Cross-sectional area of a cone(ish)

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jlt199
jlt199 on 31 Aug 2016
Answered: jlt199 on 9 Sep 2016
Morning all,
I have a surface that looks something like a lopsided squished cone, hollow in the middle.
I would like to take the cross-sectional area at different heights, but I need some help. I'm sure it shouldn't be too difficult but I can't figure it out today. I can use the countour function to plot the contours at different heights, but not find the area of the cross-section.
Can anyone help me please?

Accepted Answer

John D'Errico
John D'Errico on 31 Aug 2016
And polyarea won't suffice to compute the area of a polygon? It should.
Just generate the contours as desired. Then use polyarea. Easy.
  6 Comments
jlt199
jlt199 on 9 Sep 2016
Thanks for your help John, I have just got back to this problem after having to leave it to write reports :(
I was as surprised by the level of noise as you, it's only in about 5 of about several hundred surfaces, so I missed it originally.
I'm having a hard time working out the structure of the matrix C which is output from the contour3 function, I have tried looking at the code for contour3, but really didn't understand what was going on. Can anyone help me with this? I would like to isolate polygons as suggested, but I can't understand the data structure.
Another thought I had was to just send the portion of the surface that contains the "horn" to the contour3 function, but I can't think how to do that either.
If anyone can help with either of these two problems I would be very grateful.
This is the surface I am currently working with:
Many thanks
jlt199
jlt199 on 9 Sep 2016
Ok, I've figured out the structure of C now. Now I just need to figure out what to do with it...

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More Answers (2)

Chad Greene
Chad Greene on 31 Aug 2016
Edited: Chad Greene on 31 Aug 2016
I'd use my C2xyz function which is on File Exchange to easily get the x,y values of a contour line. Below I'm using the built-in peaks data as an example dataset and getting the area of the polygon bounded by the z=6 line.
[X,Y,Z] = peaks(1000);
pcolor(X,Y,Z);
shading interp
colorbar
zval = 6;
hold on
C = contour(X,Y,Z,zval*[1 1],'k');
[x,y,z] = C2xyz(C);
A = polyarea(x{1},y{1})
A =
0.6661
  2 Comments
Sean de Wolski
Sean de Wolski on 31 Aug 2016
How is C2xyz different than contourc?
Chad Greene
Chad Greene on 9 Sep 2016
Hey Sean, the C2xyz function simply converts the difficult-to-interpret C matrix into more intuitive x and y values.

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jlt199
jlt199 on 9 Sep 2016
Thanks, I've managed to get it working in most cases. Except where the noise gets horrendous.
Many thanks for your time

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