{"paper":{"title":"Homeomorphic approximation of the intersection curve of two rational surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"cs.CG","authors_text":"Jin-San Cheng, Liyong Shen, Xiaohong Jia","submitted_at":"2012-03-02T12:23:34Z","abstract_excerpt":"We present an approach of computing the intersection curve $\\mathcal{C}$ of two rational parametric surface $\\S_1(u,s)$ and $\\S_2(v,t)$, one being projectable and hence can easily be implicitized. Plugging the parametric surface to the implicit surface yields a plane algebraic curve $G(v,t)=0$. By analyzing the topology graph $\\G$ of $G(v,t)=0$ and the singular points on the intersection curve $\\mathcal{C}$ we associate a space topology graph to $\\mathcal{C}$, which is homeomorphic to $\\mathcal{C}$ and therefore leads us to an approximation for $\\mathcal{C}$ in a given precision."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0442","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"}