The octagon of opposition.

Meshing the hyperbolic octagon

This short report describes a preliminary study of a method computing meshes of the standard hyperbolic octagon that respects its symmetries. A prototype software was written, using the 2D meshing package of the CGAL library [1, 10] and a software computing hyperbolic triangulations, currently under development [4]. Key-words: Hyperbolic geometry, Poincaré disk, Schwarz triangle, mesh ∗ This wo...

The Octagon Abstract Domain

This article presents the octagon abstract domain, a relational numerical abstract domain for static analysis by abstract interpretation. It allows representing conjunctions of constraints of the form ±X ± Y ≤ c where X and Y range among program variables and c is a constant in Z, Q, or R automatically inferred. Abstract elements are represented using modified Difference Bound Matrices and we u...

The Valuations of the Near Octagon I4

The maximal and next-to-maximal subspaces of a nonsingular parabolic quadric Q(2n, 2), n ≥ 2, which are not contained in a given hyperbolic quadric Q+(2n − 1, 2) ⊂ Q(2n, 2) define a sub near polygon In of the dual polar space DQ(2n, 2). It is known that every valuation of DQ(2n, 2) induces a valuation of In. In this paper, we classify all valuations of the near octagon I4 and show that they are...

The valuations of the near octagon G4

The Octagon Abstract Domain Library