Approximation of ordered sets of points by geometric...

G - Physics – 06 – T

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G06T 11/20 (2006.01)

Patent

CA 2685352

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.

L'invention concerne un ensemble ordonné de points physiques, comportant chacun un point nominal et un écart admissible associé, qui est lissé par une séquence d'éléments géométriques déterminés par un procédé d'intersection de polytopes dans un espace paramétrique. Un premier faisceau d'éléments géométriques reliant un premier sous-groupe de points physiques est généré et appliqué sur un premier polytope. Un deuxième faisceau d'éléments géométriques reliant un deuxième sous-groupe de points physiques est généré et appliqué sur un deuxième polytope. Si l'intersection entre le premier polytope et le deuxième polytope n'est pas nulle, les points dans la région d'intersection correspondent à des éléments géométriques qui lissent les points physiques dans les deux sous-groupes combinés. Le procédé est répété de façon itérative pour des sous-groupes supplémentaires. Le point central de la région d'intersection finale correspond à un élément géométrique optimal lissé.

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