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Course Announcement for Fall 1998:

Computational Geometries

CSCI 7000-Section 003, call #84296

CSCI 4830-Section 003, call #84295

MW 4:00-5:15 pm; Stadium 135.

This course will be both a survey and an exploration of the ways in
which computational media and geometry intersect -- we will not look at
just one notion of "computational geometry", but several. In
re-examining geometry as a computational discipline, we will make use
of a variety of software tools, possibly including the Geometer's
Sketchpad, HyperGami, and Ray Dream Designer. As such, students taking
this course must be prepared to play with a variety of computational
systems.

The course is offered to both undergraduates (as CSCI 4830) and
graduate students (as CSCI 7000; graduate students will have somewhat
more demanding assignments).

Prerequisite or Co-Requisite: Students are strongly encouraged to
have taken CSCI 3104 or 5454, or an equivalent course.

Topics to be covered:

- Differential geometry and biological
morphology through turtle graphics (3 weeks)

"Closed-path" theorem,
multiple polygons, spirals, recursive and space-filling curves,
L-systems in 2- and 3D, turtle paths on surfaces

- Fractal geometry through iterated function systems (3 weeks)

Definitions of dimension; using iterated function systems to create
fractal sets; Julia sets

- Explorations in classical geometry. (2 weeks)

Computational media as "conjecture support" in Euclidean geometry

- Computational Experiments in solid geometry (3 weeks)

Representations of solid objects; operations on solids; polyhedral modelling

- Algorithms in "Classical Computational Geometry" (4 weeks)

Convex hull; Point-location problems; Voronoi diagrams

Readings include Abelson and diSessa, *Turtle Geometry*; Barnsley,
*Fractals Everywhere*; Preparata and Shamos, *Computational
Geometry*.