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cass: fix forward computation of easting (fixes #3432), and use itera…
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…tive generic inversion to make GIGS 5108 roundtripping tests succeed

The error on the sign after "nu * A * (1. - A2 * T * (C1 ...") dates
back to PROJ origins. All other independent implementations (Apache SIS
cf
/~https://github.com/apache/sis/blob/a04bd4b29816c91fc4dfc66135b8de5e962933a0/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/CassiniSoldner.java,
CSMAP cf
/~https://github.com/normanb/CS-Map/blob/1d8f2db7f13194a99dc218d4cd91754c64a2a774/Source/CS_csini.c)
use the same formulas as EPSG guidance note which is consistent with
Snyder's Map projections - A working manual). So align on them, so that
everyone is consistent (and hopefully right).

While doing it, I've modified the inverse method to use the generic
inversion method to improve its accuracy, which make it possible to
enable the 5108.gie tests that were previously failing on the 1000
iterations roundtripping.
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@rouault
rouault committed Nov 4, 2022
1 parent 4586998 commit c34f791
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Showing 8 changed files with 48 additions and 29 deletions.
4 changes: 2 additions & 2 deletions src/generic_inverse.cpp
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Expand Up @@ -41,7 +41,7 @@
*
* Starts with initial guess provided by user in lpInitial
*/
PJ_LP pj_generic_inverse_2d(PJ_XY xy, PJ *P, PJ_LP lpInitial) {
PJ_LP pj_generic_inverse_2d(PJ_XY xy, PJ *P, PJ_LP lpInitial, double deltaXYTolerance) {
PJ_LP lp = lpInitial;
double deriv_lam_X = 0;
double deriv_lam_Y = 0;
Expand All @@ -51,7 +51,7 @@ PJ_LP pj_generic_inverse_2d(PJ_XY xy, PJ *P, PJ_LP lpInitial) {
PJ_XY xyApprox = P->fwd(lp, P);
const double deltaX = xyApprox.x - xy.x;
const double deltaY = xyApprox.y - xy.y;
if (fabs(deltaX) < 1e-10 && fabs(deltaY) < 1e-10) {
if (fabs(deltaX) < deltaXYTolerance && fabs(deltaY) < deltaXYTolerance) {
return lp;
}

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2 changes: 1 addition & 1 deletion src/proj_internal.h
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Expand Up @@ -875,7 +875,7 @@ void pj_clear_vgridshift_knowngrids_cache();

void pj_clear_sqlite_cache();

PJ_LP pj_generic_inverse_2d(PJ_XY xy, PJ *P, PJ_LP lpInitial);
PJ_LP pj_generic_inverse_2d(PJ_XY xy, PJ *P, PJ_LP lpInitial, double deltaXYTolerance);



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11 changes: 8 additions & 3 deletions src/projections/adams.cpp
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Expand Up @@ -296,7 +296,9 @@ static PJ_LP adams_inverse(PJ_XY xy, PJ *P)
lp.lam = fabs(lp.phi) >= M_HALFPI ? 0 :
std::max(std::min(xy.x / 2.62205760 / cos(lp.phi), 1.0), -1.0) * M_PI;

return pj_generic_inverse_2d(xy, P, lp);

constexpr double deltaXYTolerance = 1e-10;
return pj_generic_inverse_2d(xy, P, lp, deltaXYTolerance);
}

static PJ_LP peirce_q_square_inverse(PJ_XY xy, PJ *P)
Expand Down Expand Up @@ -339,7 +341,9 @@ static PJ_LP peirce_q_square_inverse(PJ_XY xy, PJ *P)
}
else /* if( xy.x <= 0 && xy.y <= 0 ) */
lp.lam = -M_PI / 2;
return pj_generic_inverse_2d(xy, P, lp);

constexpr double deltaXYTolerance = 1e-10;
return pj_generic_inverse_2d(xy, P, lp, deltaXYTolerance);
}

static PJ_LP peirce_q_diamond_inverse(PJ_XY xy, PJ *P)
Expand Down Expand Up @@ -382,7 +386,8 @@ static PJ_LP peirce_q_diamond_inverse(PJ_XY xy, PJ *P)
lp.phi = -M_PI / 4;
}

return pj_generic_inverse_2d(xy, P, lp);
constexpr double deltaXYTolerance = 1e-10;
return pj_generic_inverse_2d(xy, P, lp, deltaXYTolerance);
}

static PJ *setup(PJ *P, projection_type mode) {
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16 changes: 8 additions & 8 deletions src/projections/cass.cpp
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Expand Up @@ -43,7 +43,7 @@ static PJ_XY cass_e_forward (PJ_LP lp, PJ *P) { /* Ellipsoidal, forward
const double A2 = A * A;

xy.x = nu * A * (1. - A2 * T *
(C1 - (8. - T + 8. * C) * A2 * C2));
(C1 + (8. - T + 8. * C) * A2 * C2));
xy.y = M - Q->m0 + nu * tanphi * A2 *
(.5 + (5. - T + 6. * C) * A2 * C3);
if( Q->hyperbolic )
Expand Down Expand Up @@ -82,13 +82,13 @@ static PJ_LP cass_e_inverse (PJ_XY xy, PJ *P) { /* Ellipsoidal, inverse
lp.lam = D * (1. + T1 * D2 *
(-C4 + (1. + 3. * T1) * D2 * C5)) / cos (phi1);

if( Q->hyperbolic )
{
// EPSG guidance note 7-2 suggests a custom approximation for the
// 'Vanua Levu 1915 / Vanua Levu Grid' case, but better use the
// generic inversion method
lp = pj_generic_inverse_2d(xy, P, lp);
}
// EPSG guidance note 7-2 suggests a custom approximation for the
// 'Vanua Levu 1915 / Vanua Levu Grid' case, but better use the
// generic inversion method
// Actually use it in the non-hyperbolic case. It enables to make the
// 5108.gie roundtripping tests to success, with at most 2 iterations.
constexpr double deltaXYTolerance = 1e-12;
lp = pj_generic_inverse_2d(xy, P, lp, deltaXYTolerance);

return lp;
}
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3 changes: 2 additions & 1 deletion src/projections/wink2.cpp
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Expand Up @@ -48,7 +48,8 @@ static PJ_LP wink2_s_inverse(PJ_XY xy, PJ *P)
lpInit.phi = xy.y;
lpInit.lam = xy.x;

return pj_generic_inverse_2d(xy, P, lpInit);
constexpr double deltaXYTolerance = 1e-10;
return pj_generic_inverse_2d(xy, P, lpInit, deltaXYTolerance);
}


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2 changes: 1 addition & 1 deletion test/CMakeLists.txt
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Expand Up @@ -80,7 +80,7 @@ proj_add_gie_test("GIGS-5104" "gigs/5104.gie")
proj_add_gie_test("GIGS-5105.2" "gigs/5105.2.gie")
proj_add_gie_test("GIGS-5106" "gigs/5106.gie")
proj_add_gie_test("GIGS-5107" "gigs/5107.gie")
#proj_add_gie_test("GIGS-5108" "gigs/5108.gie")
proj_add_gie_test("GIGS-5108" "gigs/5108.gie")
proj_add_gie_test("GIGS-5109" "gigs/5109.gie")
#proj_add_gie_test("GIGS-5110" "gigs/5110.gie")
proj_add_gie_test("GIGS-5111.1" "gigs/5111.1.gie")
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14 changes: 13 additions & 1 deletion test/gie/builtins.gie
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Expand Up @@ -850,6 +850,18 @@ expect -0.001790493 0.000895247
accept -200 -100
expect -0.001790493 -0.000895247

-------------------------------------------------------------------------------
# test point from EPSG Guidance Note 7.2
operation +proj=cass +lat_0=10.4416666666667 +lon_0=-61.3333333333333 \
+x_0=86501.46392052 +y_0=65379.0134283 \
+a=6378293.64520876 +b=6356617.98767984 +to_meter=0.201166195164
-------------------------------------------------------------------------------

tolerance 0.1 mm
accept -62 10
expect 66644.94040882 82536.21873655
roundtrip 1

-------------------------------------------------------------------------------
# Hyperbolic variant: test point from EPSG Guidance Note 7.2
operation +proj=cass +hyperbolic +a=6378306.376305601 +rf=293.466307 \
Expand All @@ -859,7 +871,7 @@ operation +proj=cass +hyperbolic +a=6378306.376305601 +rf=293.466307 \

tolerance 0.1 mm
accept 179.99433652777776 -16.841456527777776
expect 16015.289017555102 13369.660053668682
expect 16015.28901692 13369.66005367
roundtrip 1

===============================================================================
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25 changes: 13 additions & 12 deletions test/gigs/5108.gie.failing → test/gigs/5108.gie
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Expand Up @@ -4,18 +4,19 @@ Test 5108, Cassini-Soldner, v2-0_2011-06-28.

--------------------------------------------------------------------------------

# GDM2000
<4742> +proj=longlat +ellps=GRS80 <>
<gie-strict>

# GDM2000 / Johor Grid
<3377> +proj=cass +lat_0=2.121679744444445 +lon_0=103.4279362361111 +x_0=-14810.562 +y_0=8758.32 +ellps=GRS80 +units=m <>
use_proj4_init_rules true

# GDM2000
# <4742> +proj=longlat +ellps=GRS80 <>

<gie>
# GDM2000 / Johor Grid
# <3377> +proj=cass +lat_0=2.121679744444445 +lon_0=103.4279362361111 +x_0=-14810.562 +y_0=8758.32 +ellps=GRS80 +units=m <>

--------------------------------------------------------------------------------
operation +proj=pipeline
+step +init=epsg:4742 +inv
operation +proj=pipeline \
+step +init=epsg:4742 +inv \
+step +init=epsg:3377
--------------------------------------------------------------------------------
tolerance 0.05 m
Expand Down Expand Up @@ -87,8 +88,8 @@ accept 104 5
expect 48630.563 327067.097

--------------------------------------------------------------------------------
operation +proj=pipeline
+step +init=epsg:3377 +inv
operation +proj=pipeline \
+step +init=epsg:3377 +inv \
+step +init=epsg:4742
--------------------------------------------------------------------------------
tolerance 0.05 m
Expand Down Expand Up @@ -160,8 +161,8 @@ accept 48630.563 327067.097
expect 104 5

--------------------------------------------------------------------------------
operation +proj=pipeline
+step +init=epsg:4742 +inv
operation +proj=pipeline \
+step +init=epsg:4742 +inv \
+step +init=epsg:3377
--------------------------------------------------------------------------------
tolerance 0.006 m
Expand Down Expand Up @@ -232,4 +233,4 @@ tolerance 0.006 m
accept 104 5
roundtrip 1000

</gie>
</gie-strict>

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