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Topic: Uniform tessellation

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	Tessellation - Wikipedia, the free encyclopedia
		A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps.
		The four color theorem states that for every tessellation of the plane, with a set of four available colors, each tile can be colored in one color such that no tiles of equal color meet at a curve of positive length.
		Copies of an arbitrary quadrilateral can form a tessellation with 2-fold rotational centers at the midpoints of all sides, and translational symmetry with as minimal set of translation vectors a pair according to the diagonals of the quadrilateral, or equivalently, one of these and the sum or difference of the two.
	en.wikipedia.org /wiki/Tessellation (1457 words)

	Uniform Tessellations and Polyhedra (Site not responding. Last check: 2007-10-31)
		If a convex uniform polyhedron is enclosed in a sphere concentric with the polyhedron, then the faces of the polyhedron may be projected onto the sphere.
		The result is a tessellation of the sphere; it is "uniform" in that each face is a regular spherical polygon and the vertices are all alike in the same sense as for polyhedra.
		Given a uniform tessellation, the dual vertices are at the centers of the original faces.
	www.monmouth.com /~chenrich/UniformTessellations.html (2796 words)

	Fullerenes on other surfaces
		uniform polyhedra, stellated regular and semi-regular polyhedra or infinite polyhedra) [21].
		For example, different uniform 4-valent polyhedra of the type (3,q,3,q) (q=7,8,9,10,12,18) could be used for the derivation of the corresponding "perfect" fullerenes with q-gonal holes on a double torus (g=2) (Fig.
		In the same way, the uniform tessellations of the type (4,q,4,q) (q=5,6,8,12) or (5,10,5,10) of a double torus may result in different finite general fullerenes.
	members.tripod.com /~modularity/ful7.htm (396 words)

	Kaleidoscopes (Site not responding. Last check: 2007-10-31)
		The triangle PQR is a fundamental region for the group, as are all the triangles obtained from it by sequences of reflections.
		Uniform tessellations can be generalized to the Euclidean and hyperbolic kaleidoscope groups.
		Besides the uniform tessellations and polyhedra, there are also dual uniform tessellations and polyhedra.
	www.monmouth.com /~chenrich/Kaleidoscopes.html (1066 words)

	Earth tessellation II (Site not responding. Last check: 2007-10-31)
		The stress field derived from the fracture tessellation is consistent with a uniformly and simultaneously expanding Gondwana, as predicted by the hypothesis of Anderson (1982).
		The scale of the fracture tessellation was a function of the strength of the Gondwanan lithosphere and the geometry of a spherical shell.
		This is consistent with the hypothesis of Anderson (1982) that the geoid anomaly marks the paleoposition of Gondwana, and that Gondwana spread outward from the anomaly as it broke apart.
	www.mantleplumes.org /EarthTess2.html (3628 words)

	Uniform tessellation - Wikipedia, the free encyclopedia
		In mathematics, a uniform tessellation is a tessellation of a d-dimensional space, or a (hyper)surface, such that all its vertices are identical, i.e., there is the same combination and arrangement of faces at each vertex.
		When applied to Euclidean space, the tessellation is most often assumed to be by polyhedra.
		Examples of 3D regular tessellations are those of layers of right prisms according to the three regular tessellations in 2D; that with square cuboids is in a way the most regular, especially with cubes, because then it is congruent in three independent directions.
	en.wikipedia.org /wiki/Uniform_tessellation (140 words)

	Tessellation (Site not responding. Last check: 2007-10-31)
		A tessellation of the plane is a collection of plane figures that fill the plane with no overlaps and no gaps.
		A regular tessellation is a tessellation made up of congruent regular polygons.
		Other types of tessellations are considered, depending on types of figures and types of pattern: regular vs. irregular, periodical vs. aperiodical, symmetric vs. asymmeric, fractal, etc.
	bopedia.com /en/wikipedia/t/te/tessellation.html (152 words)

	UNIFORM - A Uniform Random Number Generator
		The fundamental underlying random number generator in UNIFORM is based on a simple, old, and limited linear congruential random number generator originally used in the IBM System 360.
		CVT is a library of MATLAB routines which compute elements of a Centroidal Voronoi Tessellation.
		UNIFORM is also available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version
	www.csit.fsu.edu /~burkardt/m_src/uniform/uniform.html (605 words)

	Multidimensional Glossary (Site not responding. Last check: 2007-10-31)
		It corresponds to a uniform isochoric polychoron in the rox regiment whose cells are 120 identical small rhombidodekahedra (in a small rhombidodekahedron, the faces are the 30 squares of a rhombicosidodecahedron together with twelve decagons; its vertex figure is the butterfly quadrilateral).
		The uniform polytope constructed by completely truncating the alternate vertices of a measure polytope, that is, truncating half its vertices by hyperplanes that pass through a truncated vertex’s edge-neighboring vertices.
		The vertex figures of the uniform polychora in the ico regiment are all facetings of the cube.
	members.aol.com /Polycell/glossary.html (16070 words)

	Tesselations
		Tessellations involving star polygons were first described in a paper "Memoir sur les Figures Isoscèles" by A.Badoureau published in the Journal de l'Ecole Polytechnique (1881).
		All of the tessellations and edge networks on these pages (including the hyperbolics) were generated using Melinda Green and Don Hatch's excellent "Tyler" applet.
		In a number of instances, a number of tessellations can be formed which share the same network of edges and vertices (a "network").
	web.ukonline.co.uk /polyhedra/tessellations/tessel.htm (367 words)

	Gamasutra - Features - "Using NURBS Surfaces in Real-time Applications" [11.17.99]
		The first, which is used by the sample code, is to use uniform tessellation and pre-evaluate the basis functions and their derivatives at the tessellation points.
		Depending on the application, it may still be quicker to tessellate the surface at every frame rather than having to fetch the generated vertices from memory (with corresponding cache misses).
		Tessellation - Although a uniform tessellation algorithm is easy to implement and can run fast, in some instances other algorithms may provide better performance/quality.
	www.gamasutra.com /features/19991117/macri_05.htm (1518 words)

	Elastic properties of model random three-dimensional open-cell solids-Voronoi tessellations
		It is worth noting that the tessellation of the BCC array (the tetrakaidecahedral cell model discussed above) is a reasonable approximation to the foam introduced by Lord Kelvin [Weaire and Fortes, 1994,Warren and Kraynik, 1997,Grenestedt, 1999].
		In this study, we wish to examine foams that have a roughly uniform cell size, but which are still random and isotropic.
		The open-cell Voronoi tessellations of these distributions showed a polydisperse size distribution since the seed points may now be bunched in regions (see Figure 7).
	ciks.cbt.nist.gov /~garbocz/opencell/node4.html (1125 words)

	[No title]
		For tessellations of many thousands of spots, a quick and very dirty way around this problem is to simply fill in the zeros with other integers.
		In its present form, the function "tessinvert" requires that each vertex of the tessellation either have exactly three adjacent vertices, or else be a dummy vertex.
		If the tessellation's cells are not convex, that problem is detected by "tessinvertc2" but the program keeps on running anyway.
	www.stat.ucla.edu /~frederic/papers/tess/readme.txt (703 words)

	UNIFORM - A Uniform Random Number Generator
		UNIFORM is a library of FORTRAN90 routines, using single or double precision arithmetic, which return a sequence of uniformly distributed pseudorandom numbers.
		CVT is a FORTRAN90 library which computes elements of a Centroidal Voronoi Tessellation.
		UNIFORM is also available in a C version and a C++ version and a FORTRAN77 version and a MATLAB version
	www.csit.fsu.edu /~burkardt/f_src/uniform/uniform.html (730 words)

	Elastic moduli of model random three-dimensional closed-cell cellular solids - Voronoi tessellations
		The most common models of cellular solids are generated by Voronoi tessellation of distributions of 'seed-points' in space.
		The cells of the Kelvin foam are uniformly shaped, fill space, and satisfy Plateau's law of foam equilibrium (three faces meet at angles of 120º, and four struts join at 109.5º).
		Data at the two lowest densities were obtained for 3 realizations of the 26 cell model, and the remainder were obtained for 5 realizations of the 122 cell model.
	ciks.cbt.nist.gov /~garbocz/closedcell/node5.html (579 words)

	Interactive Rendering of Sculptured Models
		The criteria for this tessellation are based on the sizes of triangles and their deviation from the surface in the screen space.
		For triangulating the trimmed surfaces we draw the trim curves on the uniform tessellation mesh, leaving out the triangles totally trimmed out and cutting the triangles that are partially trimmed.
		Dynamic tessellation of the interior of each visible super-surface, and feeding this triangular approximation of the super-surface to polygonal simplification algorithm, would result in various discrete levels of detail of the model.
	www.cs.unc.edu /~geom/RENDER/render.html (738 words)

	8. Voronoi Tessellation & Percolation
		The application of a non parametric percolation to the tessellation cells exceeding this noise level leads directly to a source list which is free of any assumptions about the source geometry.
		The algorithm used here for the construction of this tessellation is a two-dimensional adaption of the recipe described by Tanemura, Ogawa, and Ogita [2] for three dimensions.
		We use open boundaries on a plane, finite-area surface, where the constructibility of the out most cells is guaranteed by restricting the tessellation to the central region of the area actually covered by the photon distribution.
	ledas-cxc.star.le.ac.uk /udocs/docs/swdocs/detect/html/node16.html (3205 words)

	Earth tessellation (Site not responding. Last check: 2007-10-31)
		The tessellation of polygons is mathematically precise and intolerant, fixed by projection of a single pentagon.
		Initial opening of the Central Atlantic may have moved Gondwana and its fracture tessellation off the outbreak point of CAMP, displacing the younger parts of the hotspot tessellation with respect to the Cape Verde (or Fernando) hotspot.
		The overall congruence of the hotspots to the tessellation implies, however, that Gondwana was largely stagnant during Late Jurassic-Early Cretaceous magmatic outbreaks, consistent with a loop in the Gondwanan apparent polar wander path (DeWitt et al.
	www.mantleplumes.org /EarthTess.html (1243 words)

	Tessellation of 4x4 Bezier Patches for the Intel Pentium III Processor
		There are three basic steps in the tessellation process: taking samples of the parametric surface, connecting these samples into triangles, and generating the tessellated surface vertices.
		Since our tessellation is not dependent on the position of the control points of the Bezier patch, we can use one CBezierTessellation object for all the Bezier patches in our application.
		There is a big difference between the tessellation of screen space surfaces and the tessellation of object space surfaces.
	www.gamasutra.com /features/20000317/barad_pfv.htm (1780 words)

	Extensible 3D (X3D), ISO/IEC 19775-1:2004, Part 1 -- 27 NURBS Component
		Tessellation in object space and the internal computation of the equivalent to an X3D IndexedFaceSet.
		To avoid cracks at the junction of two surfaces, tessellation values of a whole set of surfaces can be specified in a NurbsSet.
		For implementations doing tessellations based on chord length, tessellation values less than zero are interpreted as the maximum chord length deviation in pixels.
	www.web3d.org /x3d/specifications/ISO-IEC-19775-X3DAbstractSpecification/Part01/components/nurbs.html (3254 words)

	Hyperbolic Planar Tesselations
		Each tesselation is represented by a Schlafli symbol of the form {p,q}, which means that q regular p-gons surround each vertex.
		The Omnitruncated {3,7} is the "most nearly planar" of all semiregular or regular hyperbolic tesselations, in the sense that if you tried to construct it from Euclidean planar polygons, the sum of the angles at each vertex would be as small as possible while exceeding 360 degrees.
		We can color each vertex of the uniform tiling (or Schwarz polygon of the dual) "even" or "odd" depending on whether it is generated as an even or odd number of reflections of a fixed initial vertex (or Schwarz polygon of the dual, respectively), i.e.
	www.hadron.org /~hatch/HyperbolicTesselations (1397 words)

	Taj Mahal - Wikipedia, the free encyclopedia
		The design is completely uniform and consistent on all sides of the building.
		Floors and walkways throughout use contrasting tiles or blocks in tessellation patterns.
		The lower walls of the tomb are white marble dados that have been sculpted with realistic bas relief depictions of flowers and vines.
	en.wikipedia.org /wiki/Taj_Mahal (5874 words)

	Tessellations of the Euclidean, Elliptic and Hyperbolic Plane -- from Mathematica Information Center
		Tess is a package for generation and drawing of Archimedean (including regular and uniform) tessellations in Euclidean (E2), Elliptic (S2 - polyhedra), and Lobachevskian (L2, or hyperbolic) plane.
		The tiles of Archimedean tessellations are regular polygons and all vertices are of the same type.
		Beside the drawing of tessellations, the program provides additional data, such as: geometry and type of tessellation, number of possible realizations, angles of tiles and transformation rules between neighboring vertices.
	library.wolfram.com /infocenter/MathSource/4540 (196 words)

	46glossT
		If only one shape is repeated in a tessellation, the tessellation is called a same-tile tessellation.
		Covering a surface with uniform shapes so there are no gaps or overlaps, except possibly gaps around the edges.
		A tessellation created by translating (sliding) curves from one side of a figure (such as a square) to the opposite side.
	www.auburn.wednet.edu /everydaymath/46glossary/46glosst.htm (780 words)

	CECS 361 Computer Graphics I
		This should achieve a uniform expanding and shrinking motion with tail fixed at origin.
		Use the following function to tessellate the polygons in the OpenGL part of the assignment (the compiler should not produce any warning messages since the callback functions are typecast to GLvoid pointer to a function.
		If you just use regular convex polygon drawing without tessellation as in the following sample code, then your dinosaur will be incorrectly drawn as shown in the figure below.
	meru.cecs.missouri.edu /courses/cecs361/assignments/asst6.html (756 words)

	ScienceDaily: Uniform uniform colors needed by humans
		If fact, if someone, somewhere hadn't thought to make team uniforms the same color, the scientists say we might be watching NBA finals or World Cup soccer matches with only two players and a referee.
		Halberda and Assistant Professor of Psychology Lisa Feigenson say their research suggests uniform uniform colors allow people to overcome the usual limit, because the 'color coding' enables them to perceive separate individuals as a single set.
		Tessellation -- A tessellation or tiling of the plane is a collection of plane figures that fill the plane with no overlaps and no gaps.
	www.sciencedaily.com /upi/?feed=Science&article=UPI-1-20060622-15105300-bc-us-uniformcolors.xml (1626 words)

	centroidal voronoi tessellations
		A centroidal Voronoi tessellation (CVT) is a Voronoi tessellation of a given set such that the associated generating points are centroids (centers of mass with respect to a given density function) of the corresponding Voronoi regions.
		We are now studying methods for computing these tessellations, the underlying mathematical theory and their applications.
		In computer graphics and also in mesh generation, it is well known that Voronoi tessellations and their dual Delaunay tessellations (formed by joining adjacent Vornoi generators) are useful tools in the construction of unstructured tetrahedral mesh.
	www.math.psu.edu /qdu/Res/Pic/gallery3.html (794 words)

	Hyperbolic Star Tessellations
		Regular, semi-regular and uniform tessellations can all be generated.
		An excellent introduction to the Hyperbolic Plane and beautiful images of regular (non-starred) tessellations has been generated by Don Hatch (one of the co-authors of Tyler) - it is linked here.
		The above image shows a tessellation with a vertex figure of 7/2, 3, 7/2, 3, 7/2, 3.
	web.ukonline.co.uk /polyhedra/tessellations/hyperbolic/hyperbolic.htm (377 words)

	Octahedron
		Octahedra and tetrahedra can be mixed together to form a vertex, edge, and face-uniform tiling of space, called the octet truss by Buckminster Fuller.
		This is the only such tiling save the regular tessellation of cubes, and is one of the 28 Andreini tessellations.
		Another is a tessellation of octahedra and cuboctahedra.
	www.brainyencyclopedia.com /encyclopedia/o/oc/octahedron.html (577 words)

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