User-controllable Polycube Map for Manifold Spline Construction
ACM Solid and Physical Modeling 2008
Hongyu Wang, Miao Jin, Ying He, Xianfeng Gu, Hong Qin
Polycube T-spline has been formulated elegantly that can unify Tsplines
and manifold splines to define a new shape representation
for surfaces of arbitrary topology by using polycube map as its
parametric domain. Naturally, The data fitting quality using polycube
T-splines hinges on the construction of underlying polycube
maps. However, existing methods for polycube map construction
exhibit some disadvantages. For example, existing approaches for
polycube map construction either require projection of points from
a 3D surface to its polycube approximation, which is therefore very
difficult to handle the cases when two shapes differ significantly; or
compute the map by conformally deforming the surfaces and polycubes
to the common canonical domain and then construct the map
using function composition, which is challenging to control the location
of singularities and makes it hard for the data-fitting and
hole-filling processes later on.
This paper proposes a novel framework of user-controllable polycube
maps, which can overcome the disadvantages of the conventional
methods and is much more efficient and accurate. The current
approach allows users to directly select the corner points of the
polycubes on the original 3D surfaces, then construct the polycube
maps by using the new computational tool of discrete Euclidean
ricci flow. We develop algorithms for computing such polycube
maps, and show that the resulting user-controllable polycube map
serves as an ideal parametric domain for constructing spline surfaces
and other applications. The location of singularities can be
interactively placed where no important geometric features exist.
Experimental results demonstrate that the manifold splines built
upon the proposed polycube maps can achieve the same fitting accuracy
by using much fewer control points, and subsequently make
the entire hole filling process much easier to accomplish.