Issue No. 05 - May (2012 vol. 18)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2011.102
Kexiang Wang , Dept. of Comput. Sci., Stony Brook Univ., Stony Brook, NY, USA
Xin Li , Dept. of Electr. & Comput. Eng., Louisiana State Univ., Baton Rouge, LA, USA
Bo Li , Dept. of Comput. Sci., Stony Brook Univ., Stony Brook, NY, USA
Huanhuan Xu , Dept. of Electr. & Comput. Eng., Louisiana State Univ., Baton Rouge, LA, USA
Hong Qin , Dept. of Comput. Sci., Stony Brook Univ., Stony Brook, NY, USA
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 T-splines, 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/patching/merging. 2) They have guaranteed semistandardness so that the functions and derivatives evaluation is very efficient. 3) Their restricted support regions of blending functions prevent control points from influencing other nearby domain regions that stay opposite to the immediate boundaries. These features are highly desirable for certain applications such as isogeometric analysis. We conduct extensive experiments on converting complicated solid models into RTP-splines, and demonstrate the proposed spline to be a powerful and promising tool for volumetric modeling and other scientific/engineering applications where data sets with multiattributes are prevalent.
splines (mathematics), solid modelling, isogeometric analysis, volumetric data modeling, RTP-splines scheme, restricted trivariate polycube splines scheme, trivariate T-splines, tensor-product B-splines, polycube structure, parametric domain, strictly bounds blending function, space filling, bounding volume, anchor points, local refinement, exterior cell removal, anchors removal, one-piece continuous representation, domain trimming, domain patching, domain merging, blending function, Splines (mathematics), Solid modeling, Solids, Surface reconstruction, Surface topography, Computational modeling, polycube mapping., Trivariate splines, polycube splines
Bo Li, Xin Li, Kexiang Wang, Huanhuan Xu and Hong Qin, "Restricted Trivariate Polycube Splines for Volumetric Data Modeling," in IEEE Transactions on Visualization & Computer Graphics, vol. 18, no. , pp. 703-716, 2012.