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A Sufficient Convexity Condition for Parametric bézier surface over Rectangle

American Journal of Computational Mathematics 2020年第2期10卷 252-265页

作者： Sai Hao Xianghuai Dong National Engineering Research Center of Die & Mold CAD Shanghai Jiaotong University Shanghai China

surface convexity is a key issue in computer aided geometric design, which is widely applied in geometric modeling field, such as physical models, industrial design, automatic manufacturing, etc. In this paper, a sufficient convexity condition of the parametric bézier surface over rectangles is proposed, which is firstly considered as a sufficient convexity condition for the bézier control grid. The condition is proved by De Casteljau surface subdivision arithmetic, in which the recursive expressions elaborate that the control grid eventually converges to the surface. At last, two examples for the modeling of interpolation-type surface are discussed, one of which is a general surface and the other is a degenerate surface.

关键词： Convexity Condition bézier surface De Casteljau Arithmetic Interpolation-Type surface

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CONSTRUCTION OF bEzier surfaceS FROM PRESCRIbED bOUNDARY

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Journal of Computational Mathematics 2023年第4期41卷 551-568页

作者： Yongxia Hao Ting Li School of Mathematical Sciences Jiangsu UniversityZhenjiang 212000China

In this paper,we present a method for generating bézier surfaces from the boundary information based on a general second order functional and a third order functional associated with the triharmonic *** solving simple linear equations,the internal control points of the resulting bézier surface can be obtained as linear combinations of the given boundary control *** is a generalization of previous works on Plateau-bezier problem,harmonic,biharmonic and quasi-harmonic bézier *** representative examples show the effectiveness of the presented method.

关键词： bézier surface boundary control points Quadratic functional Triharmonic equation

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Convexity and Positivity of bivariate Quadratic bézier surfaces over a Rectangle

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Journal of Shanghai University(English Edition) 2001年第1期5卷 20-28页

作者： DING You dong School of Computer Engineering and Science, Shanghai University, Shanghai 200072, China School of Computer Engineering and Science Shanghai University Shanghai China

With the help of several discriminants about the zero points of a quartic polynomial, the sufficient and necessary conditions for the positivity and nonnegativity of the quartic polynomial over an interval I(-∞,+∞) was derived. based on these conclusions, the sufficient and necessary conditions for the positivity and convexity of the 2×2 bézier surface over a rectangle were obtained. A simple sufficient condition was deduced also and finally several examples were given.

关键词： bézier surface convexity positivity discriminant

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The Effects of Shape Parameters for surface Joining with High Order Geometric Continuity

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Computer Aided Drafting,Design and Manufacturing 1998年第1期8卷 20-28页

作者： Lu Xiaolin Ma Lizhuang He Zhijun 2

The necessary and sufficient conditions and an algorithm to reach continuity between adjacent bézier patches are presented. The effects of shape parameters for surface connection of G4 geometric continuity are investigated in detail. The algorithm can be generalized directly to the case of surface joining with higher order geometric continuity. It has important applications in surface modeling and surface joining.

关键词： bézier surface surface modeling geometric continuity

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Geometric Modeling of Rape (brassica napus L.) during Seedling Stage

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Agricultural Science & Technology 2011年第7期12卷 1085-1087页

作者：赵丽丽温维亮彭亚宇郭新宇陆声链杜建军国家农业信息化工程技术研究中心北京100097 首都师范大学信息工程学院北京100048 湖南省武冈市双牌中学湖南武冈422400

[Objective] The paper was to study the geometric modeling of rape（brassica napus L.） during seedling stage.[Method] based on the analysis and observation of morphological structure and growth process of rape during seedling stage,a characteristic parameters-based three-dimensional mathematical model of rape and its visible method was *** individual control parameters were extracted according to the morphological structures of various organs of *** sizes of leaf and petiole model were constructed by using cubic bézier *** cylinder with different upper and lower bottom area was adopted as the main stem ***,three-dimensional reconstruction of whole Rape plant during seedling stage was achieved through the operations of rotation,scaling and splicing.[Result] This method had certain controllability,which was also easy and convenient,and could quickly use to build the geometric model of rape during seedling stage.[Conclusion] The results provided reference for study on structural model of rape.

关键词： bézier surface brassica napus L Geometric modeling Visualization

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