Robust Voronoi Partitioning for Scaffold Architecture via Learned-σ Centroids and Stable Normal Flow

We present a robust Voronoi-based partitioning workflow for scaffold architecture that resolves two chronic bottlenecks in Convex Fair Partition (CFP): unstable centroid updates in Lloyd’s algorithm and brittle, scale-sensitive Jacobian probes in the normal-flow stage. We replace the uniform centroid with a Gaussian-weighted ("fuzzy") centroid and learn its scale  from simple polygon features, stabilizing updates in skewed or boundary-clipped cells. We also introduce a scale-aware, edge-capped step size δ for forward finite differences, ensuring numerically resolvable probes that remain safe near edges. On 500 convex polygons (5,000 seeds each), learned-σ delivers order-of-magnitude savings for coarse partitions (≈99% time reduction at 4 regions) while remaining on par for 7–10 regions. The adaptive δ reduces iterations and wall-time for ≥6 regions by ~20–35% (up to ~37% at larger sizes). Both modules are drop-in and rely only on local geometry, making them practical for 3D bioprinting workflows and downstream transport simulation.