How to calculate a curvature of 3D isosurface?

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zilorina 2020-1-15

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https://ww2.mathworks.cn/matlabcentral/answers/500399-how-to-calculate-a-curvature-of-3d-isosurface

评论： darova 2020-1-17

I have isosurface(X, Y, Z, W, level) in 3D and I would like to calculate its curvature. So far I was using the following code: https://nl.mathworks.com/matlabcentral/fileexchange/24937-curvature-calculations-on-triangular-3d-surface

This code (as well as other analogical codes that I saw on fileexchange) will take the triangulation of my surface as an input parameter (i.e., the mesh). But I was wondering maybe there is a simpler way to calculate the curvature of the surface since I have a smooth surface that has been already fitted into my triangulated point cloud?

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Answer 1

darova 2020-1-15

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https://ww2.mathworks.cn/matlabcentral/answers/500399-how-to-calculate-a-curvature-of-3d-isosurface#answer_410235

You can use surfnorm to extract normal vectors from surface

Choose close enough vectors to calculate curvature

Angle between vectors:

Distance between points: L

Curvature radius:

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zilorina 2020-1-17

It is more complicated for 3d surface. Indeed you would need to calculate normals on triangular mesh (i.e., first, for triangles, then for vertices). I do not think surfnorm works for triangular mesh (isosurface). Then the problem will consist of calculating pricncipal curvatures (minimum and maximum curvatures out of all directions) from the second fundamental form.