插值曲率线与特征线的B样条曲面构造  

Construction of B-spline Surfaces Interpolating Curvature and Feature Curves

作　　者：王飞 陈发来[1] 童伟华 Wang Fei;Chen Falai;Tong Weihua(School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026)

机构地区：[1]中国科学技术大学数学科学学院,合肥230026

出　　处：《计算机辅助设计与图形学学报》2018年第12期2193-2202,共10页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(11571338;61877056)

摘　　要：插值三维线框模型的曲面构造是几何建模中的一个重要研究问题.对于给定的三维线框模型,利用B样条乘积理论、微分几何的基础知识以及薄板样条能量,提出一种构造插值三维线框模型的B样条曲面的算法.首先将线框模型中的曲线分为曲率线(曲面以该线为曲率线)、特征线(曲面在该线处为G0连续)及光滑拼接线(曲面在该线处为G1连续),并对于曲率线及光滑拼接线推导了B样条曲面控制顶点所满足的条件;然后利用薄板样条能量求解出满足约束条件的光顺B样条曲面.上述算法能够构造出更光顺的曲面,被广泛地应用于B样条曲面构造领域.通过对若干模型进行测试,结果验证了文中算法的正确性与有效性.Construction of surfaces interpolating 3D curve network is an important research problem in geometric modeling.Given a 3D curve network,a new method is proposed to interpolate the curve network by using the product of two B-spline functions,the fundamental knowledge of differential geometry and the thin-plate-spline energy optimization.The curve segments are specified into three categories:curvature lines of the B-spline surface,feature lines across which the B-spline surface is G0 continuous,and smooth lines at which the B-spline surface is G1 continuous.We derive constraint conditions of the control points of the B-spline surface at the curvature lines and smooth lines.Then the B-spline surface patches are constructed by minimizing the thin-plate-spline energy together with the curvature line and smooth constraints.That is fair surfaces using above method which is widely used in the construction of B-spline surfaces.We perform experiments on several models.The results demonstrate the correctness and effectiveness of our method.

关 键 词：曲率线 特征线 B样条曲面 薄板样条能量 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]