[Proj] Transverse Mercator algorithm

Irwin Scollar al001 at uni-koeln.de
Tue May 27 04:57:52 EDT 2008

A way to speed up TM calculation with enhanced accuracy was published 
by Knud Poder in 1989:

Implementation of Co-ordinate Transformations. NKG Nordiske 
Forskarkurser, Ebeltoft September 1988, Moderne Teknik i Geodaesi og 
Opmaling, 243 - 280. Kort & Matrikelstyrelsen, Copenhagen 1989.

It uses Clenshaw summation for the series expansions. See also 
Tscherning & Poder:


Clenshaw summation can be applied to almost any algorithm containing 
series expansions to gain speed.

As far as accuracy is concerned, analysis of this should also take 
into account the limitations of floating point processing when a 32 
bit machine is being used.  This is not a problem with 64 bit 
hardware and compilers.

For a real-time tracking application, I coded with the native 10 byte 
extended IEEE Floating Point representation available in Intel and 
compatible processors and offered by some compilers rather than the 
double precision used in much published code.  Howevere, the hardware 
support in the processor may be slowed by cache misses due to non-4 
byte boundary conditions on some machines. Higher speed at the 
expense of accuracy might perhaps be obtained by using SSE 
instructions via one of the Intel compilers or with hand-coded 
assembler for SSE4, but I haven't tried it.

Irwin Scollar

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