We present an abstraction of the effect of procedures through convex sets of transition matrices. Conditional branching is handled by postponing the conditional evaluation after the procedure call. In order to obtain an effective analysis convex sets are represented by polyhedra. For an efficient implementation we approximate polyhedra by means of simplices. In [CH78], Cousot and Halbwachs pres...

The well-known duality and Petrie duality operations on maps have natural analogs for abstract polyhedra. Regular polyhedra that are invariant under both operations have a high degree of both “external” and “internal” symmetry. The mixing operation provides a natural way to build the minimal common cover of two polyhedra, and by mixing a regular polyhedron with its five other images under the d...

In this lecture, we will cover some basic material on the structure of polyhedra and linear programming. There is too abundant material on this topic to be covered in a few classes, so pointers will be given for further reading. For algorithmic and computational purposes one needs to work with rational polyhedra. Many basic results, however, are valid for both real and rational polyhedra. There...

The infinite models in integer programming can be described as the convex hull of some points or as the intersection of half-spaces derived from valid functions. In this paper we study the relationships between these two descriptions. Our results have implications for finite dimensional corner polyhedra. One consequence is that nonnegative continuous functions suffice to describe finite dimensi...

This paper 1 presents a new approach to detect and localise contact between concave deformable polyhedra. In this case there are many contact points between two polyhedra, the proposed algorithm detect and localise the contact in linear time O(n). It returns also the direction of this contact and the value of the maximum inter-penetration between the two convex-hulls of these two polyhedra.

Given an ordinary polyhedron P in the three dimensional Euclidean space, diierent tetrahedralizations of P may contain diierent numbers of tetrahedra. Minimal tetrahedralization is a tetrahedralization with the minimum number of tetrahedra. In this paper, we present some properties of the graph of polyhedra. Then we identify a class of polyhedra and show that this kind of polyhedra can be minim...

This paper presents an interactive visualization tool, Archimedean Kaleidoscope (AK), aimed at supporting learner’s exploration of polyhedra. AK uses metamorphosis as a technique to help support the learner’s mental construction of relationships among different polyhedra. AK uses the symmetric nature of the Platonic solids as the foundation for exploring the way in which polyhedra are related. ...

Alpha is a functional language based on systems of aane recurrence equations over polyhedral domains. We present an extension of Alpha to deal with sparse polyhedral domains. Such domains are modeled by Z-polyhedra, namely the intersection of lattices and polyhedra. We summarize the mathematical closure properties of Z-polyhedra, and we show how the important features of Alpha, namely normaliza...

We present two methods for lossy compression of normal vectors through quantization using “base” polyhedra. The first revisits subdivision-based quantization. The second uses fixed-precision barycentric coordinates. For both, we provide fast (de)compression algorithms and a rigorous upper bound on compression error. We discuss the effects of base polyhedra on the error bound and suggest polyhed...

The notion of d-code is extended to general polyhedra by defining maximum sets of vertices with pairwise separation > or =d. Codes are enumerated and classified by symmetry for all regular and semiregular polyhedra and their duals. Partial results are also given for the series of medials of Archimedean polyhedra. In chemistry, d-codes give a model for maximal addition to or substitution in poly...