High Fidelity Interval Assignment

Quadrilateral meshing algorithms impose certain constraints on the number of intervals or mesh edges of the curves bounding a surface. When constructing a conformal mesh of a collection of adjoining surfaces, the constraints for all of the surfaces must be simultaneously satisfied. These constraints can be formulated as an integer linear program. Not all solutions to this problem are equally desirable, however. The user typically indicates a goal (soft-set) or required (hard-set) number of intervals for each curve. The hard-sets constrain the problem further, while the soft-sets influence the objective function. This paper describes an algorithm for solving this interval assignment problem. The objective is to have a solution such that for each curve the positive or negative difference between its goal and assigned intervals is small relative to its goal intervals. The algorithm solves a series of linear programs, which comes close to minimizing the maximum vector of such differences. Then the algorithm solves a nearby mixed-integer linear program to satisfy certain “sum-even” constraints. The algorithm reliably produces intervals that are very close to the user’s desires, although it runs more slowly than previous algorithms. keywords. interval assignment, mixed-integer linear programming, conformal meshing, mesh control