D-NURBS: a physics-based framework for geometric design

摘要

Presents dynamic non-uniform rational B-splines (D-NURBS), anphysics-based generalization of NURBS. NURBS have become a de factonstandard in commercial modeling systems. Traditionally, however, NURBSnhave been viewed as purely geometric primitives, which require thendesigner to interactively adjust many degrees of freedom-control pointsnand associated weights-to achieve the desired shapes. The conventionalnshape modification process can often be clumsy and laborious. D-NURBSnare physics-based models that incorporate physical quantities into thenNURBS geometric substrate. Their dynamic behavior, resulting from thennumerical integration of a set of nonlinear differential equations,nproduces physically meaningful, and hence intuitive shape variation.nConsequently, a modeler can interactively sculpt complex shapes tonrequired specifications not only in the traditional indirect fashion, bynadjusting control points and setting weights, but also through directnphysical manipulation, by applying simulated forces and local and globalnshape constraints. We use Lagrangian mechanics to formulate thenequations of motion for D-NURBS curves, tensor-product D-NURBS surfaces,nswung D-NURBS surfaces and triangular D-NURBS surfaces. We apply finitenelement analysis to reduce these equations to efficient numericalnalgorithms computable at interactive rates on common graphicsnworkstations. We implement a prototype modeling environment based onnD-NURBS and demonstrate that D-NURBS can be effective tools in a widenrange of computer-aided geometric design (CAGD) applications