Issue No.05 - May (2013 vol.19)

pp: 787-798

Huanhuan Xu , Sch. of Electr. Eng. & Comput. Sci., Louisiana State Univ., Baton Rouge, LA, USA

Wuyi Yu , Sch. of Electr. Eng. & Comput. Sci., Louisiana State Univ., Baton Rouge, LA, USA

Shiyuan Gu , Dept. of Math., Louisiana State Univ., Baton Rouge, LA, USA

Xin Li , Sch. of Electr. Eng. & Comput. Sci., Louisiana State Univ., Baton Rouge, LA, USA

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2012.173

ABSTRACT

We propose a biharmonic model for cross-object volumetric mapping. This new computational model aims to facilitate the mapping of solid models with complicated geometry or heterogeneous inner structures. In order to solve cross-shape mapping between such models through divide and conquer, solid models can be decomposed into subparts upon which mappings is computed individually. The biharmonic volumetric mapping can be performed in each subregion separately. Unlike the widely used harmonic mapping which only allows C

^{0}continuity along the segmentation boundary interfaces, this biharmonic model can provide C^{1}smoothness. We demonstrate the efficacy of our mapping framework on various geometric models with complex geometry (which are decomposed into subparts with simpler and solvable geometry) or heterogeneous interior structures (whose different material layers can be segmented and processed separately).INDEX TERMS

Computational modeling, Harmonic analysis, Mathematical model, Equations, Geometry, Shape, Boundary conditions,biharmonic mapping, Volumetric mapping

CITATION

Huanhuan Xu, Wuyi Yu, Shiyuan Gu, Xin Li, "Biharmonic Volumetric Mapping Using Fundamental Solutions",

*IEEE Transactions on Visualization & Computer Graphics*, vol.19, no. 5, pp. 787-798, May 2013, doi:10.1109/TVCG.2012.173REFERENCES