Triangles in arrangements of lines

Arrangements of Lines with a Large Number of Triangles

An arrangement of lines is constructed by choosing n diagonals of the regular 2/i-gon. This arrangement is proved to form at least n(n 3)/3 triangular cells.

Triangles in Euclidean Arrangements

The number of triangles in arrangements of lines and pseudolines has been object of some research Most results however concern arrangements in the projective plane In this article we add results for the number of triangles in Euclidean arrange ments of pseudolines Though the change in the embedding space from projective to Euclidean may seem small there are interesting changes both in the resul...

Arrangements of Pseudocircles: Triangles and Drawings

A pseudocircle is a simple closed curve on the sphere or in the plane. The study of arrangements of pseudocircles was initiated by Grünbaum, who defined them as collections of simple closed curves that pairwise intersect in exactly two crossings. Grünbaum conjectured that the number of triangular cells p3 in digon-free arrangements of n pairwise intersecting pseudocircles is at least 2n−4. We p...

Approximating Shortest Paths in Arrangements of Lines

On Envelopes of Arrangements of Lines

[Gr72] Graham R., " An efficient algorithm for determining the convex hull of a planar set, " In-A simple algorithm for determining the envelope of a set of lines, " Information [To91] Toussaint G.T., " Computing morphological properties of arrangements of lines, " Proc. [Ve87] Vegter G., " Computing the bounded region determined by finitely many lines in the plane, " Technical Report 87-03, [Z...