Stabbing numbers of triangulations
Jonathan Shewchuk
jrs at CS.Berkeley.EDU
Mon Mar 1 15:59:57 PST 1999
It is well known that a tetrahedralization of n vertices in E^3 may have
Theta(n^2) tetrahedra.
My main question:
- Consider a line passing through a tetrahedralization. What is the
(asymptotically) largest number of tetrahedra the line can intersect?
If it's o(n^2), is there a proof? If it's Theta(n^2), is there an
example?
If anyone knows an answer to this, I would be very grateful to hear it.
Some additional questions:
- How about in dimensions higher than 3?
- What if the triangulation is Delaunay?
Thanks,
Jonathan Shewchuk
Computer Science Division
University of California at Berkeley
jrs at cs.berkeley.edu
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