References & Citations
Mathematics > Differential Geometry
Title: Envelopes of straight line families in the plane
(Submitted on 14 Jul 2023 (v1), last revised 7 May 2024 (this version, v3))
Abstract: There is a widespread method to represent the envelope when a given hyperplane family creates an envelope. However, one sometimes encounters cases when the widespread method fails to represent the desired envelope precisely, and is confused. At the same time, one wants to find a correct method to draw the envelope precisely.
In this article, focused on straight line families in the plane, an easy to understand explanation is given on the recently discovered correct method to represent the envelope precisely. Moreover, it is explained when and why the widespread method fails to represent the precise shape of envelope as well.
Submission history
From: Takashi Nishimura [view email][v1] Fri, 14 Jul 2023 08:53:10 GMT (254kb,D)
[v2] Sat, 16 Dec 2023 09:17:27 GMT (255kb,D)
[v3] Tue, 7 May 2024 09:48:35 GMT (256kb,D)
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