By Jin Akiyama, Hiro Ito, Toshinori Sakai

This e-book constitutes the completely refereed post-conference complaints of the sixteenth jap convention on Discrete and computational Geometry and Graphs, JDCDGG 2013, held in Tokyo, Japan, in September 2013.

The overall of sixteen papers integrated during this quantity was once conscientiously reviewed and chosen from fifty eight submissions. The papers characteristic advances made within the box of computational geometry and concentrate on rising applied sciences, new technique and functions, graph concept and dynamics.

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Additional info for Discrete and Computational Geometry and Graphs: 16th Japanese Conference, JCDCGG 2013, Tokyo, Japan, September 17-19, 2013, Revised Selected Papers

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A . This yields: It is well-known that ra = R cos R dA ≤ y/2 −y/2 y/2 θra da = −y/2 a y dx R cos da = 2R sin dx R R 2R so dA/dx ≤ 2R sin y/(2R). For a stadium of length x, the area on the sphere is bounded by A(x, y) as desired. A (1/x − x) × x stadium can be inscribed within any x × 1/x paper rectangle. By Proposition 2, this stadium only occupies A(1/x − x, x) area on the sphere. The remaining paper only has an area of x2 − πx2 /4. Upper Bound 3. x × 1/x paper can wrap an R-sphere only if 4πR2 ≤ x2 − πx2 /4 + A(1/x − x, x).

Cicerone and G. Di Stefano 1. x is a point p interior to some edge e of P . Hence the cut [v, x] is either a b, b -pcut or a a, c -pcut. In both cases, the new angles at p are convex and then they do not need further cuts. So, one cut is sufficient to “remove” the concave vertex v from P . 2. x coincides with a vertex v of P , but v is not forbidden. Also in this case no further cuts are needed to “remove” the concave vertex v from P . This proves that the above approach uses µ(P ) octilinear cuts exactly.

Variations and generalizations of the problem are studied in [6,8–10,12–14,19,28,30–34,37–39]. In addition, Dubins’ characterization plays a fundamental role in establishing the existence as well as the optimality of curvature-constrained paths. Jacobs and Canny [23] showed that even in the presence of obstacles it suffices to restrict attention to paths of Dubins form between obstacle contacts and that if such a path exists then the shortest such path is well-defined. Fortune and Wilfong [20] give a super-exponential time algorithm for determining the existence of, but not actually constructing, such a path.

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