Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 2004. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 31)

TORNAI , R. , Shape modification of cubic B-spline curves by means of knot pairs

Shape modification of' cubic B-spline curves by means of knot pairs 67 (1) Vj — l = VJ <U< Vj + I = Vj+

2 < Vj+

3 (2) Vj. 1 < Vj = U < Vj +

1 = fj+2 < t'i+3 (3) T'J-1 = Vj <U< Uj + 1 < Vj + 2 = Vj+3 (4) Vj- 1 < Vj = Ü < Vj +1 < v

j

+2 - C

J

+3 The resulted region can be seen in Fig. 1. f). 4. Results By fixing one parameter and choosing two parameters for unknown, we got a system of two equations having two unknown parameters. (So it has a solution.) These three parameters shall not be necessarily neighbours. The resulted new areas will overlap partly. However points can be chosen from these areas, where from up to now coidd not. References [1] 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 5th International Conference on Information Visualisation

, London, IEEE CSPress, 63-68, 2001. [2] JUHÁSZ I., HOFFMANN M., The effect of knot, modifications on the shape of B-spline curves, Journal for Geometry and Graphics 5 (2001), 111-119. [3] HOFFMANN M., On the derivatives of a special family of B-spline curves, Acta Acad. Paed. Agriensis 28 (2001), 61-68. [4] JUHÁSZ I., HOFFMANN M., Knot modification of B-spline curves, in: SzirmayKalos, L, Renner, G. (eds.): I. Magyar Számítógépes Grafika és Geometria Konferencia

, Budapest, (2002), 38-44. [5] HOFFMANN M., JUHÁSZ L, Geometric aspects of knot modification of B-spline surfaces, Journal for Geometry and Graphics 6 (2002), 141-149. [6] JUHÁSZ I., HOFFMANN M., Modifying A knot of B-spline curves, Computer Aided Geometric Design 20 (2003), 243-245. [7] JUHÁSZ L, HOFFMANN M., Constrained shape modification of cubic B-spline curves by means of knots, Computer-Aided Design 36 (2004), 437-445. [8] JUHÁSZ I., A shape modifiaction of B-spline curves by symmetric translation of two knots, Acta Acad. Paed. Agriensis 28 (2001), 69-77. [9] PLEGL, L., TILLER, W., The NURBS book

, SpringerVerlag, 1995. [10] FOWLER, B., BARTELS, R., Constrained-based curve manipulation, IEEE Computer Graphics and Applications 13 (1993), 43 49. [11] ZHENG, J.M., CHAN, K. W., GIBSON, I., A new approach for direct manipulation of free-form curve, Computer Graphics Forum 17 (1998), 327 334.