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Increasing the degree of closed B-spline curves

✍ Scribed by I. Juhász; Zs. Bancsik

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
306 KB
Volume
38
Category
Article
ISSN
0895-7177

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✦ Synopsis

we consider such sequences of closed B-spline curves the elements of which differ only in their degree; i.e., they share the same control polygon. First, we prove that a sequence obtained in this way converges to the point that represents the arithmetic mean of the common control points (their position vectors) as the degree tends to infinity. Then, we show that this property can be generalized to closed rational B-spline curves in which case the limit is the weighted arithmetic mean of control points.

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