tidy3d.plugins.autograd.invdes.make_curvature_penalty

class make_curvature_penalty

Bases:

Create a penalty function based on the curvature of a set of points.

Parameters:

• min_radius (float) – The minimum radius of curvature.

• alpha (float, optional) – Scaling factor for the penalty, by default 1.0.

• kappa (float, optional) – Exponential factor for the penalty, by default 10.0.

• eps (float, optional) – A small value to avoid division by zero, by default 1e-6.

Returns:

A function that computes the curvature penalty for a given set of points.

Return type:

Callable

Notes

The penalty function is defined as:

\[p(r) = \frac{\mathrm{exp}(-\kappa(r - r_{min}))}{1 + \mathrm{exp}(-\kappa(r - r_{min}))}\]

This formula was described by A. Micheals et al. “Leveraging continuous material averaging for inverse electromagnetic design”, Optics Express (2018).

Inherited Common Usage