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Ari Rappoport, Alla Sheffer, Michel Bercovier, "VolumePreserving FreeForm Solids," IEEE Transactions on Visualization and Computer Graphics, vol. 2, no. 1, pp. 1927, March, 1996.  
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@article{ 10.1109/2945.489383, author = {Ari Rappoport and Alla Sheffer and Michel Bercovier}, title = {VolumePreserving FreeForm Solids}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {2}, number = {1}, issn = {10772626}, year = {1996}, pages = {1927}, doi = {http://doi.ieeecomputersociety.org/10.1109/2945.489383}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  VolumePreserving FreeForm Solids IS  1 SN  10772626 SP19 EP27 EPD  1927 A1  Ari Rappoport, A1  Alla Sheffer, A1  Michel Bercovier, PY  1996 KW  Freeform solids KW  freeform deformations (FFD) KW  volume preservation KW  energy constraints KW  continuity constraints KW  physicsbased modeling KW  Uzawa's algorithm. VL  2 JA  IEEE Transactions on Visualization and Computer Graphics ER   
Abstract—Some important trends in geometric modeling are the reliance on solid models rather than surfacebased models and the enhancement of the expressive power of models, by using freeform objects in addition to the usual geometric primitives and by incorporating physical principles. An additional trend is the emphasis on interactive performance. In this paper we integrate all of these requirements in a single geometric primitive by endowing the trivariate tensor product freeform solid with several important physical properties, including volume and internal deformation energy. Volume preservation is of benefit in several application areas of geometric modeling, including computer animation, industrial design and mechanical engineering. However, previous physicsbased methods, which usually have used some forms of "energy," have neglected the issue of volume (or area) preservation. We present a novel method for modeling an object composed of several tensorproduct solids while preserving the desired volume of each primitive and ensuring highorder continuity constraints between the primitives. The method utilizes the Uzawa algorithm for nonlinear optimization, with objective functions based on deformation energy or least squares. We show how the algorithm can be used in an interactive environment by relaxing exactness requirements while the user interactively manipulates freeform solid primitives. On current workstations, the algorithm runs in realtime for triquadratic volumes and close to realtime for tricubic volumes.
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