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A Certified Cubic B-Spline Interpolation Method with Tangential Direction Constraints

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Journal of Systems Science & Complexity 2024年第3期37卷 1271-1294页

作者： HE Shitao shen liyong WU Qin YUAN Chunming School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

Curve interpolation with B-spline is widely used in various areas. This problem is classic and recently raised in application scenario with new requirements such as path planning following the tangential vector field under certified error in CNC machining. This paper proposes an algorithm framework to solve Hausdorff distance certified cubic B-spline interpolation problem with or without tangential direction constraints. The algorithm has two stages: The first stage is to find the initial cubic B-spine fitting curve which satisfies the Hausdorff distance constraint;the second stage is to set up and solve the optimization models with certain constraints. Especially, the sufficient conditions of the global Hausdorff distance control for any error bound are discussed, which can be expressed as a series of linear and quadratic constraints. A simple numerical algorithm to compute the Hausdorff distance between a polyline and its B-spline interpolation curve is proposed to reduce our *** results are presented to show the advantages of the proposed algorithms.

关键词： Cubic B-spline Hausdorff distance interpolation tangential direction

“双一流”建设高校教育基金会筹资模型与实践策略

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国家教育行政学院学报 2024年第7期319卷 80-87页

作者：沈黎勇杨维东浙江大学浙江杭州310058 华北电力大学北京102206

高校教育基金会高质量履行筹资使命,既是凝聚慈善资源以优化办学投入的迫切需求,也是实现高等教育内涵式发展和支撑中国式教育现代化的题中之义。厘清高校筹资价值和现实瓶颈,基于对“双一流”建设高校教育基金会的结构化剖析,构建“目... 详细信息

高校教育基金会高质量履行筹资使命,既是凝聚慈善资源以优化办学投入的迫切需求,也是实现高等教育内涵式发展和支撑中国式教育现代化的题中之义。厘清高校筹资价值和现实瓶颈,基于对“双一流”建设高校教育基金会的结构化剖析,构建“目标子系统-过程子系统-支撑子系统”相互作用的筹资模型,深化并拓展筹资模型的要素和内涵。为保障筹资模型的高效运行,应着力把握好三对关系,即问题导向和价值导向的平衡、筹资生产关系的协同调整和筹资要素的协同配置、支持制约和反馈影响的传导互动,并立足不同子系统维度下的关键构成要素及其特征差异,助力提升高校筹资水平和加快世界一流大学建设。

关键词： “双一流”建设高校教育基金会筹资模型实践策略

Foreword to the Special Topic

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Journal of Systems Science & Complexity 2021年第1期34卷 1-2页

作者： shen liyong WU Wenyuan School of Mathematical Sciences University of Chinese Academy of SciencesChinese Academy of SciencesBeijing 100049China Chongqing Institute of Green and Intelligent Technology Chinese Academy of SciencesChongqing 400714China

This issue contains the following seven papers as the proceeding of the Eleventh Conference of Computer Mathematics (CM2019), held at Chengdu, Sichuan Province, October 24–27,2019. In the conference, the contributed papers were selected by the Program Committee for presentation at the symposium and went through a standard refereeing process after the symposium. We are therefore extremely grateful to the Program Committee members and the reviewers for their work in evaluating the submissions before and after the conference.

关键词： symposium submission Chengdu

Local spatial properties based image interpolation scheme using SVMs

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Journal of Systems Engineering and Electronics 2008年第3期19卷 618-623页

作者： Ma liyong shen Yi Ma Jiachen School of Information Science and Engineering Harbin Inst. of Technology Weihai 264209 P. R. China

Image interpolation plays an important role in image process applications. A novel support vector machines （SVMs） based interpolation scheme is proposed with increasing the local spatial properties in the source image as SVMs input patterns. After the proper neighbor pixels region is selected, trained support vectors are obtained by training SVMs with local spatial properties that include the average of the neighbor pixels gray values and the gray value variations between neighbor pixels in the selected region. The support vector regression machines are employed to estimate the gray values of unknown pixels with the neighbor pixels and local spatial properties information. Some interpolation experiments show that the proposed scheme is superior to the linear, cubic, neural network and other SVMs based interpolation approaches.

关键词： image processing interpolation support vector machines local spatial properties support vectorregression.

Determination and(Re)Parametrization of Rational Developable Surfaces

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Journal of Systems Science & Complexity 2015年第6期28卷 1426-1439页

作者： shen liyong PREZ-DíAZ Sonia School of Mathematical Sciences University of Chinese Academy of Sciences Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems Science Chinese Academy of Sciences Key Laboratory of Big Data Mining and Knowledge management Chinese Academy of Sciences Dpto de Física y Matemáticas Universidad de Alcalá

The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the standard parametric form, but it can also be in the implicit form which is commonly used in algebraic geometry. Not all algebraic developable surfaces have rational parametrizations. In this paper, the authors focus on the rational developable surfaces. For a given algebraic surface, the authors first determine whether it is developable by geometric inspection, and then give a rational proper parametrization in the affrmative case. For a rational parametric surface, the authors also determine the developability and give a proper reparametrization for the developable surface.

关键词： Parametrization proper rational developable surface reparametrization

GENERATING EXACT NONLINEAR RANKING FUNCTIONS BY SYMBOLIC-NUMERIC HYBRID METHOD

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Journal of Systems Science & Complexity 2013年第2期26卷 291-301页

作者： shen liyong WU Min YANG Zhengfeng ZENG Zhenbing School of Mathematical Sciences Graduate University of Chinese Academy of Sciences Shanghai Key Laboratory of Trustworthy Computing East China Normal University

This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial *** authors first transform the problem into a parameterized polynomial optimization problem,and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming(SDP).A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function,and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop *** last,the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients.

关键词： Program verification ranking function semidefinite programming symbolic-numeric hybrid method.

PROPER REPARAMETRIZATION FOR INHERENTLY IMPROPER UNIRATIONAL VARIETIES

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Journal of Systems Science & Complexity 2011年第2期24卷 367-380页

作者： liyong shen Engwee CHIONH Xiao-Shan GAO Jia LI School of Mathematical Sciences Graduate University Chinese Academy of Sciences Beijing 100049 China School of Computing National University of Singapore 117543 Singapore. Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems Science ChineseAcademy of Sciences Beijing 100190 China. Beijing Electrical Science and Technology Institute Beijing 100070 China.

In this paper, a class of lattice supports in the lattice space Zm is found to be inherently improper because any rational parametrization from Cm to Cm defined on such a support is improper. The improper index for such a lattice support is defined to be the gcd of the normalized volumes of all the simplex sub-supports. The structure of an improper support S is analyzed and shrinking transformations are constructed to transform S to a proper one. For a generic rational parametrization RP defined on an improper support S, we prove that its improper index is the improper index of S and give a proper reparametrization algorithm for RP. Finally, properties for rational parametrizations defined on an improper support and with numerical coefficients are also considered.

关键词： BKK bound chow form improper lattice supports improper rational parametrizations,reparametrization support transformation.

Tool Orientation Optimization and Path Planning for 5-Axis Machining

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Journal of Systems Science & Complexity 2021年第1期34卷 83-106页

作者： YUAN Chunming MI Zhenpeng JIA Xiaohong LIN Fengming shen liyong KLMM Academy of Mathematics and Systems SciencesChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

Tool path generation is a fundamental problem in 5-axis CNC machining, which consists of tool orientation planning and cutter-contact(CC) point planning. The planning strategy highly depends on the type of tool cutters. For ball-end cutters, the tool orientation and CC point location can be planned separately;while for flat end cutters, the two are highly dependent on each other. This paper generates a smooth tool path of workpiece surfaces for flat end mills from two stages: Computing smooth tool orientations on the surface without gouging and collisions and then designing the CC point path. By solving the tool posture optimization problem the authors achieve both the path smoothness and the machining efficiency. Experimental results are provided to show the effectiveness of the method.

关键词： 5-axis CNC machining flat end cutter tool path planning tool posture optimization

IMPLICITIZATION USING UNIVARIATE RESULTANTS

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Journal of Systems Science & Complexity 2010年第4期23卷 804-814页

作者： liyong shen Chunming YUAN School of Mathematical Sciences Graduate University Chinese Academy of Sciences Beijing 100049 China Key Laboratory of Mathematics Mechanization Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational space curves and rational surfaces by implicitization with univaxiate resultant computations. This method is more efficient than the other algorithms in finding implicit equations for this class of rational curves and surfaces.

关键词： Implicitization rational space curves rational surfaces resultants.