Approximating curve by a single segment of B-Spline or Bézier curve directly in CAD environment

• Autorzy: Sobolak Mariusz , Połowniak Piotr , Marciniec Adam , Jagiełowicz Patrycja Ewa

Identyfikatory

DOI

10.2478/amst-2019-0016

• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

Bézier curve; curve approximation; design of experiment; algorithms of simulated annealing

PL

krzywa Béziera; aproksymacja krzywej; projekt eksperymentu; algorytmy wyżarzania symulowanego

• Wydawca: Komitet Budowy Maszyn PAN ; De Gruyter
• Czasopismo: Advances in Manufacturing Science and Technology
• Rocznik: 2020
• Tom: Vol. 44, nr 3
• Strony: 84--92
• Opis fizyczny: Bibliogr. 10 poz., rys., tab., wykr.

Twórcy

autor

Sobolak Mariusz

• Faculty of Mechanical Engineering and Aeronautics, Rzeszow University of Technology, Rzeszów, Poland

autor

Połowniak Piotr

• Faculty of Mechanical Engineering and Aeronautics, Rzeszow University of Technology, Rzeszów, Poland

autor

Marciniec Adam

• Faculty of Mechanical Engineering and Aeronautics, Rzeszow University of Technology, Rzeszów, Poland

autor

Jagiełowicz Patrycja Ewa

• Faculty of Mechanical Engineering and Aeronautics, Rzeszow University of Technology, Rzeszów, Poland

Bibliografia

• [1] G. Farin: Curves and surfaces for computer aided geometric design: a practical guide. 3rd ed. Academic Press, Boston, MA 1993.
• [2] H. Prautzsch, W. Boehm, M. Paluszny: Bézier and B-spline techniques. Springer-Verlag, Heidelberg 2002.
• [3] H.N. Fittera, A.B. Pandey, D.D. Patel, J.M. Mistry: A review on approaches for handling Bézier curves in CAD for manufacturing. Procedia Eng., 97(2014), 1155-1166.
• [4] F. Higuchi, S. Gofuku, T. Maekawa, H. Mukundan, N.M. Patrikalakis: Approximation of involute curves for CAD-system processing. Eng. Comput., 23(2007), 207-214.
• [5] Y.J. Ahn, C. Hoffmann, Y.S. Kim: Curvature continuous offset approximation based on circle approximation using quadratic Bézier biarcs. Comput.-Aided Des., 43(2011), 1011-1017.
• [6] S.H. Kim, Y.J. Ahn: An approximation of circular arcs by quartic Bézier curves. Comput.-Aided Des., 39(2007), 490-493.
• [7] J. Sánchez-Reyes: Bézier representation of epitrochoids and hypotrochoids. Comput.-Aided Des., 31(1999), 747-750.
• [8] M. Batsch, T. Markowski, S. Legutko, G.M. Krolczyk: Measurement and mathematical model of convexo-concave Novikov gear mesh. Measurement, 125(2018), 516-525.
• [9] S. Babu, K.M. Abubacker: Development of involute profiled spur gear model with excel spreadsheet, solidworks and CAD technique. Int. J. Mech. Eng., 5(2018), 5-11.
• [10] G.G. Rey, G.B. Gordillo: Parametric geometric modeling of a spur gear using solidworks. Gear Solutions., 15(2017), 30-36.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).