2026-04-14T06:40:54Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/264842025-07-17T03:49:02Zcom_2072_1033col_2072_452950

Order types and cross-sections of line arrangements in R^3 Aichholzer, Oswin Fabila-Monroy, Ruy Hurtado Díaz, Fernando Alfredo Pérez Lantero, Pablo Ruiz Vargas, Andrés Urrutia Galicia, Jorge Vogtenhuber, Birgit Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional Computational geometry Geometria computacional We consider sets L = {l1,...., ln} of n labeled lines in general position in R3, and study the order types of point sets fp1; : : : ; png that stem from the intersections of the lines in L with (directed) planes II, not parallel to any line of L, i.e., the proper cross-sections of L. As a main result we show that the number of different order types that can be obtained as cross-sections of L is O(n9), and that this bound is tight. Peer Reviewed Postprint (published version) 2014 Conference report Aichholzer, O. [et al.]. Order types and cross-sections of line arrangements in R^3. A: Canadian Conference on Computational Geometry. "Proceedings 26th Canadian Conference on Computational Geometry". 2014, p. 1-6. https://hdl.handle.net/2117/26484 eng https://projects.cs.dal.ca/cccg2014/proceedings/papers/paper39.pdf Restricted access - publisher's policy 6 p. application/pdf