This course is given at Tel Aviv University during the 2nd semester.
Prerequisites are Linear Algebra and interest in Visualization.

Visualizing Multidimensional Geometry and its Applications

Prof. Alfred Inselberg (aiisreal@math.tau.ac.il) - Office 325 Kaplun Bldg.

SYLLABUS

· First lecture : Introduction to Scientific, Information and Multidimensional Visualization - Course overview.

· Projective Geometry - Foundations, Duality, Homogeneous Coordinates, Invariants - 2 lectures.

· Parallel Coordinates in the Plane - Dualities, Transformations, Visual & Automatic Data Mining - 1 lecture.

· Lines in N-space - 2 lectures

- Representations of Lines

- Distance & Proximity Properties

- Application : Collision Avoidance Algorithms for Air Traffic Control, and others.

· Coplanarity - 2.5 lectures

- 2 Representations of Planes, Flats & Hyperplanes

- Recursive Mapping

- “Near Coplanarity” & Applications : Data mining, Geometric Modeling , Computer Vision, Statistics.

· Curves - 2 lectures including chapter on Envelopes .

· Topologies of lines & Flats. Applications : Computer Vision & Geometric Modeling – 0.5 lecture .

· Hypersurfaces in N-Space - 2 representations. Developable, Ruled, Quadratic & more general surfaces. Detecting properties from their representation and approximations of complex surfaces. Interior point Algorithms, more on Data Mining, A Decision Support System and models of Processes (Trade-Off Analysis, Sensitivities and Interelations, Impact of Constraints, a little on Optimization) and an Automatic Rule Finder (Classifier for Data Mining) - 1.5 lectures.

· Time permitting - students can choose and lecture on various topics in Visualization, e.g. Visualizing : The Internet, Fluid Flow, Neural Networks and others.

The course notes (the lectures given in class) will be available to the students. Exercises will be assigned and graded weekly.

Course grade = .2 (exercise grades) + .8 (project grade)