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2020-10-31proj_create_ellipsoidal_2D/3D_cs(): doc improvementEven Rouault
2020-10-27merc.cpp + phi2.cpp: Avoid declaring multiple variables in 1 statement.Charles Karney
2020-10-27Use nm units in builtins.gie. Remove backward looking comments in code.Charles Karney
2020-10-26Fix/add some comments.Charles Karney
2020-10-26Use sincos optimization in merc_e_forward. Revised timing data...Charles Karney
Times per call in ns = nanoseconds. Fedora 31 Ubuntu 18 g++-9.3.1 g++-7.5.0 fwd inv fwd inv old merc 207 461 217 522 new merc 159 457 137 410 etmerc 212 196 174 147 The new forward method is now 25% faster (resp 35% faster) on Fedora 31 (resp Ubuntu 18). The new inverse method is the same speed (resp 20% faster) on Fedora 31 (resp Ubuntu 18). The accuracy is hardly affected: rms error increases from 0.30 nm to 0.33 nm, max error increases from 1.83 nm to 1.84 nm (a barely noticeable degradation).
2020-10-26phi2.cpp: Slight cosmetic changes to sinpsi2tanphi.Charles Karney
2020-10-26lcc.cpp: fix abs -> fabsCharles Karney
Also some corrected information... Timing UPDATED -------------- Sorry the previous timing data was wrong. Here are corrected values.. Here's what I get with g++ -O3 on two Linux machines with recent versions of g++. As always, you should take these with a grain of salt. Times per call in ns = nanoseconds. Fedora 31 Ubuntu 18 g++-9.3.1 g++-7.5.0 fwd inv fwd inv old merc 207 461 217 522 new merc 228 457 168 410 etmerc 212 196 174 147 The new forward method is the 10% slower (resp 20% faster) on Fedora 31 (resp Ubuntu 18). The new inverse method is the same speed (resp 20% faster) on Fedora 31 (resp Ubuntu 18). Roughly speaking the speed comparison is a wash. Maybe we should pay attention more to the Fedora 31 results since these are with a newer version of the compiler. I would still make the argument that a 20% time penalty (which in a full PROJ pipeline would probably be no more than a 5% penalty) would be a worthwhile price to pay for a more robust implementation of the projection.
2020-10-26phi2.cpp: remove unused static consts + minor code tweakCharles Karney
2020-10-26Address comments by @schwehrCharles Karney
2020-10-26Try to fix compiler complaints for max and constexpr sqrtCharles Karney
2020-10-26Update Mercator projectionCharles Karney
Introduction ------------ The existing formulation for the Mercator projection is "satisfactory"; it is reasonably accurate. However for a core projection like Mercator, I think we should strive for full double precision accuracy. This commit uses cleaner, more accurate, and faster methods for computing the forward and inverse projections. These use the formulation in terms of hyperbolic functions that are manifestly odd in latitude psi = asinh(tan(phi)) - e * atanh(e * sin(phi)) (phi = latitude; psi = isometric latitude = Mercator y coordinate). Contrast this with the existing formulation psi = log(tan(pi/4 - phi/2)) - e/2 * log((1 + e * sin(phi)) / (1 - e * sin(phi))) where psi(-phi) isn't exactly equal to -psi(phi) and psi(0) isn't guaranteed to be 0. Implementation -------------- There's no particular issue implementing the forward projection, just apply the formulas above. The inverse projection is tricky because there's no closed form solution for the inverse. The existing code for the inverse uses an iterative method from Snyder. This is the usual hokey function iteration, and, as usual, the convergence rate is linear (error reduced by a constant factor on each iteration). This is OK (just) for low accuracy work. But nowadays, something with quadratic convergence (e.g., Newton's method, number of correct digits doubles on each iteration) is preferred (and used here). More on this later. The solution for phi(psi) I use is described in my TM paper and I lifted the specific formulation from GeographicLib's Math::tauf, which uses the same underlying machinery for all conformal projections. It solves for tan(phi) in terms of sinh(psi) which as a near identity mapping is ideal for Newton's method. For comparison I also look at the approach adopted by Poder + Engsager in their TM paper and implemented in etmerc. This uses trigonometric series (accurate to n^6) to convert phi <-> chi. psi is then given by psi = asinh(tan(chi)) Accuracy -------- I tested just the routines for transforming phi <-> psi from merc.cpp and measured the errors (converted to true nm = nanometers) for the forward and inverse mapping. I also included in my analysis the method used by etmerc. This uses a trigonometric series to convert phi <-> chi = atan(sinh(psi)), the conformal latitude. forward inverse max rms max rms old merc 3.60 0.85 2189.47 264.81 etmerc 1.82 0.38 1.42 0.37 new merc 1.83 0.30 2.12 0.31 1 nm is pretty much the absolute limit for accuracy in double precision (1 nm = 10e6 m / 2^53, approximately), and 5 nm is probably the limit on what you should routinely expect. So the old merc inverse is considerably less accurate that it could be. The old merc forward is OK on accuracy -- except that if does not preserve the parity of the projection. The accuracy of etmerc is fine (the truncation error of the 6th order series is small compared with the round-off error). However, situation reverses as the flattening is increased. E.g., at f = 1/150, the max error for the inverse projection is 8 nm. etmerc is OK for terrestrial applications, but couldn't be used for Mars. Timing ------ Here's what I get with g++ -O3 on various Linux machines with recent versions of g++. As always, you should take these with a grain of salt. You might expect the relative timings to vary by 20% or so when switching between compilers/machines. Times per call in ns = nanoseconds. forward inverse old merc 121 360 etmerc 4e-6 1.4 new merc 20 346 The new merc method is 6 times faster at the forward projection and modestly faster at the inverse projection (despite being more accurate). The latter result is because it only take 2 iterations of Newton's method to get full accuracy compared with an average of 5 iterations for the old method to get only um accuracy. A shocking aspect of these timings is how fast etmerc is. Another is that forward etmerc is streaks faster that inverse etmerc (it made be doubt my timing code). Evidently, asinh(tan(chi)) is a lot faster to compute than atan(sinh(psi)). The hesitation about adopting etmerc then comes down to: * the likelihood that Mercator may be used for non-terrestrial bodies; * the question of whether the timing benefits for the etmerc method would be noticeable in a realistic application; * need to duplicate the machinery for evaluating the coefficients for the series and for Clenshaw summation in the current code layout. Ripple effects ============== The Mercator routines used the the Snyder method, pj_tsfn and pj_phi2, are used in other projections. These relate phi to t = exp(-psi) (a rather bizarre choice in my book). I've retrofitted these to use the more accurate methods. These do the "right thing" for phi in [-pi/2, pi/2] , t in [0, inf], and e in [0, 1). NANs are properly handled. Of course, phi = pi/2 in double precision is actually less than pi/2, so cos(pi/2) > 0. So no special handling is needed for pi/2. Even if angles were handled in such a way that 90deg were exactly represented, these routines would still "work", with, e.g., tan(pi/2) -> inf. (A caution: with long doubles = a 64-bit fraction, we have cos(pi/2) < 0; and now we would need to be careful.) As a consequence, there no need for error handling in pj_tsfn; the HUGE_VAL return has gone and, of course, HUGE_VAL is a perfectly legal input to tsfn's inverse, phi2, which would return -pi/2. This "error handling" was only needed for e = 1, a case which is filtered out upstream. I will note that bad argument handling is much more natural using NAN instead of HUGE_VAL. See issue #2376 I've renamed the error condition for non-convergence of the inverse projection from "non-convergent inverse phi2" to "non-convergent sinh(psi) to tan(phi)". Now that pj_tsfn and pj_phi2 now return "better" results, there were some malfunctions in the projections that called them, specifically gstmerc, lcc, and tobmerc. * gstmerc invoked pj_tsfn(phi, sinphi, e) with a value of sinphi that wasn't equal to sin(phi). Disaster followed. I fixed this. I also replaced numerous occurrences of "-1.0 * x" by "-x". (Defining a function with arguments phi and sinphi is asking for trouble.) * lcc incorrectly thinks that the projection isn't defined for standard latitude = +/- 90d. This happens to be false (it reduces to polar stereographic in this limit). The check was whether tsfn(phi) = 0 (which only tested for the north pole not the south pole). However since tsfn(pi/2) now (correctly) returns a nonzero result, this test fails. I now just test for |phi| = pi/2. This is clearer and catches both poles (I'm assuming that the current implementation will probably fail in these cases). * tobmerc similarly thinks that phi close to +/- pi/2 can't be transformed even though psi(pi/2) is only 38. I'm disincline to fight this. However I did tighten up the failure condition (strict equality of |phi| == pi/2). OTHER STUFF =========== Testing ------- builtins.gei: I tightened up the tests for merc (and while I was about it etmerc and tmerc) to reflect full double precision accuracy. My test values are generated with MPFR enabled code and so should be accurate to all digits given. For the record, for GRS80 I use f = 1/298.2572221008827112431628366 in these calculations. pj_phi2_test: many of the tests were bogus testing irrelevant input parameters, like negative values of exp(-psi), and freezing in the arbitrary behavior of phi2. I've reworked most for the tests to be semi-useful. @schwehr can you review. Documentation ------------- I've updated merc.rst to outline the calculation of the inverse projection. phi2.cpp includes detailed notes about applying Newton's method to find tan(phi) in terms of sinh(psi). Future work ----------- lcc needs some tender loving care. It can easily (and should) be modified to allow stdlat = +/- 90 (reduces to polar stereographic), stdlat = 0 and stdlat_1 + stdlat_2 = 0 (reduces to Mercator). A little more elbow grease will allow the treatment of stdlat_1 close to stdlat_2 using divided differences. (See my implementation of the LambertConformalConic class in GeographicLib.) All the places where pj_tsfn and pj_phi2 are called need to be reworked to cut out the use of Snyder's t = exp(-psi() variable and instead use sinh(psi). Maybe include the machinery for series conversions between all auxiliary latitudes as "support functions". Then etmerc could use this (as could mlfn for computing meridional distance). merc could offer the etmerc style projection via chi as an option when the flattening is sufficiently small.
2020-10-26Bump ABI version numbers for 7.2 releaseKristian Evers
2020-10-25Add +proj=col_urban projection, implementing a EPSG projection method used ↵Even Rouault
by a number of projected CRS in Colombia (fixes #589)
2020-10-25Fix issues spotted by cppcheckEven Rouault
2020-10-25More typo fixesEven Rouault
2020-10-25Fix typos spotted by scripts/fix_typos.shEven Rouault
2020-10-24projsync: fix --list-files to be compatible with filtering optionsEven Rouault
2020-10-23PROJStringFormatter::getUsedGridNames(): recognize +file= parameter of ↵Even Rouault
operation +proj=tinshift
2020-10-23Add logic to handle interpolationCRS in PROJBasedOperation and ↵Even Rouault
ConcatenatedOperation
2020-10-23AuthorityFactory::createCoordinateOperation(): correctly compute accuracy of ↵Even Rouault
concatenated operation when there is a conversion step
2020-10-23WKT1_ESRI export: try to export Geographic3D and Projected3D CRS when we can ↵Even Rouault
find a corresponding ellipsoidal vertical datum
2020-10-23Database: import ESRI VERTCS that uses a (geodetic) datum to express ↵Even Rouault
ellipsoidal height
2020-10-23WKT1_ESRI export: generate VERTCS[...,DATUM[...,SPHEROID[]] syntax when ↵Even Rouault
ellipsoidal height is found
2020-10-22WKT1_ESRI export: export CompoundCRS as PROJCS[...],VERTCS[...] or ↵Even Rouault
GEOGCS[...],VERTCS[...]
2020-10-22WKT parser: accept ESRI VERTCS[...,DATUM[...,SPHEROID[]] syntax to express ↵Even Rouault
ellipsoidal heights
2020-10-22WKT parser: accept implicit compoundCRS from ESRI WKT, like ↵Even Rouault
"PROJCS[...],VERTCS[...]"
2020-10-22WKTParser::createFromWKT(): minor adjustement for DATUM[],PRIMEM[] constructsEven Rouault
The WKT parser on the second part was called with "RIMEM[...]" (leading P skipped), which has no visible consequence, as we didn't care about the actual value of the keyword due to how we used it. But this is better fixing that. Only applies to recent master changes.
2020-10-20VerticalCRS: morph CRS and datum name using ESRI aliases on import from / ↵Even Rouault
export to WKT1:ESRI
2020-10-20Improve identification of compound CRS from ESRI WKT1, and for compound CRS ↵Even Rouault
whose result is not in the DB but whose horiz and vertical parts are known
2020-10-20projinfo: make '-q -o WKT1:ESRI' workEven Rouault
2020-10-20Orthographic projection: do not add f=0 to PROJ string if the ellipsoid is a ↵Even Rouault
sphere (fixes GDAL PDS4 tests)
2020-10-19C API: add proj_context_clone() (#2383)Alan D. Snow
Fixes #2382
2020-10-18Merge pull request #2381 from rouault/fix_1453Even Rouault
Add multi-line PROJ string export capability, and use it by default in projinfo (unless --single-line is specified) (fixes #1543)
2020-10-17CompoundCRS with ellipsoidal height: make sure the vertical axis has ↵Even Rouault
'ellipsoid height' as name and 'h' as abbreviation
2020-10-16projinfo: restrict PROJ multiline output to coordinate operations onlyEven Rouault
2020-10-16Add multi-line PROJ string export capability, and use it by default in ↵Even Rouault
projinfo (unless --single-line is specified) (fixes #1543)
2020-10-16Merge pull request #2370 from rouault/epsg10Even Rouault
Update to EPSG 10.003 and make code base robust to dealing with WKT CRS with DatumEnsemble
2020-10-11C API: add proj_dynamic_datum_get_frame_reference_epoch()Even Rouault
2020-10-11Database query: add ↵Even Rouault
AuthorityFactory::ObjectType::DYNAMIC_GEODETIC_REFERENCE_FRAME and DYNAMIC_VERTICAL_REFERENCE_FRAME, and make corresponding C API work
2020-10-11Database: add a frame_reference_epoch column in vertical_datum to be able to ↵Even Rouault
handle dynamic vertical datums, and instanciate them properly from database
2020-10-10WKT2:2019 import/export: handle DATUM (at top level object) with PRIMEMEven Rouault
This is a peculiarity of the WKT grammar. Despite ISO 19111 saying that the prime meridian is a component of the datum, in WKT, they are placed at the same level, for backward compatibility with earlier WKT versions. So handle exporting and importing that. The fix is only for situation where DATUM is the top level object (was working fine otherwise), which is a uncommon use case. And to limit the amount of issue, on export emit the prime meridian only if it is not Greenwich.
2020-10-09Merge pull request #2369 from rouault/fix_2368Even Rouault
promoteTo3D(): add a remark with the original CRS identifier (fixes #2368)
2020-10-09projinfo: fix usage formattingEven Rouault
2020-10-08promoteTo3D(): add a remark with the original CRS identifier (fixes #2368)Even Rouault
``` $ projinfo EPSG:32631 --3d WKT2:2019 string: PROJCRS["WGS 84 / UTM zone 31N", [ ...snip ] REMARK["Promoted to 3D from EPSG:32631"]] ```
2020-10-08Make GeographicCRS::is2DPartOf3D() work with DatumEnsembleEven Rouault
2020-10-08Make proj_create_crs_to_crs() / cs2cs work with CRS with DatumEnsembleEven Rouault
2020-10-08Add C API to work with datum ensembleEven Rouault
Add: - proj_crs_get_datum_ensemble() - proj_crs_get_datum_forced() - proj_datum_ensemble_get_member_count() - proj_datum_ensemble_get_accuracy() - proj_datum_ensemble_get_member() Make proj_create_geographic_crs_from_datum() and proj_create_geocentric_crs_from_datum() accept a datum ensemble.
2020-10-08createGeodeticCRS(): more DatumEnsemble compatibility in the case when ↵Even Rouault
creating from text_definition
2020-10-08Make createOperations() work with DatumEnsembleEven Rouault
2020-10-08Make CRS identification work with CRS with DatumEnsembleEven Rouault
generated by cgit v1.2.3 (git 2.25.1) at 2025-12-28 10:02:59 +0000