Abstract: We propose an approach for computing a cone spline surface fitting to a given model. For a given surface, our algorithm first calculates an initial developable surface to approximate it, which is then seg- mented into a set of regions by clustering on axis lines of local fitting cones to the developable surface. Shape parameters of conical patches are determined by solving a surface fitting problem with geometric constraints of cones. A precise cone spline surface is constructed by mapping the optimized conical patches to the space of cone spline surfaces. The experimental results demonstrate the capability of the proposed method to convert a surface into a smooth composition of conical patches which facilities the manufacturing of surface models.