Towards computing complete parameter ranges in parametric modeling

TL;DR

This paper introduces an automatic method to compute complete allowable parameter ranges in multi-parameter parametric modeling, ensuring geometric constraint solvability and improving over existing incomplete approaches.

Contribution

It presents a novel approach combining constrained optimization and swarm algorithms to accurately determine full parameter ranges in multi-parameter design scenarios.

Findings

Successfully computes complete parameter ranges in experiments.

Outperforms existing methods by avoiding missed feasible values.

Efficiently integrates Lagrange multipliers and NichePSO for range calculation.

Abstract

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.