Polycube Splines
Computer-Aided Design (CAD) 2008
Hongyu Wang, Ying He, Xin Li, Xianfeng Gu,Hong Qin
This paper proposes a new concept of polycube splines and develops novel modeling techniques for using the polycube splines in solid modeling
and shape computing. Polycube splines are essentially a novel variant of manifold splines which are built upon the polycube map, serving as
its parametric domain. Our rationale for defining spline surfaces over polycubes is that polycubes have rectangular structures everywhere over
their domains except a very small number of corner points. The boundary of polycubes can be naturally decomposed into a set of regular
structures, which facilitate tensor-product surface definition, GPU-centric geometric computing, and image-based geometric processing. We
develop algorithms to construct polycube maps, and show that the introduced polycube map naturally induces the affine structure with a finite
number of extraordinary points. Besides its intrinsic rectangular structure, the polycube map may approximate any original scanned data-set
with a very low geometric distortion, so our method for building polycube splines is both natural and necessary, as its parametric domain
can mimic the geometry of modeled objects in a topologically correct and geometrically meaningful manner. We design a new data structure
that facilitates the intuitive and rapid construction of polycube splines in this paper. We demonstrate the polycube splines with applications in
surface reconstruction and shape computing.