A C^1 Continuous Algorithm to Optimize Parameterizations of NURBS Surfaces

In order to generate closer approximations to the arc-length parameterization of NURBS surfaces, an algorithm based on C1 continuous piecewise-cubic re-parameterization is presented. Firstly, the four boundaries of NURBS surfaces are calculated. Secondly, the Hermite basis function is used to transform the differential geometric representation of NURBS surfaces, and iso-parametric lines of u and v are recalculated, and the formulated energy function of the four optimized boundaries is derived. Finally, the parameters are optimized by the L-BFGS method, and a C1 continuous algorithm which generates closer approximations to the arc-length parameterization is implemented. Experiments on iso-parametric distribution and texture mapping of NURBS surfaces under MFC and OpenGL environments show the effectiveness of our algorithm.