Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 2001. Sectio Mathematicae (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 28)
HOFFMANN, M., On the derivatives of a special family of B-spline curves
68 M. Hoffman Ii value and even the osculating planes coincide. This plane is a constant plane and defined by three control points of the original B-spline curve. Natural extensions of these results would be desired for B-spline curves of arbitrary degree, but the derivatives of these curves in the direction M; should be calculated by recursive formulae of the derivatives of the basis functions and these formulae have not been found yet. References [1] Au, C. K., YUEN, M. M. F., Unified approach to NURBS curve shape modification , computer-Aided Design, 27, 85-93 (1995). [2] BOEHM, W., Inserting new knots into B-spline curves , Computer-Aided Design, 12, 199-201 (1980). [3] FOWLER, B., BARTELS, R., Constra.int-ba.sed curve manipulation , IEEE Computer Graphics and Applications, 13, 43-49 (1993). [4] JUHÁSZ, I., Weight-based shape modification of NURBS curves , Computer Aided Geometric Design, 16, 377-383 (1999). [5] JUHÁSZ, I., A shape modification of B-spline curves by symmetric translation of two knots , Acta Acac.1. Paed. Agriensis, 27, (to appear) (2001). [6] JUHÁSZ, I., HOFFMANN, M., The effect of knot modifications on the shape of B-spline curves , Journal for Geometry and Graphics (to appear) (2001) [7] HOFFMANN, M., JUHÁSZ, I., Shape control of cubic B-spline and NURBS curves by knot modifications, in:Banissi, E. et al.(eds):Proc. of the 5 i/ l International Conference on Information Visualisation, London, IEEE Computer Society Press, 63-68 (2001) [8] PIEGL , L., Modifying the shape of rational B-splines. Part 1: curves , ComputerAided Design, 21, 509-518 (1989). [9] PIEGL, L., TILLER, W., The NURBS book, Springer-'Verlag, (1995). [10] SÁNCHEZ-REYES, J., A simple technique for NURBS shape modification, IEEE Computer Graphics and Applications, 17, 52-59 (1997). Miklós Hoffmann Károly Eszterházy College Department of Mathematics H-3300 Eger, Hungary Leányka str. 4. e-mail: liofi@ektf.hu
