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About this paper
Ana Dodik, Isabella Yu, Kartik Chandra, Jonathan Ragan-Kelley, Joshua Tenenbaum, Vincent Sitzmann, Justin Solomon
The mescher representation models impossible objects by storing screen-space vertex positions and depth changes along edges. It keeps each triangle locally coherent while allowing depth changes around loops to remain inconsistent. Discrete exterior calculus supports operations including smoothing, heat diffusion, and geodesic distances. In comparisons, all three representations render, while cut and bent representations show artifacts in tested processing operations.
Key insights
- Human perception of impossible objects is fundamentally local, relying on spatially localized cues rather than requiring a globally consistent 3D embedding.
- Discrete Exterior Calculus (DEC) provides a suitable mathematical framework for describing and operating on geometries that are locally consistent but globally inconsistent.
- The Hodge decomposition of the relative depth 1-form allows for a formal classification of impossibility, where a non-zero harmonic component signifies an impossible object.
Summary by alphaXiv.
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