Klothoide -- clothoide -- Euler spiral

- Die Klothoide(Spinnlinie) ist eine Kurve, deren Krümmung linear zu ihrer Bogenlänge zunimmt.
http://www.math.hmc.edu/~gu/curves_and_surfaces/curves/clothoid.html

- how to draw clothoid in matlab between known points?
>>dt = .01 ;
>>t=(-2*pi):dt:(2*pi) ;
>>x = cumtrapz(sin(t.^2)) * dt ;
>>y = cumtrapz(cos(t.^2)) * dt ;
>>plot(x,y,'b-') ;

- the clothoid (cornu) curve has the characteristic that its curvature is proportional to
arclength along the curve as measured from the clothoid's origin.

- Klothoide- Cornu-Spirale
- Die Klothoide wird als Übergangsbogen bei Kurven im Straßenbau und im Eisenbahnbau eingesetzt.

- Klothoidengleichung :
- Der Krümmungsradius dieser Kurve ist umgekehrt proportional zur Länge des Bogens:




http://scholar.lib.vt.edu/theses/available/etd-07312007-160005/unrestricted/Thesis_final.pdf

- Euler spiral is a curve whose curvature changes linearly with its curve length.
- Euler spirals are also commonly referred to as (spiros), (clothoids) or (Cornu spirals).
- The Clothoid is also called Euler spiral and Spiral of Cornu, is a curve whose curvature is equal to its arclength. It has the parametric formula:
- the Integrand sin(x²/2) ,  Integral(0,t)sin(x²/2)dx
http://xahlee.org/SpecialPlaneCurves_dir/Clothoid_dir/clothoid.pdf
http://xahlee.org/SpecialPlaneCurves_dir/specialPlaneCurves.html
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Clothoid Loop -- Circular Loop
http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/shawna_sastamoinen/Clothoid_Loop.htm
What is a spiral?
A spiral is a curve ,which runs around a center in a special way.
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The clothoid (double spiral) is a curve, whose curvature grows with the distance from the origin.
The radius of curvature is opposite proportional to its arc measured from the origin.
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- Teststrecken, werden aus den Elementen aufgebaut : Gerade,Klothoide und Kurve.
1.Gerade – 2.Klothoide – 3.Kreis – 4.Klothoide – 5.Kreis – 6.Klothoide – 7.Gerade
- Der Krümmungsverlauf über die Strecke
- Klothoidenmodell & Einspurmodell
- Klothoiden-Bahnkurve
- Das Klothoidenmodell beschreibt das Krümmungsverlauf  im Straßenbau .
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