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curvspace

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22 Mar 2005 (Updated )

Generate evenly spaced points along an existing curve in 2D or 3D.

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Description

CURVSPACE(P,N) generates N points that interpolates a curve (represented by a set of points) with an equal spacing. Each row of P defines a point, which means that P should be a n x 2 (2D) or a n x 3 (3D) matrix.

(Example)
x = -2*pi:0.5:2*pi;
y = 10*sin(x);
z = linspace(0,10,length(x));
N = 50;
p = [x',y',z'];
q = curvspace(p,N);

The above example creates 50 evenly spaced points along a sinusoidal curve.

Acknowledgements

This file inspired Kirchhoff Vortex Contour Dynamics Simulation.

MATLAB release MATLAB 5.3.1 (R11.1)
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Comments and Ratings (11)
20 Dec 2013 Francesca

This function is very good! You solved me a very big problem! Thank you!

10 Aug 2013 John D'Errico

Not vectorized, and purely linear interpolation. Better is my own interparc, also here on the fex.

http://www.mathworks.com/matlabcentral/fileexchange/34874-interparc

For example, given 4 points around a circle, try this:

t = linspace(0,2*pi,5)';
xy = [cos(t),sin(t)];

tic,xyi = interparc(100,xy(:,1),xy(:,2),'lin');toc
Elapsed time is 0.001540 seconds.

tic,xyc = curvspace(xy,100);toc
Elapsed time is 0.004692 seconds.

So the unvectorized code is slower. And if we plot the points, we see a diamond results, thus connect the dots interpolation.

plot(xyc(:,1),xyc(:,2),'b-')

You can use interparc to get a nice smooth curve instead. Of course, it will be slower, since it is actually finding the true distance along the interpolated spline curve.

xyi = interparc(100,xy(:,1),xy(:,2),'cs');
plot(xyi(:,1),xyi(:,2),'b-')

The help is good enough, and I see plentiful internal comments, so well done there. The code is reasonable, although a bit loopy.

10 Aug 2013 ted p teng  
31 Jan 2012 TCH

great job. I have implemented an equivalent function in the following link, :-.
http://www.mathworks.com/matlabcentral/fileexchange/34796-arbitrary-equal-division-function
purely could be a reference.

22 Apr 2011 Erhong  
08 Jan 2009 Andrea Tagliasacchi

thanks a lot, I didn't want to lose time re-implementing it!

17 Jan 2007 Sven Mensing

Thank you for your excellent function. If you replace the distance by

function l = distance(x,y)
l = sqrt(sum((x-y).^2,2));

and calculate the distance between the points as follows:

dist_bet_pts = distance ( p(1:(length(p)-1),:), p(2:length(p),:));

you can increase the speed of curvspace by 300%.

Thanks again

Sven Mensing

25 Mar 2006 Daniel Daniel

Works Great! This is an incredibly useful tool. Unlike Matlab's interp functions the X-data does not have to be distint.

Thankyou for this handy function.

03 Feb 2006 Valer Jurcak

Works fine, thaks. Please make N input also as percentual legth.
if N < 1 % e.g. 0.1 make new point every 10% of totaldist.
N = N * totaldist;
end

18 May 2005 meng mingyang

It's not as my imagination,but it illumined me .Thank you!

18 May 2005 meng mingyang

useful program! It's exact what I want!
Thank you very much!

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