Chebyshev approximation to data by geometric elements

1993 ◽  
Vol 5 (10) ◽  
pp. 509-522 ◽  
Author(s):  
Rudolf Drieschner
Keyword(s):  
Chebyshev Approximation ◽  
Geometric Elements

Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

1970 ◽  
Vol 28 ◽  
pp. 360-361
Author(s):  
John W. Coleman
Keyword(s):  
Boundary Conditions ◽  
High Performance ◽  
Force Fields ◽  
Optical Design ◽  
Direct Conversion ◽  
Design Engineering ◽  
Design Data ◽  
Scalar Potentials ◽  
Geometric Elements ◽  
At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

Criteria for evaluation of the coordinate measurements quality of parts geometric parameters at pilot-experimental production

2019 ◽  
pp. 3-8
Author(s):  
N.Yu. Bobrovskaya ◽  
M.F. Danilov
Keyword(s):  
Quality Indicators ◽  
Quality Management System ◽  
Technical Specification ◽  
Experimental Production ◽  
Technological Heredity ◽  
Coordinate Measurements ◽  
Reasonable Choice ◽  
The Stability ◽  
Geometric Elements

The criteria of the coordinate measurements quality at pilot-experimental production based on contemporary methods of quality management system and traditional methods of the measurements quality in Metrology are considered. As an additional criterion for quality of measurements, their duration is proposed. Analyzing the problem of assessing the quality of measurements, the authors pay particular attention to the role of technological heredity in the analysis of the sources of uncertainty of coordinate measurements, including not only the process of manufacturing the part, but all stages of the development of design and technological documentation. Along with such criteria as the degree of confidence in the results of measurements; the accuracy, convergence, reproducibility and speed of the results must take into account the correctness of technical specification, and such characteristics of the shape of the geometric elements to be controlled, such as flatness, roundness, cylindrical. It is noted that one of the main methods to reduce the uncertainty of coordinate measurements is to reduce the uncertainty in the initial data and measurement conditions, as well as to increase the stability of the tasks due to the reasonable choice of the basic geometric elements (measuring bases) of the part. A prerequisite for obtaining reliable quality indicators is a quantitative assessment of the conditions and organization of the measurement process. To plan and normalize the time of measurements, the authors propose to use analytical formulas, on the basis of which it is possible to perform quantitative analysis and optimization of quality indicators, including the speed of measurements.

The Geometrical Feature Recognition Method of Part Drawing

2011 ◽  
Vol 415-417 ◽  
pp. 523-526
Author(s):  
Yan Dong ◽  
Mei Li
Keyword(s):  
Feature Recognition ◽  
Graph Matching ◽  
Geometric Feature ◽  
Recognition Method ◽  
Recognition Mechanism ◽  
Chemical Database ◽  
Geometry Feature ◽  
Constraint Structure ◽  
Geometric Elements ◽  
Fine Tune

This paper put forward a geometry feature recognition method of part drawing based on graph matching. Describe the constraints structure of geometric feature in geometric elements and those constraint relationships. Match sub-graph in contour closure graphics and those combination. Using linear symbol notation of chemical compounds in chemical database for reference, encode to constraint structure of geometry graphics, establish recognition mechanism of geometric characteristics by structure codes. Taking the fine-tune screw and fork parts for example, this method has been proved to be effective.

Algorithm for Spatial Straightness Evaluation Using Theories of Linear Complex Chebyshev Approximation and Semi-infinite Linear Programming

2005 ◽  
Vol 128 (1) ◽  
pp. 167-174 ◽  
Author(s):  
LiMin Zhu ◽  
Ye Ding ◽  
Han Ding
Keyword(s):  
Linear Programming ◽  
Chebyshev Approximation ◽  
Approximation Problem ◽  
Linear Complex ◽  
Infinite Linear Programming ◽  
Minimum Zone ◽  
Effectiveness And Efficiency ◽  
Primal And Dual ◽  
Straightness Error ◽  
Infinite Linear

This paper presents a novel methodology for evaluating spatial straightness error based on the minimum zone criterion. Spatial straightness evaluation is formulated as a linear complex Chebyshev approximation problem, and then reformulated as a semi-infinite linear programming problem. Both models for the primal and dual programs are developed. An efficient simplex-based algorithm is employed to solve the dual linear program to yield the straightness value. Also a general algebraic criterion for checking the optimality of the solution is proposed. Numerical experiments are given to verify the effectiveness and efficiency of the presented algorithm.

scholarly journals Chebyshev approximation by interpolating rationals

1984 ◽  
Vol 40 (4) ◽  
pp. 310-312
Author(s):  
Charles B Dunham
Keyword(s):  
Chebyshev Approximation

Research on Situated Reconstitution of Non-Manifold Polyhedral from Function-to-Form Mapping

2013 ◽  
Vol 774-776 ◽  
pp. 1766-1769
Author(s):  
Zhi Gang Xu ◽  
Zi Xiang Li ◽  
Jin Wang ◽  
Tao Tao Liu ◽  
Chun Po Sun
Keyword(s):  
Design Automation ◽  
Algebraic Reasoning ◽  
Top Down ◽  
Automation Systems ◽  
Geometric Elements

Situated reconstitution is proposed in this paper to cope with un-manifold polyhedral from the function to form mapping processes. Specifically the situated reconstitution is not simply re-arrangement of geometric elements, mainly face entities in the un-manifold polyhedral, rather it needs a complex geometric/algebraic reasoning to reconstitute a manifold object, novel mathematical as well as AI techniques are introduced in this paper, several tools are developed to testify the proposed situated reconstitution in the “top-down” design automation systems.

Polynomial Chebyshev approximation of a complex transfer function

Computing ◽  
1971 ◽  
Vol 8 (3-4) ◽  
pp. 335-342
Author(s):  
C. Dierick ◽  
Y. Kamp
Keyword(s):  
Transfer Function ◽  
Chebyshev Approximation
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