{"paper":{"title":"B$\\acute{e}$zier curves based on Lupa\\c{s} $(p,q)$-analogue of Bernstein polynomials in CAGD","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GR","authors_text":"D.K. Lobiyal, Khalid Khan","submitted_at":"2015-05-07T18:36:37Z","abstract_excerpt":"In this paper, we use the blending functions of Lupa\\c{s} type (rational) $(p,q)$-Bernstein operators based on $(p,q)$-integers for construction of Lupa\\c{s} $(p,q)$-B$\\acute{e}$zier curves (rational curves) and surfaces (rational surfaces) with shape parameters. We study the nature of degree elevation and degree reduction for Lupa\\c{s} $(p,q)$-B$\\acute{e}$zier Bernstein functions. Parametric curves are represented using Lupa\\c{s} $(p,q)$-Bernstein basis. We introduce affine de Casteljau algorithm for Lupa\\c{s} type $(p,q)$-Bernstein B$\\acute{e}$zier curves. The new curves have some properties"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01810","kind":"arxiv","version":5},"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"}