Physics Based Geometric Design

Geometric modeling has proved to be crucial to computer graphics and computer aided geometric design CAGD During the past several decades numerous geometric formulations have been proposed for a large variety of geometric modeling applications In this paper we survey the diversity of shape representations ranging from the primitive polynomial to the sophisticated Non Uniform Rational B Spline NURBS We demonstrate that among various geometric representations NURBS have become an industrial standard primarily because of their many superior properties By reviewing commonly used design paradigms such as interpolation approximation interactive modi cation and variational optimization we can also show that these conventional geometric design techniques are generally awk ward when designers are confronted by complex real world objects This is primarily because they only allow free form primitives such as NURBS to be indirectly manipulated through numerous degrees of freedom DOFs To overcome the disadvantages of this indirect process we summarize the prior work of physics based modeling and review dynamic NURBS D NURBS as a physics based generalization of geometric NURBS for shape design D NURBS can unify the features of the industry standard NURBS geometry with the many demonstrated conveniences of interaction within the new physics based design framework We demonstrate that D NURBS can not only serve as a basis for the future research of physics based geometric design but also become readily appropriate for a large variety of important applications in graphics vision and scienti c visualization