Optimizing equiareality of NURBS surfaces using composite Möbius transformations

The equiareality of NURBS surfaces greatly affects the results of visualization and tessellation applications, especially when dealing with extruding and intruding shapes. To obtain more equiareal parameterizations of NURBS surfaces than the Möbius based method, an optimization algorithm is presented in this paper based on the more flexible composite reparameterization functions. For fixed knots, the optimal composite reparameterization can be obtained using the Levenberg–Marquardt method. For a given tolerance, a uniform subdivision scheme is interleaved with the optimization procedure and this process finishes until the change of the equiareal deviation energy is less than the given tolerance. Examples are given to show the performance of our algorithm for visualization and tessellation applications.