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大学・研究所にある論文を検索できる 「平面曲線のオイラーの弾性曲線および対数型美的曲線へのフェアリング」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

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平面曲線のオイラーの弾性曲線および対数型美的曲線へのフェアリング

グライフ, ズリタ, セバスティアン, エリアス ZURITA SEBASTIÁN ELÍAS, GRAIFF 九州大学

2022.09.22

概要

The process of fairing or fitting of a curve is widely used in industrial design and architecture. It is a process that helps to construct and create new objects. In this thesis, with reverse engineering applications in mind, we provide methods to characterize a given curve by two kind of curves: the Euler's elastica and the log-aesthetic curve.

In a first part, we provide tools to approximate a given discrete planar curve to an integrable discrete analogue of the Euler's elastica. In doing this, we review the properties and results of the discrete Euler's elastica proposed by A. I. Bobenko and Y. B. Suris, and we use an explicit solution in terms of the Jacobi elliptic functions to construct an algorithmic method to fair a general discrete planar segment.

In a second part, we present an algorithm to fair a given planar curve by a log-aesthetic curve, which is anchor in the result that a general log-aesthetic curve segment can be recovered by applying similarity transformation to a base case.

Finally, we use our findings in two concrete applications. We characterize the profile keylines of Japanese handmade pantiles by using the integrable discrete analogue of the Euler's elasticae, and we characterize some simple profile lines of a car's roof by log-aesthetic curves.

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