lerp
lerp(a, b, t): the value t of the way from a (t = 0) to b (t = 1), a + (b - a)t. Exact for exact inputs; t outside 0..1 extrapolates. (With five arguments, lerp is the numerical-methods interpolation.)
a(number) --b(number) --t(number) --
Noise And Easing
inverseLerp
The t with lerp(a, b, t) = v: (v - a)/(b - a).
a(number) --b(number) --v(number) --
remap
v moved from the range a1..b1 to the range a2..b2 (linearly, not clamped).
v(number) --a1(number) --b1(number) --a2(number) --b2(number) --
clamp
v limited to the range lo..hi.
v(number) --lo(number) --hi(number) --
smoothstep
0 below e0, 1 above e1, and the smooth S-curve t^2(3 - 2t) between (t = (x - e0)/(e1 - e0)), as in GLSL.
e0(number) --e1(number) --x(number) --
smootherstep
Like smoothstep() but with 6t^5 - 15t^4 + 10t^3, flat to the second derivative at both ends (Perlin's fade curve).
e0(number) --e1(number) --x(number) --
ease
An easing curve at t (0 at t = 0, 1 at t = 1): "cubicInOut" (default), "linear", "quadIn", "quadOut", "quadInOut", "cubicIn", "cubicOut", "sineIn", "sineOut", "sineInOut" (Penner's easing equations). Exact where the answer is.
t(number) --curve(string) -- optional
tween
From a to b along an easing curve: lerp(a, b, ease(t, curve)).
a(number) --b(number) --t(number) --curve(string) -- optional
noise
Perlin noise: a smooth random-looking value in about -1..1 at x, (x, y) or (x, y, z); 0 at whole numbers. Ken Perlin's improved noise; seed(n) picks a different field (the same n, the same field).
x(number) --y(number) -- optionalz(number) -- optional
fbm
Fractal noise: 'octaves' layers of noise(), each twice the frequency and half the strength of the last (fractal Brownian motion), about -1..1. Octaves 1 to 16.
x(number) --y(number) --z(number) -- optionaloctaves(number) --