  In parametric design, the geometric model is edited by changing relevant
parameters in the parametric model, which is commonly done sequentially on
multiple parameters. Without guidance on allowable parameter ranges that can
guarantee the solvability of the geometric constraint system, the user could
assign improper parameter values to the model's parameters, which would further
lead to a failure in model updating. However, current commercial CAD systems
provide little support for the proper parameter assignments. Although the
existing methods can compute allowable ranges for individual parameters, they
face difficulties in handling multi-parameter situations. In particular, these
methods could miss some feasible parameter values and provide incomplete
allowable parameter ranges. To solve this problem, an automatic approach is
proposed in this paper to compute complete parameter ranges in multi-parameter
editing. In the approach, a set of variable parameters are first selected to be
sequentially edited by the user; before each editing operation, the
one-dimensional ranges of the variable parameters are presented as guidance. To
compute the one-dimensional ranges, each variable parameter is expressed as an
equality-constrained function, and its one-dimensional allowable range is
obtained by calculating the function range. To effectively obtain the function
range which can hardly be calculated in a normal way, the function range
problem is converted into a constrained optimization problem, and is then
solved by Lagrange multiplier method and the Niching particle swarm
optimization algorithm (the NichePSO). The effectiveness and efficiency of the
proposed approach is verified by several experimental results.
