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Compass Construction of Bézier Curves and B-Splines

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Abstract

This article reveals a mathematical bridge between compass-only geometric constructions and parametric curves. A set of construction algorithms are presented which are used to locate points on any Bézier curve or B-Spline by using an abstract compass. These constructions aim to translate the B-Spline definition of Paul de Casteljau into the modified versions of compass-only constructions explained by Aleksandr Kostovskii. Several computer scripts are developed and used to simulate these constructions while calculating and minimizing their computational complexities. The mathematical bridge explained in this article is expected to bring back to mind the synthetic and axiomatic roots of design geometries.

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  1. Faculty of Architecture, İstanbul Bilgi University, Santralistanbul Campus, Eski Silahtarağa Elektrik Santralı Kazım Karabekir Cad. No: 2/13, 34060, Eyüp, İstanbul, Turkey

    Tuğrul Yazar

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Yazar, T. Compass Construction of Bézier Curves and B-Splines. Nexus Netw J 23, 789–811 (2021). https://doi.org/10.1007/s00004-020-00542-9

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