smoothMin¶
Once continuously differentiable approximation of min(x1, x2)
FastSmoothBuildings.Utilities.smoothMin, function (source)
Purpose
Once continuously differentiable approximation of min(x1, x2), without events (see Smoothing).
Equations
y = regStep(x2 − x1, x1, x2, Δx): y = x1 when x2 − x1 > Δx, y = x2 when x2 − x1 < −Δx, and in between a weighted mean of the two arguments whose weight goes from 0 to 1 along the cubic of regStep.
The result is exact outside the blend and continuous with its first derivative (C1). Inside the blend it lies between the two arguments, at most 0.087 Δx above min(x1, x2); it equals it when x1 = x2.
Use
deltaX (> 0) is the half width of the blend, in the unit of the arguments. The arguments are those
of Buildings.Utilities.Math.Functions.smoothMin.
Revisions¶
- October 2026: moved from trano's
FastModel.Utilities.