Abstract:
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In advanced computer-aided design systems, an object is defined by a
collection of geometric elements along with a set of geometric
constraints between them. Given the values assigned to the constraint
parameters, solving the geometric problem consists of computing the
coordinates of the points of the geometric elements defining 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 take values in given
intervals. As a result, the coordinates of the points are also
intervals. In this situation, known geometric constraint solving
techniques cannot solve directly the geometric problem.
In this paper, we report on an interval-based method to solve
geometric problems with interval parameters. We assume that we are
given a construction plan for a geometric problem, and an assignment
of interval values to the constraint parameters. We present an
algorithm that computes precise and rigorous intervals for the
coordinates of the points. We illustrate the performance of the
algorithm with a case study. |