Smoothed Subpixel Projection (SSP)

This is a repository for code implementing the smoothed subpixel projection (SSP) scheme for topology optimization, which blends density-based and level-set methods in a differentiable way, along with related techniques, as described in the papers:

• A. M. Hammond, A. Oskooi, I. M. Hammond, M. Chen, S. E. Ralph, and S. G. Johnson, “Unifying and accelerating level-set and density-based topology optimization by subpixel-smoothed projection,” Optics Express, vol. 33, pp. 33620–33642, July 2025. Editor's Pick.
• G. Romano, R. Arrieta, and S. G. Johnson, “Differentiating through binarized topology changes: Second-order subpixel-smoothed projection,” arXiv.org e-Print archive, 2601.10737, January 2026.
• R. Arrieta, G. Romano, and S. G. Johnson, “Hyperparameter-free minimum-lengthscale constraints for topology optimization,” arXiv.org e-Print archive, 2507.16108, July 2025.

Installation

Install the PyPI distribution:

pip install ssp-topopt

The Python import package is ssp_topopt:

from ssp_topopt import conic_filter, get_conic_radius_from_eta_e, ssp1_bilinear

For local development:

python -m pip install -e ".[dev]"