检索结果-南通市图书馆

degree elevation from Bzier curve to C-Bzier curve with corner cutting form

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics(A Journal of Chinese Universities) 2016年第2期31卷 165-176页

作者： SHEN Wan-qiang WANG Guo-zhao School of Science Jiangnan University Wuxi 214122 China Department of Mathematics Zhejiang University Hangzhou 310027 China State Key Lab of CAD & CG Zhejiang University Hangzhou 310027 China.

The existing results of curve degree elevation mainly focus on the degree of algebraic polynomials. The paper considers the elevation of degree of the trigonometric polynomial, from a Bezier curve on the algebraic polynomial space, to a C-Bezier curve on the algebraic and trigonometric polynomial space. The matrix of degree elevation is obtained by an operator presentation and a derivation pyramid. It possesses not a recursive presentation but a direct expression. The degree elevation process can also be represented as a corner cutting form.

关键词： Curve modeling Bezier curve C-Bezier curve degree elevation Corner cutting.

degree elevation AND KNOT INSERTION FOR GENERALIZED BEZIER SURFACES AND THEIR´APPLICATION TO ISOGEOMETRIC ANALYSIS

在线全文

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2024年第5期42卷 1197-1225页

作者： Mengyun Wang Ye Ji Chungang Zhu School of Mathematical Sciences Dalian University of TechnologyDalian 116024China Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province Dalian 116024China

Generalized B´ezier surfaces are a multi-sided generalization of classical tensor product B´ezier surfaces with a simple control structure and inherit most of the appealing properties from B´ezier ***,the original degree elevation changes the geometry of generalized B´ezier surfaces such that it is undesirable in many applications,*** *** this paper,we propose an improved degree elevation algorithm for generalized B´ezier surfaces preserving not only geometric consistency but also parametric *** on the knot insertion of B-splines,a novel knot insertion algorithm for generalized B´ezier surfaces is also *** the proposed algorithms are employed to increase degrees of freedom for multi-sided computational domains parameterized by generalized B´ezier surfaces in isogeometric analysis,corresponding to the traditional p-,h-,and *** examples demonstrate the effectiveness and superiority of our method.

关键词： Generalized Bézier surface degree elevation Knot insertion Isogeometric analysis Refinement

De Casteljau Algorithm and degree elevation of Toric Surface Patches

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2021年第1期34卷 21-46页

作者： LI Jinggai JI Ye ZHU Chungang School of Mathematical Sciences Dalian University of TechnologyDalian 116024 Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province Dalian University of TechnologyDalian 116024China

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.

关键词： De Casteljau algorithm degree elevation depth elevation isogeometric analysis toric surface patches

Non-uniform B-spline curves with multiple shape parameters

在线全文

学校读者我要写书评

暂无评论

Journal of Zhejiang University-Science C(Computers and Electronics) 2011年第10期12卷 800-808页

作者： Juan CAO Guo-zhao WANG School of Mathematical Sciences Xiamen University Xiamen 361005 China Department of Mathematics Zhejiang University Hangzhou 310027 China

We introduce a kind of shape-adjustable spline curves defined over a non-uniform knot *** curves not only have the many valued properties of the usual non-uniform B-spline curves,but also are shape adjustable under fixed control *** method is based on the degree elevation of B-spline curves,where maximum degrees of freedom are added to a curve parameterized in terms of a non-uniform *** also discuss the geometric effect of the adjustment of shape parameters and propose practical shape modification algorithms,which are indispensable from the user's perspective.

关键词： Non-uniform B-spline Shape parameter degree elevation

The structure of uniform B-spline curves with parameters

在线全文

学校读者我要写书评

暂无评论

Progress in Natural Science:Materials International 2008年第3期18卷 303-308页

作者： Juan Cao , Guozhao Wang Institute of Image Processing and Computer Graphic, Department of Mathematics, Zhejiang University, Hangzhou 310027, China Institute of Image Processing and Computer Graphic Department of Mathematics Zhejiang University Hangzhou 310027 China

The shape-adjustable curve constructed by uniform B-spline basis function with parameter is an extension of uniform B-spline curve. In this paper, we study the relation between the uniform B-spline basis functions with parameter and the B-spline basis functions. Based on the degree elevation of B-spline, we extend the uniform B-spline basis functions with parameter to ones with multiple parameters. Examples show that the proposed basis functions provide more flexibility for curve design.

关键词： Uniform B-spline Shape parameter Shape-adjustable curve degree elevation

A Type of Triangular Ball Surface and its Properties

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Journal of Computer Science & Technology 1998年第1期13卷 63-72页

作者：胡事民王国瑾孙家广 DepartmentofComputerScienceandTecnology TsinghuaUniversityBeijing100084P.R.China

A new type of bivariate generalized Ball basis function on a triangle is presented for free-form surface design. Some properties of the basis function are given, then degree elevation, recursive evaluation and some other properties of the generalized Ball surfaces are also derived. It is shown that the proposed recursive evaluation algorithm is more efficient than those of the old surfaces.

关键词： Triangular Ball surfaces degree elevation recursive evaluation.

SOME RECURRENCE FORMULAS FOR BOX SPLINES AND CONE SPLINES

在线全文

学校读者我要写书评

暂无评论

Analysis in Theory and Applications 2004年第4期20卷 297-306页

作者： Patrick J. Van Fleet Department of Mathematics University of St. Thomas St. Paul MN 55105 USA

A degree elevation formula for multivariate simplex splines was given by Micchelli and extended to hold for multivariate Dirichlet splines in [8]. We report similar formulae for multivariate cone splines and box splines. To this end, we utilize a relation due to Dahmen and Micchelli that connects box splines and cone splines and a degree reduction formula given by Cohen, Lyche, and Riesenfeld in [2].

关键词： box spline cone spline degree elevation

Identification of Planar Sextic Pythagorean-Hodograph Curves

在线全文

学校读者我要写书评

暂无评论

Journal of Mathematical Research with Applications 2017年第1期37卷 59-72页

作者： Hui WANG Chungang ZHU Caiyun LI School of Mathematical Sciences Dalian University of Technology School of Science Dalian University of Technology

Pythagorean-hodograph(PH) curves offer computational advantages in Computer Aided Geometric Design, Computer Aided Design, Computer Graphics, Computer Numerical Control machining and similar applications. In this paper, three methods are utilized to construct the identifications of planar regular sextic PH curves. The first exhibits purely the control polygon legs’ constraints in the complex form. Such reconstruction of a PH sextic can be elaborated by C1 Hermite data and another one condition. The second uses polar representation in two cases. One of them can produce a family of convex sextic PH curves related with a quintic PH curve, and the other one may naturally degenerate a sextic PH curve to a quintic PH curve. In the third identification, we use some odd PH curves to construct a family of sextic PH curves with convexity-preserving property.

关键词： Pythagorean-hodograph sextic curves control polygon degree elevation geometric characteristic

CONVERSION FORMULAS FOR RATIONAL BEZIER SURFACES

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Computer Aided Drafting,Design and Manufacturing 1996年第1期6卷 18-24页

作者： Hu Shimin Wang Guozhao

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... 详细信息

关键词： ss: rational Bezier patch degree elevation conversion formula parameter transformation