Asymptotically Efficient Triangulations of the d -Cube
نویسندگان
چکیده
منابع مشابه
Asymptotically efficient triangulations of the d-cube
Triangulating the regular d-cube I = [0, 1] in a “simple” way has many applications, like solving differential equations by finite element methods or calculating fixed points. See, for example, [7]. Determining the smallest number of simplices needed has brought special attention both from a theoretical point of view and from an applied one (see [6, Section 14.5.2] for a recent survey). Before ...
متن کامل. C O ] 1 1 A pr 2 00 2 ASYMPTOTICALLY EFFICIENT TRIANGULATIONS OF THE d - CUBE
We describe a method to triangulate P × Q which is very useful to obtain triangulations of the d-cube I of good asymptotic efficiency. The main idea is to triangulate P × Q from a triangulation of Q and another of P ×∆, where ∆ is a simplex of dimension m− 1, which is supposed to be smaller than dim(Q) = n− 1. Last triangulation will induce a triangulation of P ×∆. Thus, considering P := I and ...
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The hyperdeterminant of format 2 × 2 × 2 × 2 is a polynomial of degree 24 in 16 unknowns which has 2894276 terms. We compute the Newton polytope of this polynomial and the secondary polytope of the 4-cube. The 87959448 regular triangulations of the 4-cube are classified into 25448 Dequivalence classes, one for each vertex of the Newton polytope. The 4-cube has 80876 coarsest regular subdivision...
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In 19] we introduced a new algorithm for computing planar triangulations of faceted surfaces for surface parameter-ization. Our algorithm computes a mapping that minimizes the distortion of the surface metric structures (lengths, angles, etc.). Compared with alternative approaches, the algorithm provides a signiicant improvement in robustness and applicability; it can handle more complicated su...
متن کاملOn the coverings of the d-cube for d<=6
The cut number S(d) of the d-cube is the minimum number of hyperplanes in R that slice, that is cut the edges while avoiding vertices, all the edges of the d-cube. The cut number problem for the hypercube of dimensions d ≥ 4 was posed by P. O’Neil more than thirty years ago [17]. The identity S(3) = 3 is easy and that of S(4) = 4 is a well-known result, see [5,6,18]. However, the conjecture of ...
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ژورنال
عنوان ژورنال: Discrete and Computational Geometry
سال: 2003
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-003-2845-5