Rational Spherical Splines For Genus Zero Shape Modeling
Ying He, Xianfeng Gu and Hong Qin
Proceedings of IEEE International Conference on Shape Modeling and Applications 2005
Traditional approaches for modeling a closed manifold
surface with either regular tensor-product or triangular
splines (defined over an open planar domain) require decomposing
the acquired geometric data into a group of
charts, mapping each chart to a planar parametric domain,
fitting an open surface patch of certain degree to each chart,
and finally, trimming the patches (if necessary) and stitching
all of them together to form a closed manifold. In this
paper, we develop a novel modeling method which does not
need any cutting or patching operations for genus zero surfaces.
Our new approach is founded upon the concept of
spherical splines proposed by Pfeifle and Seidel. Our work
is strongly inspired by the fact that, for genus zero surfaces,
it is both intuitive and necessary to employ spheres as
their natural domains. Using this framework, we can convert
genus zero mesh to a single rational spherical spline
whose maximal error deviated from the original data is less
than a user-specified tolerance. With the rational spherical
splines, we can model sharp features and edit both the
global shape and the local details with ease. Furthermore,
we can accurately compute the differential quantities without
resorting to any numerical approximations. We conduct
several experiments in order to demonstrate the efficacy of
our approach for reverse engineering, shape modeling, and
interactive graphics.