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1
Content available Approximating curve by a single segment of B-Spline or Bézier curve directly in CAD environment
Sobolak Mariusz, Połowniak Piotr, Marciniec Adam, Jagiełowicz Patrycja Ewa
Advances in Manufacturing Science and Technology
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2020
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Vol. 44, nr 3
84--92
EN
The paper presents the method of approximating curves with a single segment of the B-Spline and Bézier curves. The method for determining a single curve segment using the optimization methods in the CATIA environment is shown. The algorithms of simulated annealing and design of experiment are used for optimization. For the same purpose, a new original procedure for determining the distance between the given curves using explicit parameters in the CATIA environment was also used. This approximation of the cyclic curves results in the curve oscillation as shown in the examples. The results show that the approximation method with Bézier curve using control points as “free” points can be applied to obtain the best results of approximation.
2
Content available A new technique to design planar dipole antennas by using Bezier curve and Particle Swarm Optimization
Homsup N., Silabut W., Kesornpatumanum V., Boonek P., Kuhirun W.
Archives of Electrical Engineering
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2016
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Vol. 65, nr 3
513--525
EN
This research presents a new technique which includes the principle of a Bezier curve and Particle Swarm Optimization (PSO) together, in order to design the planar dipole antenna for the two different targets. This technique can improve the characteristics of the antennas by modifying copper textures on the antennas with a Bezier curve. However, the time to process an algorithm will be increased due to the expansion of the solution space in optimization process. So as to solve this problem, the suitable initial parameters need to be set. Therefore this research initialized parameters with reference antenna parameters (a reference antenna operates on 2.4 GHz for IEEE 802.11 b/g/n WLAN standards) which resulted in the proposed designs, rapidly converted into the goals. The goal of the first design is to reduce the size of the antenna. As a result, the first antenna is reduced in the substrate size from areas of 5850 mm2 to 2987 mm2 (48.93% approximately) and can also operates at 2.4 GHz (2.37 GHz to 2.51 GHz). The antenna with dual band application is presented in the second design. The second antenna is operated at 2.4 GHz (2.40 GHz to 2.49 GHz) and 5 GHz (5.10 GHz to 5.45 GHz) for IEEE 802.11 a/b/g/n WLAN standards.
3
Content available On a method of the rapid approximation of a cubic Bèzier curve by quadratic Bèzier curves
Biły B.
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska
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2014
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z. 4
57--71
EN
In this paper the approximation of a cubic Bèzier curve by quadratic Bèzier curves is presented. For some method of the choose of quadratic Bèzier curves, the error of approximation, measured with the Frèchet distance is especially simple to calculate. Moreover, this error is easy to predict also for parts of a given cubic Bèzier curve. Both these features give us the opportunity, with some caution, of rapid approximation, where required precision is granted.
PL
W artykule zaprezentowano aproksymację krzywej Bèziera trzeciego stopnia za pomocą krzywych Bèziera drugiego stopnia. Dla pewnej metody wyboru krzywych Bèziera drugiego stopnia błąd aproksymacji, mierzony odległością Frècheta, jest szczególnie łatwy do policzenia. Co więcej, błąd ten łatwo policzyć także dla fragmentów wyjściowej krzywej. Obie te właściwości, z pewnymi zastrzeżeniami, umożliwiają szybką aproksymację z wymaganą dokładnością.
4
Content available Ocena dynamiczna wybranych sposobów łączenia elementów trasy o zróżnicowanej krzywiźnie
Koc W., Palikowska K.
TTS Technika Transportu Szynowego
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2012
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R. 19, nr 9
1785--1807, CD
PL
Artykuł przedstawia porównanie właściwości dynamicznych kubicznych krzywych C-Bezier i PH krzywych Bezier piątego stopnia na tle krzywej typu K0 uzyskanej przy zastosowaniu uniwersalnej metody modelowania krzywizny. Właściwości dynamiczne i możliwości zastosowania wymienionych krzywych w projektowaniu dróg kolejowych omówiono na przykładach łączenia krzywą przejścia dwóch łuków kołowych odwrotnych oraz dwóch łuków zgodnych (bez przypadku zawierania się jednego łuku w drugim).
EN
Comparison of the dynamic properties of the cubic C-Bezier curves and the PH quintic Bezier curves against the K0 curve obtained using universal modeling curvature method is presented in the article. The dynamic properties and application prospects of the mentioned curves in the railway route design are presented on two cases of joining two circular arcs: with S-shaped and C-shaped transition curves (without the case when one circle is inside the other).
5
Content available remote Generating new styles of Chinese strokes based on statistical model
Xu M., Dong J.
TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
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2007
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Vol. 11, No 1-2
129-136
EN
Chinese calligraphy is one of the most important Chinese arts: a form of entertainment as well as an embodiment of figurative thinking. In this paper, a statistical model-based approach to generating new styles of Chinese character strokes is proposed. Original calligraphy samples are aligned in a common co-ordinate frame and a training set consisting of landmarks is generated semi-automatically. The most significant features of the training set are extracted and a statistical model is built in order to generate strokes in new styles. The Bezier curve is used to fit the discrete contour data.
6
Content available remote 3D reconstruction of parametric curves: recovering the control points
Bhuiyan M. A., Hama H.
Machine Graphics and Vision
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2004
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Vol. 13, No. 4
307-328
EN
This article introduces a new curve reconstruction method based on recovering the control points of parametric cubic curves. The method developed here has two stages: finding the 3D control points of parametric curves and reconstruction of free curves. The 3D control points of curves are computed from 2D image sequences by using projective reconstruction of the 3D control points and the bundle adjustment algorithm. The relationships among parametric curves, such as Hermite curves, Bézier curves and B-spline curves, are established so that a curve of any model can be achieved for best fitting. Some experiments are performed to show the performance and effectiveness of the algorithm. The method is based on the slope following and learning algorithm, which provides an efficient way of finding the 3D control points of any type of cubic Bézier curves. This method, which is an extension of our previous work on recovering control points of 2D Bézier curves, can automatically fit a set of data points with piecewise geometrically continuous cubic parametric curves. The experimental results demonstrate that our method is a fast and efficient way of recovering 3D control points of parametric curves, matching free curves and shape reforming.
7
Content available Bezier approach to smoothing zig-zag data for use in ship maneuvering model identification
Artyszuk J.
Annual of Navigation
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2002
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No. 4
5-12
EN
The Bezier curve is used as a basis of zig-zag data approximation. It improves an estimate of external excitations acting during such a type of maneuver. In addition to the previous report about a turning test modeling, this makes available most of the existing full-scale trial results for the force-based identification of ship maneuvering mathematical model.
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