نتایج جستجو برای: convex polygon domain
تعداد نتایج: 464581 فیلتر نتایج به سال:
In this paper we present a natural and simple procedure to compute all feasible allocation points of a (non-convex) polygon within a (non-convex) polygonal bounded region. This procedure can be seen as a basis of more sophisticated and efficient algorithms for the same task, or for related problems such as finding a single placement point.
Let n ≥ 3 be an integer. A convex lattice n-gon is a polygon whose n vertices are points on the integer lattice Z 2 and whose interior angles are strictly less than π. Let a n denote the least possible area enclosed by a convex lattice n-gon, then [1, 2, 3] {a n } ∞ n=3 = n 1 2
We present a polynomial-time algorithm for a variant of the Euclidean traveling salesman tour where n vertices are on the boundary of a convex polygon P and m vertices form the boundary of a convex polygonal obstacle Q completely contained within P . In the worst case the algorithm needs O(m lg m+ mn) time and O(nm + m) space.
Three open problems on folding/unfolding are discussed: (1) Can every convex polyhedron be cut along edges and unfolded at to a single nonoverlapping piece? (2) Given gluing instructions for a polygon, construct the unique 3D convex polyhedron to which it folds. (3) Can every planar polygonal chain be straightened?
We show that bisecting a polygon into two equal (possibly disconnected) parts with the smallest possible total perimeter is NP-complete, and it is in fact NP-hard to approximate within any ratio. In contrast, we give a dynamic programming algorithm which nds a subdivision into two parts with total perimeter at most that of the optimum bisection, such that the two parts have areas within of each...
A selection of points drawn from a convex polygon, no two with the same vertical or horizontal coordinate, yields a permutation in a canonical fashion. We characterise and enumerate those permutations which arise in this manner and exhibit some interesting structural properties of the permutation class they form. We conclude with a permutation analogue of the celebrated Happy Ending Problem. 1 ...
This paper studies the chromatic number of the following four flip graphs (under suitable definitions of a flip): • the flip graph of perfect matchings of a complete graph of even order, • the flip graph of triangulations of a convex polygon (the associahedron), • the flip graph of non-crossing Hamiltonian paths of a convex point set, and • the flip graph of triangles in a convex point set. We ...
A well-studied problem is that of unfolding a convex polyhedron into a simple planar polygon. In this paper, we study the limits of unfoldability. We give an example of a polyhedron with convex faces that cannot be unfolded by cutting along its edges. We further show that such a polyhedron can indeed be unfolded if cuts are allowed to cross faces. Finally, we prove that \open" polyhedra with co...
A well-studied problem is that of unfolding a convex polyhedron into a simple planar polygon. In this paper, we study the limits of unfoldability. We give an example of a polyhedron with convex faces that cannot be unfolded by cutting along its edges. We further show that such a polyhedron can indeed be unfolded if cuts are allowed to cross faces. Finally, we prove that “open” polyhedra with co...
We show that for any convex object Q in the plane, the average distance from the Fermat-Weber center of Q to the points in Q is at least ∆(P )/7, where ∆(P ) is the diameter of P , and that there exists a convex object for which this distance is ∆(P )/6. We use this result to obtain a linear-time approximation scheme for finding an approximate Fermat-Weber center of a convex polygon Q.
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