eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-03-09
58:1
58:17
10.4230/LIPIcs.STACS.2022.58
article
High Quality Consistent Digital Curved Rays via Vector Field Rounding
Tokuyama, Takeshi
1
Yoshimura, Ryo
2
Department of Computer Science, School of Engineering, Kwansei Gakuin University, Sanda, Japan
Graduate School of Information Science and Technology, The University of Tokyo, Japan
We consider the consistent digital rays (CDR) of curved rays, which approximates a set of curved rays emanating from the origin by the set of rooted paths (called digital rays) of a spanning tree of a grid graph. Previously, a construction algorithm of CDR for diffused families of curved rays to attain an O(√{n log n}) bound for the distance between digital ray and the corresponding ray is known [Chun et al., 2019]. In this paper, we give a description of the problem as a rounding problem of the vector field generated from the ray family, and investigate the relation of the quality of CDR and the discrepancy of the range space generated from gradient curves of rays. Consequently, we show the existence of a CDR with an O(log ^{1.5} n) distance bound for any diffused family of curved rays.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol219-stacs2022/LIPIcs.STACS.2022.58/LIPIcs.STACS.2022.58.pdf
Computational Geometry
Discrepancy Theory
Consistent Digital Rays
Digital Geometry