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:
“Many people will say to working mothers, in effect, “I don’t think you can have it all.” The phrase for “have it all” is code for “have your cake and eat it too.” What these people really mean is that achievement in the workplace has always come at a price—usually a significant personal price; conversely, women who stayed home with their children were seen as having sacrificed a great deal of their own ambition for their families.”
—Anne C. Weisberg (20th century)
“Watteau is no less an artist for having painted a fascia board while Sainsbury’s is no less effective a business for producing advertisements which entertain and educate instead of condescending and exploiting.”
—Stephen Bayley (b. 1951)
“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)