matinf 4170/9170 - lecture 4 - 8/2-2017 filematinf 4170/9170 - lecture 4 - 8/2-2017 last time:...
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MATINF 4170/9170 - Lecture 4 - 8/2-2017
Last time: section 1.6 and 2.1• B-splines
Today: chapter 2.2 and onwards • Properties of B-splines• Knot vectors• Spline spaces• Spline curves• Matrix representation• Evaluation
B-splines, basic properties
Knotvectors
Spline functions
p=1 and t=(0,0,1,2,4,7,8,9,9)
Quadratic spline functionsExample: Variation diminishing spline approximation (Ex. 2.9)
(t*3,f(t*3))
s(x)
B-spline control polygons
Spline function properties
Spline curves
Matrix representations of B-splines (2.3)Linear B-splines on an interval
Recall the recursion formula
Quadratic B-splines on an interval
Cubic B-splines on an interval
Recall the recursion formula
General matrix formulation on an interval
Example
Evaluation of splines - Alg 2.20
Implementation of alg 2.20
This is Algorithm 1.3
You will do this in Oblig 2
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