A Data structure for solving geometric construction problems with interval parameters

In advanced computer-aided design systems, an object is defined by a finite collection of points, linear segments, and circular segments, and a finite set of geometric constraints relating these points and segments. Given a set of values for the constraint parameters, the geometric problem consists of computing the coordinates of the points of the object. Traditionally, constraint parameters have been considered to be exact values. In many applications, however, it is more realistic to consider that some dimensions of the object may have tolerances and, therefore, that the corresponding constraint parameters are intervals. In this situation, the geometric problem becomes indeed more difficult to solve because the resulting coordinates of the points are also intervals. In this paper, we show how constructible geometric problems can be solved when the constraint parameters are intervals.