(1) Suppose I have a FLAT finite 2 dimensional region and take S samples
from different (point) sites at t different times for t=1,2,3..n
BOTH the location AND number of samples taken at each time step t
will in general be different (ie change in time).
What statistic(s) would best give a measure of how the spatial
arrangment of the sampling regime changes at each time step in:-
(a) a relative sense (the points may be translated)
(b) an absolute sense (relative to some fixed reference frame)?
For example, the samples might be the temperatures of a tank of fluid
at different surface locations respectively (a) not taking into account
the sampling locations relative to the tank bottom, (b)taking into
account sampling locations relative to the tank bottom.
(2) Question (1) again but now with the samples taken 3 dimensionally
ie not confined to the fluid surface.
(3) Suppose I have a continuous finite 2 dimensional surface within
fixed boundaries which changes in shape at times t=1,2,3,..n (for
example the membrane of a drum). What statistic(s) would be
be used to measure how much the overall shape changes at each time step?
All comments and suggestions are very welcome.
Many thanks,
Eric Grist
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