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Journal articles on the topic 'Curva de Bézier'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Rizal, Syamsul, and Dong-Seong Kim. "Image Transmission in Military Network Using Bézier Curve." Journal of Advances in Computer Networks 3, no. 2 (2015): 141–45. http://dx.doi.org/10.7763/jacn.2015.v3.156.

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2

Li, Juncheng, and Dongbiao Zhao. "An Investigation on Image Compression Using the Trigonometric Bézier Curve with a Shape Parameter." Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/731648.

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A trigonometric Bézier curve analogous to the cubic polynomial Bézier curve, with a shape parameter, is presented in this work. The proposed curve inherits properties similar to those of cubic polynomial Bézier curve, and the shape of the curve can be adjusted by altering the value of the shape parameter while the control polygon is fixed. With the shape parameter, the proposed curve can be made closer to the given control polygon than the general cubic Bézier curve. Then, image compression using the trigonometric Bézier curve approximation method is investigated. Experimental results show tha

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3

Li, Caiyun, and Chungang Zhu. "Designing Developable C-Bézier Surface with Shape Parameters." Mathematics 8, no. 3 (2020): 402. http://dx.doi.org/10.3390/math8030402.

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Developable surface plays an important role in geometric design, architectural design, and manufacturing of material. Bézier curve and surface are the main tools in the modeling of curve and surface. Since polynomial representations can not express conics exactly and have few shape handles, one may want to use rational Bézier curves and surfaces whose weights control the shape. If we vary a weight of rational Bézier curve or surface, then all of the rational basis functions will be changed. The derivation and integration of the rational curve will yield a high degree curve, which means that th

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4

Wu, Zhi, Chu yi Song, and De xi Bao. "An Approximation Method of Bézier Curve." Computer and Information Science 10, no. 4 (2017): 67. http://dx.doi.org/10.5539/cis.v10n4p67.

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It is proved that the linear space constructed by power base is a banach space under 2-norm by using approximation method. For the Bézier curve--the elements in banach space, the linear combination of the low-order S power base is used to approximate optimal the high-order Bernstein base function. The original Bézier curve is instituted by the linear combination of low-order S power base and the optimal approximation element of the original Bézier curve is obtained.

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5

Hu, Gang, Huanxin Cao та Suxia Zhang. "Approximate Multidegree Reduction ofλ-Bézier Curves". Mathematical Problems in Engineering 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/8140427.

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Besides inheriting the properties of classical Bézier curves of degreen, the correspondingλ-Bézier curves have a good performance in adjusting their shapes by changing shape control parameter. In this paper, we derive an approximation algorithm for multidegree reduction ofλ-Bézier curves in theL2-norm. By analysing the properties ofλ-Bézier curves of degreen, a method which can deal with approximatingλ-Bézier curve of degreen+1byλ-Bézier curve of degreem (m≤n)is presented. Then, in unrestricted andC0,C1constraint conditions, the new control points of approximatingλ-Bézier curve can be obtained

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6

BiBi, Samia, Md Yushalify Misro, Muhammad Abbas, Abdul Majeed, and Tahir Nazir. "G3 Shape Adjustable GHT-Bézier Developable Surfaces and Their Applications." Mathematics 9, no. 19 (2021): 2350. http://dx.doi.org/10.3390/math9192350.

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In this article, we proposed a novel method for the construction of generalized hybrid trigonometric (GHT-Bézier) developable surfaces to tackle the issue of modeling and shape designing in engineering. The GHT-Bézier developable surface is obtained by using the duality principle between the points and planes with GHT-Bézier curve. With different shape control parameters in their domain, a class of GHT-Bézier developable surfaces can be established (such as enveloping developable GHT-Bézier surfaces, spine curve developable GHT-Bézier surfaces, geodesic interpolating surfaces for GHT-Bézier su

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7

Louzazni, Mohamed, Sameer Al-Dahidi, and Marco Mussetta. "Fuel Cell Characteristic Curve Approximation Using the Bézier Curve Technique." Sustainability 12, no. 19 (2020): 8127. http://dx.doi.org/10.3390/su12198127.

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Accurate modelling of the fuel cell characteristics curve is essential for the simulation analysis, control management, performance evaluation, and fault detection of fuel cell power systems. However, the big challenge in fuel cell modelling is the multi-variable complexity of the characteristic curves. In this paper, we propose the implementation of a computer graphic technique called Bézier curve to approximate the characteristics curves of the fuel cell. Four different case studies are examined as follows: Ballard Systems, Horizon H-12 W stack, NedStackPS6, and 250 W proton exchange membran

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8

Nuntawisuttiwong, Taweechai, and Natasha Dejdumrong. "An Approximation of Bézier Curves by a Sequence of Circular Arcs." Information Technology and Control 50, no. 2 (2021): 213–23. http://dx.doi.org/10.5755/j01.itc.50.2.25178.

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Some researches have investigated that a Bézier curve can be treated as circular arcs. This work is to proposea new scheme for approximating an arbitrary degree Bézier curve by a sequence of circular arcs. The sequenceof circular arcs represents the shape of the given Bézier curve which cannot be expressed using any other algebraicapproximation schemes. The technique used for segmentation is to simply investigate the inner anglesand the tangent vectors along the corresponding circles. It is obvious that a Bézier curve can be subdivided intothe form of subcurves. Hence, a given Bézier curve can

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9

Ammad, Muhammad, and Md Yushalify Misro. "Construction of Local Shape Adjustable Surfaces Using Quintic Trigonometric Bézier Curve." Symmetry 12, no. 8 (2020): 1205. http://dx.doi.org/10.3390/sym12081205.

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Based on quintic trigonometric Bézier like basis functions, the biquintic Bézier surfaces are modeled with four shape parameters that not only possess the key properties of the traditional Bézier surface but also have exceptional shape adjustment. In order to construct Bézier like curves with shape parameters, we present a class of quintic trigonometric Bézier like basis functions, which is an extension of a traditional Bernstein basis. Then, according to these basis functions, we construct three different types of shape adjustable surfaces such as general surface, swept surface and swung surf

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10

Majeed, Abdul, Muhammad Abbas, Amna Abdul Sittar, Mohsin Kamran, Saba Tahseen, and Homan Emadifar. "New Cubic Trigonometric Bezier-Like Functions with Shape Parameter: Curvature and Its Spiral Segment." Journal of Mathematics 2021 (September 13, 2021): 1–13. http://dx.doi.org/10.1155/2021/6330649.

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This work presents the new cubic trigonometric Bézier-type functions with shape parameter. Basis functions and the curve satisfy all properties of classical Bézier curve-like partition of unity, symmetric property, linear independent, geometric invariance, and convex hull property and have been proved. The C 3 and G 3 continuity conditions between two curve segments have also been achieved. To check the applicability of proposed functions, different types of open and closed curves have been constructed. The effect of shape parameter and control points has been observed. It is observed that, by

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11

Said Mad Zain, Syed Ahmad Aidil Adha, Md Yushalify Misro, and Kenjiro T. Miura. "Generalized Fractional Bézier Curve with Shape Parameters." Mathematics 9, no. 17 (2021): 2141. http://dx.doi.org/10.3390/math9172141.

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The construction of new basis functions for the Bézier or B-spline curve has been one of the most popular themes in recent studies in Computer Aided Geometric Design (CAGD). Implementing the new basis functions with shape parameters provides a different viewpoint on how new types of basis functions can develop complex curves and surfaces beyond restricted formulation. The wide selection of shape parameters allows more control over the shape of the curves and surfaces without altering their control points. However, interpolated parametric curves with higher degrees tend to overshoot in the proc

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12

BiBi, Samia, Muhammad Abbas, Kenjiro T. Miura, and Md Yushalify Misro. "Geometric Modeling of Novel Generalized Hybrid Trigonometric Bézier-Like Curve with Shape Parameters and Its Applications." Mathematics 8, no. 6 (2020): 967. http://dx.doi.org/10.3390/math8060967.

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The main objective of this paper is to construct the various shapes and font designing of curves and to describe the curvature by using parametric and geometric continuity constraints of generalized hybrid trigonometric Bézier (GHT-Bézier) curves. The GHT-Bernstein basis functions and Bézier curve with shape parameters are presented. The parametric and geometric continuity constraints for GHT-Bézier curves are constructed. The curvature continuity provides a guarantee of smoothness geometrically between curve segments. Furthermore, we present the curvature junction of complex figures and also

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13

Li, Fenhong, Gang Hu, Muhammad Abbas, and Kenjiro T. Miura. "The Generalized H-Bézier Model: Geometric Continuity Conditions and Applications to Curve and Surface Modeling." Mathematics 8, no. 6 (2020): 924. http://dx.doi.org/10.3390/math8060924.

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The local controlled generalized H-Bézier model is one of the most useful tools for shape designs and geometric representations in computer-aided geometric design (CAGD), which is owed to its good geometric properties, e.g., symmetry and shape adjustable property. In this paper, some geometric continuity conditions for the generalized cubic H-Bézier model are studied for the purpose of constructing shape-controlled complex curves and surfaces in engineering. Firstly, based on the linear independence of generalized H-Bézier basis functions (GHBF), the conditions of first-order and second-order

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14

王, 芳. "Rational Bézier Curve and Its Application." Advances in Applied Mathematics 06, no. 08 (2017): 935–41. http://dx.doi.org/10.12677/aam.2017.68112.

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15

Erkan, Esra, and Salim Yüce. "Serret-Frenet Frame and Curvatures of Bézier Curves." Mathematics 6, no. 12 (2018): 321. http://dx.doi.org/10.3390/math6120321.

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The aim of this study is to view the role of Bézier curves in both the Euclidean plane E 2 and Euclidean space E 3 with the help of the fundamental algorithm which is commonly used in Computer Science and Applied Mathematics and without this algorithm. The Serret-Frenet elements of non-unit speed curves in the Euclidean plane E 2 and Euclidean space E 3 are given by Gray et al. in 2016. We used these formulas to find Serret-Frenet elements of planar Bézier curve at the end points and for every parameter t. Moreover, we reconstruct these elements for a planar Bézier curve, which is defined by t

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16

Molinari, José Robyson Aggio, and Franciéle Maria de Souza Retslaff. "Curvas de Bézier no software Geogebra e suas aplicações." Revista do Instituto GeoGebra Internacional de São Paulo. ISSN 2237-9657 8, no. 2 (2019): 026–43. http://dx.doi.org/10.23925/2237-9657.2019.v8i2p026-043.

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Este trabalho teve como objetivo, o estudo das Curvas de Bézier, tanto a parte geométrica, quanto a parte algébrica. A parte geométrica foi construída no software Geogebra e a parte algébrica pelo polinômio de Bernstein. Foram estudadas as propriedades: fecho convexo, interpolação de pontos finais, design das curvas e pseudo controle local. Diversas são as aplicações com as Curvas de Bézier e neste estudo há mais uma aplicação inédita para a área florestal, sendo o cálculo do volume de árvores em pé, para a espécie Pinus Elliottii. Com as Curvas de Bézier, foi possível o cálculo do volume com

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17

AYDIN, TUBA AĞIRMAN. "A MATRIX PRESENTATION OF HIGHER ORDER DERIVATIVES OF BÉZIER CURVE AND SURFACE." Journal of Science and Arts 21, no. 1 (2021): 77–90. http://dx.doi.org/10.46939/j.sci.arts-21.1-a08.

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In this study, the Bézier curves and surfaces, which have an important place in interactive design applications, are expressed in matrix form using a special matrix that gives the coefficients of the Bernstein base polynomial. The matrix forms of higher order derivatives of the Bézier curves and surfaces are obtained. It is demonstrated by numerical examples that the bidirectional transition between the control points and parametric equations of the Bézier curves and surfaces can be easily achieved using these matrix forms. In addition, it is demonstrated that this type of curve and surface, w

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18

Shen, Wan-qiang, and Guo-zhao Wang. "Degree elevation from Bézier curve to C-Bézier curve with corner cutting form." Applied Mathematics-A Journal of Chinese Universities 31, no. 2 (2016): 165–76. http://dx.doi.org/10.1007/s11766-016-3369-0.

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19

Maqsood, Sidra, Muhammad Abbas, Gang Hu, Ahmad Lutfi Amri Ramli, and Kenjiro T. Miura. "A Novel Generalization of Trigonometric Bézier Curve and Surface with Shape Parameters and Its Applications." Mathematical Problems in Engineering 2020 (May 25, 2020): 1–25. http://dx.doi.org/10.1155/2020/4036434.

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Adopting a recurrence technique, generalized trigonometric basis (or GT-basis, for short) functions along with two shape parameters are formulated in this paper. These basis functions carry a lot of geometric features of classical Bernstein basis functions and maintain the shape of the curve and surface as well. The generalized trigonometric Bézier (or GT-Bézier, for short) curves and surfaces are defined on these basis functions and also analyze their geometric properties which are analogous to classical Bézier curves and surfaces. This analysis shows that the existence of shape parameters br

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20

Naseer, Salma, Muhammad Abbas, Homan Emadifar, Samia Bi Bi, Tahir Nazir, and Zaheer Hussain Shah. "A Class of Sextic Trigonometric Bézier Curve with Two Shape Parameters." Journal of Mathematics 2021 (June 26, 2021): 1–16. http://dx.doi.org/10.1155/2021/9989810.

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In this paper, we present a new class of sextic trigonometric Bernstein (ST-Bernstein, for short) basis functions with two shape parameters along with their geometric properties which are similar to the classical Bernstein basis functions. A sextic trigonometric Bézier (ST-Bézier, for short) curve with two shape parameters and their geometric characteristics is also constructed. The continuity constraints for the connection of two adjacent ST-Bézier curves segments are discussed. Shape control parameters can provide an opportunity to modify the shape of curve as designer desired. Some open and

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21

Park, Hae Yeon, and Young Joon Ahn. "Isoparametric Curve of Quadratic F-Bézier Curve." Journal of the Chosun Natural Science 6, no. 1 (2013): 46–52. http://dx.doi.org/10.13160/ricns.2013.6.1.046.

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22

Abbas, Muhammad, Norhidayah Ramli, Ahmad Abd Majid, and Jamaludin Md Ali. "The Representation of Circular Arc by Using Rational Cubic Timmer Curve." Mathematical Problems in Engineering 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/408492.

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In CAD/CAM systems, rational polynomials, in particular the Bézier or NURBS forms, are useful to approximate the circular arcs. In this paper, a new representation method by means of rational cubic Timmer (RCT) curves is proposed to effectively represent a circular arc. The turning angle of a rational cubic Bézier and rational cubic Ball circular arcs without negative weight is still not more than4π/3andπ, respectively. The turning angle of proposed approach is more than Bézier and Ball circular arcs with easier calculation and determination of control points. The proposed method also provides

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23

Shao, Lejun, and Hao Zhou. "Curve Fitting with Bézier Cubics." Graphical Models and Image Processing 58, no. 3 (1996): 223–32. http://dx.doi.org/10.1006/gmip.1996.0019.

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24

Sederberg, T. W., and T. Nishita. "Curve intersection using Bézier clipping." Computer-Aided Design 22, no. 9 (1990): 538–49. http://dx.doi.org/10.1016/0010-4485(90)90039-f.

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25

COX, M. G., and P. M. HARRIS. "The Approximation of a Composite Bézier Cubic Curve by a Composite Bézier Quadratic Curve." IMA Journal of Numerical Analysis 11, no. 2 (1991): 159–80. http://dx.doi.org/10.1093/imanum/11.2.159.

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26

Zube, Severinas. "Interpolation method for quaternionic-Bezier curves." Lietuvos matematikos rinkinys 59 (December 20, 2018): 13–18. http://dx.doi.org/10.15388/lmr.a.2018.03.

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27

Purwar, Anurag, and Qiaode Jeffrey Ge. "On the Effect of Dual Weights in Computer Aided Design of Rational Motions." Journal of Mechanical Design 127, no. 5 (2005): 967–72. http://dx.doi.org/10.1115/1.1906263.

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In recent years, it has become well known that rational Bézier and B-spline curves in the space of dual quaternions correspond to rational Bézier and B-spline motions. However, the influence of weights of these dual quaternion curves on the resulting rational motions has been largely unexplored. In this paper, we present a thorough mathematical exposition on the influence of dual-number weights associated with dual quaternions for rational motion design. By deriving the explicit equations for the point trajectories of the resulting motion, we show that the effect of real weights on the resulti

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28

CHUON, CHANSOPHEA, SUMANTA GUHA, PAUL JANECEK, and NGUYEN DUC CONG SONG. "SIMPLIPOLY: CURVATURE-BASED POLYGONAL CURVE SIMPLIFICATION." International Journal of Computational Geometry & Applications 21, no. 04 (2011): 417–29. http://dx.doi.org/10.1142/s0218195911003743.

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A curvature-based algorithm to simplify a polygonal curve is described, together with its implementation. The so-called SimpliPoly algorithm uses Bézier curves to approximate pieces of the input curve, and assign curvature estimates to vertices of the input polyline from curvature values computed for the Bézier approximations. The authors' implementation of SimpliPoly is interactive and available freely on-line. Additionally, a third-party implementation of SimpliPoly as a plug-in for the GNU Blender 3D modeling software is available. Empirical comparisons indicate that SimpliPoly performs as

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29

Hu, Gang, Xiaomin Ji, Xinqiang Qin та Suxia Zhang. "Shape Modification forλ-Bézier Curves Based on Constrained Optimization of Position and Tangent Vector". Mathematical Problems in Engineering 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/735629.

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Besides inheriting the properties of classical Bézier curves of degreen, the correspondingλ-Bézier curves have a good performance on adjusting their shapes by changing shape control parameter. Specially, in the case where the shape control parameter equals zero, theλ-Bézier curves degenerate to the classical Bézier curves. In this paper, the shape modification ofλ-Bézier curves by constrained optimization of position and tangent vector is investigated. The definition and properties ofλ-Bézier curves are given in detail, and the shape modification is implemented by optimizing perturbations of c

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30

Li, Jing-Gai, and Chun-Gang Zhu. "Curve and surface construction based on the generalized toric-Bernstein basis functions." Open Mathematics 18, no. 1 (2020): 36–56. http://dx.doi.org/10.1515/math-2020-0004.

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Abstract The construction of parametric curve and surface plays an important role in computer aided geometric design (CAGD), computer aided design (CAD), and geometric modeling. In this paper, we define a new kind of blending functions associated with a real points set, called generalized toric-Bernstein (GT-Bernstein) basis functions. Then, the generalized toric-Bézier (GT-Bézier) curves and surfaces are constructed based on the GT-Bernstein basis functions, which are the projections of the (irrational) toric varieties in fact and the generalizations of the classical rational Bézier curves/su

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31

Abu Hasan, Zabidi, Zainor Ridzuan Yahya, Nur Afifah Rusdi, and Nurshazneem Roslan. "Curve Reconstruction In Different Cubic Functions Using Differential Evolution." MATEC Web of Conferences 150 (2018): 06030. http://dx.doi.org/10.1051/matecconf/201815006030.

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This paper discusses the comparison on using two types of curves for curve reconstruction. Differential Evolution (DE) is used to optimize the parameter in the related spline function. DE minimized the Sum Square Error (SSE) to find the best curve that fit the data. The two curves namely cubic Bézier and cubic Ball is used for comparison purposes. For the curve reconstruction, the cubic Ball consumes less calculation time compare to cubic Bézier and gives better curve approximation based on the errors result. Visualization and numerical comparison shall be given.

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32

CHEN, Xiao. "Disk Bézier Curve Approximation of the Offset Curve." Journal of Software 16, no. 4 (2005): 616. http://dx.doi.org/10.1360/jos160616.

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33

Galdames Bravo, Orlando. "Modelización con curvas y superficies de Bézier." Modelling in Science Education and Learning 4 (June 5, 2011): 181. http://dx.doi.org/10.4995/msel.2011.3071.

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<p>Las curvas de Bézier, un instrumento matemático para la modelización de curvas y superficies, nacieron como una aplicación concreta en el seno de la industria automovilística. El presente artículo pretende recuperar este ejemplo para mostrar como ciertos desarrollos matemáticos que surgieron directamente en la industria, pueden utilizarse como contenidos en la enseñanza universitaria. Explicaremos cómo y por qué surgen, y también su formulación matemática junto con alguno de los problemas que plantea. Para finalizar describimos una experiencia en el aula y extraemos algunas conclusion

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Xu, Wei Xiang, Liu Qiang Wang, and Xu Min Liu. "Quadratic TC-Bézier Curves with Shape Parameter." Advanced Materials Research 179-180 (January 2011): 1187–92. http://dx.doi.org/10.4028/www.scientific.net/amr.179-180.1187.

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Quadratic TC-Bézier curves with shape parameter is constructed in a special space, it shares most optimal properties as those of the quadratic Bézier curves and its shape can be adjusted by changing the parameter value in . The circle and ellipse can be represented with this curve accurately. Presents G1 condition of quadratic TC-Bézier curves, the results have definite geometric meanings and can be applied to surface modeling conveniently.

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Huang, Youdu, Huaming Su, and Hongwei Lin. "A simple method for approximating rational Bézier curve using Bézier curves." Computer Aided Geometric Design 25, no. 8 (2008): 697–99. http://dx.doi.org/10.1016/j.cagd.2008.03.001.

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Lin, Qun, and J. G. Rokne. "Intersection test and blossoming perturbation for disk parametric curves and ball parametric surfaces." Mathematical Problems in Engineering 2006 (2006): 1–28. http://dx.doi.org/10.1155/mpe/2006/29643.

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Errors in curve and surface representation due to inaccuracies in the data are considered and accounted for by introducing disk parametric curves and ball parametric surfaces. Intersection test algorithms and interval extensions using blossoming are discussed for each of the three cases of Bézier curves, tensor product surfaces, and triangular patches. A stability analysis is also performed for each of the three cases. It is shown that under certain restrictions disk Bézier curves and triangular ball Bézier patches are stable with respect to perturbations of the control disks (balls); whereas

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Liu, Xiaomin, Muhammad Abbas, Gang Hu, and Samia BiBi. "Degree Reduction of Q-Bézier Curves via Squirrel Search Algorithm." Mathematics 9, no. 18 (2021): 2212. http://dx.doi.org/10.3390/math9182212.

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Q-Bézier curves find extensive applications in shape design owing to their excellent geometric properties and good shape adjustability. In this article, a new method for the multiple-degree reduction of Q-Bézier curves by incorporating the swarm intelligence-based squirrel search algorithm (SSA) is proposed. We formulate the degree reduction as an optimization problem, in which the objective function is defined as the distance between the original curve and the approximate curve. By using the squirrel search algorithm, we search within a reasonable range for the optimal set of control points o

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Park, Yungeom, U. Jin Choi, and Ha-Jine Kimn. "Approximate conversion of Bézier curves." Bulletin of the Australian Mathematical Society 51, no. 1 (1995): 153–62. http://dx.doi.org/10.1017/s0004972700013988.

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The methods for generating a polynomial Bézier approximation of degree n − 1 to an nth degree Bézier curve, and error analysis, are presented. The methods are based on observations of the geometric properties of Bézier curves. The approximation agrees at the two endpoints up to a preselected smoothness order. The methods allow a detailed error analysis, providing a priori bounds of the point-wise approximation error. The error analysis for other authors’ methods is also presented.

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39

Ait-Haddou, Rachid, and Walter Herzog. "Convex subdivision of a Bézier curve." Computer Aided Geometric Design 19, no. 8 (2002): 663–71. http://dx.doi.org/10.1016/s0167-8396(02)00161-9.

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40

Lin, Hongwei, Ligang Liu, and Guojin Wang. "Boundary evaluation for interval Bézier curve." Computer-Aided Design 34, no. 9 (2002): 637–46. http://dx.doi.org/10.1016/s0010-4485(01)00130-0.

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Hussain, Maria, Sana Zafar, and Malik Zawwar Hussain. "Energy-Minimizing Cubic H-Bézier Curve." Journal of Testing and Evaluation 49, no. 4 (2020): 20190750. http://dx.doi.org/10.1520/jte20190750.

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42

Wu, Bei-bei, and Chuan-qing GU. "A new fractional rational Bézier curve." Journal of Shanghai University (English Edition) 9, no. 3 (2005): 216–18. http://dx.doi.org/10.1007/s11741-005-0080-4.

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43

Montès, P. "Kriging interpolation of a Bézier curve." Computer-Aided Design 23, no. 10 (1991): 713–16. http://dx.doi.org/10.1016/0010-4485(91)90025-r.

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44

Yu, Leiyan, Xianyu Wang, Zeyu Hou, Zaiyou Du, Yufeng Zeng, and Zhaoyang Mu. "Path Planning Optimization for Driverless Vehicle in Parallel Parking Integrating Radial Basis Function Neural Network." Applied Sciences 11, no. 17 (2021): 8178. http://dx.doi.org/10.3390/app11178178.

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To optimize performances such as continuous curvature, safety, and satisfying curvature constraints of the initial planning path for driverless vehicles in parallel parking, a novel method is proposed to train control points of the Bézier curve using the radial basis function neural network method. Firstly, the composition and working process of an autonomous parking system are analyzed. An experiment concerning parking space detection is conducted using an Arduino intelligent minicar with ultrasonic sensor. Based on the analysis of the parallel parking process of experienced drivers and the i

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Wang, Cheng Wei. "α Extension of the Cubic Ball Curve". Applied Mechanics and Materials 235 (листопад 2012): 85–89. http://dx.doi.org/10.4028/www.scientific.net/amm.235.85.

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Ball curve； curve design； shape parameter Abstract. Ball curve is found similar to Bézier curve，also it has a good property of shape preserving，and in some respects，it has better properties than the Bézier curve. Therefore, In the shape design，Ball curve is paid more and more attention, it has a wide application. By introducing the concept of weights in NURBS curve into a blending technique, the paper extends the representation of the cubic Ball curve. The generalized cubic Ball curve is denoted as α extension cubic Ball curve, whose shape-control capability is shown to be much better than tha

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Cai, Hua Hui, Yan Cheng, and Yong Hong Zhu. "Multi-Degree Reduction of DP Curves with Constraints of Endpoints Continuity." Applied Mechanics and Materials 215-216 (November 2012): 669–73. http://dx.doi.org/10.4028/www.scientific.net/amm.215-216.669.

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In this paper, we presented a constrained multi-degree reduction algorithm of DP curves based on the transformation between the DP and Bézier curves. We first correct the conversion formula between Bernstein basis and DP basis. And then, we deal with multi-degree reduction of NP curves by degree reduction of Bézier curve.

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Liu, Xu Min, Xian Peng Yang, and Yan Ling Wu. "Biquadratic TC-Bézier Curves with Shape Parameter." Key Engineering Materials 467-469 (February 2011): 57–62. http://dx.doi.org/10.4028/www.scientific.net/kem.467-469.57.

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Shape controlling is a popular topic in curves and surfaces design with free form. In this paper, a new curve, to be called Biquadratic TC-Bézier curves with shape parameter , is constructed in the space . We show that such curves share the same properties as the traditional Bézier curves in polynomial spaces. The shape of new curves, representing circle and ellipse accurately, can be adjusted by changing the value of the parameter . Then we give the G1 continuity conditions of Biquadratic TC-Bézier curves with shape parameter and its application in surfaces modeling.

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SARFRAZ, MUHAMMAD. "SOME ALGORITHMS FOR CURVE DESIGN AND AUTOMATIC OUTLINE CAPTURING OF IMAGES." International Journal of Image and Graphics 04, no. 02 (2004): 301–24. http://dx.doi.org/10.1142/s0219467804001427.

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A new multipurpose curve technique has been introduced which is meant to automatically provide a fit to any ordered data in a plane. The technique is particularly economical for designing purposes as well as for the visualization of a large amount of data sets. A more flexible class of cubic functions is the basis of this technique. This class of functions involves two control parameters, to produce more flexible shapes than ordinary Bézier cubics or Hermite cubics, in each segment. These functions, together with the control parameters, are utilized to fit a design curve in an interactive way.

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Kagami, Yoshiyuki, Takashi Emura, and Masayuki Hiyama. "Vision-based playback method of wheeled mobile robots." Robotica 18, no. 3 (2000): 281–86. http://dx.doi.org/10.1017/s026357479900257x.

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This paper describes a new vision-based playback method of a wheeled mobile robot. The path of the robot is divided into straight line parts and curved line parts. The curved line parts were approximated by a Bézier curve to decrease the volume of data. In order to track the curved line parts with good accuracy, tracking errors were detected by referring to two pre-recorded images on one part of the curve. Then, the errors were corrected by adjusting the control points of the Bézier curve. Outdoor experiments demonstrated good repeatability by using the proposed method.

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Hu, Gang, Cuicui Bo, Junli Wu, Guo Wei, and Fei Hou. "Modeling of Free-Form Complex Curves Using SG-Bézier Curves with Constraints of Geometric Continuities." Symmetry 10, no. 11 (2018): 545. http://dx.doi.org/10.3390/sym10110545.

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The modeling of free-form engineering complex curves is an important subject in product modeling, graphics, and computer aided design/computer aided manufacturing (CAD/CAM). In this paper, we propose a novel method to construct free-form complex curves using shape-adjustable generalized Bézier (or SG-Bézier, for short) curves with constraints of geometric continuities. In order to overcome the difficulty that most of the composite curves in engineering cannot often be constructed by using only a single curve, we propose the necessary and sufficient conditions for G1 and G2 continuity between t

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