Nonrealizability proofs in computational geometry

Computational Proofs in Dynamics

OTTER Proofs in Tarskian Geometry

We report on a project to use OTTER to find proofs of the theorems in Tarskian geometry proved in Szmielew’s part (Part I) of [9]. These theorems start with fundamental properties of betweenness, and end with the development of geometric definitions of addition and multiplication that permit the representation of models of geometry as planes over Euclidean fields, or over real-closed fields in ...

Parleda: a Library for Parallel Processing in Computational Geometry Applications

ParLeda is a software library that provides the basic primitives needed for parallel implementation of computational geometry applications. It can also be used in implementing a parallel application that uses geometric data structures. The parallel model that we use is based on a new heterogeneous parallel model named HBSP, which is based on BSP and is introduced here. ParLeda uses two main lib...

Computability in Computational Geometry

We promote the concept of object directed computability in computational geometry in order to faithfully generalise the wellestablished theory of computability for real numbers and real functions. In object directed computability, a geometric object is computable if it is the effective limit of a sequence of finitary objects of the same type as the original object, thus allowing a quantitative ...

Computational Geometry

This column is devoted to non-crossing configurations in the plane realized with straight line segments connecting pairs of points from a finite ground set. Graph classes of interest realized in this way include matchings, spanning trees, spanning cycles, and triangulations. We review some problems and results in this area. At the end we list some open problems.