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Originally Posted by Astronouth7303
... distance is defined as the sum of the absolute values of the [differences of] the [coordinates].
OR: dT = |AX - BX| + |AY - BY| + |AZ - BZ| + ...
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Shouldn't your definition for the taxicab distance (d
T) be written
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dT(A, B) = |AX - BX| + |AY - BY| + |AZ - BZ| + ...
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And with Rob's hints, I think I figured out your "segment" formula:
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A segment = {P | dT(P, A) + dT(P, B) = dT(A, B)}
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If I indeed understand it correctly, a "segment" turns out to be all points on or within a rectangle* with points A and B at opposite corners.
*Or a rectangular prism in three dimensions, or a rectangular hyper-prism in more than three.