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Issue No.09 - Sept. (2013 vol.19)
pp: 1539-1551
Bo Li , Dept. of Comput. Sci., Stony Brook Univ., Stony Brook, NY, USA
Xin Li , Sch. of Electr. Eng. & Comput. Sci., Louisiana State Univ., Baton Rouge, LA, USA
Kexiang Wang , Dept. of Comput. Sci., Stony Brook Univ., Stony Brook, NY, USA
Hong Qin , Dept. of Comput. Sci., Stony Brook Univ., Stony Brook, NY, USA
This paper develops a novel volumetric parameterization and spline construction framework, which is an effective modeling tool for converting surface meshes to volumetric splines. Our new splines are defined upon a novel parametric domain called generalized polycubes (GPCs). A GPC comprises a set of regular cube domains topologically glued together. Compared with conventional polycubes (CPCs), the GPC is much more powerful and flexible and has improved numerical accuracy and computational efficiency when serving as a parametric domain. We design an automatic algorithm to construct the GPC domain while also permitting the user to improve shape abstraction via interactive intervention. We then parameterize the input model on the GPC domain. Finally, we devise a new volumetric spline scheme based on this seamless volumetric parameterization. With a hierarchical fitting scheme, the proposed splines can fit data accurately using reduced number of superfluous control points. Our volumetric modeling scheme has great potential in shape modeling, engineering analysis, and reverse engineering applications.
Splines (mathematics), Shape, Solid modeling, Computational modeling, Solids, Topology, Algorithm design and analysis,volumetric parameterization, Volumetric spline, generalized polycube
Bo Li, Xin Li, Kexiang Wang, Hong Qin, "Surface Mesh to Volumetric Spline Conversion with Generalized Polycubes", IEEE Transactions on Visualization & Computer Graphics, vol.19, no. 9, pp. 1539-1551, Sept. 2013, doi:10.1109/TVCG.2012.177
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