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Chhandomay Mandal, Hong Qin, Baba C. Vemuri, "Dynamic Modeling of Butterfly Subdivision Surfaces," IEEE Transactions on Visualization and Computer Graphics, vol. 6, no. 3, pp. 265287, JulySeptember, 2000.  
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@article{ 10.1109/2945.879787, author = {Chhandomay Mandal and Hong Qin and Baba C. Vemuri}, title = {Dynamic Modeling of Butterfly Subdivision Surfaces}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {6}, number = {3}, issn = {10772626}, year = {2000}, pages = {265287}, doi = {http://doi.ieeecomputersociety.org/10.1109/2945.879787}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  Dynamic Modeling of Butterfly Subdivision Surfaces IS  3 SN  10772626 SP265 EP287 EPD  265287 A1  Chhandomay Mandal, A1  Hong Qin, A1  Baba C. Vemuri, PY  2000 KW  Dynamic modeling KW  physicsbased geometric design KW  geometric modeling KW  CAGD KW  subdivision surfaces KW  deformable models KW  finite elements KW  interactive techniques. VL  6 JA  IEEE Transactions on Visualization and Computer Graphics ER   
Abstract—In this paper, we develop integrated techniques that unify physicsbased modeling with geometric subdivision methodology and present a scheme for dynamic manipulation of the smooth limit surface generated by the (modified) butterfly scheme using physicsbased “force” tools. This procedurebased surface model obtained through butterfly subdivision does not have a closedform analytic formulation (unlike other wellknown splinebased models) and, hence, poses challenging problems to incorporate mass and damping distributions, internal deformation energy, forces, and other physical quantities required to develop a physicsbased model. Our primary contributions to computer graphics and geometric modeling include: 1) a new hierarchical formulation for locally parameterizing the butterfly subdivision surface over its initial control polyhedron, 2) formulation of dynamic butterfly subdivision surface as a set of novel finite elements, and 3) approximation of this new type of finite elements by a collection of existing finite elements subject to implicit geometric constraints. Our new physicsbased model can be sculpted directly by applying synthesized forces and its equilibrium is characterized by the minimum of a deformation energy subject to the imposed constraints. We demonstrate that this novel dynamic framework not only provides a direct and natural means of manipulating geometric shapes, but also facilitates hierarchical shape and nonrigid motion estimation from large range and volumetric data sets using very few degrees of freedom (control vertices that define the initial polyhedron).
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