Geometric Modeling

G22.3033.002 Spring 2001

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Course Information

Syllabus

Description: Geometry is used in modeling the world in many disciplines. For instance, in industrial design (of machine parts, of complex systems like a submarine, etc). But geometric modeling is also used in the geosciences and their many applications in socio-economic planning, demographic research, natural resource management, utility planning, environmental assessment, urban design, etc. We will study geometric modeling in the above two domains: in mechanical design and in geographical information systems. The former is essentially in 3-dimensions while the latter can be kept in 2-dimensions for our purposes. This will provide a rough partition of the semester into two parts.

This is a hands-on course, where you will implement algorithms and learn about real datasets. There will be a final project. Graphics programming will be based on Java2D (or OpenGL). What you will learn:
        -- computational geometry
        -- geometric design (curves and surfaces)
        -- geographical information systems
        -- important geospatial datasets
        -- numerical non-robustness issues and solutions
        -- visualization issues

Here is the topic coverage:

1. COMPUTATIONAL GEOMETRY (3 weeks)
        point problems:
                convex hull
                Delaunay triangulation
                Voronoi diagrams
        line problems:
                segment intersection
                arrangement
        query problems:
                point location
                shortest paths
                range searching

2. ROBUSTNESS ISSUES (1 week)
        this topic is also dispersed among the other
        lectures.

3. GEOGRAPHICAL INFORMATON SYSTEMS (4 weeks)
        nature of georeferenced datasets
                map layers
                Tiger dataset
                DEM dataset
                ARC/INFO
        visualization interface
                thinwire issues
                raster vs. vector data
        analysis and query subsystem
                example of geographic analysis
                concepts of distances
                data structure

4. GEOMETRIC DESIGN (6 weeks)
        Representation of Solids
                CSG
                B-Reps
        Classification Problem
        Boolean Operations
        Curves and Surfaces
                implicit representation
                parametric representation
                conversions
                intersection problems
 

Textbook and References

Course Work

There are 3 components:
-- regular homework including programming assignments.  There
       will be about 5 homeworks.
       Graphics programming can be in Java2D and Java3D
       (or, if you prefer, you can use OpenGL based on C/C++).
-- final project
-- class presentation and participation

Links