A simple algorithm for determining the envelope of a set of lines
Information Processing Letters
Journal of Algorithms
There exist 6n/13 ordinary points
Discrete & Computational Geometry
Finding an ordinary conic and an ordinary hyperplane
Nordic Journal of Computing
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Given an arrangement of n not all coincident lines in the Euclidean plane we show that there can be no more than $\lfloor 4n/3\rfloor$ wedges (i.e. two-edged faces) and give explicit examples to show that this bound is tight. We describe the connection this problem has to the problem of obtaining lower bounds on the number of ordinary points in arrangements of not all coincident, not all parallel lines, and show that there must be at least $\lfloor(5{\it n} + 6)/39\rfloor$ such points.