4-D Objects ```Name: Name Status: N/A Age: N/A Location: N/A Country: N/A Date: Around 1993 ``` Question: 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? Replies: 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. Topper 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 Click here to return to the Mathematics Archives

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