The containment model for composite positional tolerance evaluation

The composite positional tolerance evaluation problem for planar point features and circular tolerance zones is defined and characterized under necessary and sufficient conditions. This model is then generalized to the circular feature case, and the solution to the circular feature–circular tolerance zone problem is characterized analogous to the point feature model. The circular feature–circular tolerance zone problem is formulated as a containment model and solved as a constrained nonlinear program. The three-dimensional spherical containment model is also formulated and numerical examples are used to illustrate the methodology in the two- and three-dimensional cases.