Abstract: A scheme for delayed tesselation of Catmull/Clark surfaces is described where only changes of the control mesh and changes in visibility create workload. Tesselation is performed on demand and is typically spread over a number of frames, so that the number of perceivable frame-rate drops is minimized. No special preprocessing stage is necessary, and applications have the greatest freedom for control-mesh manipulation. The tesselation scheme is ideally suited for interactive applications such as modeling and animation. The number of operations for computing regular tesselations is analyzed, and the most expensive part is optimized. The display procedure uses precomputed index arrays to switch between different adaptive triangulations at no additional cost.