# Radius of curvature of a crater on a surface

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John on 26 Nov 2013
Commented: Sean de Wolski on 3 Dec 2013
I need to be able to use MATLAB to measure the radius of curvature of a "dimple" on a surface. I cannot post the images here, but imagine a nice rounded surface with a dimple or crater in it, as if something impacted it and left a forever dent.
I've seen some code on here regarding radius of curvature, but I cannot make it work for what I have. My images are imported as "STL" files, and as of now, I can only plot them using the scatter3 command, meaning I have a surface, but not a smooth one... one with scatter plot dots everywhere. You can easily visualize it, though.
Is there a way to do this? If ML can find the slope change where the surface stops and crater starts, it can give me the points for the "circle" to use, and I'm sure it can measure the depth, but as for the radius of curvature of that hole, I'm at a loss.
Any ideas?
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John on 26 Nov 2013
When the STL file is imported, it dumps data into a two-part structure: faces and vertices.

Sean de Wolski on 26 Nov 2013
Edited: Sean de Wolski on 26 Nov 2013
So you'll need to first determine all of the faces that are within the dimple. If the rest of the mesh is convex, you could do this by looking at vertices that are not part of the convex hull and all of the faces that contain these vertices. Once you have this information, calculation of the radius of curvature just becomes algebra.
For calculating the convex hull:
Sean de Wolski on 3 Dec 2013
Hi John,
I don't think duplicate values would describe the error you're seeing. It's really difficult for me to come up with an example without a file. But I do have some time on a plane Thursday and Friday so I could try then. Essentially, the goal would be to create an isosurface of a Death Star, probably by taking two partially overlapping spheres and removing the small sphere from both...

Image Analyst on 26 Nov 2013
I've never used STL files, but if you can get a topographic image (with pixel value being the height values) then you can threshold, and call regionprops(binaryImage, 'EquivDiameter') to get the equivalent circular diameter (ECD).
Image Analyst on 27 Nov 2013
I haven't used it, and don't have plans to. I assume you contacted the author.

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