1. Literature: Serious Articles etc.

2. Visualization: Various tools and methods.

3. Scientific Computing: Visualization of simulations requiring 4D displays.

4. (Pre-)College: High School and Undergraduate math level.

1. David Banks, *"Interactive Manipulation and Display of
Two-Dimensional Surfaces in Four-Dimensional Space" * in 1992
Symposium on Interactive 3D Graphics, pp. 197

Comment: A paper primarily on intuitive manipulation of
surfaces in four dimensions. Usage of multiple devices for input
and intersecting with planes to allow seeing the internal
structure of the surface.

2. AJ. Hanson and RA. Cross, * "Interactive Visualization
Methods for Four Dimensions" * in Proceedings of
Visualization '93, San Jose, CA, October 25-29, 1993, pp. 196

Comment: Not yet available.

3. SR. Hollasch, "
*Four-Space Visualization of 4D Objects
*" Master's Thesis, Arizona State University, 1991

Comment: A good introduction in extending 3D graphics techniques
and mathematical background into 4D.

4. AJ. Hanson and PA. Heng, "*Illuminating the Fourth
Dimension *", *IEEE* Computer Graphics and Appl., Vol. 12, No. 4,
pp. 54

Comment: Not yet available.

5. G. Ferrar,
*Arbitrary-Dimensional Solid Object Display Algorithm*.

Comment: Not yet available.

1. T. Banchoff, Brown University,
*Flatland-Hypergraphics*.

Comment: A leader in 4D visualization.

2. Center for Innovative Computer Applications, Indiana
University, *
Four-Dimensional Dice Simulation*

Comment: A very nice movie of a rotation of a 4-dimensional
dice, which appeared in *SIGGRAPH*

3. Center for Innovative Computer Applications, Indiana
University, *
Visualizing Fermat's Last Theorem*

Comment: Fermat's Last Theorem, before the proof was known.

4. R. Koch, UOregon, Java program that can display and rotate *
all possible three and four dimensional regular solids*

Comment: Cubes, tetrahedra, octahedra and so on in 3 and 4 dimensions.

5. P. Fleckenstein, Rochester Institute of Technology *
N-dimensional Ray Tracing*

Comment: Intersecting a 4-D object with a space, and making a
movie out of it.

6. N. Jackiw,
*The Geometer's Sketchpad*

Comment: A very nice Java Applet focusing on how to start from
1D cube and work your way up to a 4D cube.

7. H. van der Wal,
*
HyperCube Game*.

Comment: A neat game in three and four dimensions, of trying to
avoid hitting a hypercube with a ball. Allows for stereo vision
as well.

8. J Bailey, *
Four Dimensional Rubik's cube*.

Comment: One way of thinking about a 4D rubik cube.

9. Another such list.

Comment: Geometry-concerned list of 4D stuff.

1. Lattice QCD at the Ohio State university:
*Eigenmode of the Dirac operator.*

Comment: Fourth dimension treated as time, and turned into a
movie, a common practice.

2. TR. Nelson and DH. Pretorius,
*Interactive Acquisition, Analysis and Visualization of
Sonographic Volume Data*, Intl. Journal of Imaging
Systems and Technologies, Vol. 8, 1997, pp. 26

Comment: Another common practice, data acquired in a 3D cubical
lattice, with an associated value at each point, requires four-dimensional
visualization. Also known as volume rendering.

3. Yale Medical School, *Shape-Based
Analysis of Nonrigid Motion* list of articles.

Comment: Some examples include: Myocardial Motion and Function
Assessment; Shape-Based 4D Left Ventricular Myocardial Function
Analysis; A Sequential Filter for Temporal Analysis of Cardial
Motion and much more.

4.A. Anderson, Watermodeling:
*A 4-Dimensional GIS/CADD-Based Decision Support System for
Managing Environmental Remediation Projects*

Comment: Another area in which 4D vis. is of importance is GIS
systems, dealing with more than just land, eg. atmosphere, water
bodies etc.

5. Medical Imaging, MRI, PET, CT, SECT and Ultrasound *Volume Segmentation*.

Comment:

1. The Geometer's Sketchpad.

Comment: A very nice Java Applet focusing on how to start from
1D cube and work your way up to a 4D cube.

2. A Hypergame!.

Comment: A neat game in three and four dimensions, of trying to
avoid hitting a hypercube with a ball. Allows for stereo vision
as well.

3. Question corner at the University of Toronto Mathematics
Network:
*
Euclidean Geometry in Higher Dimensions*.

Comment: A simple guide into higher dimensions.

4. A. Sheppard, Hampshire College Summer Studies in Mathematics,
outline of a course for gifted high school students: Images From The Fourth Dimension.

Comment: Not yet available.

Dimitrios Mitsouras Last modified: Mon Nov 23 05:14:53 EST 1998