[Proj] Grown error if re-projecting from 4269 to LCC (2285) and backward multiple times

[Thomas Knudsen]

Hi Oscar,

Regarding LCCA:

I can see that the functions for computing dr and its derivative can be
easily inlined, by defining them as macros, rather than functions.

The call to fabs() is probably, on most platforms, converted to a builtin,
so I would not touch that.

The meridional arc length function, pj_mlfn(), is fairly simple and COULD
be inlined, but at the cost of future agony if the function is one day
updated,
so I would prefer to keep it as is until actual profiling shows it to be a
serious problem.

Are there any other obvious speed problems in PJ_lcca (ignoring everything
under the PROJECTION() call, which is setup functionality, executed only
once, and hence not so speed critical).


Regarding LCC:

The iteration you mention goes on in the pj_phi2() function in pj_phi2.c.

By strengthening the convergence criterion to 1e-12, the 1000 iteration
roundtrip deviation for LCC was reduced to 0.005 mm, which certainly
is more acceptable.

By strengthening to 1e-13, the 1000 roundtrip deviation was below 0.0001 mm.

I have, however, not yet had time to measure what the time cost of this
improvement
amounts to. Once I have hard numbers, I will post them to the list, and
probably suggest that we switch - either from LCC to LCCA, or from stop
criterion of 1e-10 to 1e-12.

/Thomas


2017-11-01 12:29 GMT+01:00 vanadovv at hetnet.nl <vanadovv at hetnet.nl>:

> Hi Thomas,
>
>
> LCCA: good suggestion!
> As far as I can tell, there are two significant differences between LCC
> and LCCA.
> LCC has an iteration loop criterion (in the inverse) of 1e-10, whereas
> LCCA is somewhat more accurate with 1e-12.
> Furthermore LCCA works with a Newton iteration scheme. This could be
> faster than iteration by successive approximation, but there are a couple
> of minor inefficiencies in the code, like function calls instead of inline,
> but YMMV.
>
>
> Oscar van Vlijmen
>
>
>
> ----Origineel Bericht----
> Van : knudsen.thomas at gmail.com
> Datum : 01/11/2017 07:58
> Aan : vanadovv at hetnet.nl, proj at lists.maptools.org
> Onderwerp : Re: [Proj] Grown error if re-projecting from 4269 to LCC
> (2285) and backward multiple times
>
> Oscar,
>
> I certainly agree that the deviation is quite high - my comment was more
> related
> to the expection of exact roundtrips, which I find unrealistic.
>
> Nevertheless, looking into the PROJ.4 code, I see there is an alternative
> implementation of LCC, called LCCA, which I had forgotten about, which
> actually seems to roundtrip exactly.
>
> In the master branch of PROJ.4, over at  https://github.com/OSGeo/proj.4,
> and comming in the next release, there is a tool "gie" for doing (a.o.)
> roundtrip tests. It is still lacking in docs, but I think you can follow
> this example:
>
> With this input file:
>
> $ cat lcc-lcca.gie
>
> BEGIN
>
> -------------------------------------------------------------------------------
>
> operation +proj=lcc +lat_1=48.73333333333333 +lat_2=47.5 \
>                     +lat_0=47  +lon_0=-120.8333333333333 \
>                     +x_0=500000.0001016001 +y_0=0        \
>                     +units=us-ft +ellps=GRS80 +towgs84=0,0,0  +no_defs
> -------------------------------------------------------------------------------
>
> tolerance   0.0010 mm
> accept     -118.5293900000000300   48.7408309999860520
> roundtrip   1000
>
>
> -------------------------------------------------------------------------------
>
> operation +proj=lcca +lat_1=48.73333333333333 +lat_2=47.5 \
>                      +lat_0=47  +lon_0=-120.8333333333333 \
>                      +x_0=500000.0001016001 +y_0=0        \
>                      +units=us-ft +ellps=GRS80 +towgs84=0,0,0  +no_defs
> -------------------------------------------------------------------------------
>
> tolerance   0.0 mm
> accept     -118.5293900000000300   48.7408309999860520
> roundtrip   1000
> END
>
> I get this output:
>
> $ gie lcc-lcca.gie
>
> -------------------------------------------------------------------------------
>
> Reading file '..\..\..\proj\lcc-lcca.gie'
> -------------------------------------------------------------------------------
>
> +proj=lcc +lat_1=48.73333333333333 +lat_2=47.5 +lat_0=47  +lon_0=-120....
> -------------------------------------------------------------------------------
>
>      FAILURE in lcc-lcca.gie(11):
>      roundtrip deviation: 1.550 mm, expected: 0.001 mm
> -------------------------------------------------------------------------------
>
> total:  1 tests succeeded,   1 tests FAILED!
> -------------------------------------------------------------------------------
>
>
> i.e. lcca roundtrips exactly, while lcc diverges heavily.
>
> So Dmitry: This seems to be your workaround - define your projection using
> lcca,
> rather than letting the epsg-list select lcc for you.
>
> /Thomas
>
>
>
>
>
>
>
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