UE-Brzier （unified and extended Brzier） basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brz...UE-Brzier （unified and extended Brzier） basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brzier-like bases, UE-Brzier basis func-tions are not orthogonal. In this paper, a group of orthogonal basis is constructed based on UE-Brzier basis. The transformation matrices between UE-Brzier basis and the proposed orthogonal basis are also solved.展开更多
In this paper, a simple method for merging of Bezier curves is presented by using constrained optimization method. The use of the “discrete” coefficient norm in L2 sense greatly simplifies the merging process. Furth...In this paper, a simple method for merging of Bezier curves is presented by using constrained optimization method. The use of the “discrete” coefficient norm in L2 sense greatly simplifies the merging process. Furthermore, continuity at the endpoint of curves are considered in the merging process.展开更多
In this paper, we investigate the inherent relationship between two types of rational Bezier surfaces. We present a conversion formula for rational Bezier surfaces from triangular patches to rectangular patches with s...In this paper, we investigate the inherent relationship between two types of rational Bezier surfaces. We present a conversion formula for rational Bezier surfaces from triangular patches to rectangular patches with straight forward geometric interpretations, an inverse process of such conversion is also considered.展开更多
Abstract Generalized B-splines have been employed as geometric modeling and numerical simu- lation tools for isogeometric analysis （IGA for short）. However, the previous models used in IGA, such as trigonometric gen...Abstract Generalized B-splines have been employed as geometric modeling and numerical simu- lation tools for isogeometric analysis （IGA for short）. However, the previous models used in IGA, such as trigonometric generalized B-splines or hyperbolic generalized B-splines, are not the unified mathematical representation of conics and polynomial parametric curves/surfaces. In this paper, a unified approach to construct the generalized non-uniform B-splines over the space spanned by {α（t）,β（t）,ξ（t）, η（t）, 1, t,……. , tn-4} is proposed, and the corresponding isogeometric analysis framework for PDE solving is also studied. Compared with the NURBS-IGA method, the proposed frameworks have several advantages such as high accuracy, easy-to-compute derivatives and integrals due to the non-rational form. Furthermore, with the proposed spline models, isogeometric analysis can be performed on the computational domain bounded by transcendental curves/surfaces, such as the involute of circle, the helix/helicoid, the catenary/catenoid and the cycloid. Several numerical examples for isogeometrie heat conduction problems are presented to show the effectiveness of the proposed methods.展开更多
Spirals are curves with one-signed, monotone increasing or decreasing curvature. They are commonly useful in a variety of applications, either for aesthetic or for engineering requirements. In this paper we propose a ...Spirals are curves with one-signed, monotone increasing or decreasing curvature. They are commonly useful in a variety of applications, either for aesthetic or for engineering requirements. In this paper we propose a new iterative subdivision scheme for generating planar spiral segments from two points and their tangent vectors. The subdivision process consists of two main steps, computing new points and adjusting tangent vectors adaptively for each iteration. We categorize this iterative scheme as geometry driven because we utilize the old points and their tangent vectors whereas most other iterative schemes rely only on the old points. Some numerical examples are presented to show the advantageous properties of the new scheme.展开更多
A new kind of spline with variable frequencies, called ωB-spline, is presented. It not only unifies B-splines, trigonometric and hyperbolic polynomial B-splines, but also produces more new types of splines, ωB-splin...A new kind of spline with variable frequencies, called ωB-spline, is presented. It not only unifies B-splines, trigonometric and hyperbolic polynomial B-splines, but also produces more new types of splines, ωB-spline bases are defined in the space spanned by {coso） t, sino）t, ], t, ..., t^n, ...} with the sequence of frequencies m where n is an arbitrary nonnegative integer, ωB-splines persist all desirable properties of B-splines. Furthermore, they have some special properties advantageous for modeling free form curves and surfaces.展开更多
基金Supported by National Science Foundation of China(No.60904070,61272032)the Natural Science Foundation of Zhejiang Province(No.LY12F02002,Y1111101)
文摘UE-Brzier （unified and extended Brzier） basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brzier-like bases, UE-Brzier basis func-tions are not orthogonal. In this paper, a group of orthogonal basis is constructed based on UE-Brzier basis. The transformation matrices between UE-Brzier basis and the proposed orthogonal basis are also solved.
文摘In this paper, a simple method for merging of Bezier curves is presented by using constrained optimization method. The use of the “discrete” coefficient norm in L2 sense greatly simplifies the merging process. Furthermore, continuity at the endpoint of curves are considered in the merging process.
文摘In this paper, we investigate the inherent relationship between two types of rational Bezier surfaces. We present a conversion formula for rational Bezier surfaces from triangular patches to rectangular patches with straight forward geometric interpretations, an inverse process of such conversion is also considered.
基金supported by Zhejiang Provincial Natural Science Foundation of China under Grant No.LR16F020003the National Nature Science Foundation of China under Grant Nos.61472111,61602138+1 种基金the Open Project Program of the State Key Lab of CAD&CG(A1703)Zhejiang University
文摘Abstract Generalized B-splines have been employed as geometric modeling and numerical simu- lation tools for isogeometric analysis （IGA for short）. However, the previous models used in IGA, such as trigonometric generalized B-splines or hyperbolic generalized B-splines, are not the unified mathematical representation of conics and polynomial parametric curves/surfaces. In this paper, a unified approach to construct the generalized non-uniform B-splines over the space spanned by {α（t）,β（t）,ξ（t）, η（t）, 1, t,……. , tn-4} is proposed, and the corresponding isogeometric analysis framework for PDE solving is also studied. Compared with the NURBS-IGA method, the proposed frameworks have several advantages such as high accuracy, easy-to-compute derivatives and integrals due to the non-rational form. Furthermore, with the proposed spline models, isogeometric analysis can be performed on the computational domain bounded by transcendental curves/surfaces, such as the involute of circle, the helix/helicoid, the catenary/catenoid and the cycloid. Several numerical examples for isogeometrie heat conduction problems are presented to show the effectiveness of the proposed methods.
基金Supported partially by the National Natural Science Foundation of China (Grant Nos. 60673032, 60773179)the National Basic Research Program of China (Grant No. 2004CB318000)the Scientific Starting Foundation of Hangzhou Dianzi University
文摘Spirals are curves with one-signed, monotone increasing or decreasing curvature. They are commonly useful in a variety of applications, either for aesthetic or for engineering requirements. In this paper we propose a new iterative subdivision scheme for generating planar spiral segments from two points and their tangent vectors. The subdivision process consists of two main steps, computing new points and adjusting tangent vectors adaptively for each iteration. We categorize this iterative scheme as geometry driven because we utilize the old points and their tangent vectors whereas most other iterative schemes rely only on the old points. Some numerical examples are presented to show the advantageous properties of the new scheme.
基金the National Natural Science Foundation of China(Grant No.60773179)Foundation of State Key Basic Research 973 Development Programming Item of China(Grant No.G2004CB318000)
文摘A new kind of spline with variable frequencies, called ωB-spline, is presented. It not only unifies B-splines, trigonometric and hyperbolic polynomial B-splines, but also produces more new types of splines, ωB-spline bases are defined in the space spanned by {coso） t, sino）t, ], t, ..., t^n, ...} with the sequence of frequencies m where n is an arbitrary nonnegative integer, ωB-splines persist all desirable properties of B-splines. Furthermore, they have some special properties advantageous for modeling free form curves and surfaces.
