Approximation of ordered sets of points by geometric elements via overlapping polytopes

An apparatus for approximating an ordered set of physical points in physical space, each physical point comprising a nominal point and an associated allowable deviation, comprising:

• means for generating a first bundle of geometric elements connecting a first subgroup of physical points selected from the ordered set of physical points, wherein the deviation of each geometric element in the first bundle from each nominal point in the first subgroup is not greater than the allowable deviation associated with each nominal point in the first subgroup;
• means for mapping the first bundle to a first polytope in a parametric space, wherein each geometric element in the first bundle is mapped to a corresponding parametric point in the first polytope;
• means for generating a second bundle of geometric elements connecting a second subgroup of physical points selected from the ordered set of physical points, wherein the deviation of each geometric element in the second bundle from each nominal point in the second subgroup is not greater than the allowable deviation associated with each nominal point in the second subgroup;
• and
• means for mapping the second bundle to a second polytope in the parametric space, wherein each geometric element in the second bundle is mapped to a corresponding parametric point in the second polytope.

A non-transitory computer readable medium storing computer instructions for approximating an ordered set of physical points in physical space, each physical point comprising a nominal point and an associated allowable deviation, the computer instructions defining the steps of:

• generating a first bundle of geometric elements connecting a first subgroup of physical points selected from the ordered set of physical points, wherein the deviation of each geometric element in the first bundle from each nominal point in the first subgroup is not greater than the allowable deviation associated with each nominal point in the first subgroup;
• mapping the first bundle to a first polytope in a parametric space, wherein each geometric element in the first bundle is mapped to a corresponding parametric point in the first polytope;
• generating a second bundle of geometric elements connecting a second subgroup of physical points selected from the ordered set of physical points, wherein the deviation of each geometric element in the second bundle from each nominal point in the second subgroup is not greater than the allowable deviation associated with each nominal point in the second subgroup;
• and
• mapping the second bundle to a second polytope in the parametric space, wherein each geometric element in the second bundle is mapped to a corresponding parametric point in the second polytope.