Nuke’s Smooth Ramp Functions

Nuke’s Ramp node can produce linear and smooth gradients. Here are its formulas. I have reverse-engineered them by trial and error after reading up on interpolation formulas like smoothstep (nicely summed up on this website).

In these formulas, “x” denotes a value from 0 to 1. The result falls into the [0-1] range as well and needs to be scaled by the desired end color if you want an RGB ramp.

// linear
y = x
// plinear: perceptually linear in rec709
y = pow(x, 3)
// smooth: traditional smoothstep
y = x*x*(3 - 2*x)
// smooth0: Catmull-Rom spline, smooth start, linear end
y = x*x*(2 - x)
// smooth1: Catmull-Rom spline, linear start, smooth end
y = x*(1 + x*(1 - x))

Here’s a ramp macro for Fusion which allows you to draw ramps directly onto an image like in Nuke. Fusion’s own BG tool is of course much more flexible, but it requires you to merge its gradient manually and it has no easy switch for smoothstep gradients.


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