The rapid and precise evaluation of curve & surface parameterizations has wide application. In the paper we present a parameterization technique for cubic B spline subdivision curves with sharp feature. The eigenstructure of the subdivision matrix is analyzed. The subdivision matrix and control points are projected into the eigenspace of matrix. The technique can deal with curve fitting with sharp features directly. The vertices with maximal curvature are as the initial fitting vertices. With the parameterization technique given in this paper

the curve segment with sharp feature is constructed; and the distance between the original data and the curve is also calculated. The fitting vertices are located at the extremities of curve segment; during error estimation it can improve computation speed and avoid mismatching when the target curve is self intersection or when two branches are too close.