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Relevant bibliographies by topics / Non-uniform B-spline curves

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Journal articles

Academic literature on the topic 'Non-uniform B-spline curves'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Non-uniform B-spline curves"

1

Dube, Mridula, and Reenu Sharma. "Cubic TP B-Spline Curves with a Shape Parameter." International Journal of Engineering Research in Africa 11 (October 2013): 59–72. http://dx.doi.org/10.4028/www.scientific.net/jera.11.59.

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In this paper a new kind of splines, called cubic trigonometric polynomial B-spline (cubic TP B-spline) curves with a shape parameter, are constructed over the space spanned by As each piece of the curve is generated by three consecutive control points, they posses many properties of the quadratic B-spline curves. These trigonometric curves with a non-uniform knot vector are C1 and G2 continuous. They are C2 continuous when choosing special shape parameter for non-uniform knot vector. These curves are closer to the control polygon than the quadratic B-spline curves when choosing special shape

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2

Munira, Ali, Nur Najmiyah Jaafar, Abdul Aziz Fazilah, and Z. Nooraizedfiza. "Review on Non Uniform Rational B-Spline (NURBS): Concept and Optimization." Advanced Materials Research 903 (February 2014): 338–43. http://dx.doi.org/10.4028/www.scientific.net/amr.903.338.

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This 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. The formulation of NURBS showing that NURBS curves and surfaces requires three important parameters in controlling the curve and also modifying the shape of the curves and surfaces. Yet, curves and surfaces fitting are still the major problems in the geometrical modeling. With this, the researches that have bee

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3

Li, Ai Min, and Hai Bo Tian. "A Multiresolution Fairing Approach for NURBS Curves." Applied Mechanics and Materials 215-216 (November 2012): 1205–8. http://dx.doi.org/10.4028/www.scientific.net/amm.215-216.1205.

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Curve fairing has an important influence on curve editing and geometric modeling. Though there has been several different kinds of fairing methods, Multiresolution curve fairing has higher efficiency and simpler algorithms. Different from existing multiresolution curve fairing, a new multiresolution approach is presented based on non-uniform semiorthogonal B-spline wavelets, which can be applied for NURBS curve fairing. It has no restriction to B-spline curves’ knot sequence. This method effectively overcomes the limit of uniform or quasi-uniform B-spline wavelets for fairing. A detailed examp

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4

Majeed, Abdul, Muhammad Abbas, Faiza Qayyum, Kenjiro T. Miura, Md Yushalify Misro, and Tahir Nazir. "Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter." Mathematics 8, no. 12 (2020): 2102. http://dx.doi.org/10.3390/math8122102.

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Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ∈[0,4]. All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and ha

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5

Wang, Kai, and Guicang Zhang. "New Trigonometric Basis Possessing Denominator Shape Parameters." Mathematical Problems in Engineering 2018 (October 24, 2018): 1–25. http://dx.doi.org/10.1155/2018/9569834.

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Four new trigonometric Bernstein-like bases with two denominator shape parameters (DTB-like basis) are constructed, based on which a kind of trigonometric Bézier-like curve with two denominator shape parameters (DTB-like curves) that are analogous to the cubic Bézier curves is proposed. The corner cutting algorithm for computing the DTB-like curves is given. Any arc of an ellipse or a parabola can be exactly represented by using the DTB-like curves. A new class of trigonometric B-spline-like basis function with two local denominator shape parameters (DT B-spline-like basis) is constructed acco

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6

Dung, Van Than, and Tegoeh Tjahjowidodo. "A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting." PLOS ONE 12, no. 3 (2017): e0173857. http://dx.doi.org/10.1371/journal.pone.0173857.

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7

Hu, Liangchen, Huahao Shou, and Shiaofen Fang. "A PIA optimization algorithm for non-uniform B-spline curves and surfaces." International Journal of Modelling and Simulation 37, no. 3 (2017): 167–77. http://dx.doi.org/10.1080/02286203.2017.1309260.

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8

Tuo, Ming-Xiu, Gui-Cang Zhang, and Kai Wang. "A New Quasi Cubic Rational System with Two Parameters." Symmetry 12, no. 7 (2020): 1070. http://dx.doi.org/10.3390/sym12071070.

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The purpose of this article is to develop a new system for the construction of curves and surfaces. Making the new system not only has excellent properties of the orthodox Bézier and the B-spline method but also has practical properties such as variation diminishing and local shape adjustability. First, a new set of the quasi-cubic rational (QCR) system with two parameters is given, which is verified on an optimal normalized totally positive system (B-system). The related QCR Bézier curve is defined, and the de Casteljau-type algorithm are given. Next, a group of non-uniform QCR B-spline syste

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9

Li, J.-G., M.-M. Qiu, T.-H. Zhang, and Z.-X. Li. "A practical real-time non-uniform rational B-spline curve interpolator for computer numerical control machining." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226, no. 4 (2011): 1068–83. http://dx.doi.org/10.1177/0954406211418026.

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Non-uniform rational B-spline (NURBS) interpolator, a key technique in computer numerical control (CNC) machining, has many advantages over linear and circular interpolator. A practical real-time NURBS interpolator based on an off-line algorithm, which is developed to handle the limitation of velocity and acceleration, is presented in this article. Two processing modules are employed to realize the real-time interpolator. In one module, a NURBS curve is split into shorter NURBS curves or approximated as continuous line segments according to the minimum splitting length first, and then the velo

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10

Zhang, Wen Jie. "The Research of the NURBS Curve Interpolation Algorithm." Advanced Engineering Forum 2-3 (December 2011): 614–18. http://dx.doi.org/10.4028/www.scientific.net/aef.2-3.614.

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In this article, the definition, the nature and the parameter of the NURBS (Non-Uniform Rational B-spline) curves are defined, the more thorough analysis and research of the real-time NURBS curve interpolation algorithm and the feed rate adaptive control are carried out.

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