Sharpness-knob → profile exponent map: n = 2^(3 − 4s). In (1 − p²)^n space SMALLER exponents are boxier, so the map runs opposite to the gaussian-family β: s = 0 → n = 8 (spiky), s = 0.5 → n = 2 (the default quartic), s = 1 → n = 0.5 (boxy).
n = 2^(3 − 4s)
(1 − p²)^n
Sharpness-knob → profile exponent map:
n = 2^(3 − 4s). In(1 − p²)^nspace SMALLER exponents are boxier, so the map runs opposite to the gaussian-family β: s = 0 → n = 8 (spiky), s = 0.5 → n = 2 (the default quartic), s = 1 → n = 0.5 (boxy).