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September 3, 2002, 22:25 
curvature

#1 
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Hi, there:
Does anybody know how to calculate the curvature of a convolution surface? Thanks. 

September 3, 2002, 22:32 
sorry ,I post it again!

#2 
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sorry,
The question should be: Does anybody know how to calculate the curvature of a "revolution" surface? 

September 4, 2002, 02:39 
Re: sorry ,I post it again!

#3 
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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. 

September 4, 2002, 06:04 
Re: sorry ,I post it again!

#4 
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Try using the following in Google as search terms
"curvature of a revolution surface" ......leave out the quotes when using Google. 

September 4, 2002, 22:24 
Re: sorry ,I post it again!

#5 
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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 hemicircle rotate, a sphere is formed. I think now you know what I mean. 

September 4, 2002, 22:59 
Re: sorry ,I post it again!

#6 
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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.


September 24, 2002, 10:28 
Re: sorry ,I post it again!

#7 
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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 ).


September 24, 2002, 11:17 
Re: sorry ,I post it again!

#8 
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Oops!! the square root should by a power 3/2; i.e. the cude of the square root.


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