US 8,274,512 B2Granted

System and method for polytopic mesh refinement

AssigneeSandia Corporation

InventorsJackson R. Mayo, David C. Thompson, Philippe P. Pebay

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Abstract

A method is disclosed for partitioning an input polytope into a conformal set of polytopes according to a subdivision pattern specified on lower-dimensional boundaries of the input polytope. A feature of this method is that it is applicable to any dimension. For input polytopes that are hexahedra isomorphic to a 3-dimensional cube, all members of the conforming partition will be hexahedra isomorphic to a 3-dimensional cube. A further feature of the invention is that it preserves convexity; a convex input polytope will result in a conformal partition comprising convex polytopes. Finally, the method may be used to process large conformal meshes of input polytopes in parallel and produce a globally conformal partition without the requirement of communication between processes.

Claims17

Dependent claims

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.

7 more elements

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 the input polytope and the conformal set polytopes are hexahedra isomorphic to a 3-dimensional cube.

1 more element

Dependencies are inferred from the claim text.

Facts

Application: 12/476,335Filed 2 Jun 2009 · us provisional application
Priority: 4 Jun 2008
Published: US 2010/0045673 A125 Feb 2010
Granted: 25 Sep 2012
Term ends: Not estimatedThe source records don’t support an estimate.

Classification3 codes

G06T 17/20
Three-dimensional [3D] modelling for computer graphics: finite element generation, e.g. wire-frame surface description, tesselation
G06T 9/001
Image coding: model-based coding, e.g. wire frame
G06T
Image data processing or generation, in general