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For obtaining better curvature distributions of subdivision surfaces, various improvements for Loop's subdivision scheme (C. Loop, 1987) on triangular surface meshes have been made. A careful analysis shows that the fast evaluation technique of the subdivision surface proposed by Stam is no longer usable to these improved schemes. This paper describes a fast evaluating algorithm for improved Loop's subdivision surfaces. The algorithm is applicable to a vast class of subdivision schemes for triangular surface meshes. Using the proposed algorithm, one can evaluate the subdivision surface at any domain point for any set of input subdivision masks and a control mesh.