Automated Translation of High Order Complex Geometry from a Cad Model into a Surface Based Combinatorial Geometry Format

Abstract

The descriptions of higher order complex geometry in CAD systems are fundamentally different from and seemingly incompatible with the surface based combinatorial geometry (SBCG) format for describing the same geometry in the context of general ray-tracing applications such as radiation transport. A computer implemented process translates the high order complex geometry embodied in CAD software to the SBCG format. The translation process is comprised of a set of lower-level algorithms that operate on two data sets which are commonly available from commercial CAD software systems. The first data set is a list of trimmed surfaces which make up a given part. These data are typically available from one of the standard geometry representations such as IGES, STEP, or ACIS, at least one of which is supported by each of the major CAD systems (e.g. ProEngineer). The second data set is nodal data: an appropriately dense grouping of point coordinates, designated as either inside or outside the part. These data may be obtained by discretizing solid geometry both within and external to the part of interest using standard FE tools (e.g. ProMechanica). The process translates these two data sets into a list of analytic surfaces and a well-posed zoning statement and then optimizes that statement.

1 . A method for translating high order complex geometry from a computer aided design (CAD) model to a surface based combinatorial geometry format, comprising: 
 Writing a list of trimmed surfaces from the CAD model, said trimmed surfaces being a bounded representation of a geometric surface in space;    Generating lists of nodes that lie within the part or within any void spaces represented in the CAD model;    Translating the trimmed surfaces into a list of analytic surfaces including bounding surfaces and ambiguity surfaces; and    Formulating a well-posed zoning statement from the list of analytic surfaces and the list of nodes.    
   
   
       2 . The method of  claim 1 , wherein the lists of nodes are generated by, 
 Writing two lists of candidate nodes that cover the part and the void spaces, and    Refining these lists of nodes such that the first one consists of only nodes that lie within the part but away from any of the analytic surfaces and the second one consists of only nodes that lie within the void spaces but away from any of the analytic surfaces.    
   
   
       3 . The method of  claim 2 , wherein the lists of candidate nodes are written using a mesh or random node generation.  
   
   
       4 . The method of  claim 3 , wherein a finite element (FE) program generates the mesh.  
   
   
       5 . The method of  claim 1 , wherein the translation and formulation comprise: 
 Calculating analytic bounding surfaces from the trimmed surfaces to provide the bounding surfaces;    Forming the ambiguity surfaces required for a well-posed zoning statement by comparing the bounding surfaces to each other; and    Comparing each node to each of the analytic surfaces to create a sequence of nodal zoning statements, said unique nodal zoning statements together forming the well-posed zoning statement.    
   
   
       6 . The method of  claim 5 , wherein the list of trimmed surfaces includes a number of entities, a type designator for each entity and a translation matrix, said extraction of untrimmed spatial primitives comprising: 
 Examining each entity to determine a type of geometric object; and    Mapping the entity to the analytic bounding surface for the geometric object with the proper translation.    
   
   
       7 . The method of  claim 6 , wherein the analytic forms for b-spline planes, toroids, spheres, revolved planes, cylinders or revolved cone objects are extracted from the information regarding trimmed surfaces.  
   
   
       8 . The method of  claim 5 , wherein forming the ambiguity surfaces comprises: 
 Performing a pair-wise comparison of all the bounding surfaces;    Determining whether a condition exists between each pair of bounding surfaces;    and, if so,    Generating a specific analytical ambiguity surface to differentiate regions of space that the bounding surfaces may be insufficient to distinguish.    
   
   
       9 . The method of  claim 8 , wherein the ambiguity surfaces are generated using a library that contains a plurality of pair-wise comparisons, the associated conditions and the formulae for the ambiguity surfaces.  
   
   
       10 . The method of  claim 5 , wherein each nodal zoning statement comprises a string of signed numbers that designate the binary positional relationship to each of the analytic surfaces.