Trivariate B-spline Approximation of Spherical Solid Objects

Junho Kim, Seung-Hyun Yoon and Yunjin Lee
Volume: 10, No: 1, Page: 23 ~ 35, Year: 2014
10.3745/JIPS.2014.10.1.023
Keywords: Trivariate B-spline Approximation, Volume Mesh Parameterization, Topological Sphere Model, Harmonic Mapping
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Abstract
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 hape 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 usercontrollability 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.

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Cite this article
IEEE Style
Junho Kim, Seung-Hyun Yoon, and Yunjin Lee, "Trivariate B-spline Approximation of Spherical Solid Objects," Journal of Information Processing Systems, vol. 10, no. 1, pp. 23~35, 2014. DOI: 10.3745/JIPS.2014.10.1.023.

ACM Style
Junho Kim, Seung-Hyun Yoon, and Yunjin Lee, "Trivariate B-spline Approximation of Spherical Solid Objects," Journal of Information Processing Systems, 10, 1, (2014), 23~35. DOI: 10.3745/JIPS.2014.10.1.023.