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Cornu spiral

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1: 7.20 Mathematical Applications
§7.20(ii) Cornu’s Spiral
Then the set { x ( t ) , y ( t ) } is called Cornu’s spiral: it is the projection of the corkscrew on the { x , y } -plane. …
See accompanying text
Figure 7.20.1: Cornu’s spiral, formed from Fresnel integrals, is defined parametrically by x = C ( t ) , y = S ( t ) , t [ 0 , ) . Magnify
2: 7.21 Physical Applications
§7.21 Physical Applications
Fresnel integrals and Cornu’s spiral occurred originally in the analysis of the diffraction of light; see Born and Wolf (1999, §8.7). More recently, Cornu’s spiral appears in the design of highways and railroad tracks, robot trajectory planning, and computer-aided design; see Meek and Walton (1992). …
3: 7.3 Graphics
See accompanying text
Figure 7.3.3: Fresnel integrals C ( x ) and S ( x ) , 0 x 4 . Magnify