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This paper presents a new approach for fitting a subdivision surface from an irregular and dense triangle mesh of arbitrary topological type. All feature edges and feature vertices of the original mesh model are first identified. A topology- and feature-preserving mesh simplification algorithm is developed to further simplify the dense triangle mesh into a coarse mesh. A subdivision surface with exactly the same topology and sharp features as that of the simplified mesh is finally fitted from a subset of the vertices of the original dense mesh. During the fitting process, both the position masks and subdivision rules are used for setting up the fitting equation. Examples are provided to demonstrate the proposed approach.