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When adding and subtracting vectors to keep track of Zanzi's movements within the material plane relative to the Hall of Justice portal, the Stone of Recall has to multiply vectors in component form by both positive and negative scalar multiples (k values), and it memorises the directional information of these calculations by using the bindings of rope wrapped around it as a data storage area while it undertakes dot product calculations on these vectors according to u.v = (u subone)(v subone) + (u subtwo)(v subtwo) and also the angle between vectors according to cos theta = (u.v)/(|u|.|v|). Because the Stone of Recall needs to associate the numbers produced by dot product multiplication of vector components with the directional information of the added and subtracted scalar-multiplied vectors to enable Zanzi's return to the Hall of Justice portal, it fails to function with the rope bindings unravelled - the loss of the memorised data means that it cannot associate the dot product values of vectors with the directional information for those same vectors.
When playing Neverwinter Nights the Game Player sees events unfolding as a rendered 2D representation of the game's material and other planes, but for characters immersed within the game these planes are as three dimensional as space appears to be in the Game Player's "real" world. So the Stone of Recall actually uses the 3D coordinate system (x, y, z) to keep track of Zanzi's movements relative to the Hall of Justice portal.