An Object-oriented Framework for Curves and Surfaces with Applications

In computer graphics and geometric modeling one generally faces the problem to integrate a variety of curve and surface types into a single program. Object-oriented design ooers the opportunity to use the inherent hierarchical structure of curves and surfaces to solve this problem. This paper presents an object-oriented framework together with its C++ implementation that starts from an abstract class of general diierentiable curves and surfaces and in turn reenes 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 diierential geometry, and blending illustrate the approach. x1. Introduction In this paper we present an object-oriented framework together with its C++ implementation that starts from an abstract class of general diierentiable curves and surfaces and in turn reenes this design to various parametric representations of curves and surfaces 19, 26]. This design includes all of the standard curve and surface types and provides a powerful and uniform interface for applications. In Section 2 after a short introduction into object-oriented design and classes we present our approach to order the types of curves and surfaces into a hierarchical structure and review implementation features and selected curve and surface classes.