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M There seems to be a contradiction between your response to my wk 4 question regarding shadows and then this chapter. When I asked about how we would perceive the shadow of a four dimensional object in our three dimensional world, your response was that we would register it as a fuzzy cloud like structure. But then in the chapter you discussed shadows as distorted cubes, or parallelepipeds.
I was wondering if any four dimensional graphics were used in the everyday animation of today. Are there any special effects that we register as two dimensional that are in fact four? One thing that is interesting about two dimensional graphics is the way that we perceive them as three dimensional objects. Using correct shading and perspective, the line between the dimensions can be almost eliminated. Another example of this is in the IMAX theatres. Even though the movie screen is two dimensional, by wrapping it around the viewer, it appears multidimensional. In fact, it is a two dimensional picture warped into three space.
Another question: if we were to represent an extremely irregular shape in the fourth dimension, would there be any pattern to where the points would be extended? For example, if you were to take a human face and extend each coordinate on the face, what would the result be visually? If there is no obvious vertex connection, or parallel plane, how do you know where to place the new coordinate? Is there a rule?
Also, when did people start really questioning the perception of the fourth dimension as time?
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