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In this contribution, we present the description of a B-spline curve. We deal with creation of its basis function as well as with creation of the curve itself from entered control points. Following the literature, we formed an algorithm for B-spline modelling and we used it for the planar and spatial curve. The planar curve is made of chosen points. The spatial curve approximates the trajectory of a real vehicle, which trajectory was obtained by the set of measured points. The modelled curve very exactly describes the polygon created from the linked control points. With the lowering degree of the curve, this one is more clamping to the given polygon and for the extreme case it is transformed to the polygon itself. The advantage of the B-spline curve use is, for example in comparison with a Bézier curve, high adaptability, which is expressed in its parameters - besides entered control points, these are knots generated on the curve and degree of the curve.

using B-splines and Runge-Kutta methods, N.A.T 2010, Studia Univ “Babes-Bolyai” Cluj-Napoca, Vol. LVI, Number 2, pag 515-526, June 2011. [6] L.F. Shampine, I. Gladwell, S. Thomson, Solving ODEs with Matlab, Cambridge University Press, 2003.

References [1] L. Debnath, Partial Differential Equations for Scientists and Engineers, Birkhäuser, Boston, 1997. [2] S. Kutluay, A. Esen, I. Dag, Numerical solutions of the Burgers’ equation by the least squares quadratic B-spline finite element method, J. Comp. Appl. Math., 167 (2004) 21-33. [3] L. R. T. Gardner, G. A. Gardner, A. Dogan, A Petrov-Galerkin finite element scheme for Burgers equation, Arab. J. Sci. Eng., 22 (1997) 99-109. [4] A. H. A. Ali, L. R. T. Gardner, G. A. Gardner, A Collocation method for Burgers equation using cubic splines, Comp. Meth

, Ottawa, Canada, July, 1999. 9. B. Gregorski, B. Hamann and K. Joy, “Reconstruction of B-spline surfaces from scattered data points”, In Proceedings of Computer Graphics International, Geneva, Switzerland, 2000.

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. Figure 12 Tangent segment to the curve. Having the points P 1 , P 2 , P 3 , P 4 it is possible to create a Bézier curve segment (3D Curve command in the FreeStyle module). The type of creation by the control points should be chosen and appropriate points should be selected ( Figure 13 ). Figure 13 The Bézier curve creating; 1—approximated circular arc, 2—Bézier curve, and 3—Bézier polygon. The curve approximation is realized in a similar way to that shown earlier for the B-Spline curve. The variable parameters in this case are the lengths of the tangent segments