Euler Spiral - Code For Producing An Euler Spiral

Code For Producing An Euler Spiral

The following Sage code produces the second graph above. The first four lines express the Euler spiral component. Fresnel functions could not be found. Instead, the integrals of two expanded Taylor series are adopted. The remaining code expresses respectively the tangent and the circle, including the computation for the center coordinates.

var('L') p = integral(taylor(cos(L^2), L, 0, 12), L) q = integral(taylor(sin(L^2), L, 0, 12), L) r1 = parametric_plot(, (L, 0, 1), color = 'red') r2 = line(, rgbcolor = 'blue') x1 = p.subs(L = 1) y1 = q.subs(L = 1) R = 0.5 x2 = x1 - R*sin(1.0) y2 = y1 + R*cos(1.0) r3 = circle((x2, y2), R, rgbcolor = 'green') show(r1 + r2 + r3, aspect_ratio = 1, axes=false)

The following is Mathematica code for the Euler spiral component (it works directly in wolframalpha.com):

ParametricPlot[ {FresnelC] t]/Sqrt], FresnelS] t]/Sqrt]}, {t, -10, 10}]

Read more about this topic:  Euler Spiral

Famous quotes containing the words code, producing and/or spiral:

    Motion or change, and identity or rest, are the first and second secrets of nature: Motion and Rest. The whole code of her laws may be written on the thumbnail, or the signet of a ring.
    Ralph Waldo Emerson (1803–1882)

    Having behind us the producing masses of this nation and the world, supported by the commercial interests, the labor interests, and the toilers everywhere, we will answer their demand for a gold standard by saying to them: You shall not press down upon the brow of labor this crown of thorns, you shall not crucify mankind upon a cross of gold.
    —Administration in the State of Neva, U.S. public relief program (1935-1943)

    The spiral is a spiritualized circle. In the spiral form, the circle, uncoiled, unwound, has ceased to be vicious; it has been set free.
    Vladimir Nabokov (1899–1977)