[hammock]

Imagine you are watching the ball, but instead of traveling along a line, it is tracing a circle- however you are viewing it from the one-dimensional angle. Is that smoothstep, or would that be a different equation? They look similar to my naked eye.

[ycombobreaker]

The reason smoothstep looks similar to a sinusoid is because it is a polynomial approximation. I remember Dan Perlin discussing it in his (book|paper|website), but googling around doesn't seem to show anything that I remember. For Perlin Noise, a sinusoid was the highest-quality interpolation because it was continuous everywhere, even at the endpoints. Smooth-step is discontinuous at the endpoints, but it is close enough for discrete computer graphics.

[dietrichepp]

Do you mean "smooth everywhere"? The Weierstrauss function is continuous everywhere, but you wouldn't use it for interpolation:

http://en.wikipedia.org/wiki/Weierstrass_function

[ycombobreaker]

Yes, thank you. After reading a bit more, smoothness is what I'm looking for. One of the _derivatives_ of the smoothstep is discontinuous at the endpoint.

[sesqu]

I wouldn't call smoothstep an approximation to a sinusoid - both are sigmoidal, but that's about it. This smoothstep in particular is just a natural cubic spline interpolator, arguably the simplest sigmoidal interpolating function.

[tellarin]

Minor correction: Ken Perlin - http://mrl.nyu.edu/~perlin/

[ycombobreaker]

Thank you!

[madelfio]

Smoothstep is a polynomial approximation of a sine wave through (0, 0) and (1, 1), but it's pretty darn close.

http://www.onlinefunctiongrapher.com/?f=3*x%5E2-2*x%5E3|.5-c...

[matthewrobertso]

That would be a sinusoidal function. Smoothstep looks similar but is different.