Gradient Descent in the ALPS: Abstracted Low-Poly Stylization and Fabrication

Abstract

Low-poly vector art represents an image with a small set of flat-shaded polygons and a limited color palette, making results easy to edit and fabricate. We introduce ALPS, an optimization-based approach that models an image as a 2D polygonal mesh and refines topology, geometry, and colors via score distillation while enforcing mesh validity constraints such as non-overlap, manifoldness, and a bijective mapping. A fine-to-coarse strategy based on mesh simplification helps navigate discrete topology changes during optimization. By constraining colors to a fixed palette, ALPS produces clean vector outputs that can be turned into physical artifacts such as mosaics, embroidery, crocheting, patchwork, and stencils.