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Date: Around 1993

Hi, I could not find the 2 books that were recommended to me, about the 4-D objects. But, maybe someone can help me. I made a computer program to draw 3-D Objects and project them in the 2-D monitor. It also draws 3D functions. I made a function to convert the 3D coordinate (x,y,z) to a screen coordinate (x,y), and it works really well. What I want to do now, if it is possible, is to make a function to convert 4D coordinates (x,y,z,w) in 3-D or 2-D coordinates, so I can draw a 4-D object (or a function) on my screen, and see what it looks like. Can I do that? My program works fine in projecting and rotating 3-D objects, but what about different kinds of projections?

Pedro, I really hate to seem discouraging, but this does not seem possible to me. It is theoretically possible to "project" a 4-D object into a 3-D space (just like we can "project" a 3-D object, like a cube, onto a 2-D surface, which is a plane). However, to project a 3-D object onto a 2-D surface (like a computer screen) we also have to use lines, colors, and/or shading to present us with an illusion of what the third dimension looks like. In principle, one might be able to do something like this with a 4-D object, but it does not seem possible to do it in 2-D (on a computer screen) with a 4- D object. If you can solve this problem, publish it in a computer graphics journal! Good luck.


Actually, it is not that hard to display 4 dimensions on a 2 dimensional screen (or sheet of paper) as long as your data has the right form. There is a book on ways people have displayed up to 6 dimensions of data - I think it was called The Visual Representation of Information. A simple example of 4 dimensional display is placing arrows (which represent 2 dimensions) on the points of a two dimensional grid. This is often done to represent currents, or magnetic fields, for example. Color can actually represent 3 dimensions (1 for redness, 1 for greenness, and 1 for overall brightness, for example), so a 2-D color graph could give 5 dimensions of data. Actually, there is a 6-dimensional graph in the April Scientific American, displaying possible origins of new universes (see p. 24). Actually, it looks of uniform brightness, so maybe there are only 5 dimensions on display. The main problem with displaying higher dimensions is that it is impossible to treat all the dimensions in the same way. So 2 (or at most 3) will look like spatial dimensions, and the others just have to look like something else (arrows or colors). Hope this helps!

Arthur Smith

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