NURBS曲面C^1连续参数优化算法  

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

作　　者：李效伟 杨义军[2] Li Xiaowei;Yang Yijun(School of Data Science and Computer,Shandong Women’s University,Ji’nan 250300;School of Computer Science&Technology,Shandong University,Qingdao 266237)

机构地区：[1]山东女子学院数据科学与计算机学院,济南250300 [2]山东大学计算机科学与技术学院,青岛266237

出　　处：《计算机辅助设计与图形学学报》2019年第11期1882-1888,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61872224);山东省重点研发计划项目(2015GGX106006);教育部产学合作协同育人项目(201801258006,201801258008);山东女子学院高水平科研项目培育基金(2019GSPSJ08)

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.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.

关 键 词：NURBS曲面 边界曲线 数值优化 C1连续性 弧长参数化 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]