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at the origin. The point to emphasize is that the coordinate space used to
describe the points remained constant (even if we called it different names
at different times), while we imaged the points moving in space. A trans-
formation thus interpreted is sometimes called an active transformation.
Alternatively, we can think of the same process as a passive transfor-
mation. In the passive paradigm, we imagine the points being stationary
while we move the coordinate space used to describe those points. In either
case, the coordinates of the points are the same at each step. It's all in how
we choose to view the situation. Earlier, our perspective was fixed with the
coordinate space, because we were thinking of the transformation in active
terms. Now we show the dual perspective, which is fixed relative to the
object.
Absolute perspective
Local perspective
Robot
object
space
Robot
upright
space
World
space
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