# Meschers: Geometry Processing of Impossible Objects

arXiv: https://arxiv.org/abs/2605.14960 · HTML: https://mlsanity.com/paper/2605.14960/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 72 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 9 of 9)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [Visual Anagrams: Generating Multi-View Optical Illusions with Diffusion Models](https://mlsanity.com/paper/2311.17919/) (2023)
- [Diffusion Illusions: Hiding Images in Plain Sight](https://mlsanity.com/paper/2312.03817/) (2023)
- [Factorized Diffusion: Perceptual Illusions by Noise Decomposition](https://mlsanity.com/paper/2404.11615/) (2024)
- [Designing Perceptual Puzzles by Differentiating Probabilistic Programs](https://mlsanity.com/paper/2204.12301/) (2022)
- [Toward Quantifying Ambiguities in Artistic Images](https://mlsanity.com/paper/2008.09688/) (2020)
- [Algebraic Smooth Occluding Contours](https://mlsanity.com/paper/2306.01973/) (2023)

## Built on by (most cited first, 1 of 1)

- [JanusMesh: Fast and Zero-Shot 3D Visual Illusion Generation via Cross-Space Denoising](https://mlsanity.com/paper/2606.20563/) (2026)

## Abstract (arXiv)

Impossible objects, geometric constructions that humans can perceive but that cannot exist in real life, have been a topic of intrigue in visual arts, perception, and graphics, yet no satisfying computer representation of such objects exists. Previous work embeds impossible objects in 3D, cutting them or twisting/bending them in the depth axis. Cutting an impossible object changes its local geometry at the cut, which can hamper downstream graphics applications, such as smoothing, while bending makes it difficult to relight the object. Both of these can invalidate geometry operations, such as distance computation. As an alternative, we introduce Meschers, meshes capable of representing impossible constructions akin to those found in M.C. Escher's woodcuts. Our representation has a theoretical foundation in discrete exterior calculus and supports the use-cases above, as we demonstrate in a number of example applications. Moreover, because we can do discrete geometry processing on our representation, we can inverse-render impossible objects. We also compare our representation to cut and bend representations of impossible objects.