[compgeom-discuss] looking for an easy proof/reference

[Masud Hasan <mhasan2010@gmail.com>]

Dear Colleagues,
 
I was looking for an easy proof/reference for the following:
 
Given a sphere Q and a convex polyhedron P fixed inside Q with P containing the center of Q. To cut P out of Q by guillotine cuts the total cutting cost must be at least \pi*R^2, where cost of a cut is its area and R is the radius of Q.
 
A 2D version can be proven easily. However, 3D generalization of the proof looks cumbersome.
 
Best regards,
Masud

-- 
Dr. Masud Hasan
Assistant Professor
Department of Computer Science and Engineering
Bangladesh University of Engineering and Technology
Dhaka-1000, Bangladesh
Phone: 9665650-80, Ext: 7738 http://teacher.buet.ac.bd/masudhasan
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