Envelopes created by circle families in the plane
Yongqiao Wang, Takashi Nishimura
TL;DR
This paper thoroughly investigates the mathematical properties of envelopes formed by circle families in the plane, addressing fundamental questions about their existence, representation, quantity, and relationships.
Contribution
It provides comprehensive solutions to all four basic problems related to envelopes generated by circle families in the plane, advancing geometric theory.
Findings
All four basic problems are solved.
Established conditions for the existence of envelopes.
Characterized the relationships among different envelope definitions.
Abstract
In this paper, on envelopes created by circle families in the plane, all four basic problems (existence problem, representation problem, problem on the number of envelopes, problem on relationships of definitions) are solved.
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Taxonomy
TopicsAdvanced Theoretical and Applied Studies in Material Sciences and Geometry · Computational Geometry and Mesh Generation · Optimization and Packing Problems