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We present an automatic method to produce a Catmull-Clark subdivision surface that fits a given input mesh. Its control mesh is coarse and adaptive, and it is obtained by simplifying an initial mesh at high resolution. Simplification occurs progressively via local operators and addresses both quality of surface and faithfulness to the input shape throughout the whole process. The method is robust and performs well on rather complex shapes. Displacement mapping or normal mapping can be applied to approximate the input shape arbitrarily well.