منابع مشابه
The Nine Morse Generic Tetrahedra
From computational geometry comes the notion of a Gabriel graph of a point set in the plane. The Gabriel graph consists of those edges connecting two points of the point set such that the circle whose diameter is the edge does not contain any point of the point set in its interior. We define a generalization of the Gabriel graph to n dimensions: the Morse poset. Using Morse theory we prove that...
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Extending a similar result about triangles, we show that each Heronian tetrahedron may be positioned with integer coordinates. More generally, we show the following: if an integral distance set in R can be positioned with rational coordinates, then it can in fact be positioned with integer coordinates. The proof, which uses the arithmetic of quaternions, is tantamount to an algorithm.
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When solving an algorithmic problem involving a polyhedron in R, it is common to start by partitioning the given polyhedron into simplier ones. The most common process is called triangulation and it refers to partitioning a polyhedron into tetrahedra in a face-to-face manner. In this paper instead of triangulations we will consider tilings by tetrahedra. In a tiling the tetrahedra are not requi...
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We present a flexible and highly efficient hardware-assisted volume renderer grounded on the original Projected Tetrahedra (PT) algorithm. Unlike recent similar approaches, our method is exclusively based on the rasterization of simple geometric primitives and takes full advantage of graphics hardware. Both vertex and geometry shaders are used to compute the tetrahedral projection, while the vo...
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We determine the numbers of integral tetrahedra with diameter d up to isomorphism for all d ≤ 1000 via computer enumeration. Therefore we give an algorithm that enumerates the integral tetrahedra with diameter at most d in O(d5) time and an algorithm that can check the canonicity of a given integral tetrahedron with at most 6 integer comparisons. For the number of isomorphism classes of integra...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2008
ISSN: 0895-4801,1095-7146
DOI: 10.1137/060656395