) building the B-spline volume over the extended domain with restricted boundaries; 3) inserting duplicate knots by adding anchor points and performing local refinement; and 4) removing exterior cells and anchors. Besides local refinement inherited from general Tsplines, the RTP-splines have a few attractive properties as follows: 1) They naturally model solid objects with complicated topologies/ bifurcations using a one-piece continuous representation without domain trimming/pat...

• Type: Journal
• Year: 2012
• Where: TVCG
• Authors: Kexiang Wang, Xin Li, Bo Li 0014, Huanhuan Xu, Hong Qin
• Keywords: Anchor Points, B Spline, Hardware, Tensor Product, TVCG 2012