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Unformatted text preview: e into a set of knot spans [ti, ti+1)
The Bsplines can be defined by * Bspline Basis Bspline Basis (2) Producing Curves by BSplines
• The basis functions are multiplied to the control
points and to define arbitrary curves 0
10/10/2008 t
3 Lecture 5 m+1 Knots
• The knots produce a vector that defines the
domain of the curve
• The knots must be in the increasing order
• But not necessarily uniform
• If uniformly sampled and the degree is 3
uniform cubic bspline 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Knots
Here is an example of nonuniform knots http://i33www.ira.uka.de/applets/mocca/html/noplugin/BSplineBasis/AppBSplineBasis/index.html Some Terms
• Order k: the number of control points that affect the sampled
value
• Degree k1 (the basis functions are polynomials of degree k1)
• Control points Pi (i=0,…,m)
• Knots : tj, (j=0,…, n)
• An important rule : n – m = k
• The domain of function tk1 ≦ t ≦tm+1 – Below, k = 4, m = 9, domain, t3 ≦ t ≦t10 0 t
3 m+1 Clamped Bsplines
• The first and last knot values are repeated with
multiplicity equal to the order (= degree + 1)
• The end points pass the control point
• For cubic Bsplines, the multiplicity of the first /
last knots must be 4 (repeated four times) Controlling the shape of Bsplines
• Moving the control points is...
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This document was uploaded on 03/26/2014.
 Spring '14

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