Sinclair, Robert; Tanaka, Minoru A bound on the number of endpoints of the cut locus. (English) Zbl 1111.53004 LMS J. Comput. Math. 9, 21-39 (2006). Summary: The authors provide strong experimental evidence for an upper bound on the number of endpoints of the cut locus from a point on a 2-surface of revolution. This bound is equal to the minimal number of intervals of monotone non-increasing or non-decreasing Gaussian curvature along one meridian from one pole to the other. Cited in 7 Documents MSC: 53A05 Surfaces in Euclidean and related spaces 53-04 Software, source code, etc. for problems pertaining to differential geometry 53C22 Geodesics in global differential geometry 68U05 Computer graphics; computational geometry (digital and algorithmic aspects) Keywords:Gaussian curvature; 2-surface of revolution; experimental evidence Software:Loki; Thaw PDFBibTeX XMLCite \textit{R. Sinclair} and \textit{M. Tanaka}, LMS J. Comput. Math. 9, 21--39 (2006; Zbl 1111.53004) Full Text: DOI Link References: [1] Sakai, Transl. Math. Monogr. 149 (1996) [2] Bleecker, Colloq. Math. 44 pp 263– (1981) [3] Gooch, Non-photorealistic rendering (2001) · Zbl 1055.68136 [4] DOI: 10.2307/1971259 · Zbl 0436.53047 [5] Elerath, J. Differential Geom. 15 pp 187– (1980) · Zbl 0526.53043 [6] DOI: 10.2307/1967147 · JFM 33.0670.02 [7] Besse, Ergeb. Math. Grenz-geb. 93 (1978) [8] DOI: 10.1090/S0002-9947-03-03163-5 · Zbl 1035.53047 [9] DOI: 10.1006/aima.2000.1923 · Zbl 0992.53026 [10] Tsuji, Proc. School of Sci., Tokai Univ. 32 pp 23– (1997) [11] Tanaka, Mem. Fac. Set, Kyushu Univ. Ser. A, Mathematics 46 pp 251– (1992) [12] DOI: 10.2307/1986219 · JFM 36.0669.01 [13] DOI: 10.1215/S0012-7094-36-00208-9 · Zbl 0013.32201 [14] DOI: 10.1215/S0012-7094-35-00126-0 · Zbl 0012.27502 [15] Margerin, Differential geometry: Riemannian geometry 54 pp 465– (1993) [16] Mongoldt, J. Reine Angew. Math. 91 pp 23– (1881) [17] Ma, Nanjing Daxue Xuebao Shuxue Bannian Kan 4 pp 106– (1987) [18] DOI: 10.2307/2370645 · JFM 56.0600.03 [19] Jacobi, Gesammelte Werke, C. G. J. Jacobi (1884) [20] Itoh, Experiment. Math. 13 pp 309– (2004) · Zbl 1093.53003 [21] Gravesen, Asian J. Math. 9 pp 103– (2005) · Zbl 1080.53005 [22] DOI: 10.2969/jmsj/04440631 · Zbl 0789.53023 [23] Struik, Lectures on classical differential geometry (1988) · Zbl 0697.53002 [24] Sinclair, Experiment. Math. 12 pp 477– (2003) · Zbl 1073.53007 [25] Sinclair, Experiment. Math. 11 pp 1– (2002) · Zbl 1052.53001 [26] Shiohama, The geometry of total curvature on complete open surfaces 159 (2003) · Zbl 1086.53056 [27] DOI: 10.1145/97880.97901 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.