How to write a function of a curve?

Question

jljl 2012-8-28

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/46886-how-to-write-a-function-of-a-curve

评论： Walter Roberson 2020-4-9

采纳的回答： Friedrich

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!

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Friedrich 2012-8-28

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/46886-how-to-write-a-function-of-a-curve#answer_57298

编辑：Friedrich 2012-8-28

在 MATLAB Online 中打开

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

9 个评论
显示 7更早的评论隐藏 7更早的评论

Friedrich 2012-8-29

编辑：Friedrich 2012-8-29

在 MATLAB Online 中打开

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 2020-4-8

在 MATLAB Online 中打开

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 2020-4-9

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

请先登录，再进行评论。

How to write a function of a curve?

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

采纳的回答

9 个评论
显示 7更早的评论隐藏 7更早的评论

更多回答（0 个）

另请参阅

类别

标签

Community Treasure Hunt

How to write a function of a curve?

0 个评论 显示 -2更早的评论隐藏 -2更早的评论

采纳的回答

9 个评论 显示 7更早的评论隐藏 7更早的评论

更多回答（0 个）

另请参阅

类别

标签

Community Treasure Hunt

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

9 个评论
显示 7更早的评论隐藏 7更早的评论