Patent ID: 8274512

Claim:
A method using a computer including program code for providing a conformal set of polytopes that partition a non-simplicial n-dimensional input polytope according to a selection made by an indicator function of one or more of the input polytope m-boundaries, where 1≦m≦n−1, and wherein vertices of the conformal set of polytopes comprise vertices of the input polytope, vertices placed on m-boundaries of the input polytope indicated by the indicator function, and zero or more vertices placed on the input polytope l-boundaries for any m+1≦l≦n−1 and contained within the interior of the input polytope, comprising: listing the input polytope itself if no m-boundaries are selected by the indicator function, or listing a conformal set of polytopes defined by the vertices of the input polytope, the vertices placed on m-boundaries of the input polytope indicated by the indicator function, and the vertices on the l-boundaries for any m+1≦l≦n−1 and in the interior of the input polytope, wherein the conformal set of polytopes are output to a visual display, a printed report, a mass storage device, a simulator, or a combination thereof, wherein providing the set of polytopes defined by said vertices comprises: listing the input polytope itself if no boundaries are selected by the indicator function, or applying a homothetic transform h({right arrow over (x)})={right arrow over (O)}+c({right arrow over (x)}−{right arrow over (O)}) wherein {right arrow over (O)} is a homothetic center interior to the input polytope, {right arrow over (x)} is an untransformed point, h({right arrow over (x)}) is a transformed point, and 0<c<1 is a contraction factor, and joining corresponding (n−2)-boundaries of the input polytope and transformed polytope with (n−1)-planes such that a level-0 partition is constructed; applying (n−l)-bound homothetic transforms to any member of the level-0 partition that shares an m-boundary with the input polytope that is selected by the indicator function to obtain a level-1 partition; applying (n−l)-bound homothetic transforms to any member of the level-(l−1) partition for l=2, 3, . . . , n−m, that shares an m-boundary with the input polytope that is selected by the indicator function to obtain a level-l partition; and listing all members of the level-(n−m) partition and any members of the previous partitions not covered by members of the level-(n−m) partition.