PHYSICS BASED GEOMETRIC DESIGN

Abstract

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 modification 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 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 cannot 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 scientific visualization.