How to write a function of a curve?

Hi Everyone,

I'm trying to write a function which takes in 4 inputs, not x, and to return a curve as an output.

eg: f(x)= (1-x)^2

Is this possible? Without defining the variable x?

I'm new to Matlab and would appreciate any help, links or simple code to outline how this could be done.

Cheers!

Answer 1

[Friedrich]

Hi,

try an anonymous function.

http://www.mathworks.com/help/matlab/matlab_prog/anonymous-functions.html

So for example

>> f = @(x,y,z,zz) x + y + z + zz

f = 

      @(x,y,z,zz)x+y+z+zz

>> f(1,2,3,4)

ans =

      10

If your function is too complex, consider writing a function in a seperate m-file (save this in a file called f.m):

function out = f(x,y,z,zz)
      out = x + y + z + zz
end

[jljl]

Thank you for the extremely fast reply, but I am trying to write a function eg:

function out = f(x,y,z,zz)

    % some calculations which end up with (1-t)^2 
    % or (t^2 +4t)

    out = f(t)
end

Is this possible?

[Walter Roberson]

Do you mean that you are writing a recursive function ?

[jljl]

Yes I am writing a recursive function.

[jljl]

I am trying to write the bspline basis function that returns a function of one unknown.

function y = bspline_basis(j,n,t)
  % j: interval index
  % n: order
  % t: knot sequence

   % code for the recurrence relation for a bspline basis function
   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
% output: eg. the function y(x) = (x - t(j+1))^2
end

In other words, I want the output to be the function of the curve. Hope I am making sense. Thank you for all the comments/ replies.

[Friedrich]

Hi,

I would suggest looking into that book

Piegl, Les and Tiller, Wayne. The NURBS book (2nd ed.) page 70

You can implement this pretty smart without recursion (assuming closed B-Splines)

function [N] = basisfuns(p,i,u,U)

%returns functionsvalues of basisfunctions in point u
%p degree, i index,u value, U knotvector
%Piegl, Les and Tiller, Wayne. The NURBS book (2nd ed.)
%page 70

N = zeros(1,p+1);
left = zeros(1,p);
right = zeros(1,p);
N(1) = 1;

for j=1:p
    left(j)  = u - U(i-j+1);
    right(j) = U(i+j) - u;
    saved = 0;
    for r = 0:j-1
        temp = N(r+1)/(right(r+1) + left(j-r));
        N(r+1) = saved+right(r+1)*temp;
        saved = left(j-r)*temp;
    end
    N(j+1) = saved;
end

Also in the case you need an algorithm for finding the index i:

function [i] = findspan(p,U,u)

%return index i for knotspan, w.r.t. value u
%p degree, U knotvector, u value
%Piegl, Les and Tiller, Wayne. The NURBS book (2nd ed.)
%page 68

n = size(U,2) - (p+1);
if u == U(n+1)
    i = n;
    return
end

low = p;
high = n+1;
mid = ceil((low + high) / 2);
while u < U(mid) || u >= U(mid+1)
    if u < U(mid)
        high = mid;
    else
        low = mid;
    end
    mid = ceil((low + high) /2);
end

i = mid;

end

And if you want the value on the curve and not only the values of the basis functions do this:

function [C] = curvepoint(p,U,P,u)

%returns functionvalue C on b-spline curve
%p degree, U knotvector, P controlpoints, u value
%Piegl, Les and Tiller, Wayne. The NURBS book (2nd ed.)
%page 82

span = findspan(p,U,u);
N = basisfuns(p,span,u,U);
C = zeros(1,size(P,2));
for i = 0:p
    C = C + N(i+1)*P(span-p+i,:);
end

end

And a lot more very nice and pretty fast algorithms (all in C, so you need to "translate" them to MATLAB) can be found there. Also for surfaces and volumes. Take a look its worth it ;)

[CS]

in your "basisfuns(p,i,u,U)', when it gets to the line "left(j) = u - U(i-j+1)", MATLAB gives the error "Array indices must be positive integers or logical values". Why? How to solve this?

[Walter Roberson]

Hossein Sehhat what values are you passing to curvepoint ?

[CS]

I didn't get to the curvepoint yet.

I want to give the values for u as

u=0:5

It gives the error "Unable to perform assignment because the left and right sides have a different number of elements.".

I want to draw on the same chart the 2 nd, 3rd, and 4th degree B-spline curves for the seven control points. Thus, the value for p would be 2, 3, and 4, for the 2nd, 3rd, and 4th degrees. Also, the value of u should be continous to be able to plot the curve. Considering u=0:5, MATLAB gave me the above error (as can be seen in the above functions, the value of u is specified at only one point.).

How should I solve these and plot the curves?

Appreciate your help!

[Walter Roberson]

The code is only designed for scalar u, and would require significant rewrites for nonscalar u.