Geometric classification tests using interval arithmetic in b-rep solid modeling

Abstract

In this work, the use of interval arithmetic is considered to increase robustness of geometric classification algorithms in B-Rep solid modeling systems. The classification algorithms, also known as incidence tests, are important to keep the consistency between topology and geometry in a solid model during the application of Boolean operations. An error in the incidence test has deep impact over the steps that follow the Boolean operations and can damage the result, generating an inconsistent solid. The interval arithmetic incorporates approximation errors, so that, it eliminates the need of defining a fixed tolerance to do the comparison between floating-point numbers. However, it is not possible to directly convert floating-point algorithms to interval arithmetic, so that, it is necessary to reformulate the entire algorithm. Another important step in the Boolean operation is the determination of intersection points where the use of interval arithmetic can have side effects as intervals with large dimensions, and may cause incidence tests failures. It is necessary to control the growth of the intervals based on the geometry and topology. This work will introduce the application of interval arithmetic to a B-Rep solid modeler.