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