Issue No. 05 - May (2013 vol. 19)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2012.173
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
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 C0 continuity along the segmentation boundary interfaces, this biharmonic model can provide C1 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).
Computational modeling, Harmonic analysis, Mathematical model, Equations, Geometry, Shape, Boundary conditions
Huanhuan Xu, Wuyi Yu, Shiyuan Gu and Xin Li, "Biharmonic Volumetric Mapping Using Fundamental Solutions," in IEEE Transactions on Visualization & Computer Graphics, vol. 19, no. 5, pp. 787-798, 2013.