【摘要】 为了在曲面拼接和自由形式曲面设计中生成G1光滑的曲面,提出一种使用四阶几何偏微分方程构造B样条曲面的方法.该方法基于切梯度算子、第二切算子、Laplace-Beltrami算子和Giaquinta-Hildebrandt算子在四边形网格上的离散化及收敛性分析,在G1边界光滑约束条件下使用一般形式的四阶几何偏微分方程构造四边B样条曲面片.数值实验结果表明该方法是有效的,确能产生满足G1光滑边界条件的曲面.更多还原

【Abstract】 In this paper,a dynamic B-spline technique using general form fourth-order geometric PDEs is presented.Basing on(1) the discretizaion of tangential gradient operator,second tangential operator,Laplace-Beltrami operator and Giaquinta-Hildebrandt operator over quadrilateral meshes and(2) their convergence analysis,a novel approach for constructing geometric PDE B-spline surfaces,using general form fourth-order geometric flows is proposed in this paper.Numerical experiments show that the method is effective in the application of constructing four-sided B-spline surface patches with G1 boundary conditions.更多还原