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An Object-Oriented Framework for Curves and Surfaces with Applications

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Abstract

In computer graphics and geometric modeling one gen-
erally faces the problem to integrate a variety of curve and surface
types into a single program. Object-oriented design offers the oppor-
tunity to use the inherent hierarchical structure of curves and sur-
faces to solve this problem. This paper presents an object-oriented
framework together with its C++ implementation that starts from
an abstract class of general differentiable curves and surfaces and
in turn refines 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, and blending il-
lustrate the approach.