Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Points and triangles in the plane and halving planes in space
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Dehn-Sommerville relations, upper bound theorem, and levels in arrangements
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Counting triangle crossings and halving planes
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Cutting dense point sets in half
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
| Hi-index | 0.00 |
Let S ⊂ R3 be an n-set in general position. A plane containing three of the points is called a halving plane if it dissects S into two parts of equal cardinality. It is proved that the number of halving planes is at most &Ogr;(n2.998).As a main tool, for every set Y of n points in the plane a set N of size &Ogr;(n4) is constructed such that the points of N are distributed almost evenly in the triangles determined by Y.