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Journal articles on the topic 'Circular arcs'

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Author: Grafiati

Published: 18 May 2024

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1

Aichholzer, Oswin, Wolfgang Aigner, Franz Aurenhammer, Kateřina Čech Dobiášová, Bert Jüttler, and Günter Rote. "Triangulations with Circular Arcs." Journal of Graph Algorithms and Applications 19, no. 1 (2015): 43–65. http://dx.doi.org/10.7155/jgaa.00346.

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2

Souppez, Jean-Baptiste R. G., Patrick Bot, and Ignazio Maria Viola. "Turbulent flow around circular arcs." Physics of Fluids 34, no. 1 (January 2022): 015121. http://dx.doi.org/10.1063/5.0075875.

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3

Schiefermayr, Klaus. "Chebyshev polynomials on circular arcs." Acta Scientiarum Mathematicarum 85, no. 34 (2019): 629–49. http://dx.doi.org/10.14232/actasm-018-343-y.

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4

Glassner, Andrew. "Reconciling Circular and Elliptical Arcs." Journal of Graphics, GPU, and Game Tools 15, no. 2 (May 11, 2010): 95–98. http://dx.doi.org/10.1080/2151237x.2011.563679.

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5

Adamaszek, Michał, Henry Adams, Florian Frick, Chris Peterson, and Corrine Previte-Johnson. "Nerve Complexes of Circular Arcs." Discrete & Computational Geometry 56, no. 2 (July 13, 2016): 251–73. http://dx.doi.org/10.1007/s00454-016-9803-5.

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6

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 the easier modification in the shape of circular arc showing in several numerical examples.

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7

Cretu, Simona Mariana, and Ionuţ Daniel Geonea. "Circular-Arc Radial Cams with One Connection Arc." Applied Mechanics and Materials 896 (February 2020): 83–94. http://dx.doi.org/10.4028/www.scientific.net/amm.896.83.

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This paper deals with the geometric and kinematic analysis of the circular-arc profile cams with one connection arc. If the maximum lift of the follower is required, it is shown that it is possible to connect two circular-arcs – that are defined by center of curvature and radius – through a single circular-arc, and the connection points result. But, if the connection points of two given circular-arcs of the cam profile are required, at least two circular-arcs are needed to connect them. The specific equations for the geometric analysis for one circular-arc profile are described. Also, for two mechanisms, one with straight-line profile and another with one circular-arc connection profile, the geometric and kinematic analysis and simulations of the movements using SolidWorks and ADAMS programs are presented

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8

PAL, SHYAMOSREE, RAHUL DUTTA, and PARTHA BHOWMICK. "CIRCULAR ARC SEGMENTATION BY CURVATURE ESTIMATION AND GEOMETRIC VALIDATION." International Journal of Image and Graphics 12, no. 04 (October 2012): 1250024. http://dx.doi.org/10.1142/s0219467812500246.

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A novel algorithm to detect circular arcs from a digital image is proposed. The algorithm is based on discrete curvature estimated for the constituent points of digital curve segments, followed by a fast geometric analysis. The curvature information is used in the initial stage to find the potentially circular segments. In the final stage, the circular arcs are merged and maximized in length using the radius and center information of the potentially circular segments. Triplets of longer segments are given higher priorities; doublets and singleton arcs are processed at the end. Detailed experimental results on benchmark datasets demonstrate its efficiency and robustness.

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9

Lu, Li Zheng. "Adaptive Polynomial Approximation to Circular Arcs." Applied Mechanics and Materials 50-51 (February 2011): 678–82. http://dx.doi.org/10.4028/www.scientific.net/amm.50-51.678.

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We present a new adaptive method for approximating circular arcs in polynomial form by using the s-power series. Circular arcs can be expressed in infinite series form, we obtain the order-k Hermite interpolant by truncating at the kth term. An upper bound on the error of the interpolant is available, so we can obtain the lowest degree polynomial curve that approximates a circular arc within any user-prescribed tolerance. And this degree can be further reduced through subdivision, which generates a spline approximation with Ck continuity at the joints.

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10

Su, YuYang, BingXuan Yu, Ruixin Peng, and HongShu Yan. "Image Edge Analysis and Application Based on Least Squares Fitting Model." Highlights in Science, Engineering and Technology 9 (September 30, 2022): 298–309. http://dx.doi.org/10.54097/hset.v9i.1859.

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This paper presents an effective method to automatically segment and fit the edge contour curve data of a picture into straight line segments, circular arc segments or elliptical arc segments. Firstly, the curvature of each point is calculated, and the curvature change breakpoints are found to distinguish between straight lines, circular arcs and elliptical arcs; then, circular arc segments and elliptical arcs are distinguished by the change degree of curvature of adjacent points, and the automatic segmentation of contour edges is realized. Finally, the circular arc segment and elliptic arc segment are fitted by least squares method, based on which the length of the straight line, the direction angle of the circular arc, the rotation angle of the elliptic arc and other related information are calculated. The results show that our model can better identify the feature texture information of image edges.

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11

PIEGL, LES A., and WAYNE TILLER. "FITTING CIRCULAR ARCS TO MEASURED DATA." International Journal of Shape Modeling 08, no. 01 (June 2002): 1–21. http://dx.doi.org/10.1142/s0218654302000029.

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12

Vavpetič, Aleš. "Optimal parametric interpolants of circular arcs." Computer Aided Geometric Design 80 (June 2020): 101891. http://dx.doi.org/10.1016/j.cagd.2020.101891.

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13

Pei, Soo-Chang, and Ji-Hwei Horng. "Fitting digital curve using circular arcs." Pattern Recognition 28, no. 1 (January 1995): 107–16. http://dx.doi.org/10.1016/0031-3203(94)00086-2.

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14

Na, Hyeon-Suk. "PLANE SWEEP ALGORITHM FOR CIRCULAR ARCS." Far East Journal of Mathematical Sciences (FJMS) 103, no. 10 (May 16, 2018): 1647–78. http://dx.doi.org/10.17654/ms103101647.

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15

Cheng, C. C., C. A. Duncan, M. T. Goodrich, and S. G. Kobourov. "Drawing planar graphs with circular arcs." Discrete & Computational Geometry 25, no. 3 (April 2001): 405–18. http://dx.doi.org/10.1007/s004540010080.

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16

Liu, Zhi, Jie-qing Tan, Xiao-yan Chen, and Li Zhang. "An approximation method to circular arcs." Applied Mathematics and Computation 219, no. 3 (October 2012): 1306–11. http://dx.doi.org/10.1016/j.amc.2012.07.038.

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17

Martini, Horst, and Senlin Wu. "Halving circular arcs in normed planes." Periodica Mathematica Hungarica 57, no. 2 (December 2008): 207–15. http://dx.doi.org/10.1007/s10998-008-8207-6.

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18

Karimäki, Veikko. "Fast code to fit circular arcs." Computer Physics Communications 69, no. 1 (February 1992): 133–41. http://dx.doi.org/10.1016/0010-4655(92)90134-k.

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19

Saund, E. "Identifying Salient Circular Arcs on Curves." CVGIP: Image Understanding 58, no. 3 (November 1993): 327–37. http://dx.doi.org/10.1006/ciun.1993.1045.

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20

Saund, E. "Identifying Salient Circular Arcs on Curves." Computer Vision and Image Understanding 58, no. 3 (November 1993): 327–37. http://dx.doi.org/10.1006/cviu.1993.1047.

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21

Dawson, Robert, and Pietro Milici. "Rectification of Circular Arcs by Linkages." Mathematical Intelligencer 42, no. 1 (July 8, 2019): 18–23. http://dx.doi.org/10.1007/s00283-019-09912-9.

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22

Héra, K., and M. Laczkovich. "The Kakeya Problem for Circular Arcs." Acta Mathematica Hungarica 150, no. 2 (October 24, 2016): 479–511. http://dx.doi.org/10.1007/s10474-016-0663-5.

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23

Nuntawisuttiwong, Taweechai, and Natasha Dejdumrong. "An Approximation of Bézier Curves by a Sequence of Circular Arcs." Information Technology and Control 50, no. 2 (June 17, 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 be expressed by a sequence of calculated points on thecurve corresponding to a parametric variable t. Although the resulting points can be used in the circular arcconstruction, some duplicate and irrelevant vertices should be removed. Then, the sequence of inner angles arecalculated and clustered from a sequence of consecutive pixels. As a result, the output dots are now appropriateto determine the optimal circular path. Finally, a sequence of circular segments of a Bézier curve can be approximatedwith the pre-defined resolution satisfaction. Furthermore, the result of the circular arc representationis not exceeding a user-specified tolerance. Examples of approximated nth-degree Bézier curves by circular arcsare shown to illustrate efficiency of the new method.

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24

Worring, M., and A. W. M. Smeulders. "Digitized circular arcs: characterization and parameter estimation." IEEE Transactions on Pattern Analysis and Machine Intelligence 17, no. 6 (June 1995): 587–98. http://dx.doi.org/10.1109/34.387505.

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25

Ahn, Young Joon, and Hong Oh Kim. "Approximation of circular arcs by Bézier curves." Journal of Computational and Applied Mathematics 81, no. 1 (June 1997): 145–63. http://dx.doi.org/10.1016/s0377-0427(97)00037-x.

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26

Sabitov, I. Kh, and A. V. Slovesnov. "Approximation of plane curves by circular arcs." Computational Mathematics and Mathematical Physics 50, no. 8 (August 2010): 1279–88. http://dx.doi.org/10.1134/s0965542510080014.

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27

Sen, Malay K., B. K. Sanyal, and Douglas B. West. "Representing digraphs using intervals or circular arcs." Discrete Mathematics 147, no. 1-3 (December 1995): 235–45. http://dx.doi.org/10.1016/0012-365x(94)00167-h.

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28

Dubinin, V. N., and S. I. Kalmykov. "On polynomials with constraints on circular arcs." Journal of Mathematical Sciences 184, no. 6 (July 11, 2012): 703–8. http://dx.doi.org/10.1007/s10958-012-0892-2.

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29

Goldapp, Michael. "Approximation of circular arcs by cubic polynomials." Computer Aided Geometric Design 8, no. 3 (August 1991): 227–38. http://dx.doi.org/10.1016/0167-8396(91)90007-x.

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30

Ahn, Young Joon, and Christoph Hoffmann. "Sequence ofGnLN polynomial curves approximating circular arcs." Journal of Computational and Applied Mathematics 341 (October 2018): 117–26. http://dx.doi.org/10.1016/j.cam.2018.03.028.

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31

Murthy, T. S. R. "Evaluation of conditional multiple concentric circular arcs." Precision Engineering 8, no. 4 (October 1986): 227–31. http://dx.doi.org/10.1016/0141-6359(86)90064-4.

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32

Joseph, S. H. "Unbiased Least Squares Fitting of Circular Arcs." CVGIP: Graphical Models and Image Processing 56, no. 5 (September 1994): 424–32. http://dx.doi.org/10.1006/cgip.1994.1039.

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33

Atieg, A., and G. A. Watson. "Fitting circular arcs by orthogonal distance regression." Applied Numerical Analysis & Computational Mathematics 1, no. 1 (March 2004): 66–76. http://dx.doi.org/10.1002/anac.200310006.

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34

Lillekjendlie, Bjørn. "Circular Arcs Fitted on a Riemann Sphere." Computer Vision and Image Understanding 67, no. 3 (September 1997): 311–17. http://dx.doi.org/10.1006/cviu.1997.0529.

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35

Zhang, Zi Qiang, Qiu Sheng Yan, Zhi Dan Zheng, and Shao Bo Chen. "Error Estimate of Approximate Double Circular Arc Interpolated Method for Curve Smoothing." Materials Science Forum 471-472 (December 2004): 92–95. http://dx.doi.org/10.4028/www.scientific.net/msf.471-472.92.

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Approximate Double Circular Arc Interpolated Method which was put forward by author, is different from other circular arc interpolated methods in demanding only the corner between normal directions of each circular arcs at intersection point are less than designated allowed value but not demanding contiguous circular arcs are tangent, and makes the calculating be predigested. In order to estimate error of the method, emulated calculating is carried out, namely the course of curve being obtained by reverse engineering is simulated in this paper. The results show: if space between measure points is about 0.1mm in curve being obtained by reverse engineering, then, the most departure of smoothing results from original curve is 0.552μm for the stated example. Influence of the error on NC machining is quite small, so it can meet the needs of NC machining.

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36

Blandford, Roger D., and Israel Kovner. "Formation of arcs by nearly circular gravitational lenses." Physical Review A 38, no. 8 (October 1, 1988): 4028–35. http://dx.doi.org/10.1103/physreva.38.4028.

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37

Lu, Lizheng. "On polynomial approximation of circular arcs and helices." Computers & Mathematics with Applications 63, no. 7 (April 2012): 1192–96. http://dx.doi.org/10.1016/j.camwa.2011.12.036.

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38

Yong-Kui, Liu. "The Generation of Circular Arcs on Hexagonal Grids." Computer Graphics Forum 12, no. 1 (February 1993): 21–26. http://dx.doi.org/10.1111/1467-8659.1210021.

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39

Cappos, Justin, Alejandro Estrella-Balderrama, J. Joseph Fowler, and Stephen G. Kobourov. "Simultaneous graph embedding with bends and circular arcs." Computational Geometry 42, no. 2 (February 2009): 173–82. http://dx.doi.org/10.1016/j.comgeo.2008.05.003.

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40

AKL, SELIM G., and BINAY K. BHATTACHARYA. "COMPUTING MAXIMUM CLIQUES OF CIRCULAR ARCS IN PARALLEL*." Parallel Algorithms and Applications 12, no. 4 (January 1997): 305–20. http://dx.doi.org/10.1080/01495739708941428.

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41

Kovač, Boštjan, and Emil Žagar. "Some new quartic parametric approximants of circular arcs." Applied Mathematics and Computation 239 (July 2014): 254–64. http://dx.doi.org/10.1016/j.amc.2014.04.100.

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42

Jaklič, Gašper, Jernej Kozak, Marjeta Krajnc, and Emil Žagar. "Approximation of circular arcs by parametric polynomial curves." ANNALI DELL'UNIVERSITA' DI FERRARA 53, no. 2 (October 3, 2007): 271–79. http://dx.doi.org/10.1007/s11565-007-0012-2.

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43

Nagy, Béla, and Vilmos Totik. "Bernstein’s Inequality for Algebraic Polynomials on Circular Arcs." Constructive Approximation 37, no. 2 (May 22, 2012): 223–32. http://dx.doi.org/10.1007/s00365-012-9168-9.

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44

Erdélyi, Tamás. "Basic Polynomial Inequalities on Intervals and Circular Arcs." Constructive Approximation 39, no. 2 (September 10, 2013): 367–84. http://dx.doi.org/10.1007/s00365-013-9208-0.

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45

Truong, T. T. "ON GEOMETRIC ASPECTS OF CIRCULAR ARCS RADON TRANSFORMS FOR COMPTON SCATTER TOMOGRAPHY." Eurasian Journal of Mathematical and Computer Applications 2, no. 1 (2014): 40–69. http://dx.doi.org/10.32523/2306-3172-2014-2-1-40-69.

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46

Dekel, Avishai, and Erez Braun. "Giant Arcs – Spherical Shells?" Symposium - International Astronomical Union 130 (1988): 598. http://dx.doi.org/10.1017/s0074180900137246.

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A noticeable fact about the giant luminous arcs, which have been detected in a few high-redshift clusters of galaxies (see contributions by Petrosian and by Mellier in this volume), is that they seem to be segments of almost perfectly circular rings – in one case spanning about one third of a circle. If this is a characteristic property of these arcs, they cannot be segments of randomly-oriented three-dimensional rings, which, when viewed from a random direction, should look acircular in most cases. Perhaps the most generic source for a circular ring is a limb-brightened luminous shell – as in planetary nebulae and supernova remnants. Such shells can naturally arise, for example, from explosion-generated shocks which cooled and fragmented into stars. If the sources are shells, and the arcs are either resolved or their thickness is determined by the seeing conditions (and by the CCD pixle size), there is a very general upper-limit on the possible surface-brightness contrast between the arcs and the regions encompassed by them. For the detected arcs, without any special finetuning, this limit is ≃ 3. It might become twice as big if the shell is transparent and the interior is opaque. This limit could exclude the shell model if the preliminary claims for a detected contrast greater than 10 are confirmed. It is interesting to note that the famous ring nebula presents a similar problem. We checked several mechanisms, such as stimulated radiation, which could, in principle, enhance the observed contrast while retaining the spherical symmetry; if such a mechanism is responsible for the enhanced contrast, it should show clear imprints on the spectrum. The figure shows the surface-brightess profile for a shell of thickness d.

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47

GROSSMAN, P. A., M. BRAZIL, J. H. RUBINSTEIN, and D. A. THOMAS. "MINIMAL CURVATURE-CONSTRAINED PATHS IN THE PLANE WITH A CONSTRAINT ON ARCS WITH OPPOSITE ORIENTATIONS." International Journal of Computational Geometry & Applications 23, no. 03 (June 2013): 171–96. http://dx.doi.org/10.1142/s0218195913500064.

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The declines that provide vehicle access in an underground mine are typically designed as paths formed by concatenating line segments and circular arcs. In order to reduce wear on the ore trucks and the road surfaces and to enhance driver safety, such paths may be subject to a further constraint: each pair of consecutive arcs with opposite orientations must be separated by a straight line segment of at least a certain specified length. In order to reduce the construction and operational costs of the mine, it is desirable to minimize the lengths of such paths between any given pair of directed points. Some necessary and sufficient conditions are obtained for paths of this form to be locally or globally minimal with respect to length. In particular, it is shown that there is always a globally minimal path that contains at most four circular arcs.

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48

Xu, Dong Wei, Jian Qun Liu, Xian Fu Wu, and Wei Qiang Gao. "Design and Implementation of the Stone Elliptical Arc Contour Fitting Algorithm." Key Engineering Materials 579-580 (September 2013): 241–47. http://dx.doi.org/10.4028/www.scientific.net/kem.579-580.241.

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Elliptical arcs have been widely used in stone contours, but the circular saw of the existing stone bridge cutting machine can only cut stone contours which compose of long lines and large radius arcs. The elliptical arc is often fitted by small line segments or small arc segments, and the circular saw cannot be used to process the stone elliptical arc contour. Therefore, a better choice of fitting the elliptical arc in the stone contour is the four-arc fitting algorithm. The traditional four-arc fitting ellipse algorithm can only fit the whole ellipse, in order to fit elliptical arcs, a new fitting algorithm of four-arc fitting elliptical arc is designed. Firstly, identify the stone contour and analyze the elliptical entities section from the DXF file, and divide the elliptical arc curve into several arcs according to the angular relationship. Then adopting the Chebyshev approximation theory of four-arc fitting ellipse, the preliminary fitting of the elliptical arc is performed, and re-fit the start section and end section of the elliptical arc curve, the elliptical arc fitting algorithm is designed. In addition, the maximum value of fitting error has been calculated. Finally, by using the Visual C++ as the developing software, the stone elliptical arc contour fitting algorithm and its processing trajectory simulation are realized. Testing results show that the fitting algorithm can meet the requirements of the circular saw cutting the stone elliptical arc contour.

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49

Rababah, Abedallah. "The best uniform quadratic approximation of circular arcs with high accuracy." Open Mathematics 14, no. 1 (January 1, 2016): 118–27. http://dx.doi.org/10.1515/math-2016-0012.

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AbstractIn this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfy the properties of the best uniform approximation and yield the highest possible accuracy.

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50

Zoghi, M., M. S. Hefzy, K. C. Fu, and W. T. Jackson. "A Three-Dimensional Morphometrical Study of the Distal Human Femur." Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 206, no. 3 (September 1992): 147–57. http://dx.doi.org/10.1243/pime_proc_1992_206_282_02.

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The objective of this paper is to present a method to describe the three-dimensional variations of the geometry of the three portions forming the distal part of the human femur: the medial and lateral femoral condyles and the intercondylar fossa. The contours of equally spaced sagittal slices were digitized on the distal femur to determine its surface topography. Data collection was performed using a digitizer system which utilizes low-frequency, magnetic field technology to determine the position and orientation of a magnetic field sensor in relation to a specified reference frame. The generalized reduced gradient optimization method was used to reconstruct the profile of each slice utilizing two primitives: straight-line segments and circular arcs. The profile of each slice within the medial femoral condyle was reconstructed using two circular arcs: posterior and distal. The profile of each slice within the lateral femoral condyle was reconstructed using three circular arcs: posterior, distal and anterior. Finally, the profile of each slice within the intercondylar fossa was reconstructed using two circular arcs: proximal-posterior and anterior, and a distal-posterior straight-line segment tangent to the proximal-posterior circular arc. Combining the data describing the profiles of the different slices forming the distal femur, the posterior portions of each of the medial and lateral femoral condyles were modelled using parts of spheres having an average radius of 20 mm. The anterior portion of the lateral condyle was approximated to a right cylinder having its circular base parallel to the sagittal plane with an average radius of 26 mm. The anterior portion of the intercondylar fossa was modelled using an oblique cylinder having its circular base parallel to the sagittal plane with an average radius of 22 mm. Furthermore, it is suggested that the distal portion of the lateral femoral condyle could be modelled using parts of two oblique cones while the distal portion of the medial femoral condyle could be modelled using a part of a single oblique cone, all cones having their circular bases parallel to the sagittal plane. It is also suggested that the posterior portion of the intercondylar fossa could be modelled using two oblique cones: a proximal cone having its base parallel to the sagittal plane and a distal cone having its base parallel to the frontal plane.

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