Tiling polygons with parallelograms
نویسندگان
چکیده
منابع مشابه
Maximal Parallelograms in Convex Polygons
Given a convex polygon P of n vertices in the plane, we consider the problem of finding the maximum area parallelogram (MAP) inside P. Previously, the best algorithm for this problem runs in time O(n2), and this was achieved by utilizing some nontrivial properties of the MAP. In this paper, we exhibit an algorithm for finding the MAP in time O(n log2 n), greatly improving the previous result. T...
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The Archimedean tilings (Figure 1) and polyhedra will be familiar to many readers. They have the property that the tiles of the tiling, or the faces of the polyhedron, are regular polygons, and that the vertices form a single orbit under the symmetries of the tiling or polyhedron. (Grünbaum and Shephard [1] use Archimedean, in relation to tilings, to refer to the sequence of polygons at each ve...
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Given a simple polygon with rational coordinates having one vertex at the origin and an adjacent vertex on the x-axis, we look at the problem of the location of the vertices for a tiling of the polygon using lattice triangles (i.e., triangles which are congruent to a triangle with the coordinates of the vertices being integer). We show that the coordinate of the vertices in any tiling are ratio...
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We have all seen many of the beautiful patterns obtained by tiling the hyperbolic plane H by repeated reflection in the sides of a "kaleidoscopic" polygon. Though there are such patterns on the sphere and the euclidean plane, these positively curved and fiat geometries lack the richness we see in the hyperbolic plane. Many of these patterns have been popularized by the beautiful art of M.C. Esc...
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We study piecewise rational rotations of convex polygons with a recursive tiling property. For these dynamical systems, the set Σ of discontinuity-avoiding aperiodic orbits decomposes into invariant subsets endowed with a hierarchical symbolic dynamics (Vershik map on a Bratteli diagram). Under conditions which guarantee a form of asymptotic temporal scaling, we prove minimality and unique ergo...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1992
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02187834