Lecture 4 - 11.02.2016

B-splines

• Last time: Splines and B-splines (rest pof sec. 1 and sect 2.1)• Today: More B-spline properties (2.2-2.4)

We will study the B-splines in the expression

B-splines, basic properties

Spline functions

p=1 and t=(0,0,1,2,4,7,8,9,9)

Quadratic splines

Variation diminishing spline approximation

(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

Evaluation of splines - Alg 2.21