A performance drawback of our feature-based warping technique is that
each point in the warped volume is influenced by all
elements, since the influence fields never decay to zero. It follows
that the time to warp a volume is proportional to the number of
element pairs. An efficient C++ implementation, using incremental
calculations, needs 160 minutes to warp a single 
volume with
30 element pairs on an SGI Indigo 2.
We have implemented two optimizations which greatly accelerate the
computation of the warped volume 
, where we henceforth use
to denote either 
or 
. First, we
approximate the spatially non-linear warping function with a
piecewise linear warp [13]. Second, we introduce an
octree subdivision over 
.