Mathematical elements for computer graphics (2nd ed.)
Mathematical elements for computer graphics (2nd ed.)
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Recursive representation and application of transformation matrices of B-spline bases
Computer Aided Geometric Design
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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.