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In parametric design, changing values of parameters to get different solution instances to the problem
at hand is a paramount operation. One of the main issues when generating the solution instance for the
actual set of parameters is that the user does not know in general which is the set of parameter values
for which the parametric solution is feasible. Similarly, in constraint-based dynamic geometry, knowing
the set of critical points where construction feasibility changes would allow to avoid unexpected and
We consider parametric models in the Euclidean space with one internal degree of freedom. In this
scenario, in general, the set of values of the variant parameter for which the parametric model is realizable
and defines a valid shape is a set of intervals on the real line.
In this work we report on our experiments implementing the van der Meiden Approach to compute
the set of parameter values that bound intervals for which the parametric object is realizable. The
implementation is developed on top of a constructive, ruler-and-compass geometric constraint solver.
We formalize the underlying concepts and prove that our implementation is correct, that is, the approach
exactly computes all the feasible interval bounds.
CitationHidalgo, M.; Joan-Arinyo, R. Computing parameter ranges in constructive geometric constraint solving: Implementation and correctness proof. "Computer-aided design", Juliol 2012, vol. 44, núm. 7, p. 709-720.
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