Calculating the Plane Parameters of a Child Cube

When a new ``best so far'' fit cube is found, the cube needs to find out where it is in parameter space. The FHT does not explicitly propagate information from parent to child concerning the position of hypercubes in parameter space. Of course it would be trivial to do this, by, for instance, calculating the centre of the child relative to the centre of the parent, using equation 5.17, and passing the centre coordinates on to the child. However, since centre coordinates are needed only when an improved planar fit is found, this would involve quite a lot of wasted multiplication and division.

The method used in Needles provides each cube with the part of its ``family tree'' comprising the direct line of descent from the root to itself. It therefore knows how it is related to its parent, how its parent was related to its grandparent, and so on. A cube knows only about its own ``branch'', which is passed down to it by its parent.

The relationship between parent and child cubes is contained in the child indices $[b_1, b_2, b_3]$. Each cube therefore receives a list of such index triplets, detailing the relationships between ancestors of different generations. The list is linked backwards, i.e. from child to root. The formulae to calculate a cube's centre coordinates are simpler when the list is traversed in this direction. They are computational in nature, involving iteration when traversing the list, so we have not included them here, but they are given in the next section in procedure $cube\_centre$.