Solution Selectors: A User-Oriented Answer to the Multiple Solution Problem in Constraint Solving

Abstract

The development of solid modeling to represent the geometry of designed parts and the development of parametric modeling to control the size and shape have had significant impacts on the efficiency and speed of the design process. Designers now rely on parametric solid modeling, but often are frustrated by a problem that unpredictably causes their sketches to become twisted, contorted, or take an unexpected shape. Mathematically, this problem, known as the “multiple solution problem” occurs because the dimensions and geometric constraints yield a set of non-linear equations with many roots. In practice, this situation occurs because the dimensioning and geometric constraint information given in a CAD model is not sufficient to unambiguously and flexibly specify which configuration the user desires. This paper first establishes that only explicit, independent solution selection declarations can provide a flexible mechanism that is sufficient for all situations. The paper then describes the systematic derivation of a set of “solution selector” types by considering the occurrences of multiple solutions in combinations of mutually constrained geometric entities. The result is a set of eleven basic solution selector types and two derived types that incorporate topological information. In particular, one derived type “concave/convex” is user-oriented and may prove to be particularly useful.