Envelopes of straight line families in the plane

2023/07/14 by Takashi Nishimura, Nishimura, Takashi · 1 citation
Computer Science · Engineering · Mathematics · #57R45 #58C25 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2307.07232

openalex publication_date 2023/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Envelopes created by sphere families in Euclidean 3-space

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