# COMP 258: Fall 1999

## Lecture Notes

# COMP258, Fall 1999: Lecture Notes

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Lecture 7: Spatial index structures based on grids

B-tree, linear orderings for grids, Quad-trees
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Lecture 8: Spatial index structures based on partitioning data

R-trees, kd-trees, Binary space partition
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Lecture 9-10: 3d data structures (Dinesh)

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Lecture 11: Digital Terrain Models

USGS DEM description

Survey on terrain models, esp TINs

Progressive
terrain demo
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Lecture 12: Student talks on project proposals

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Lecture 13: Delaunay triangulation algorithms

Refer to de Berg et al. Computational Geometry: Algorithms and
Applications, chapter 9

Paper on reconstructing
Delaunay triangulations in linear time (gzipped postscript)

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Lecture 14: Simplifying Terrain Models

Heckbert and Garland survey on terrain simplification
(pdf)
from SIGGRAPH 97
course on multiresolution modeling
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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.
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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)

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Lecture 23-24: Geometry compression: Dinesh & Martin

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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.