De Casteljau algorithm and degree elevation of Bézier and NURBS curves/surfaces are two important techniques in computer aided geometric design. This paper presents the de Casteljau algorithm and degree elevation...De Casteljau algorithm and degree elevation of Bézier and NURBS curves/surfaces are two important techniques in computer aided geometric design. This paper presents the de Casteljau algorithm and degree elevation of toric surface patches, which include tensor product and triangular rational Bézier surfaces as special cases. Some representative examples of toric surface patches with common shapes are illustrated to verify these two algorithms. Moreover, the authors also apply the degree elevation of toric surface patches to isogeometric analysis. And two more examples show the effectiveness of proposed method.展开更多
Inspired by the r-refinement method in isogeometric analysis,in this paper,the authors propose a curvature-based r-adaptive isogeometric method for planar multi-sided computational domains parameterized by toric surfa...Inspired by the r-refinement method in isogeometric analysis,in this paper,the authors propose a curvature-based r-adaptive isogeometric method for planar multi-sided computational domains parameterized by toric surface patches.The authors construct three absolute curvature metrics of isogeometric solution surface to characterize its gradient information,which is more straightforward and effective.The proposed method takes the internal weights as optimization variables and the resulting parameterization is analysis-suitable and injectivity-preserving with a theoretical guarantee.Several PDEs are solved over multi-sided computational domains parameterized by toric surface patches to demonstrate the effectiveness and efficiency of the proposed method.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11671068 and 11801053。
文摘De Casteljau algorithm and degree elevation of Bézier and NURBS curves/surfaces are two important techniques in computer aided geometric design. This paper presents the de Casteljau algorithm and degree elevation of toric surface patches, which include tensor product and triangular rational Bézier surfaces as special cases. Some representative examples of toric surface patches with common shapes are illustrated to verify these two algorithms. Moreover, the authors also apply the degree elevation of toric surface patches to isogeometric analysis. And two more examples show the effectiveness of proposed method.
基金supported by the National Natural Science Foundation of China under Grant Nos.12071057,11671068,and 12001327.
文摘Inspired by the r-refinement method in isogeometric analysis,in this paper,the authors propose a curvature-based r-adaptive isogeometric method for planar multi-sided computational domains parameterized by toric surface patches.The authors construct three absolute curvature metrics of isogeometric solution surface to characterize its gradient information,which is more straightforward and effective.The proposed method takes the internal weights as optimization variables and the resulting parameterization is analysis-suitable and injectivity-preserving with a theoretical guarantee.Several PDEs are solved over multi-sided computational domains parameterized by toric surface patches to demonstrate the effectiveness and efficiency of the proposed method.
