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)
“Wise Draco comes, deep in the midnight roll
Of black artillery; he comes, though late;
In code corroborating Calvin’s creed
And cynic tyrannies of honest kings;
He comes, nor parlies; and the Town, redeemed,
Gives thanks devout; nor, being thankful, heeds
The grimy slur on the Republic’s faith implied,
Which holds that Man is naturally good,
And—more—is Nature’s Roman, never to be
scourged.”
—Herman Melville (1819–1891)
“An evil soul producing holy witness
Is like a villain with a smiling cheek,
A goodly apple rotten at the heart.”
—William Shakespeare (1564–1616)
“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)