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Subdivision surfaces have become a standard technique for free shape modeling. But subdivision schemes are cost-intensive at higher levels of subdivision, making adaptive methods indispensable for visualization and shape modeling. In this paper, we present an adaptive subdivision method based on limit surface normals. The subdivision surfaces generated by the proposed method approximate the limit surfaces better than those generated by traditional methods. Furthermore, the proposed method can be easily applied to any triangular subdivision scheme with C1 or higher degree of continuity.