G¹ B-Spline Surface Construction by Geometric Partial Differential Equations

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.