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).
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.
trimmed surfaces using the Voronoi tesselation, P.-Y. Tsai and B.
Hamann, Mississippi State U.
efficient algorithm for finding the CSG representation of a simple
polygon, D. Dobkin, L. Guibas, J. Hershberger, and J. Snoeyink, DEC
- 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.
(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.
Geometric and Solid Modeling,
Dinesh Manocha, UNC Chapel Hill.
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.
Modeling International '97, Japan, March 1997.
- Shape modeling with real functions.
U. Aizu, Japan.
- Speed-ups in constructive solid geometry, D. Eppstein, UCI, 1992.
Geometry in Action,
a collection of applications of computational geometry.
from a common source file.