• The Journal of the Korea Contents Association
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• v.10 no.4
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• pp.106-114
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• 2010

Mesh parameterization is the process of finding one-to-one mapping between an input mesh and a parametric domain. It has been considered as a fundamental tool for digital geometric processing which is required to develop several applications of digital geometries. In this paper, we propose a novel 3D volume parameterization by means that a harmonic mapping is established between a 3D volume mesh and a unit solid cube. To do that, we firstly partition the boundary of the given 3D volume mesh into the six different rectangular patches whose adjacencies are topologically identical to those of a surface cube. Based on the partitioning result, we compute the boundary condition as a precondition for computing a volume mesh parameterization. Finally, the volume mesh parameterization with a low-distortion can be accomplished by performing a harmonic mapping, which minimizes the harmonic energy, with satisfying the boundary condition. Experimental results show that our method is efficient enough to compute 3D volume mesh parameterization for several models, each of whose topology is identical to a solid sphere.

• Journal of Information Processing Systems
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• v.10 no.1
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• pp.23-35
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• 2014

Recently, novel application areas in digital geometry processing, such as simulation, dynamics, and medical surgery simulations, have necessitated the representation of not only the surface data but also the interior volume data of a given 3D object. In this paper, we present an efficient framework for the shape approximations of spherical solid objects based on trivariate B-splines. To do this, we first constructed a smooth correspondence between a given object and a unit solid cube by computing their harmonic mapping. We set the unit solid cube as a rectilinear parametric domain for trivariate B-splines and utilized the mapping to approximate the given object with B-splines in a coarse-to-fine manner. Specifically, our framework provides user-controllability of shape approximations, based on the control of the boundary condition of the harmonic parameterization and the level of B-spline fitting. Experimental results showed that our method is efficient enough to compute trivariate B-splines for several models, each of whose topology is identical to a solid sphere.