منابع مشابه
Heronian Tetrahedra Are Lattice Tetrahedra
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.
متن کاملTiling Polyhedra with Tetrahedra
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...
متن کاملHardware-Assisted Projected Tetrahedra
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...
متن کاملEnumeration of Integral Tetrahedra
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...
متن کاملOn Lattice Barycentric Tetrahedra
A lattice tetrahedron T ⊂ R3 is a tetrahedron whose four vertices are all in the lattice Z3. Lattice tetrahedra are preserved by those affine linear maps of the form ~v 7→ A~v +~b, such that A is an element of GL(3,Z) and ~b is an element of the lattice Z3. Such affine linear maps are called unimodular maps. We say that a lattice tetrahedron whose barycentre is its only non-vertex lattice point...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2007
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-006-1293-4