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In this paper, we present a new adaptive rendering method for general Catmull-Clark subdivision surfaces. The new method is based on direct evaluation of the limit surface to generate an inscribed polyhedron of the limit surface. The method generates fewer polygons in the final rendering process because inscribed approximation usually provides faster convergent rate than circumscribed approximation. 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 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.