Rotation, computer graphics

Sally, it s very difficult. Some scientists use computer graphics to help visualize 3-D cross sections of rotating 4-D objects. You pause. Do you recall I told you how easy it would be for a 4-D being to impregnate a woman without being seen ... 

Although computer graphic devices produce projections of higher dimensions on mere 2-D screens, the computer can store the location of points in higher dimensions for manipulations such as rotation and magnification. The computer can then display projections of these higher-dimensional forms from various viewpoints. In fact, the computer is frequendy used to represent higher dimen-... 

Quaternions are similar to complex numbers but of the form a + hi + cj.+ dk with one real and three imaginary parts. The addition of these 4-D numbers is fairly easy, but the multiplication is more complicated. How could such numbers have practical application It turns out that quaternions can be used to describe the orbits of pairs of pendulums and to specify rotations in computer graphics. 

Picture transformations (e.g. rotation, translation, scaling, perspective etc) in interactive computer graphics lend themselves naturally to representation in matrix notation, and implementation of the various algorithms on a vector processor is obviously straightforward and very worthwhile (particularly if moving pictures are required.). For this reason graphical applications of the MVP-9500 will not be discussed here and the interested reader is referred to one of the standard texts in this area (7). 

Even the most basic computer graphics program provides some standard facilities for the manipulation of models, including the abihty to translate, rotate and zoom the model towards and away from the viewer. More sophisticated packages can provide the scientist with quantitative feedback on the effect of altering the structure. For example, as a bond is rotated then the energy of each structure could be calculated and displayed interactively. 

Figure 45 shows that a rotation of the coordinate axes may improve variable by variable plots significantly. This method is very useful if an. interactive computer graphics terminal is available and if the dimensionality of the pattern space is not too large. A multidimensional rotation can be considered as a series of d(d-1)/2 two-dimensional rotations -... 

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