Summary: 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 offers 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 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 illustrate the approach.