{"paper":{"title":"Meschers: Geometry Processing of Impossible Objects","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"Meschers represent impossible objects as meshes that support standard geometry processing and inverse rendering.","cross_cats":["cs.CG","cs.CV"],"primary_cat":"cs.GR","authors_text":"Ana Dodik, Isabella Yu, Jonathan Ragan-Kelley, Joshua Tenenbaum, Justin Solomon, Kartik Chandra, Vincent Sitzmann","submitted_at":"2026-05-14T15:28:14Z","abstract_excerpt":"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 d"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That discrete exterior calculus can be extended to meshes representing impossible objects while preserving the validity of standard geometry operations such as distance computation and smoothing without introducing new inconsistencies.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Meschers are a new mesh representation for impossible geometric objects grounded in discrete exterior calculus that supports full discrete geometry processing including inverse rendering.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Meschers represent impossible objects as meshes that support standard geometry processing and inverse rendering.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4a7793999aab23190522f6955469a414264f92cace1116e0029f7b40920d2c58"},"source":{"id":"2605.14960","kind":"arxiv","version":1},"verdict":{"id":"5cfdd833-2204-4553-a458-cca874b39c34","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T03:05:58.675967Z","strongest_claim":"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.","one_line_summary":"Meschers are a new mesh representation for impossible geometric objects grounded in discrete exterior calculus that supports full discrete geometry processing including inverse rendering.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That discrete exterior calculus can be extended to meshes representing impossible objects while preserving the validity of standard geometry operations such as distance computation and smoothing without introducing new inconsistencies.","pith_extraction_headline":"Meschers represent impossible objects as meshes that support standard geometry processing and inverse rendering."},"references":{"count":47,"sample":[{"doi":"","year":2006,"title":"In ACM SIGGRAPH 2006 Papers","work_id":"ebc0e374-e5b1-441e-9869-f6ddab62f576","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2000,"title":"InRendering Techniques 2000: Proceedings of the Eurographics Workshop in Brno, Czech Republic, June 26–28, 2000","work_id":"6a90bc1f-f425-410f-839d-bf2cf91c9816","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2003,"title":"The Visual Computer19, 2 (2003), 105–114","work_id":"2f81cbec-da60-4a15-a204-a652bc0cd700","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1145/3596711.3596740","year":1985,"title":"Computer vision, graphics, and image processing32, 1 (1985), 29–73","work_id":"5f89b341-58c9-4218-95d5-b2f7297568e8","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"month = dec, year =","work_id":"8a1f68ba-1095-46d9-a9af-d49d9ba585f2","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":47,"snapshot_sha256":"4bff3279bf405caa1b7a34c78269e9d53d48c9f47048e53bfae4c402d4504b1d","internal_anchors":1},"formal_canon":{"evidence_count":1,"snapshot_sha256":"0d8573ef1214317ecebadc6412bb46dcb9a6d1c7d4fa38fd8992b34707df3982"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}