Euler spiral
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https://term.museum-digital.de/md-de/tag/40300
- Note
- An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). Euler spirals are also commonly referred to as spiros, clothoids, or Cornu spirals. Euler´s spiral is a type of superspiral that has the property of a monotonic curvature function.
Euler spirals have applications to diffraction computations. They are also widely used in railway and highway engineering to design transition curves between straight and curved sections of railway or roads. A similar application is also found in photonic integrated circuits. The principle of linear variation of the curvature of the transition curve between a tangent and a circular curve defines the geometry of the Euler spiral:
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