diff options
| -rw-r--r-- | docs/source/operations/projections/lcc.rst | 51 | ||||
| -rw-r--r-- | src/PJ_lcc.c | 33 | ||||
| -rw-r--r-- | test/gie/builtins.gie | 91 | ||||
| -rw-r--r-- | test/gie/more_builtins.gie | 17 |
4 files changed, 172 insertions, 20 deletions
diff --git a/docs/source/operations/projections/lcc.rst b/docs/source/operations/projections/lcc.rst index 6db2a73c..3b2032d6 100644 --- a/docs/source/operations/projections/lcc.rst +++ b/docs/source/operations/projections/lcc.rst @@ -4,6 +4,39 @@ Lambert Conformal Conic ******************************************************************************** +A Lambert Conformal Conic projection (LCC) is a conic map projection +used for aeronautical charts, portions of the State Plane Coordinate +System, and many national and regional mapping systems. It is one of +seven projections introduced by Johann Heinrich Lambert in 1772. + +It has several different forms: with one and two standard parallels +(referred to as 1SP and 2SP in EPSG guidance notes). Additionally we +provide "2SP Michigan" form which is very similar to normal 2SP, but +with a scaling factor on the ellipsoid (given as `k_0` parameter). +It is implemented as per EPSG Guidance Note 7-2 (version 54, August +2018, page 25). It is used in a few systems in the EPSG database which +justifies adding this otherwise non-standard projection. + ++---------------------+----------------------------------------------------------+ +| **Classification** | Conformal conic | ++---------------------+----------------------------------------------------------+ +| **Available forms** | Forward and inverse, spherical and elliptical projection.| +| | One or two standard parallels (1SP and 2SP). | +| | "LCC 2SP Michigan" form can be used by setting | +| | `+k_0` parameter to specify elliposid scale. | ++---------------------+----------------------------------------------------------+ +| **Defined area** | Best for regions predominantly east–west in extent and | +| | located in the middle north or south latitudes. | ++---------------------+----------------------------------------------------------+ +| **Alias** | lcc | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + .. figure:: ./images/lcc.png :width: 500 px :align: center @@ -31,3 +64,21 @@ Parameters .. include:: ../options/x_0.rst .. include:: ../options/y_0.rst + +.. option:: +k_0=<value> + + This parameter can represent two different values depending on the + form of the projection. In LCC 1SP it determines the scale factor + at natural origin. In LCC 2SP Michigan it determines the ellipsoid + scale factor. + + *Defaults to 1.0.* + +Further reading +############### + +#. `Wikipedia <https://en.wikipedia.org/wiki/Lambert_conformal_conic_projection>`_ +#. `Wolfram Mathworld <http://mathworld.wolfram.com/LambertConformalConicProjection.html>`_ +#. `John P. Snyder "Map projections: A working manual" (pp. 104-110) <https://pubs.er.usgs.gov/publication/pp1395>`_ +#. `ArcGIS documentation on "Lambert Conformal Conic" <http://desktop.arcgis.com/en/arcmap/10.3/guide-books/map-projections/lambert-conformal-conic.htm>`_ +#. `EPSG Guidance Note 7-2 (version 54, August 2018, page 25) <http://www.epsg.org/Guidancenotes.aspx>`_ diff --git a/src/PJ_lcc.c b/src/PJ_lcc.c index 34ed99cb..96aa3f2a 100644 --- a/src/PJ_lcc.c +++ b/src/PJ_lcc.c @@ -5,9 +5,9 @@ #include "proj_math.h" PROJ_HEAD(lcc, "Lambert Conformal Conic") - "\n\tConic, Sph&Ell\n\tlat_1= and lat_2= or lat_0"; + "\n\tConic, Sph&Ell\n\tlat_1= and lat_2= or lat_0, k_0="; -# define EPS10 1.e-10 +#define EPS10 1.e-10 struct pj_opaque { double phi1; @@ -15,12 +15,11 @@ struct pj_opaque { double n; double rho0; double c; - int ellips; }; static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */ - XY xy = {0.0,0.0}; + XY xy = {0., 0.}; struct pj_opaque *Q = P->opaque; double rho; @@ -31,18 +30,19 @@ static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */ } rho = 0.; } else { - rho = Q->c * (Q->ellips ? pow(pj_tsfn(lp.phi, sin(lp.phi), - P->e), Q->n) : pow(tan(M_FORTPI + .5 * lp.phi), -Q->n)); + rho = Q->c * (P->es != 0. ? + pow(pj_tsfn(lp.phi, sin(lp.phi), P->e), Q->n) : + pow(tan(M_FORTPI + .5 * lp.phi), -Q->n)); } lp.lam *= Q->n; - xy.x = P->k0 * (rho * sin( lp.lam) ); - xy.y = P->k0 * (Q->rho0 - rho * cos(lp.lam) ); + xy.x = P->k0 * (rho * sin(lp.lam)); + xy.y = P->k0 * (Q->rho0 - rho * cos(lp.lam)); return xy; } static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */ - LP lp = {0.0,0.0}; + LP lp = {0., 0.}; struct pj_opaque *Q = P->opaque; double rho; @@ -51,13 +51,13 @@ static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */ xy.y = Q->rho0 - xy.y; rho = hypot(xy.x, xy.y); - if (rho != 0.0) { + if (rho != 0.) { if (Q->n < 0.) { rho = -rho; xy.x = -xy.x; xy.y = -xy.y; } - if (Q->ellips) { + if (P->es != 0.) { lp.phi = pj_phi2(P->ctx, pow(rho / Q->c, 1./Q->n), P->e); if (lp.phi == HUGE_VAL) { proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION); @@ -78,13 +78,12 @@ static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */ PJ *PROJECTION(lcc) { double cosphi, sinphi; int secant; - struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque)); + struct pj_opaque *Q = pj_calloc(1, sizeof (struct pj_opaque)); - if (0==Q) - return pj_default_destructor (P, ENOMEM); + if (0 == Q) + return pj_default_destructor(P, ENOMEM); P->opaque = Q; - Q->phi1 = pj_param(P->ctx, P->params, "rlat_1").f; if (pj_param(P->ctx, P->params, "tlat_2").i) Q->phi2 = pj_param(P->ctx, P->params, "rlat_2").f; @@ -99,10 +98,9 @@ PJ *PROJECTION(lcc) { Q->n = sinphi = sin(Q->phi1); cosphi = cos(Q->phi1); secant = fabs(Q->phi1 - Q->phi2) >= EPS10; - if( (Q->ellips = (P->es != 0.)) ) { + if (P->es != 0.) { double ml1, m1; - P->e = sqrt(P->es); m1 = pj_msfn(sinphi, cosphi, P->es); ml1 = pj_tsfn(Q->phi1, sinphi, P->e); if (secant) { /* secant cone */ @@ -128,4 +126,3 @@ PJ *PROJECTION(lcc) { return P; } - diff --git a/test/gie/builtins.gie b/test/gie/builtins.gie index 1ee968f4..955b5b51 100644 --- a/test/gie/builtins.gie +++ b/test/gie/builtins.gie @@ -2505,11 +2505,10 @@ expect -217928.275907355 112144.329220142 accept -2 -1 expect -217928.275907355 -112144.329220142 - =============================================================================== Lambert Conformal Conic Conic, Sph&Ell - lat_1= and lat_2= or lat_0 + lat_1= and lat_2= or lat_0, k_0= =============================================================================== ------------------------------------------------------------------------------- @@ -2535,6 +2534,94 @@ expect -0.001796359 0.000904232 accept -200 -100 expect -0.001796358 -0.000904233 +------------------------------------------------------------------------------- +Tests with +k_0 (Lambert Conformal Conic 2SP Michigan). +------------------------------------------------------------------------------- +operation +proj=lcc +ellps=GRS80 +lat_1=0.5 +lat_2=2 +k_0=1.0000382 +------------------------------------------------------------------------------- +tolerance 0.1 mm +accept 2 1 +expect 222596.942614366 110664.761103214 +accept 2 -1 +expect 222765.389013083 -110537.020013748 +accept -2 1 +expect -222596.942614366 110664.761103214 +accept -2 -1 +expect -222765.389013083 -110537.020013748 + +direction inverse +accept 200 100 +expect 0.001796291 0.000904198 +accept 200 -100 +expect 0.001796290 -0.000904199 +accept -200 100 +expect -0.001796291 0.000904198 +accept -200 -100 +expect -0.001796290 -0.000904199 + + +------------------------------------------------------------------------------- +Test various corner cases, spherical projection and one standard +parallel to improve test coverage. +------------------------------------------------------------------------------- +operation +proj=lcc +ellps=GRS80 +lat_1=0.5 +lat_2=2 +------------------------------------------------------------------------------- +tolerance 0.1 mm + +accept 0 90 +expect 0 292411117.537843227 +accept 0 0 +expect 0 0 + +------------------------------------------------------------------------------- +operation +proj=lcc +ellps=sphere +lat_1=30 +lat_2=40 +------------------------------------------------------------------------------- +tolerance 0.1 mm + +accept 1 2 +expect 129391.909521100 262101.674176860 +accept 0 0 +expect 0 0 + +direction inverse + +accept 129391.909521100 262101.674176860 +expect 1 2 +accept 0 0 +expect 0 0 + +------------------------------------------------------------------------------- +operation +proj=lcc +ellps=GRS80 +lat_1=30 +------------------------------------------------------------------------------- +tolerance 0.1 mm + +accept 1 2 +expect 131833.493971117 265456.213515346 +accept 1 -2 +expect 137536.205750651 -269686.591917190 +accept -1 2 +expect -131833.493971117 265456.213515346 +accept -1 -2 +expect -137536.205750651 -269686.591917190 + +------------------------------------------------------------------------------- +operation +proj=lcc +ellps=sphere +lat_1=30 +------------------------------------------------------------------------------- +tolerance 0.1 mm + +accept 1 2 +expect 131824.206082557 267239.875053699 +accept -1 -2 +expect -137565.475967350 -271546.945608449 +accept 1 -2 +expect 137565.475967350 -271546.945608449 +accept -1 2 +expect -131824.206082557 267239.875053699 + +direction inverse + +accept 131824.206082557 267239.875053699 +expect 1 2 =============================================================================== Lambert Conformal Conic Alternative diff --git a/test/gie/more_builtins.gie b/test/gie/more_builtins.gie index 10feea70..960e5814 100644 --- a/test/gie/more_builtins.gie +++ b/test/gie/more_builtins.gie @@ -243,6 +243,23 @@ expect failure errno no_args +------------------------------------------------------------------------------- +Tests for LCC 2SP Michigan (from PJ_lcc.c) +------------------------------------------------------------------------------- +This test is taken from EPSG guidance note 7-2 (version 54, August 2018, +page 25) +------------------------------------------------------------------------------- +operation +proj=lcc +ellps=clrk66 +lat_1=44d11'N +lat_2=45d42'N +x_0=609601.2192 +lon_0=84d20'W +lat_0=43d19'N +k_0=1.0000382 +units=us-ft +------------------------------------------------------------------------------- +tolerance 5 mm +accept 83d10'W 43d45'N +expect 2308335.75 160210.48 + +direction inverse +accept 2308335.75 160210.48 +expect 83d10'W 43d45'N +------------------------------------------------------------------------------- + ------------------------------------------------------------------------------- A number of tests from PJ_helmert.c |