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 for, 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)
“Faultless honesty is a sine qua non of business life. Not alone the honesty according to the moral code and the Bible. When I speak of honesty I refer to the small, hidden, evasive meannesses of our natures. I speak of the honesty of ourselves to ourselves.”
—Alice Foote MacDougall (1867–1945)
“Death is an incident producing clay. Use it, mold it, learn from it.”
—John Gilling, British screenwriter. Dr. Knox (Peter Cushing)
“What is art,
But life upon the larger scale, the higher,
When, graduating up in a spiral line
Of still expanding and ascending gyres,
It pushes toward the intense significance
Of all things, hungry for the Infinite?
Art’s life,—and where we live, we suffer and toil.”
—Elizabeth Barrett Browning (1806–1861)