The Euler spiral is the planar curve parametrized by the Fresnel integrals. In the optical convention,The tangent has unit length and argument , so its signed curvature is , proportional to signed arc length. In Fresnel diffraction, an interval integral is the directed chord joining its endpoint parameters on the Cornu spiral. Chord length gives the interval factor's modulus, while chord direction gives its complex argument.
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An Euler spiral, also known as a "spiral of constant curvature" or "clothoid," is a curve in which the curvature changes linearly with the arc length. This means that the radius of curvature of the spiral increases (or decreases) smoothly as you move along the curve. The curvature is a measure of how sharply a curve bends, and in an Euler spiral, the curvature increases from zero at the start of the spiral to a constant value at the end.