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1.4.2 B-spline curve

A B-spline curve is defined as a linear combination of control points and B-spline basis functions given by
    (1.62)

In this context the control points are called de Boor points. The basis function is defined on a knot vector
    (1.63)

where there are elements, i.e. the number of control points plus the order of the curve . Each knot span is mapped onto a polynomial curve between two successive joints and . Normalization of the knot vector, so it covers the interval [0,1], is helpful in improving numerical accuracy in floating point arithmetic computation due to the higher density of floating point numbers in this interval [133,300].

Figure 1.10: An order four B-spline basis functions with uniform knot vector
Figure 1.11: A clamped cubic B-spline curve

A B-spline curve has the following properties:

Figure 1.12: The de Boor algorithm



Next: 1.4.3 Algorithms for B-spline Up: 1.4 B-spline curves and Previous: 1.4.1 B-splines   Contents   Index
December 2009