CS 274. Computational Geometry

Catalog Description: <Formerly 292T>. Constructive problems in computational geometry: convex hulls, triangulations, Voronoi diagrams, arrangements of hyperplanes; relationships among these problems. Search problems: advanced data structures; subdivision search; various kinds of range searches. Models of computation; lower bounds.

Units: 3.0

Prerequisites: 170 or equivalent.

Formats:
Fall: 3 hours of lecture per week
Spring: 3 hours of lecture per week

Grading basis: letter

Final exam status: No final exam


Class Schedule (Spring 2019):
MoWe 2:00PM - 3:29PM, Soda 320 – Jonathan Shewchuk

Class homepage on inst.eecs

General Catalog listing


Department Notes: Combinatorial geometry: Polygons, polytopes, triangulations, planar and spatial subdivisions. Constructions: triangulations of polygons, convex hulls, intersections of halfspaces, Voronoi diagrams, Delaunay triangulations, arrangements of lines and hyperplanes, Minkowski sums; relationships among them. Geometric duality and polarity. Numerical predicates and constructors. Upper Bound Theorem, Zone Theorem. Algorithms and analyses: Sweep algorithms, incremental construction, divide-and-conquer algorithms, randomized algorithms, backward analysis, geometric robustness. Construction of triangulations, convex hulls, halfspace intersections, Voronoi diagrams, Delaunay triangulations, arrangements, Minkowski sums. Geometric data structures: Doubly-connected edge lists, quad-edges, face lattices, trapezoidal maps, history DAGs, spatial search trees (a.k.a. range search), binary space partitions, visibility graphs. Applications: Line segment intersection and overlay of subdivisions for cartography and solid modeling. Triangulation for graphics, interpolation, and terrain modeling. Nearest neighbor search, small-dimensional linear programming, database queries, point location queries, windowing queries, discrepancy and sampling in ray tracing, robot motion planning. http://www.cs.berkeley.edu/~jrs/274/

Related Areas: