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An Object-Oriented Approach to Curves and Surfaces

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Abstract

Applications in computer graphics and geometric modeling generally require the integration
of a variety of curve and surface types into a single system. Object-oriented design offers
the opportunity to use the inherent hierarchical structure of curves and surfaces to solve
this problem. This paper presents a top down approach to the design of an object-oriented
framework for curves and surfaces together with its C++ implementation. We start from an
abstract class of general differentiable curves and surfaces and in turn refine this design
to various parametric representations of curves and surfaces. This design includes all of the
standard curve and surface types and provides a powerful and uniform interface for applications.
Examples from differential geometry, blending, and scattered data interpolation illustrate the
approach.