![](bga.png)
based algorithms or in some volume-based
algorithms which exhibit characteristics like surface-
based algorithms (Lerois, 1995). Some volume-
based algorithms can consider this but may involve
considerable user intervention ((Payne, 1992),
(Chen, 1996), (Breen, 2001)). Morphing involving
discrete mathematical functions for interpolation
((Hughes, 1992), (He, 1994), (Turk, 1999)) is
capable of traversing along only a specified
direction.
Now let us analyze the algorithm in terms of
efficiency. In field morphing, control data sets are
used to specify coordinate mapping hence time
complexity is usually Ө(nm) as all coordinates of a
single dataset are more or less influenced by all
control fields (Chen, 1995). Here ‘n’ is the size of
volume and ‘m’ is the number of control fields. In
the proposed method, control fields i.e. slices are
automatically determined during data traversal and
these control fields have little influence or control in
coordinate mapping: only coordinates of respective
boundaries are influenced. Hence if the number of
extracted coordinates from each boundary is ‘p’ and
the number of automatically defined slices (‘m’) are
considered as control fields, then time complexity is
Ө(mp + m). Here ‘mp’ can be equated with the
volume size ‘n’ hence time complexity for the
proposed algorithm is Ө(n + m) which is much less
than volume morphing using disk field Ө(nm)
(Chen, 1996).
6 CONCLUSIONS
Simplicity and flexibility are two major characteris -
tics of the proposed algorithm which have made it
more dynamic and extendible than other existing
morphing algorithms. Future work includes exten -
ding the algorithm in order to show the extendibility
of the method by incorporating influence shape
while morphing including multiple influences and
exploitation of the method in parallel/distributed
computing environment as simple data structure of
sliced body and binary subdivision is suitable for
both data as well as functional partitioning.
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