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Hong Qin, Demetri Terzopoulos, "DNURBS: A PhysicsBased Framework for Geometric Design," IEEE Transactions on Visualization and Computer Graphics, vol. 2, no. 1, pp. 8596, March, 1996.  
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@article{ 10.1109/2945.489389, author = {Hong Qin and Demetri Terzopoulos}, title = {DNURBS: A PhysicsBased Framework for Geometric Design}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {2}, number = {1}, issn = {10772626}, year = {1996}, pages = {8596}, doi = {http://doi.ieeecomputersociety.org/10.1109/2945.489389}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  DNURBS: A PhysicsBased Framework for Geometric Design IS  1 SN  10772626 SP85 EP96 EPD  8596 A1  Hong Qin, A1  Demetri Terzopoulos, PY  1996 KW  NURBS KW  geometric modeling KW  computeraided design KW  computer graphics physicsbased models KW  finite elements KW  dynamics. VL  2 JA  IEEE Transactions on Visualization and Computer Graphics ER   
Abstract—This paper presents dynamic NURBS, or DNURBS, a physicsbased generalization of NonUniform Rational BSplines. NURBS have become a de facto standard in commercial modeling systems because of their power to represent both freeform shapes and common analytic shapes. Traditionally, however, NURBS have been viewed as purely geometric primitives, which require the designer to interactively adjust many degrees of freedom (DOFs)—control points and associated weights—to achieve desired shapes. The conventional shape modification process can often be clumsy and laborious. DNURBS are physicsbased models that incorporate mass distributions, internal deformation energies, forces, and other physical quantities into the NURBS geometric substrate. Their dynamic behavior, resulting from the numerical integration of a set of nonlinear differential equations, produces physically meaningful, hence intuitive shape variation. Consequently, a modeler can interactively sculpt complex shapes to required specifications not only in the traditional indirect fashion, by adjusting control points and setting weights, but also through direct physical manipulation, by applying simulated forces and local and global shape constraints. We use Lagrangian mechanics to formulate the equations of motion for DNURBS curves, tensorproduct DNURBS surfaces, swung DNURBS surfaces, and triangular DNURBS surfaces. We apply finite element analysis to reduce these equations to efficient numerical algorithms computable at interactive rates on common graphics workstations. We implement a prototype modeling environment based on DNURBS and demonstrate that DNURBS can be effective tools in a wide range of CAGD applications such as shape blending, scattered data fitting, and interactive sculpting.
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