Adaptive Rendering of Catmull-Clark Subdivision Surfaces based on Inscribed Approximation

Subdivision provides a powerful scheme for building smooth and complex surfaces. But the number of faces in the uniformly refined meshes increases exponentially with respect to subdivision depth. Adaptive rendering reduces the number of faces needed to yield a smooth approximation to the limit surface and, consequently, makes the rendering process more efficient. In this paper, we present a new adaptive rendering method for general Catmull-Clark subdivision surfaces. Different from previous control mesh refinement based approaches, which generate approximate meshes that usually do not interpolate, but circumscribe the limit surface, our new method is based on direct evaluation of the limit surface to generate an inscribed polyhedron of the limit surface. Our method generates less polygons in the final rendering process, because in most cases, inscribed approximation provides faster convergent rate than circumscribed approximation. With explicit evaluation of general Catmull-Clark subdivision surfaces becoming available, the new adaptive rendering method can precisely measure error for every point of the limit surface. Hence, it has complete control of the accuracy of the rendering result. Cracks are avoided by using a recursive color marking process to ensure that adjacent patches or subpatches use the same limit surface points in the construction of the shared boundary. The new method performs limit surface evaluation only at points that are needed for the final rendering process. Therefore it is very fast and memory efficient. The new method is presented for the general Catmull-Clark subdivision scheme. But it can be used for any subdivision scheme that has an explicit evaluation method for its limit surface. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling curve, surface, solid and object representations;