Most of the work in the subdivision procedures ( for the
for the MFHT) goes into two stages.
Firstly, arrays are calculated that are to be passed on to children.
For the FHT plane finder these are the eight ( in general)
normalised distance arrays, whereas for the MFHT
is the only such array
arrays in general).
In both cases the calculation of an array element involves two calculations:
an addition and multiplication by two in the FHT, an addition and a division
by two in the MFHT. The second time consuming part is the voting, i.e.
the test for intersection of hyperplane with hypersphere/hypercube.
For the FHT plane finder this is just a single comparison for each of
the eight child cubes ( comparisons generally) whereas for the MFHT
line finder, 9/2 comparisons (on average) and four boolean
expressions are evaluated (for general these figures become
and respectively). All these figures are summarised in
Since increases faster than , the FHT will overtake the MFHT for speed as increases. In fact tests have shown the MFHT plane fitter to be about 25% slower than the FHT. The memory space advantage of the MFHT is also reduced, since new arrays are required at each subdivision as against eight for the FHT (which again could be altered so as to require only one array, at the cost of some loss of speed).