Towards a topology for computational geometry
The author notes that computations in finite precision can lead to impossible solutions, in particular in intersection problems that are close to singular. He proposes to deal with the problem in two steps. The first is to use different criteria for identifying two points or asserting their distinctness; another approach to the same problem is to consider the identification of two points as a fuzzy problem. The second step is to use halfspaces to test for compatible topologies (at least for computational problems of linear geometry). An unanswered problem is the construction of an algorithm that suggests coherent solutions in case the halfspace test turns up an inconsistency in the computed numbers.
scientific article; zbMATH DE number 777941