Overview of GIS
Lecture 2: GIS definition and geographic data
Lecture 3: GIS data types
Lecture 4: Lines and line simplification; ps #2
Lecture 5: Embedded planar graphs
Lecture 6: Applications of topological structure
Lecture 7: Spatial index structures based on grids
B-tree, linear orderings for grids, Quad-trees
Lecture 8: Spatial index structures based on partitioning data
R-trees, kd-trees, Binary space partition
Lecture 9-10: 3d data structures (Dinesh)
Lecture 11: Digital Terrain Models
USGS DEM descriptionSurvey on terrain models, esp TINs
Progressive terrain demo
Lecture 12: Student talks on project proposals
Lecture 13: Delaunay triangulation algorithms
Refer to de Berg et al. Computational Geometry: Algorithms and
Applications, chapter 9Paper on reconstructing Delaunay triangulations in linear time (gzipped postscript)
Lecture 14: Simplifying Terrain Models
Heckbert and Garland survey on terrain simplification
(pdf)
from SIGGRAPH 97
course on multiresolution modeling
Lectures 15-18: Simplifying Polygonal Models
Garland and Heckbert survey on polygon simplification.
(pdf) David Luebke's survey on polygon simplification. (pdf)
Carl Erikson's paper on model simplification.
Lecture 21-22: Computational Topology
Survey paper:
Computational Topology
by Dey, Edelsbrunner, Guha (gzipped .ps)
Surface modeling for molecules: Herbert Edelsbrunner, Deformable SMooth Surface Design, Disc & Comp Geom 21:87-115 (1999)
Lecture 23-24: Geometry compression: Dinesh & Martin
Lecture 25: Lower bounds in geometric computation
We looked at a number of problems that reduce to 3-SUM: Given sets
X,Y,Z of n reals each, is there an x in X, y in Y and z in Z such that
x+y=z?
On a
Class of O(n^2) Problems in Computational Geometry, by Anka Gajentaan
and Mark Overmars.
Lecture 25: Lower bounds in geometric computation