how to find the de Boor points ?

Use Task 1 to plot the cubic spline which interpolates the following 7 data points (x, y): (0, 1),(1, 3),(2, −2),(3, 0),(4, 1),(5, 0),(6, 1).

My answer:

x = [0 1 2 3 4 5 6];
y = [1 3 -2 0 1 0 1];
xx = linspace(0,6,120);
plot(xx,csapi(x,y,xx),'k-',x,y,'ro')
title('Cubic Spline Interpolant to Seven Points')

Experiment until you find the de Boor points di so that the b-spline will fall on top of the curve you obtained in part a) above. Use the same knots as in part a). How large is the number n? To assist you we provide the algorithm which constructs the cubic b-spline basis functions Ni,4(x). how to do it? thanks

[Sruthi Ayloo]

Hi Ali,

I understand that you want to you want to draw a B-spline curve using de Boor’s algorithm with the knots being same as that of the cubic spline.

The number of knots is the minimum for the degree of the B-spline curve. After looking through various sources, I found a few useful links. They are as follows:

http://www.mathworks.com/matlabcentral/fileexchange/27374-b-splines - This package activates a figure window to place B-spline control points interactively and see how the curve is drawn.

http://booksite.elsevier.com/samplechapters/9781558607378/9781558607378.PDF - This chapter talks about B-Splines in an extensive way.

Hope this helps.