For space curves of constant curvature the evolute has the same constant curvature
Modify the curve
tube thickness, 1 ... 16:
Radius, 0.1 ... 6:
slope, 0.02 ... 2:
log(Scaling factor), 0 ... 7:
The helices have the formulas
curve(t) = Rad*[cos(frq*t), sin(frq*t), slope*frq*t].
We choose frq = 1/(Rad*sqrt(1 + slope^2)) to keep the arclength of the
helix constant under parameter changes. The normals of the helix are drawn
until they meet the evolute, another helix with the same curvature.
The helix and its evolute have the same constant curvature. The convex hull of their
pair of osculating circles is the Oloid. If ``normals'' and ``osculating circles'' are selected, then the Oloid is shown.
See more images of helices