How to write the B-spline basis function?

Question

jljl 2012-8-30

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https://ww2.mathworks.cn/matlabcentral/answers/47041-how-to-write-the-b-spline-basis-function

评论： Rohitashya 2024-7-16

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Hi All,

here I have a code which creates a B-spline basis function given:

j= interval index

n= order

t= knot vector

x= variable of basis function

if true
  function [y,x] = bspline_basis(j,n,t,x)
  y = bspline_basis_recurrence(j,n,t,x);
    function y = bspline_basis_recurrence(j,n,t,x)
    y = zeros(size(x));
    if n > 1
        b = bspline_basis(j,n-1,t,x);
        dn = x - t(j+1);
        dd = t(j+n) - t(j+1);
        if dd ~= 0  % indeterminate forms 0/0 are deemed to be zero
            y = y + b.*(dn./dd);
        end
        b = bspline_basis(j+1,n-1,t,x);
        dn = t(j+n+1) - x;
        dd = t(j+n+1) - t(j+1+1);
        if dd ~= 0
            y = y + b.*(dn./dd);
        end
    else
        y(:) = t(j+1) <= x & x <= t(j+2);
    end
  end

It works fine until I try to plot the uniform quadratic basis function. Which results in:

if true
  x = [0:0.1:3];
  y = bspline_basis(0,3,[0 1 2 3],x);
  plot(x,y)
end

That doesn't look right at all as it should have a bell shape... Please advise what can be done or where the mistake it to correct it...

THANK YOU.

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Answer 1

Babak 2012-8-30

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/47041-how-to-write-the-b-spline-basis-function#answer_57501

Your function called, bspline_basis() calls a nested function called, bspline_basis_recurrence() and the nested function again calls the parent function bspline_basis().

You cannot do this because you are basically calling the same function inside itself which (in some cases) results in an infinite loop. In some other cases that you have an if loop inside your function which is not true, then you are breaking the infinite loop and getting an answer. Anyways I recommend you reformat your code.