UDC
514

DEVELOPMENT OF A GRAPHICAL SYSTEM FOR MODELING 
THE LOCUS OF POINTS EQUIDISTANT 
FROM A PAIR OF GEOMETRIC OBJECTS Development of a graphical system for modeling 
the locus of points equidistant 
from a pair of geometric objects

Published in Journal of Natural Sciences Research · Pages 57–70 · Rubric: Mathematics and mechanics
Received: 01.11.2025 Accepted: 01.11.2025 Published: 01.11.2025
Authors
In a range of applied tasks - from mobile robot navigation in dynamic environments to modeling wireless network coverage zones - there arises a need not merely to partition space by nearest neighbors, but to account for the relative influence of sources with different 'types' and 'strengths'. Classical Voronoi diagrams cannot accommodate non-uniform weights for generators (geometric objects) or handle their complex configurations. To address this problem, a unified model 
of a generalized weighted Voronoi diagram has been developed. This model allows assigning 
a custom weight (influence coefficient) to each generator type and provides interactive tools 
for parameter control. Future work plans to extend functionality by introducing new generator types – geometric objects and applying the model to agent scene orientation tasks and complex simulations.
generalized Voronoi diagram, locus, equidistant, weighted bisector
Text References
Text (PDF)
Read Download

1. Aurenhammer F. Diagrammy Voronogo / F. Aurenhammer, R. Klyayn. – Hagen: Universitet Hagen (FernUniversität in Hagen), 1996. – 101 s.

2. Vyshnepol'skiy V.I. Geometricheskie mesta tochek, ravnootstoyaschih ot dvuh zadannyh geometricheskih figur. chast' 4: geometricheskie mesta tochek, ravnoudalennyh ot dvuh sfer / V.I. Vyshnepol'skiy, E.V. Zavarihina, D.S. Peh // Geometriya i grafika. – 2021. – T. 9, № 3. – S. 12-29. – DOIhttps://doi.org/10.12737/2308-4898-2021-9-3-12-29. – EDN WGHOZY.

3. Vyshnepol'skiy V.I. Geometricheskie mesta tochek, ravnootstoyaschih ot dvuh zadannyh geometricheskih figur. chast' 5: geometricheskie mesta tochek, ravnoudalennyh ot sfery i ploskosti / V.I. Vyshnepol'skiy, E.V. Zavarihina, K.T. Egiazaryan // Geometriya i grafika. – 2021. – T. 9, № 4. – S. 22-34. – DOIhttps://doi.org/10.12737/2308-4898-2022-9-4-22-34. – EDN MGDBLH.

4. Kiselev A.P. Elementarnaya geometriya: kniga dlya uchitelya / A.P. Kiselev – Moskva: Prosveschenie, 1980. – 287 s.: il. – ISBN 978-0977985203.

5. Lazarev K.V. Principy parametricheskogo postroeniya arhitekturnoy formy na osnove biologicheskih struktur / K.V. Lazarev, E.D. Enyutina // Tradicii i innovacii 
v stroitel'stve i arhitekture. Arhitektura i gradostroitel'stvo: sbornik nauchnyh trudov. – 2021. – S. 367-378. EDN: https://elibrary.ru/QLOKZA

6. Takahashi O. Planirovanie dvizheniya na ploskosti s ispol'zovaniem obobschennyh diagramm Voronogo / O. Takahashi, R.Dzh. Shilling // IEEE Transactions on Robotics and Automation. – 1989. – Tom 5, № 2. – S. 143-150. DOI: https://doi.org/10.1109/70.88035