Rendering the Impossible: Introducing Meschers
Representing impossible objects – geometric constructions perceivable but not physically realizable – has been a challenge in computer graphics. Existing methods, like cutting or bending, disrupt geometry, hindering downstream processing. This paper introduces Meschers, a novel mesh representation based on discrete exterior calculus. Instead of 3D vertex positions, Meschers store 2D screen-space positions and per-edge depth differences, allowing representation of Escher-like impossibilities. This enables standard geometry processing operations like smoothing, heat diffusion, and geodesic distance queries, as well as inverse rendering, deforming possible shapes into impossible ones. Meschers offer new avenues for understanding human visual perception and expanding computer graphics capabilities.