Towards a topology for computational geometry

Abstract

The paper examines the implications for topology of implementing geometrical algorithms in a floating point number system. It uses fuzzy logic to define a discriminator function which can then be used in point classification, the classification itself being defined in terms of the logic of partial functions. This is then applied to the problem of a triple line intersection, and is used to validate the results of such an intersection and indicate how an invalid geometry can be perturbed to give a valid geometry.