# interpolating the 2d line to make the new coordinates equi-distant

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tafteh on 12 Feb 2013
Hi all;
I have a 2d line which is a x and y vector. I would like to interpolate that line such that the new x, y coordinates are uniformly distributed along the line. I mean I get a line which the x and y coordinate are equi-distance. As if we are moving along this curve with constant speed.
Is there any way to do this? I would appreciate if you could help me out in this.
Thanks

Sven on 12 Feb 2013
Hi Payam, try this:
pathXY = [0 0; 1 1; 10 2; 12 3]
stepLengths = sqrt(sum(diff(pathXY,[],1).^2,2))
stepLengths = [0; stepLengths] % add the starting point
cumulativeLen = cumsum(stepLengths)
finalStepLocs = linspace(0,cumulativeLen(end), 100)
finalPathXY = interp1(cumulativeLen, pathXY, finalStepLocs)
Is that what you were looking for?

tafteh on 14 Feb 2013
Thanks a ton Sven. That is the answer I needed. Appreciate it.
However, out of my cuorisity, why do we have to calculate the cumulutive sum of all the distances? Can we have the
linspace(0, sum(stepLengths), 100)
linspace(0,cumulativeLen(end), 100)?
or there any other reason to calculate the cumulativeLen vector?
thanks, Payam
Sven on 14 Feb 2013
Check out the help for the interp1 function - it takes as its first argument something that relies on the true distance between each of your input points. If you simply use linspace(0,finalDist,100), then you will be telling MATLAB "all my points are equally spaced apart" (even though they are not).
There is no difference between sum(stepLengths) and cumulativeLen(end)... it's just that I already have (and need) the cumLen so I may as well use it rather than make a new sum.