Volumetric parameterization of complex objects by respecting multiple materials

In this paper we present a methodology to create higher order parametric trivariate representations such as B-splines or T-splines, from closed triangle meshes with higher genus or bifurcations. The input can consist of multiple interior boundaries which represent inner object material attributes. Fundamental to our approach is the use of a midsurface in combination with harmonic functions to decompose the object into a small number of trivariate tensor-product patches that respect material attributes. The methodology is applicable to thin solid models which we extend using the flexibility of harmonic functions and demonstrate our technique, among other objects, on a genus-1 pelvis data set containing an interior triangle mesh separating the cortical part of the bone from the trabecular part. Finally, a B-spline representation is generated from the parameterization.

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