Interval methods for constructive geometric constraint solving problems
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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.
CitacióJoan-Arinyo, R., Mata, N., Soto-Riera, A. "Interval methods for constructive geometric constraint solving problems". 2002.