{"paper":{"title":"A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.NA","authors_text":"Alessandra Sestini, Carlotta Giannelli, Caterina Stoppato, Graziano Gentili, Rida T. Farouki","submitted_at":"2016-04-24T10:09:34Z","abstract_excerpt":"A rotation-minimizing frame $({\\bf f}_1,{\\bf f}_2,{\\bf f}_3)$ on a space curve ${\\bf r}(\\xi)$ defines an orthonormal basis for $\\mathbb{R}^3$ in which ${\\bf f}_1={\\bf r}'/|{\\bf r}'|$ is the curve tangent, and the normal-plane vectors ${\\bf f}_2$, ${\\bf f}_3$ exhibit no instantaneous rotation about ${\\bf f}_1$. Polynomial curves that admit rational rotation-minimizing frames (or RRMF curves) form a subset of the Pythagorean-hodograph (PH) curves, specified by integrating the form ${\\bf r}'(\\xi)={\\cal A}(\\xi)\\,{\\bf i}\\,{\\cal A}^*(\\xi)$ for some quaternion polynomial ${\\cal A}(\\xi)$. By introduci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07008","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"}