{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TGD3PLUQLCPEIEH2MQCGWTGIQH","short_pith_number":"pith:TGD3PLUQ","schema_version":"1.0","canonical_sha256":"9987b7ae90589e4410fa64046b4cc881c8638c42affc13c497e5738b489bbbf1","source":{"kind":"arxiv","id":"1606.00789","version":2},"attestation_state":"computed","paper":{"title":"Matrix representations by means of interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christos Konaxis, Clement Laroche, Ilias S. Kotsireas, Ioannis Z. Emiris","submitted_at":"2016-06-02T18:30:03Z","abstract_excerpt":"We examine implicit representations of parametric or point cloud models, based on interpolation matrices, which are not sensitive to base points. We show how interpolation matrices can be used for ray shooting of a parametric ray with a surface patch, including the case of high-multiplicity intersections. Most matrix operations are executed during pre-processing since they solely depend on the surface. For a given ray, the bottleneck is equation solving. Our Maple code handles bicubic patches in $\\le 1$~sec, though numerical issues might arise. Our second contribution is to extend the method t"},"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":"1606.00789","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-02T18:30:03Z","cross_cats_sorted":[],"title_canon_sha256":"d26ad0023ea9d9c2defb40ca237e34bec1989a54aba0f00aa5045ea623aa796a","abstract_canon_sha256":"2d353c2bbf6a824d1950ede127bd3221e4bbf198578ff157b977ed994d221435"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:46.612710Z","signature_b64":"6rl+V4rR6t+8ejPD9ezjdOdE2gq1gN4pYj/IKsUoVUBdQZe6LdD1rywNter10W+zdDkAzpkJDdVWIbjihnCCAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9987b7ae90589e4410fa64046b4cc881c8638c42affc13c497e5738b489bbbf1","last_reissued_at":"2026-05-18T00:42:46.612075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:46.612075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrix representations by means of interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christos Konaxis, Clement Laroche, Ilias S. Kotsireas, Ioannis Z. Emiris","submitted_at":"2016-06-02T18:30:03Z","abstract_excerpt":"We examine implicit representations of parametric or point cloud models, based on interpolation matrices, which are not sensitive to base points. We show how interpolation matrices can be used for ray shooting of a parametric ray with a surface patch, including the case of high-multiplicity intersections. Most matrix operations are executed during pre-processing since they solely depend on the surface. For a given ray, the bottleneck is equation solving. Our Maple code handles bicubic patches in $\\le 1$~sec, though numerical issues might arise. Our second contribution is to extend the method t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00789","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":"1606.00789","created_at":"2026-05-18T00:42:46.612161+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.00789v2","created_at":"2026-05-18T00:42:46.612161+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00789","created_at":"2026-05-18T00:42:46.612161+00:00"},{"alias_kind":"pith_short_12","alias_value":"TGD3PLUQLCPE","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"TGD3PLUQLCPEIEH2","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"TGD3PLUQ","created_at":"2026-05-18T12:30:44.179134+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/TGD3PLUQLCPEIEH2MQCGWTGIQH","json":"https://pith.science/pith/TGD3PLUQLCPEIEH2MQCGWTGIQH.json","graph_json":"https://pith.science/api/pith-number/TGD3PLUQLCPEIEH2MQCGWTGIQH/graph.json","events_json":"https://pith.science/api/pith-number/TGD3PLUQLCPEIEH2MQCGWTGIQH/events.json","paper":"https://pith.science/paper/TGD3PLUQ"},"agent_actions":{"view_html":"https://pith.science/pith/TGD3PLUQLCPEIEH2MQCGWTGIQH","download_json":"https://pith.science/pith/TGD3PLUQLCPEIEH2MQCGWTGIQH.json","view_paper":"https://pith.science/paper/TGD3PLUQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.00789&json=true","fetch_graph":"https://pith.science/api/pith-number/TGD3PLUQLCPEIEH2MQCGWTGIQH/graph.json","fetch_events":"https://pith.science/api/pith-number/TGD3PLUQLCPEIEH2MQCGWTGIQH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TGD3PLUQLCPEIEH2MQCGWTGIQH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TGD3PLUQLCPEIEH2MQCGWTGIQH/action/storage_attestation","attest_author":"https://pith.science/pith/TGD3PLUQLCPEIEH2MQCGWTGIQH/action/author_attestation","sign_citation":"https://pith.science/pith/TGD3PLUQLCPEIEH2MQCGWTGIQH/action/citation_signature","submit_replication":"https://pith.science/pith/TGD3PLUQLCPEIEH2MQCGWTGIQH/action/replication_record"}},"created_at":"2026-05-18T00:42:46.612161+00:00","updated_at":"2026-05-18T00:42:46.612161+00:00"}