Help with mathematical function

[Robert A. Macy]

I am not a mathematician, so not sure I can ask this
correctly, but...
I need to calculate a "spiral" integral - calculate the
area a vector, or "ray", sweeps out as a spiral collapses.
 

The tip of the vector monotonically decreases down to near
zero value.  with 500 of these spirals.  

The data array is composed of 500 by 100 complex values.
 The data along each row (500 rows) spirals down to near
zero values at the highest index value.  

I would like to calculate the area the ray sweeps out as
the spiral collapses.  

I tried a simple approach like using the area defined by
radius times the change in angle (delta angle)

average( abs(arrayvalues) ) * delta( angle(arrayvalues) )

and then integrated these values along each row.  The mesh
plots looked promising, BUT...

The angle function has a limited range so their plus minus
transitions played havoc with the results.  The spirals can
be over 700 to 1000 degrees.  

Plus, there is noise in the data, so the spiral tends to
"lump" around 0,0 not necessarily converge to it, which
again causes wild angle transitions.  However, along a row
between any two adjacent array values the data seems to be
monotonically decreasing (spiralling down) to zero values.
 

Does anyone know of a simple algorithm that will take each
vectors' end points, calculate the area, and sum that up
over the 100 values along each row?  

             - Robert -



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