July 2002
Intermediate to advanced
576 pages
15h 37m
English
Content preview from Pyramid Algorithms
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7.8 Uniform B-Splines
The simplest, most common knot vectors have evenly spaced knots—for example, knot vectors where the knots are located at the integers {…, −2,−1,0,1,2,…}. When the knots are simple knots (knots of multiplicity one) located at the integers, the knot sequence is called a uniform knot sequence and the associated B-splines are called uniform B-splines. These uniform B-splines have some especially nice properties, which we are now going to investigate.
For uniform B-splines it follows easily from the de Boor algorithm that all the B-splines of the same degree are translates of a single B-spline so that
(7.20)
(see Exercise 1
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