Computation and simulation has rapidly become a third branch of science,
standing next to the older branches of theory and experiment.
Much scientific computation is done with the finite element method
or related techniques, requiring a geometric mesh
generation stage to set up the computation, and often involving more
geometry in finding sparse decompositions of the resulting matrices.
Other scientific problems involve more directly the geometry of polyhedra
or local neighbor interactions. We include separate sections for
earth sciences, and
physics meets computational geometry, Glimm et al, 1st CGC
Worksh. Computational Geometry. The authors use combinatorial
geometry to represent discontinuities in problems of
fluid dynamics, elastic and plastic deformation, semiconductor manufacture,
Euclidean minimum spanning tree mixing model. S. Subramaniam and
S. B. Pope use geometric minimum spanning trees to model locality of
particle interactions in turbulent fluid flows. The tree structure of
the MST permits a linear-time solution of the resulting
computational geometry to computational physics, M. Pellegrini,
ERCIM News, Apr. 1996.
Marco describes his recent work on algorithms for form
factors, radiosity, and electrostatics, using integral geometry and
Monte Carlo methods in place
of the traditional finite element meshing approach.
states of a ternary fcc lattice model.
D. Avis and K. Fukuda apply their work on listing vertices of polytopes
to a problem of finding possible ground states in alloy structures.
- Ionic association in electrolyte solutions: A Voronoi
Polyhedra analysis, and
The Voronoi Polyhedra as tools for structure determination in
simple disordered systems.
J.C. Gil Montoro and J.L.F. Abascal investigate the use of Voronoi
diagrams in analyzing chemical simulations.
mixing model for turbulent reactive flows based on Euclidean minimum
spanning trees, S. Subramaniam and S. B. Pope.
- Percolation. Ted Davis of U. Minn. uses Voronoi diagrams
to simulate fluid flow through porous media.
- Rocpack - A 3D Particle Packing Algorithm".
Sphere packing applications in rocket propellant particle simulations.
Part of a larger package for simulating solid-gas combustion interfaces.
Similar ideas look likely to be useful for simulating soils or other
- Structure determination in disordered systems.
J.C.G. Montoro and J.L.F. Abascal use Voronoi polyhedra to detect
clusters in rapidly quenched liquids.
Disorder and Conductance Fluctuations in Thin Films. K. Abkemeier
and D. Grier use Delaunay triangulations of randomly perturbed lattice points
to form resistor networks that model the electrical behavior of
amorphous and polycrystalline silicon.
- Visualizing 3D spatial patterns of archaeological assemblages.
Diego Jiminez and Dave Chapman use beta-skeletons and other Delaunay-like proximity graphs
to find potential semantic connections between Mexican artifacts.
data interpretation. The Insight group at Ohio State is using
geometric techniques such as minimum spanning trees to extract features
from large meteorological data sets.
Geometry in Action,
a collection of applications of computational geometry.
from a common source file.