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Towards additive manufacturing oriented geometric modeling using implicit functions

Visual Computing for Industry,Biomedicine,and Art 2018年第1期1卷 95-110页

作者： Qingde Li Qingqi Hong Quan Qi Xinhui Ma Xie Han Jie Tian School of Engineering and Computer Science University of HullHull HU67RXUK Software School Xiamen UniversityXiamenChina School of Computer Science and Control Engineering North University of ChinaTaiyuanChina Intelligent Bioinformatics Systems Division Institute of AutomationThe Chinese Academy of SciencesBeijingChina

Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine ***,it is not an ideal solution for additive manufacturing because to digitally print a surface-represented geometric object using a certain additive manufacturing technology,the object has to be converted into a solid ***,converting a known surface-based geometric representation into a printable representation is essentially a redesign process,and this is especially the case,when its interior material structure needs to be *** specify a 3D geometric object that is ready to be digitally manufactured,its representation has to be in a certain volumetric *** this research,we show how some of the difficulties experienced in additive manufacturing can be easily solved by using implicitly represented geometric *** surface-based geometric representation is subtractive manufacturing-friendly,implicitly described geometric objects are additive manufacturing-friendly:implicit shapes are 3D printing *** implicit geometric representation allows to combine a geometric shape,material colors,an interior material structure,and other required attributes in one single description as a set of implicit functions,and no conversion is *** addition,as implicit objects are typically specified procedurally,very little data is used in their specifications,which makes them particularly useful for design and visualization with modern cloud-based mobile devices,which usually do not have very big storage ***,implicit modeling is a design procedure that is parallel computing-friendly,as the design of a complex geometric object can be divided into a set of simple shape-designing tasks,owing to the availability of shape-preserving implicit blending operations.

关键词： Additive manufacturing 3D printing-friendly CAD implicit function Isosurface Level-set function-based shape modeling implicit modeling

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Numerical method of slope failure probability based on Bishop model

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Journal of Central South University of Technology 2008年第1期15卷 100-105页

作者：苏永华赵明华张月英 Institute of Geotechnical Engineering Hunan University

Based on Bishop's model and by applying the first and second order mean deviations method, an approximative solution method for the first and second order partial derivatives of functional function was deduced according to numerical analysis theory. After complicated multi-independent variables implicit functional function was simplified to be a single independent variable implicit function and rule of calculating derivative for composite function was combined with principle of the mean deviations method, an approximative solution format of implicit functional function was established through Taylor expansion series and iterative solution approach of reliability degree index was given synchronously. An engineering example was analyzed by the method. The result shows its absolute error is only 0.78% as compared with accurate solution.

关键词： Bishop mechanical model failure probability of slope mean deviation method implicit function Taylor series dump of open-pit

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MULTI-DIMENSIONAL RIEMANN PROBLEM OF SCALAR CONSERVATION LAW

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Acta Mathematica Scientia 1999年第2期19卷 190-200页

作者：杨小舟 Shantou Univ Dept Math Shantou 515063 Guangdong Peoples R China

This paper considers multi-dimensional Riemann problem in another kind of view. The author gets solution of (1.1)(1.2) in Theorem 3.4 and proves itu uniqueness. A new method of solution constructing is applied, which is different from the usual self-similar transformation. The author also discusses some generalized concepts in multi-dimensional situation (such as 'convex condition', 'left value' and 'right value', etc). An example is finally given to demonstrate that rarefaction wave solution of (1.1)(1.2) is not self-similar.

关键词： Riemann problem conservation laws implicit function

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隐函救最小二乘曲线拟合的直接算法

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厦门大学学报(自然科学版) 1987年第5期 627-630页

作者：陈昆厦门大学物理学系

达到的小.式中N为观测点的总数,W1为权重因子,y为因变量,m代表测量值,c代表计算值。当待拟合的函数为显式函数时,y1c可由如下解析表达式直接算得

关键词： Curve fitting Direct algorithm implicit function Objec tive function

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When Does x^x~x Exist?

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Journal of Shanghai University(English Edition) 2003年第3期7卷 201-205页

作者：李常品陈关荣 Department of Mathematics College of Sciences Shanghai University Shanghai 200436 China Department of Electronic Engineering City University of Hong Kong China

This paper further explores some interesting properties of the infinite exponential series, or called tower of powers, with a rigorous proof of its convergence in a positive interval.

关键词： Infinite exponential implicit function convergence.

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The Conditions of Equivalence of a Class Germs of C~∞ functions on Banach Spaces

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Chinese Quarterly Journal of Mathematics 2011年第2期26卷 223-228页

作者： CEN Yan-bin LIU Wen-wu CEN Yi-gang Department of Mathematics Qiannan Normal College for Nationalities Duyun 558000 China School of Computer and InformatiOn Technology Beijing Jiaotong University Beijing 100044 China

In this paper,we prove the converse of gem is right equivalent is also true in[1] and[2],obtain the necessary and sufficient conditions of equivalence of a class gems of C∞ function on Banach spaces.

关键词： Banach space converse theorem Frodholm gem right equivalent implicit function

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