{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EUNY4Y3CJOHAEKNMI4CEC3BBBF","short_pith_number":"pith:EUNY4Y3C","schema_version":"1.0","canonical_sha256":"251b8e63624b8e0229ac4704416c21094021c8eb10b7e2a9fade06d40e8dc030","source":{"kind":"arxiv","id":"1810.01285","version":2},"attestation_state":"computed","paper":{"title":"Area-Preserving Geometric Hermite Interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Geoffrey McGregor, Jean-Christophe Nave","submitted_at":"2018-10-02T14:22:52Z","abstract_excerpt":"In this paper we establish a framework for planar geometric interpolation with exact area preservation using cubic B\\'ezier polynomials. We show there exists a family of such curves which are $5^{th}$ order accurate, one order higher than standard geometric cubic Hermite interpolation. We prove this result is valid when the curvature at the endpoints does not vanish, and in the case of vanishing curvature, the interpolation is $4^{th}$ order accurate. The method is computationally efficient and prescribes the parametrization speed at endpoints through an explicit formula based on the given dat"},"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":"1810.01285","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-02T14:22:52Z","cross_cats_sorted":[],"title_canon_sha256":"707358ae4a198bf1b71c7e6d5d49947fa9926dcc3154eaaa3a0ea2b0befe4139","abstract_canon_sha256":"e2ec4663a70dc022ac030ce487fc5645cd8bfb37f933436219bf7aedcd933c52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:48.891055Z","signature_b64":"5mlvEw5ZR6NGEgFmTBp0b5l+z3VlDr2TMXx3hkYwFY5nhwOlQYnhduiROgWW+RUUMT5GsQjGAv8N3v9TJs4rCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"251b8e63624b8e0229ac4704416c21094021c8eb10b7e2a9fade06d40e8dc030","last_reissued_at":"2026-05-17T23:50:48.890431Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:48.890431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Area-Preserving Geometric Hermite Interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Geoffrey McGregor, Jean-Christophe Nave","submitted_at":"2018-10-02T14:22:52Z","abstract_excerpt":"In this paper we establish a framework for planar geometric interpolation with exact area preservation using cubic B\\'ezier polynomials. We show there exists a family of such curves which are $5^{th}$ order accurate, one order higher than standard geometric cubic Hermite interpolation. We prove this result is valid when the curvature at the endpoints does not vanish, and in the case of vanishing curvature, the interpolation is $4^{th}$ order accurate. The method is computationally efficient and prescribes the parametrization speed at endpoints through an explicit formula based on the given dat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01285","kind":"arxiv","version":2},"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":"1810.01285","created_at":"2026-05-17T23:50:48.890513+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.01285v2","created_at":"2026-05-17T23:50:48.890513+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01285","created_at":"2026-05-17T23:50:48.890513+00:00"},{"alias_kind":"pith_short_12","alias_value":"EUNY4Y3CJOHA","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EUNY4Y3CJOHAEKNM","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EUNY4Y3C","created_at":"2026-05-18T12:32:22.470017+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/EUNY4Y3CJOHAEKNMI4CEC3BBBF","json":"https://pith.science/pith/EUNY4Y3CJOHAEKNMI4CEC3BBBF.json","graph_json":"https://pith.science/api/pith-number/EUNY4Y3CJOHAEKNMI4CEC3BBBF/graph.json","events_json":"https://pith.science/api/pith-number/EUNY4Y3CJOHAEKNMI4CEC3BBBF/events.json","paper":"https://pith.science/paper/EUNY4Y3C"},"agent_actions":{"view_html":"https://pith.science/pith/EUNY4Y3CJOHAEKNMI4CEC3BBBF","download_json":"https://pith.science/pith/EUNY4Y3CJOHAEKNMI4CEC3BBBF.json","view_paper":"https://pith.science/paper/EUNY4Y3C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.01285&json=true","fetch_graph":"https://pith.science/api/pith-number/EUNY4Y3CJOHAEKNMI4CEC3BBBF/graph.json","fetch_events":"https://pith.science/api/pith-number/EUNY4Y3CJOHAEKNMI4CEC3BBBF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EUNY4Y3CJOHAEKNMI4CEC3BBBF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EUNY4Y3CJOHAEKNMI4CEC3BBBF/action/storage_attestation","attest_author":"https://pith.science/pith/EUNY4Y3CJOHAEKNMI4CEC3BBBF/action/author_attestation","sign_citation":"https://pith.science/pith/EUNY4Y3CJOHAEKNMI4CEC3BBBF/action/citation_signature","submit_replication":"https://pith.science/pith/EUNY4Y3CJOHAEKNMI4CEC3BBBF/action/replication_record"}},"created_at":"2026-05-17T23:50:48.890513+00:00","updated_at":"2026-05-17T23:50:48.890513+00:00"}