Cornu spiral

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1: 7.20 Mathematical Applications

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§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. … ►

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Figure 7.20.1: Cornu’s spiral, formed from Fresnel integrals, is defined parametrically by $x=C\left(t\right)$, $y=S\left(t\right)$, $t\in [0,\mathrm{\infty })$. Magnify

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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

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Figure 7.3.3: Fresnel integrals $C\left(x\right)$ and $S\left(x\right)$, $0\le x\le 4$. Magnify

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