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Results for “Constructive Solid Geometry (CSG)”

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NASA NTRS1985

Improving the Effectiveness of Integral Property Calculation in a CSG Solid Modeling System by Exploiting Predictability

Integral property calculation is an important application for solid modeling systems. Algorithms for computing integral properties for various solid representation schemes are fairly well known. It is important to deigners and users of solid modeling systems to understand the behavior of such algorithms. Specifically the trade-off between execution time and accuracy is critical to effective use of integral property calculation. The average behavior of two algorithms for Constructive Solid Geometry (CSG) representations is investigated. Experimental results from the PADL-2 solid modeling system show that coarse decompositions can be used to predict execution time and error estimates for finer decompositions. Exploiting this predictability allow effective use of the algorithms in a solid modeling system.

Clark, A. L.↗

NASA NTRS1985

Boundary to Constructive Solid Geometry Mappings: a Focus on 2-D Issues

The problem of converting boundary representation (B-rep) to constructive solid geometry representation (CSG-rep) (and vice versa) is discussed in two phases. The first phase entails finding a CSG-rep that defines the region bounded by a polygonal profile curve. The second phase utilizes the results of the first phase to find a CSG-rep for many non-polygonal profile curves. A mathematically concise representation of a region bounded by a polygonal is presented. Namely, any polygonal region bounded by an n sided polygon may be represented by a binary tree which has at most n planar halfspaces as leaves. A structure for this representation and an algorithm for calculating is discussed.

Peterson, D. P.↗

NASA NTRS1987

Octree based automatic meshing from CSG models

Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is emphasized. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary respresentation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractors. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed.

Perucchio, Renato↗