[Proj] UNPP optimizations - was Re: Natural Earth projection
OvV_HN
ovv at hetnet.nl
Fri Mar 9 09:57:31 EST 2012
[Proj] UNPP optimizations - was Re: Natural Earth projection
support.mn at elisanet.fi support.mn at elisanet.fi
Fri Mar 9 09:13:06 EST 2012
Re:
I started to be interested about the number of iteration steps
in the inverse (iterative) conversion.. we all need maximum
speed.. so:
you could call it (Usually Near the Previous Point)
UNPP optimization ................
Reply (for what it's worth, probably 2 cents):
In the case of the Natural Earth projection the number of iteration steps
seems to be low.
Some examples:
R = 6371008.7714 m
lat, lon = 70.0,120.0; inverse needs 4 iterations
lat, lon = 80.0,120.0; inverse needs 4 iterations
lat, lon = 85.0,120.0; inverse needs 5 iterations
lat, lon = 89.0,120.0; inverse needs 7 iterations
lat, lon = 90.0,120.0; inverse needs 7 iterations
Note that the iteration loop only has a couple of multiplications and one
division.
The polynomial is efficiently calculated with a Horner scheme.
A UNPP optimized code could be quite involved. Calculating from the previous
point will certainly involve some math, but probably no time consuming
divisions or transcendentals. But after a series of points an original
calculation has to be done in order to retain accuracy. Decision tests have
to be made and these could cost some time.
I wonder if such an optimization will lead to a significant reduction in
time for very simple iterative procedures which are looped less than say 10
times.
But for relatively time consuming loops that have to be done 40 times or so
until convergence, times 10 million pixels........ optimization should be
investigated!
Oscar van Vlijmen
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