The Clothoid Computation: A Simple and Efficient Numerical Algorithm

The clothoid (also known as Cornu spiral or Euler spiral) is a curve that is characterized by its curvature being proportional to its length. This property makes it very useful as a transition curve when designing the layout of roads and railway tracks. This paper presents an analysis of two methods for computing the clothoid: the classical method, which is based on the use of explicit formulas obtained from Taylor expansions of sine and cosine functions, and an alternative algorithm, which is based on the numerical solution of the initial value problems giving the clothoid parametrization. This alternative method is simple and efficient, and its effectiveness is shown through its application to three classical problems of horizontal road alignment.