Abstract: This paper presents a reliable method for constructing a control mesh whose Doo-Sabin subdivision surface interpolates the vertices of a given mesh with arbitrary topology. The method improves on existing techniques in two respects: (1) it is guaranteed to always work for meshes of arbitrary topological type; (2) there is no need to solve a system of linear equations to obtain the control points. Extensions to include normal vector interpolation and/or shape adjustment are also discussed.