球面上の均等な点配置について

中口, 悦史

東京医科歯科大学教養部研究紀要, 2024, 55, 19-34

Number of Access:370（2025-09-09 02:05 Counts）

Identifier to cite or link to this item: https://hdl.handle.net/11094/100654

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Title
球面上の均等な点配置について
Almost even arrangement of points on a spherical surface
Creator
NRID
1000070304011 1000070304011
ORCID
0000-0003-0004-4452 0000-0003-0004-4452
researchmap permalink
e_nakaguti e_nakaguti
CreatorName
中口, 悦史 ; ナカグチ, エツシ ; Nakaguchi, Etsushi
Subject
球面
均等配置
整面凸多面体
球面螺線
球面座標格子
ポアソン点列
数理最適化
計算幾何
Spherical surface
even arrangement
regular-faced convex polyhedra
spherical spirals
spherical coordinate grids
Poisson point sequences
mathematical optimization
computational geometry
Abstract
球面上に均等に（＝均一かつ等間隔に）点を配置することは、さまざまな分野や場面で必要とされるが、線分や円周、正方形などの均等分割や、多角形の正則三角形分割のように、容易に解決されるものではないようである。本稿では、3次元球の球面上に「ほぼ」均等に点を配置する方法として、多面体、球面螺線、球面座標格子に基づく配置の例と、ランダムな配置の生成、数理最適化による配置調整を概観し、「均等な配置」とは何かを考える。
An even (i.e., uniform and equally spaced) arrangement of points on a spherical surface is required in various fields and situations; however, solving this problem, such as the equal division of line segments, circumferences or squares, or the regular triangulation of polygons, does not appear to be straightforward. This study reviews examples of arrangements based on polyhedra, spherical spirals and spherical coordinate grids, as well as the generation of random arrangements and the adjustment of arrangements by mathematical optimization, as methods of arranging points ‘almost’ evenly on the surface of a three- dimensional sphere, and considers what the phrase ‘even arrangement’should mean.
Publisher
東京医科歯科大学教養部
College of Liberal Arts and Sciences Tokyo Medical and Dental University
Source Title
東京医科歯科大学教養部研究紀要
Journal of The College of Liberal Arts and Sciences Tokyo Medical and Dental University
Volume (Issue)
55
Page
19-34
Date of Issued
2024-12-25
Language
Japanese
Handle URL
https://hdl.handle.net/11094/100654
PISSN
03863492
eISSN
2433359X
Relation.isIdenticalTo
DOI (Publisher Version)
https://doi.org/10.11480/kyoyobukiyo.55.0_19
Access Rights
open access
oaire:version
Version of Record
Category
学術雑誌論文 Journal Article