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In this paper, a new approach for fitting a subdivision surface from a dense triangle mesh is proposed. All feature edges and feature vertices of the original mesh model are first identified. A new feature- preserving mesh simplification algorithm is developed to further simplify the dense triangle mesh into a coarse mesh. A subdivision surface is finally fitted from a subset of the initial vertices of the dense triangle mesh. On the stage of fitting, our basic idea is to use the subdivision limit position (SLP) to adapt the control mesh of the subdivision surface to fit to the data points. Some examples are provided to demonstrate the proposed approach.