how to generate multiple curves with the same track length

Question

lei kong 2022-10-26

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https://ww2.mathworks.cn/matlabcentral/answers/1835838-how-to-generate-multiple-curves-with-the-same-track-length

评论： Mathieu NOE 2022-10-27

I want to know how to generate multiple curves with the same track length. In other words, how can we get the curve of a rope with a certain length (such as 1m) after its random bending.

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J. Alex Lee 2022-10-26

It seems like the harder part of this question is how to make the rules for randomly bending...after that, measuring the track length (arc length) of a curve is relatively easy, just us pythagoreas on each segment making up the curve and add it all up.

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Answer 1

Mathieu NOE 2022-10-26

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https://ww2.mathworks.cn/matlabcentral/answers/1835838-how-to-generate-multiple-curves-with-the-same-track-length#answer_1083983

在 MATLAB Online 中打开

hello

try this

% rope at rest (straight) would have length = 1 (= max(t))
n = 1000;
t = (0:n-1)./n;
max_length = 0.7; % we remove x , y points from curve s that exceed  max_length (should be < 1)
figure(1)
hold on
for ck = 1:10
    w = 2*pi*rand(1);
    x = t;
    y = rand(1).*t+cos(w.*t);
    
    % distance formula : ds² = dx² + dy² , then s = cumsum of ds
    dx = diff(x);
    dy = diff(y);
    ds = sqrt(dx.^2 + dy.^2);
    s = [0 cumsum(ds)];
    id = (s>max_length);
    x(id) = [];
    y(id) = [];
    % recompute s after points removal (to check it works);
    dx = diff(x);
    dy = diff(y);
    ds = sqrt(dx.^2 + dy.^2);
    s = sum(ds) % should remains below or equal to max_length
    
    plot(x,y);
end
hold off

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lei kong 2022-10-27

Thanks for your help! The way you calculate the length of the curve is very useful to me.

Mathieu NOE 2022-10-27

My pleasure !

if my suggestion has fullfilled your expectation, don't hesitate to accept it (or someone else answer if it better deserves your project)

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Answer 2

Matt J 2022-10-26

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1835838-how-to-generate-multiple-curves-with-the-same-track-length#answer_1083993

编辑：Matt J 2022-10-26

在 MATLAB Online 中打开

Using interparc from the File Exchange

https://www.mathworks.com/matlabcentral/fileexchange/34874-interparc?s_tid=srchtitle

format long

for i=1:4

[Px,Py,TrackLength]=makeRope(2);

TrackLength

plot(Px,Py);hold on

end

TrackLength =

1.999999999963130

TrackLength =

1.999999999957910

TrackLength =

1.999999999541550

TrackLength =

1.999999999896211

function [Px,Py,Lfinal]=makeRope(targetLength)

L=targetLength; %target length

N=100; %number of knots

px=sqrt(L)*rand(1,N); py=sqrt(L)*rand(1,N);

t=linspace(1,N,1e5);

Px=interp1(px,t,'spline');

Py=interp1(py,t,'spline');

Lc=cumsum(vecnorm(diff([Px;Py],1,2),2,1));

tc=find(L<Lc,1);

Px=Px(1:tc+1); Py=Py(1:tc+1);

Ltot=sum(vecnorm(diff([Px;Py],1,2),2,1));

pt=interparc(L/Ltot, Px,Py)';

P=[Px;Py];

[~,k]=mink( vecnorm(P-pt,2,1) ,2);

k=min(k)-1;

Px=[Px(1:k),pt(1)]-Px(1); %final points

Py=[Py(1:k),pt(2)]-Py(1);

Lfinal=sum(vecnorm(diff([Px;Py],1,2),2,1)); %confirm the length

end

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J. Alex Lee 2022-10-26

neat!

lei kong 2022-10-27

Thank you for your help. The matlab functions you used are strange to me. I need a little time to learn, and the results look good! thank you!

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