Abstract: This paper follows the basic idea of C-T subdivision algorithm and reconstructs a G¹ piecewise smooth surface from a given triangulation T(P) of arbitrary topology to fit the positions and normals at points of 《P. When the normals are not given in advance, an ‘inertia estimation’ is promoted to estimate them. Unlike the C-T subdivision algorithm of Farin, a more reasonable approach which is unaffected by the handling order of given points is proposed. Moreover, new algorithm needn't estimate and correct the position of control vertexes, instead, it calculates them at once by reasonably assigning the redundant degrees of freedom. Since the algorithm is confined to local area, it is highly efficient.