Curves and surfaces have properties that are difficult to comprehend from a purely symbolic or numeric description. Therefore, visualization is an indispensable tool for controlling the quality and for judging the aesthetic properties of these geometric objects. The same techniques can also be used advantageously for visually evaluating new algorithms and mathematical schemes. The paper describes an object-oriented framework written in c++ that provides tools for the analysis and visualization of curves and surfaces. The design of the class hierarchy is outlined, and specific applications (i.e. scattered data interpolation, blending surfaces, and differential geometry) that take advantage of this platform are presented.