differt.utils.smoothing_function

smoothing_function(x, /, smoothing_factor=1.0)

Return a smoothed approximation of the Heaviside step function.

This function is used internally for smoothing-out discontinuities in Ray Tracing, see Smoothing Discontinuities for Fully Differentiable Ray Tracing.

Parameters:

• x (Float[ArrayLike, '*#batch']) – The input array.

• smoothing_factor (Float[ArrayLike, '*#batch']) – The slope—or scaling—parameter, also noted \(\alpha\).

Return type:

Float[ArrayLike, '*batch']

Returns:

The output of the smoothing function.