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Are there situations where it makes sense for the homogeneous coordinate to be anything other than 0 or 1?


Why do we divide by c for vectors? I didn't think this would apply for vectors because we are forcibly setting the 4th coordinate to 0 for ease of computation, when technically it should be 1 if we're thinking about the associated line in homogeneous coordinates.


So for the vector, we would just ignore the divide by C part and keep the (x,y) as is?


Do we need to distinguish using a divide-by-zero check because we otherwise compute transformations with points and vectors using the same functions?


when we use c=1 we are assuming the triangle is at z=1, when c=0 it means the vector is at z=0, which makes sense because for any linear transformation it's now still from the origin.


Can we not just treat points as vectors (with respect to the origin)?


Since we cannot actually carry out the division by zero operation, does this mean we can only approximate a vector by setting c closer to 0 but can not accurately express a vector using this division method.