klotoids
Klotoids, also known as Euler spirals or clothoid curves, are mathematical curves characterized by a continuous and smooth transition in curvature. They are widely used in engineering and design, particularly in road and railway track layouts, to ensure gradual changes in directional change, thereby enhancing safety and comfort.
The defining feature of a klotoid is its curvature that varies linearly with its arc length. Specifically,
Mathematically, klotoids are often represented through Fresnel integrals, which describe their parametric equations, or via differential
In practical applications, klotoids are utilized in the design of roads, railways, roller coasters, and track
The concept of klotoids dates back to studies by Leonhard Euler in the 18th century, who sought
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