{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:XTDVZX7NR7ABY5AWESWNDM5QAM","short_pith_number":"pith:XTDVZX7N","schema_version":"1.0","canonical_sha256":"bcc75cdfed8fc01c741624acd1b3b00304bee4ff3ad796b24f1dfbc9523818f2","source":{"kind":"arxiv","id":"1308.3872","version":1},"attestation_state":"computed","paper":{"title":"A Variational Principle for Improving 2D Triangle Meshes based on Hyperbolic Volume","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Feng Luo, Jian Sun, Jie Gao, Junhui Deng, Wei Chen, Xianfeng Gu","submitted_at":"2013-08-18T16:40:31Z","abstract_excerpt":"In this paper, we consider the problem of improving 2D triangle meshes tessellating planar regions. We propose a new variational principle for improving 2D triangle meshes where the energy functional is a convex function over the angle structures whose maximizer is unique and consists only of equilateral triangles. This energy functional is related to hyperbolic volume of ideal 3-simplex. Even with extra constraints on the angles for embedding the mesh into the plane and preserving the boundary, the energy functional remains well-behaved. We devise an efficient algorithm for maximizing the ene"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1308.3872","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-08-18T16:40:31Z","cross_cats_sorted":[],"title_canon_sha256":"cf61c4df0d5ab874ef8bbdc0b2696f847bb7fe8e2da4bf749a55956e9da5af2a","abstract_canon_sha256":"7e44c237e8c81652ad41f45b43fdabe876862c29190d4d6db12d38b3727dbc1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:42.296990Z","signature_b64":"pATCvQJF/fAieNGeyHwhg7ALOoOclBfmtbUbg0f7ElWTWbPwHSwcqq8bgJtiGRecKf0M+I26I0wlQRZYjW6JCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcc75cdfed8fc01c741624acd1b3b00304bee4ff3ad796b24f1dfbc9523818f2","last_reissued_at":"2026-05-18T03:15:42.296469Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:42.296469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Variational Principle for Improving 2D Triangle Meshes based on Hyperbolic Volume","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Feng Luo, Jian Sun, Jie Gao, Junhui Deng, Wei Chen, Xianfeng Gu","submitted_at":"2013-08-18T16:40:31Z","abstract_excerpt":"In this paper, we consider the problem of improving 2D triangle meshes tessellating planar regions. We propose a new variational principle for improving 2D triangle meshes where the energy functional is a convex function over the angle structures whose maximizer is unique and consists only of equilateral triangles. This energy functional is related to hyperbolic volume of ideal 3-simplex. Even with extra constraints on the angles for embedding the mesh into the plane and preserving the boundary, the energy functional remains well-behaved. We devise an efficient algorithm for maximizing the ene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3872","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1308.3872","created_at":"2026-05-18T03:15:42.296556+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.3872v1","created_at":"2026-05-18T03:15:42.296556+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3872","created_at":"2026-05-18T03:15:42.296556+00:00"},{"alias_kind":"pith_short_12","alias_value":"XTDVZX7NR7AB","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"XTDVZX7NR7ABY5AW","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"XTDVZX7N","created_at":"2026-05-18T12:28:06.772260+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XTDVZX7NR7ABY5AWESWNDM5QAM","json":"https://pith.science/pith/XTDVZX7NR7ABY5AWESWNDM5QAM.json","graph_json":"https://pith.science/api/pith-number/XTDVZX7NR7ABY5AWESWNDM5QAM/graph.json","events_json":"https://pith.science/api/pith-number/XTDVZX7NR7ABY5AWESWNDM5QAM/events.json","paper":"https://pith.science/paper/XTDVZX7N"},"agent_actions":{"view_html":"https://pith.science/pith/XTDVZX7NR7ABY5AWESWNDM5QAM","download_json":"https://pith.science/pith/XTDVZX7NR7ABY5AWESWNDM5QAM.json","view_paper":"https://pith.science/paper/XTDVZX7N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.3872&json=true","fetch_graph":"https://pith.science/api/pith-number/XTDVZX7NR7ABY5AWESWNDM5QAM/graph.json","fetch_events":"https://pith.science/api/pith-number/XTDVZX7NR7ABY5AWESWNDM5QAM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XTDVZX7NR7ABY5AWESWNDM5QAM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XTDVZX7NR7ABY5AWESWNDM5QAM/action/storage_attestation","attest_author":"https://pith.science/pith/XTDVZX7NR7ABY5AWESWNDM5QAM/action/author_attestation","sign_citation":"https://pith.science/pith/XTDVZX7NR7ABY5AWESWNDM5QAM/action/citation_signature","submit_replication":"https://pith.science/pith/XTDVZX7NR7ABY5AWESWNDM5QAM/action/replication_record"}},"created_at":"2026-05-18T03:15:42.296556+00:00","updated_at":"2026-05-18T03:15:42.296556+00:00"}