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First, align tetrahedron t[0] with ...
Then, "initial position" ...

The "blue" tetrahedron is aligned with AA[0] as shown on the left. And assign any values of gradient and 2nd derivative to the initial tile t[0] as shown on the right: in this example, x1x2x4 and "D".

The "white" tetrahedrons shown in the left figure are the adjacent tetrahedrons t[1] and t[-1]. They are moved to the position of AA[1] and AA[-1] respectively later.