Hi, there:

Does anybody know how to calculate the curvature of a convolution surface?

Thanks.

sorry,

The question should be:

Does anybody know how to calculate the curvature of a "revolution" surface?

curvature in the rotational direction: 1/r, where r is the radius of the body (the distance from body surface to the rotational axis); curvature in the azimutal plane: Know the first and second derivatives first, then compute curvature according to a standard formula;

curvature = div ( N ), where is the unit normal vector.

Try using the following in Google as search terms

"curvature of a revolution surface" ......leave out the quotes when using Google.

I think you are wrong. I have thought it over before I come here for help!

1/r is not the curvature in any direction!!!

e.g. When a hemi-circle rotate, a sphere is formed. I think now you know what I mean.

r is not necessarily radius of revolution. There are two principal radi of cuvature for a general surface in 3D space. Refer to a book on geometry.

If you write your surface as z = f(r) where r is the radius, then the curvature is f''/sqrt(1 + f'^2) where ' = d/dr. ( If you have r = g(z) then the formulas just the same; g''/sqrt(1 + g'^2) '=d/dz ).

Oops!! the square root should by a power 3/2; i.e. the cude of the square root.