Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 2001. Sectio Mathematicae (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 28)

JUHÁSZ, I., A shape modification of B-spline curves by symmetric translation of two knots

A shape modification of B-spline curves by symmetric translation of two knots 75 Figure 3: Shape modification of a cubic B-spline curve by means of a symmetric translation of knots U{ and 5. Paths of points of the arc s

?;

+2 (u

) are also shown along with their extensions which intersect the side d

6, dy of the control polygon (n = 12, k = 4, i = 6, A G [—1,1]). 3. Rational B-spline curves The rational equivalents of the results of Section 2 can easily be found utilizing the fact that any rational B-spline (NURBS) curve can be obtained as a central projection of an integral (non-rational) B-spline curve. More precisely, the rational B-spline curve in R

r

f x V- , N,

k(u) s (

u

) = z^ Wl

d> ti 12j=o

wj

Nj (

u)