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COMPGEOM
2004
ACM
13 years 10 months ago
2004
ACM
Let P be a set of n points in Ê3 , not all in a common plane. We solve a problem of Scott (1970) by showing that the connecting lines of P assume at least 2n − 7 different dir...
COMPGEOM
2004
ACM
13 years 10 months ago
2004
ACM
Let B be a set of n unit balls in R3 . We show that the combinatorial complexity of the space of lines in R3 that avoid all the balls of B is O(n3+ε ), for any ε > 0. This re...
COMPGEOM
2004
ACM
13 years 10 months ago
2004
ACM
We prove that the geometric thickness of graphs whose maximum degree is no more than four is two. In our proofs, we present a space and time efficient embedding technique for gra...
COMPGEOM
2004
ACM
13 years 10 months ago
2004
ACM
Given a set P of n points in convex position in the plane, we prove that there exists a point p ∈ P such that the number of distinct distances from p is at least (13n−6)/36 . ...
COMPGEOM
2004
ACM
13 years 10 months ago
2004
ACM
Given a smoothly embedded 2-manifold in ¤¦¥ , we define the elevation of a point as the height difference to a canonically defined second point on the same manifold. Our de...