Equiareal parameterizations of NURBS surfaces

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The equiareality of NURBS surfaces greatly affects the results of visualization and tessellation applications, especially when dealing with extruding and intruding shapes. To improve the equiareality of given NURBS surfaces, an optimization algorithm using the Möbius transformations is presented in this paper. The optimal Möbius transformation is obtained by computing the intersection of two planar algebraic curves, whose coefficients are computed explicitly for Bézier and B-spline surfaces, while numerically for NURBS surfaces. Examples are given to show the performance of our algorithm for visualization and tessellation applications.