Harmonic Volumetric Mapping for Solid Modeling Applications
ACM Solid and Physical Modeling
Xin Li, Xiaohu Guo, Hongyu Wang, Ying He,Xianfeng Gu, Hong Qin
Harmonic volumetric mapping for two solid objects establishes a
one-to-one smooth correspondence between them. It nds its applications
in shape registration and analysis, shape retrieval, information
reuse, and material/texture transplant. In sharp contrast
to harmonic surface mapping techniques, little research has been
conducted for designing volumetric mapping algorithms due to its
technical challenges. In this paper, we develop an automatic and effective
algorithm for computing harmonic volumetric mapping between
two models of the same topology. Given a boundary mapping
between two models, the volumetric (interior) mapping is derived
by solving a linear system constructed from a boundary method
called the fundamental solution method. The mapping is represented
as a set of points with different weights in the vicinity of
the solid boundary. In a nutshell, our algorithm is a true meshless
method (with no need of specic connectivity) and the behavior of
the interior region is directly determined by the boundary. These
two properties help improve the computational efciency and robustness.
Therefore, our algorithm can be applied to massive volume
data sets with various geometric primitives and topological
types. We demonstrate the utility and efcacy of our algorithm in
shape registration, information reuse, deformation sequence analysis,
tetrahedral remeshing and solid texture synthesis.