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 s u r v ey 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

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... dustrial standard primarily because of their many superior properties. By reviewing commonly used design paradigms such a s i n terpolation, approximation, interactive modi cation and variational optimization, we can also show that these conventional geometric design techniques are generally awkward 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 o vercome 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 o f physics-based geometric design but also become readily appropriate for a large variety of important applications in graphics, vision, and scienti c visualization.