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Computer animation and the fourth dimension
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 2014 |
| Abstract | Man is a creature restricted to a world of three spa tial dimensions in which he is reasonably free to move about at will except for the arbitrary territorial bound aries imposed by different nations. Man also lives in another dimension over which he presently has no con trol other than to watch its continual forward move ment in the mechanical and electrical gadgets he has devised to measure this dimension which he calls time. Many people call time the fourth dimension, but be cause of its many unique qualities I would rather con sider time as a special dimension. Therefore, in this pa per the fourth dimension is a fourth purely spatial di mension not to be confused with time. Since we live in a world of three spatial dimensions, we are unable to visualize a fourth spatial dimension perpendicular to our three spatial dimensions. How ever, the computer is not bothered by problems of hu man visualization and is able to deal with objects in four-dimensional space as easily as it performs calcula tions for three-dimensional objects. Only a fourth num ber is required by the computer to locate a point in four dimensional space. But if the computer is to present the results of its calculations with four-dimensional ob jects to man, then the computer must come down from its digital tower and perform the necessary operations so that man can visualize and possibly obtain some intuitive feel for the results. The technique of per spective projection from four dimensions to three di mensions is particularly helpful here. In a previous paper (“A Computer Technique for Displaying n-Dimensional Hyperobjects,” Communi cations of the ACM, Vol. 10, No. 8, August 1967, pp. 469-473), I described in general the technique of perspective projection of n-dimensional hyperobjects and also the application of this technique to the produc tion of computer-generated three-dimensional movies of rotating four-dimensional hyperobjects, and in partic ular, the hypercube. The mathematical details of this previous paper will not be repeated here but a physical interpretation of the results will be explored with particular emphasis on the purely artistic effects obtainable with the technique. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://noll.uscannenberg.org/Art%20Papers/Fourth%20Dimension.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
