Polycube Splines
ACM Solid and Physical Modeling
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.