Assume that I have a camera defined by its position and direction, and its center and detail is defined as a box (three orthogonal Box Center to Face Vector Centers)
It appears that 1-3 faces of box view can appear on the basis of box position and orientation. Is there some clever way to determine which faces are visible? A clear solution for each face is to calculate 6 dot-products of normal face against face-camera vector. Is there a better way? Note: Perspective projection will be used, but I do not think it matters, the property of "face-to-face camera" is free for projecting.
I believe the method you described is a normal way of doing this. It's a very quick calculation so you do not have to worry too much about the speed. This is the same method that they use to reduce the number of calculations for the triangle intersection algorithm. If the face is not visible in front, then the method does not continue to count for that face. See this letter for a C ++ implementation of this algorithm. This is in the first half of the calculation
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