Cornu spiral
E730640
The Cornu spiral is a graphical representation of Fresnel integrals that forms a characteristic S-shaped curve used to analyze diffraction and wave propagation in optics and engineering.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
graphical representation
ⓘ
mathematical curve ⓘ tool in physical optics ⓘ |
| alsoKnownAs |
Euler spiral
NERFINISHED
ⓘ
Fresnel spiral NERFINISHED ⓘ clothoid NERFINISHED ⓘ |
| coordinateSystem | Cartesian coordinates NERFINISHED ⓘ |
| definedBy | Fresnel integrals NERFINISHED ⓘ |
| domainOfParameter | real numbers ⓘ |
| field |
civil engineering
ⓘ
mathematical physics ⓘ optics ⓘ transportation engineering ⓘ |
| hasParametricEquation |
x(t) = C(t) = ∫₀ᵗ cos(πu²/2) du
ⓘ
y(t) = S(t) = ∫₀ᵗ sin(πu²/2) du ⓘ |
| hasProperty |
approaches asymptotic points as parameter → ±∞
ⓘ
curvature proportional to arc length ⓘ curvature varies linearly with arc length ⓘ passes through the origin ⓘ smoothly varying curvature ⓘ |
| namedAfter | Alfred Cornu NERFINISHED ⓘ |
| relatedTo |
Fresnel diffraction theory
NERFINISHED
ⓘ
Fresnel integrals C(x) and S(x) ⓘ Gaussian beam optics NERFINISHED ⓘ spiral easement ⓘ transition curves ⓘ |
| represents | Fresnel integrals ⓘ |
| shape | S-shaped curve ⓘ |
| symmetricAbout |
both coordinate axes
ⓘ
origin ⓘ |
| usedIn |
Fresnel diffraction
NERFINISHED
ⓘ
antenna theory ⓘ aperture diffraction calculations ⓘ computer-aided geometric design ⓘ diffraction analysis ⓘ edge diffraction calculations ⓘ engineering ⓘ highway transition curves ⓘ optical system design ⓘ physical optics ⓘ radio wave propagation ⓘ railway track transition design ⓘ robot path planning ⓘ wave propagation analysis ⓘ |
| usedTo |
construct Fresnel diffraction patterns
ⓘ
determine diffraction field amplitudes ⓘ graphically evaluate Fresnel integrals ⓘ visualize phase and amplitude variations ⓘ |
| visualizationMethod | plot of C(t) versus S(t) ⓘ |
Referenced by (2)
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