By Jin Akiyama, Hiro Ito, Toshinori Sakai, Yushi Uno

ISBN-10: 3319485318

ISBN-13: 9783319485317

ISBN-10: 3319485326

ISBN-13: 9783319485324

This booklet constitutes the completely refereed post-conference lawsuits of the 18th eastern convention on Discrete and Computational Geometry and Graphs, JDCDGG 2015, held in Kyoto, Japan, in September 2015.

The overall of 25 papers integrated during this quantity used to be conscientiously reviewed and chosen from sixty four submissions. The papers function advances made within the box of computational geometry and concentrate on rising applied sciences, new method and purposes, graph idea and dynamics.

This lawsuits are devoted to Naoki Katoh at the get together of his retirement from Kyoto University.

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Extra resources for Discrete and Computational Geometry and Graphs: 18th Japan Conference, JCDCGG 2015, Kyoto, Japan, September 14-16, 2015, Revised Selected Papers

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Comput. 14, 182–196 (1984) 17. : Computational Geometry: An Introduction. Springer, Berlin (1990) 18. : Line-constrained k-median, k-means, and k-center problems in the plane. -S. ) ISAAC 2014. LNCS, vol. 8889, pp. 3–14. Springer, Heidelberg (2014). 1007/978-3-319-13075-0 1 Dissection with the Fewest Pieces is Hard, Even to Approximate Jeffrey Bosboom1(B) , Erik D. Demaine1 , Martin L. edu Abstract. We prove that it is NP-hard to dissect one simple orthogonal polygon into another using a given number of pieces, as is approximating the fewest pieces to within a factor of 1 + 1/1080 − ε.

2. [Up phase] While v is the right child of p(v) (the parent of v) do v = p(v). Let vr be right child of v. (a) Update x = min{x, m(vr )}. (b) If x > λ(vr ) then set v = p(v), and repeat Step 2. Else let v = vr . 3. [Down phase] Let vl be the left child of vertex of v. (a) Update x = min{x, m(vl )}. (b) If x ≤ λ(vl ) then set v = vl else set v = vr . (c) If v is a leaf lj , set xout = min{x, rj } and stop. Else repeat Step 3. Once the first piercing point is identified, and if it doesn’t pierce all the active intervals on the x-axis, then we invoke UpDown(xin , Tρ , cy ) again with xin set to xout returned from the first invocation, to find the second piercing point, and so forth.

Reversible Nets of Polyhedra 19 (a) D1 : N1 : + ⇒ (b) (c) Fig. 9. A swirl net of a regular tetrahedron. (k = 1, 2, . . , n) inside N1 (Fig. 9(b)). Then, any such D2 doesn’t intersect D1 . (Fig. 9(c)). As in Theorem 2, dissect N1 along D2 into n pieces P1 , . . , Pn , and then connect them in sequence using n − 1 hinges on the perimeter of N1 to form a chain. Fix one of the end-pieces of the chain and rotate the remaining pieces then forming net N2 which is obtained by cutting P along D2 (Fig.

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