Approximation of the ordered set of points with geometric elements through the overlapping polytope

摘要

An ordered set of physical points, each comprising a nominal point and an associated allowable deviation, is approximated by a sequence of geometric elements determined by a method of intersecting polytopes in a parametric space. A first bundle of geometric elements connecting a first subgroup of physical points is generated and mapped to a first polytope. A second bundle of geometric elements connecting a second subgroup of physical points is generated and mapped to a second polytope. If the intersection between the first polytope and the second polytope is not null, the points in the intersection region correspond to geometric elements which approximate the physical points in the combined two subgroups. The process is repeated iteratively for additional subgroups. The center point of the final intersection region corresponds to an approximate best-fit geometric element.