Approlab is an interactive surface modeling and visualization tool that is ideal for 3D design and as a plug-in for mathematical/scientific applications such as Mathematica. Approlab enables the generation, manipulation, and control of complex mathematical models with cursor control speed and flexibility. In addition to implementations of industry-standard NURBS plus Bezier curves and surfaces, Approlab features patent-pending approximation methods: Uniform Parabolic Splines (UPS), Uniform Exponential Splines (UES) and Interpolation Pre-Wavelets. Coupled with matrix manipulation algorithms and accelerated OpenGL pipeline implementation, these features enable complex 3D objects and scenes to be manipulated in real time on personal computers running Windows XP. Fully shaded models respond at cursor speed to zoom, pan and rotate functions. Approlab includes multiple light sources, fog, transparency, color and texture mapping. Objects constructed in Approlab can be exported.