Geometry in Action: CSG

Constructive Solid Geometry and Solid Modeling

Geometric questions related to solid modeling include conversion between different representations including boundary nets, constructive solid geometry (representations involving Boolean combinations of simple base shapes), and hierarchical decomposition; combination (such as intersection and union) of shapes; blending surfaces; and data structures for graphical rendering of models. More could be done to connect the models used in computational geometry (typically polyhedra) with those in computer aided design (typically involving splines or other higher order curves and surfaces).

Alpha shapes, defined by H. Edelsbrunner and others at U. Illinois, provide a useful algorithmic tool for modeling shapes, especially those formed by unions of spheres.
Annotated bibliography on object representation schemes for 3d graphics, H.-G. Park, Air Force Inst. Tech.
BRL-CAD CSG system, Army Research Lab.
Constructive solid geometry bibliography, Ian Grimstead, U. Wales.
Decomposing trimmed surfaces using the Voronoi tesselation, P.-Y. Tsai and B. Hamann, Mississippi State U.
An efficient algorithm for finding the CSG representation of a simple polygon, D. Dobkin, L. Guibas, J. Hershberger, and J. Snoeyink, DEC SRC, 1989.
Geometric and solid modeling links, Jeongyoon Lee, Korea.
The Gnu Triangulated Surface library. Providing robust primitives for mesh representation, constructive solid geometry operations, and Delaunay triangulation.
HEXAR (Cray Research) is an automatic unstructured hexahedral mesh generation package that starts working directly from computer-aided design (CAD) surface data.
Information Geometers Ltd., publishers of books on geometry, CAD/CAM, and graphics including the CSG proceedings.
Integrating Geometric and Solid Modeling, Dinesh Manocha, UNC Chapel Hill.
A Mathematical Framework for Sculptured Solids in Exact CSG Representation, Jai Menon and Baining Guo, 5th MSI Worksh. Comp. Geom.
Object Representation by Means of Nonminimal Division Quadtrees and Octrees. This paper by Ayala et al., in ACM Trans. on Graphics, describes quadtree methods in solid modeling.
Raindrop Geomagic Inc. geometric modeling and visualization software.
Representation and Evaluation of Boolean Combinations of NURBS Solids, Shankar Krishnan, Dinesh Manocha, and Atul Narkhede, 5th MSI Worksh. Comp. Geom.
Shape Modeling International '97, Japan, March 1997.
Shape modeling with real functions. U. Aizu, Japan.
Speed-ups in constructive solid geometry, D. Eppstein, UCI, 1992.

Part of Geometry in Action, a collection of applications of computational geometry.
David Eppstein, Theory Group, ICS, UC Irvine.

Semi-automatically filtered from a common source file.