2014/11/20 by Panagiotis Sidiropoulos, Sidiropoulos, Panagiotis
Computer Science · Materials Science · #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Probability (math.PR) #Textile materials and evaluations
paper · pdf · doi:10.48550/arxiv.1411.5639
openalex publication_date 2014/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work studies the chord length distribution, in the case where both ends lie on a N-dimensional hypersphere (N ≥ 2). Actually, after connecting this distribution to the recently estimated surface of a hyperspherical cap \citeSLi11, closed-form expressions of both the probability density function and the cumulative distribution function are straightforwardly extracted, which are followed by a discussion on its basic properties, among which its dependence from the hypersphere dimension. Additionally, the distribution of the dot product of unitary vectors is estimated, a problem that is related to the chord length.