Tessellation of Curved Surfaces under Highly Varying Transformations

We pursue the problem of step size determination for tessellating arbitrary degree polynomial and rational Bézier patches, under highly varying modeling and viewing transformations, to within post-viewing size and/or deviation thresholds specified in display coordinates. The technique involves the computation of derivative bounds of surfaces in modeling coordinates, and the mapping of these bounds into world coordinates (or lighting coordinates), where tessellation takes place by using norms of modeling transformations. A key result of this work is a closed form expression for the maximum scale a perspective transformation is capable of at an arbitrary point in space. This result allows the mapping of thresholds from DC into WC (LC). In practice, while the step size determination needs to take place during every traversal, the costly operations of finding derivative bounds, computing norms of modeling transformations, and factoring viewing transformations take place at creation time.