# How to eliminate "undercuts" of a 2d curve?

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paul harder on 6 Dec 2021
Commented: Star Strider on 9 Dec 2021
I have a curve made up of a 2d vector of points which has "undercuts". I'd like to create a new curve which eliminates these undercuts. In the figure below, I want to turn the blue curve into the red curve. I could figure out something from scratch (maybe just march along x and skip indices where x does not increase,) but I suspect this can be done with existing functions. In the end, I'd also like to end up with an even point spacing in x, but I can handle that with interp1 after the fact if needed. thanks
John D'Errico on 6 Dec 2021
I don't know of any simple solution, using existing tools. You will need to just write it. To the extent that this will use existing low level tools, you can describe that anyway you want. But no off the shelf tool exists that I can think of.

William Rose on 7 Dec 2021
Edited: William Rose on 7 Dec 2021
xin=data(:,1);
yin=data(:,2);
xout(1)=xin(1);
yout(1)=yin(1);
i=2; j=1;
while i<=length(data)
if xin(i)>xout(j)
xout(j+1)=xin(i);
yout(j+1)=yin(i);
i=i+1;
j=j+1;
else
i=i+1;
end
end
plot(xin,yin,'-b.',xout,yout,'-rx');
Produces the plot below.
The undercutting in the plot above is a bit different than in your drawing. To get results as in your drawing, modify as follows: change the code so it only removes undercuts where y is decreasing, on the first pass. Then negate the output y-vector, to turn the output of pass 1 upside down, and run it through the filter again. Then negate the output y-vector of pass 2, to turn it right-side up. Flippng it in time is an alterative to negation, and would give the same result.
William Rose on 9 Dec 2021
@Star Strider, you are certainly correct. We collaborated with physicians at Nemours Children's Hospital and Shriners Childrens Hospital in Philadelphia. Subjects included patients with brachial plexus birth injuries and scoliosis.

R2020b

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