Triangles Formed via Poisson Nearest Neighbors
Steven R. Finch
TL;DR
This paper investigates the geometric properties of triangles formed by Poisson point processes, analyzing joint densities of sides and angles, and extends results to specific constrained triangle configurations.
Contribution
It introduces new joint density results for Poissonian triangles and explores analogous properties for staked and anchored triangle variants.
Findings
Derived joint densities for sides and angles of Poissonian triangles
Extended analysis to staked and anchored triangle configurations
Provided insights into geometric structures formed by Poisson points
Abstract
We start with certain joint densities (for sides and for angles) corresponding to pinned Poissonian triangles in the plane, then discuss analogous results for staked and anchored triangles.
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Taxonomy
TopicsMathematics and Applications · Point processes and geometric inequalities · Computational Geometry and Mesh Generation