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On the Bertrand Pairs of Open Non-Uniform Rational B-Spline Curves
2021B-spline curves are used basically in Computer-Aided Design (CAD), Computer-Aided Geometric Design (CAGD), and Computer-Aided Modeling (CAM). In determining the invariants of curves and surfaces at any point, there are some difficulties in expressing it analytically and calculating its invariants at the desired point.
İncesu, Muhsin +2 more
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EVELOPMENT OF NON-UNIFORM RATIONAL TYPE-2 FUZZY B-SPLINE CURVE MODELING
Advances in Differential Equations and Control Processes, 2020Type-2 fuzzy set offers an opportunity to define a fuzzy control point with type-2 levels of uncertainty. We discuss the development of non-uniform B-spline curve model based on type-2 fuzzy set theory and also a type-2 level of NURBS curve model. First we define type-2 fuzzy control points and type-2 fuzzy weight using a type-2 fuzzy number.
Wahab, Abd. Fatah +2 more
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On Non-Uniform Rational B-Splines Surface Neural Networks
Neural Processing Letters, 2008A novel bi-variate non-uniform rational B-splines (NURBS) surface neural network consisting of four hidden layers is proposed in this paper. The blending functions are selected as the activation functions for the neurons in one of the hidden layers, instead of the commonly used sigmoid functions.
Ming-Yang Cheng +2 more
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Adapting Non-Uniform Rational B-Spline Fitting Approaches to Metamodeling
Volume 3: 25th Computers and Information in Engineering Conference, Parts A and B, 2005Modern engineering design requires the exploration of complex nonlinear design spaces that relate large numbers of design variables and performance criteria. Effective exploration and decision making requires the availability of efficient representations of high dimensional design spaces.
Cameron J. Turner, Richard H. Crawford
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Graph analysis of non-uniform rational B-spline-based metamodels
Engineering Optimization, 2014Over the past decade metamodels, also known as surrogate models, based on non-uniform rational B-splines (NURBs) have been developed. These metamodels exhibit unique properties that enable a wide range of computationally efficient analyses. Thus far, the analysis of these metamodels has been of a geometric nature, but in this article an approach based ...
John C. Steuben, Cameron J. Turner
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General Form Tolerance Evaluation Using Non-Uniform Rational B-Splines
Volume 3: 22nd Design Automation Conference, 1996Abstract Tolerance evaluation is critical to quality assurance in modern manufacturing. In contrast to traditional measurement which relies on specific hard gauges, coordinate measuring machines provide more flexibility for dimensional measurement and tolerance evaluations.
Hong-Tzong Yau, Kuei-Wu Chen
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Feedrate control for non-uniform rational B-spline motion command generation
Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2006This paper presents a real-time feedrate-controlled interpolator (FCI) for accurate feedrate control of computer numerical controlled (CNC) machine tools along non-uniform rational B-spline (NURBS) curves for precision machining. Unlike most of the existing interpolators that are developed based on the Taylor's expansion, the proposed method uses a ...
C W Cheng, M C Tsai, J Maciejowski
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Non-uniform-rational-B-splines (NURBS) in illumination design
Frontiers in Optics, 2003After a brief explanation of NURBS concepts [1], this work considers the use of NURBS surfaces in illumination system design. An important design case is creating a uniform illuminance distribution on a target plane. This work demonstrates an optimization design approach that results in an efficient faceted reflector system.
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An approach to representing heterogeneous non-uniform rational B-spline objects
Transactions of Tianjin University, 2011The representation method of heterogeneous material information is one of the key technologies of heterogeneous object modeling, but almost all the existing methods cannot represent non-uniform rational B-spline (NURBS) entity. According to the characteristics of NURBS, a novel data structure, named NURBS material data structure, is proposed, in which ...
Ting Zang, Anping Xu
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Review on Non Uniform Rational B-Spline (NURBS): Concept and Optimization
Advanced Materials Research, 2014This paper is to provide literature review of the Non Uniform Rational B-Splines (NURBS) formulation in the curve and surface constructions. NURBS curves and surfaces have a wide application in Computer Aided Geometry Design (CAGD), Computer Aided Design (CAD), image processing and etc.
Ali Munira +3 more
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