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李效伟, 杨义军. NURBS曲面C^1连续参数优化算法[J]. 计算机辅助设计与图形学学报, 2019, 31(11): 1882-1888. DOI: 10.3724/SP.J.1089.2019.17703
引用本文: 李效伟, 杨义军. NURBS曲面C^1连续参数优化算法[J]. 计算机辅助设计与图形学学报, 2019, 31(11): 1882-1888. DOI: 10.3724/SP.J.1089.2019.17703
Li Xiaowei, Yang Yijun. A C^1 Continuous Algorithm to Optimize Parameterizations of NURBS Surfaces[J]. Journal of Computer-Aided Design & Computer Graphics, 2019, 31(11): 1882-1888. DOI: 10.3724/SP.J.1089.2019.17703
Citation: Li Xiaowei, Yang Yijun. A C^1 Continuous Algorithm to Optimize Parameterizations of NURBS Surfaces[J]. Journal of Computer-Aided Design & Computer Graphics, 2019, 31(11): 1882-1888. DOI: 10.3724/SP.J.1089.2019.17703

NURBS曲面C^1连续参数优化算法

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

  • 摘要: 为了在NURBS曲面上生成满足C1连续的近似弧长参数化等参线,将NURBS曲面4条边界的积分能量函数作为目标函数,提出一种基于分段三次重新参数化的曲面参数优化算法.首先推导出NURBS曲面4条边界的参数表达式;然后使用Hermite基函数变换NURBS曲面u和v方向参数,重新计算参数化等参线,导出变换后的4条边界的积分能量函数;最后通过数值优化算法计算出曲面的最优参数表示.在MFC和OpenGL环境下实现了多个NURBS曲面的等参线分布和纹理映射实验,结果表明该算法是有效的.

     

    Abstract: 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.

     

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