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.

中文翻译：

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贝塞尔曲线和 B 样条的罗盘构造

本文揭示了仅罗盘几何结构和参数曲线之间的数学桥梁。提出了一组构造算法，用于通过使用抽象罗盘在任何贝塞尔曲线或 B 样条曲线上定位点。这些构造旨在将 Paul de Casteljau 的 B 样条定义转换为 Aleksandr Kostovskii 解释的仅罗盘构造的修改版本。一些计算机脚本被开发并用于模拟这些结构，同时计算和最小化它们的计算复杂性。预计本文中解释的数学桥会让人想起设计几何的综合和公理根源。