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| Original file line number | Diff line number | Diff line change |
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| /****************************************************************************** | ||
| * Project: PROJ.4 | ||
| * Purpose: Convert between ellipsoidal, geodetic coordinates and | ||
| * cartesian, geocentric coordinates. | ||
| * | ||
| * Formally, this functionality is also found in the PJ_geocent.c | ||
| * code. | ||
| * | ||
| * Actually, however, the PJ_geocent transformations are carried | ||
| * out in concert between 2D stubs in PJ_geocent.c and 3D code | ||
| * placed in pj_transform.c. | ||
| * | ||
| * For pipeline-style datum shifts, we do need direct access | ||
| * to the full 3D interface for this functionality. | ||
| * | ||
| * Hence this code, which may look like "just another PJ_geocent" | ||
| * but really is something substantially different. | ||
| * | ||
| * Author: Thomas Knudsen, thokn@sdfe.dk | ||
| * | ||
| ****************************************************************************** | ||
| * Copyright (c) 2016, Thomas Knudsen / SDFE | ||
| * | ||
| * Permission is hereby granted, free of charge, to any person obtaining a | ||
| * copy of this software and associated documentation files (the "Software"), | ||
| * to deal in the Software without restriction, including without limitation | ||
| * the rights to use, copy, modify, merge, publish, distribute, sublicense, | ||
| * and/or sell copies of the Software, and to permit persons to whom the | ||
| * Software is furnished to do so, subject to the following conditions: | ||
| * | ||
| * The above copyright notice and this permission notice shall be included | ||
| * in all copies or substantial portions of the Software. | ||
| * | ||
| * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS | ||
| * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | ||
| * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL | ||
| * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | ||
| * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING | ||
| * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER | ||
| * DEALINGS IN THE SOFTWARE. | ||
| *****************************************************************************/ | ||
|
|
||
| #define PJ_LIB__ | ||
| #include <projects.h> | ||
| #include <geocent.h> | ||
| #include <assert.h> | ||
| #include <stddef.h> | ||
| #include <math.h> | ||
| #include <errno.h> | ||
| PROJ_HEAD(cart, "Geodetic/cartesian conversions"); | ||
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| static void *cart_freeup (PJ *P, int errlev) { /* Destructor */ | ||
| if (0==P) | ||
| return 0; | ||
|
|
||
| if (0!=errlev) | ||
| pj_ctx_set_errno (P->ctx, errlev); | ||
|
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| if (0==P->opaque) | ||
| return pj_dealloc (P); | ||
|
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| pj_dealloc (P->opaque); | ||
| return pj_dealloc(P); | ||
| } | ||
|
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|
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| /* Adapts cart_freeup to the format defined for the PJ object */ | ||
| static void freeup (PJ *P) { | ||
| cart_freeup (P, 0); | ||
| return; | ||
| } | ||
|
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|
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| /************************************************************** | ||
| CARTESIAN / GEODETIC CONVERSIONS | ||
| *************************************************************** | ||
| This material follows: | ||
| Bernhard Hofmann-Wellenhof & Helmut Moritz: | ||
| Physical Geodesy, 2nd edition. | ||
| Springer, 2005. | ||
| chapter 5.6: Coordinate transformations | ||
| (HM, below), | ||
| and | ||
| Wikipedia: Geographic Coordinate Conversion, | ||
| https://en.m.wikipedia.org/wiki/Geographic_coordinate_conversion | ||
| (WP, below). | ||
| The cartesian-to-geodetic conversion is based on Bowring's | ||
| celebrated method: | ||
| B. R. Bowring: | ||
| Transformation from spatial to geographical coordinates | ||
| Survey Review 23(181), pp. 323-327, 1976 | ||
| (BB, below), | ||
| but could probably use some TLC from a newer and faster | ||
| algorithm: | ||
| Toshio Fukushima: | ||
| Transformation from Cartesian to Geodetic Coordinates | ||
| Accelerated by Halley’s Method | ||
| Journal of Geodesy, February 2006 | ||
| (TF, below). | ||
| These routines are probably not as robust at those in | ||
| geocent.c, at least thay haven't been through as heavy | ||
| use as their geocent sisters. Some care has been taken | ||
| to avoid singularities, but extreme cases (e.g. setting | ||
| es, the squared eccentricity, to 1), will cause havoc. | ||
| **************************************************************/ | ||
|
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|
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| /*********************************************************************/ | ||
| static double semiminor_axis (double a, double es) { | ||
| /*********************************************************************/ | ||
| return a * sqrt (1 - es); | ||
| } | ||
|
|
||
| /*********************************************************************/ | ||
| static double normal_radius_of_curvature (double a, double es, double phi) { | ||
| /*********************************************************************/ | ||
| double s = sin(phi); | ||
| if (es==0) | ||
| return a; | ||
| /* This is from WP. HM formula 2-149 gives an a,b version */ | ||
| return a / sqrt (1 - es*s*s); | ||
| } | ||
|
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|
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| /*********************************************************************/ | ||
| static double second_eccentricity_squared (double a, double es) { | ||
| /********************************************************************** | ||
| Follows the definition, e'2 = (a2-b2)/b2, but uses the identity | ||
| (a2-b2) = (a-b)(a+b), for improved numerical precision. | ||
| ***********************************************************************/ | ||
| double b = semiminor_axis (a, es); | ||
| return (a - b) * (a + b) / (b*b); | ||
| } | ||
|
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|
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| /*********************************************************************/ | ||
| static XYZ cartesian (LPZ geodetic, PJ *P) { | ||
| /*********************************************************************/ | ||
| double N, h, lam, phi, cosphi = cos(geodetic.phi); | ||
| XYZ xyz; | ||
|
|
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| N = normal_radius_of_curvature(P->a, P->es, geodetic.phi); | ||
| phi = geodetic.phi; | ||
| lam = geodetic.lam; | ||
| h = geodetic.z; | ||
|
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| /* HM formula 5-27 (z formula follows WP) */ | ||
| xyz.x = (N + h) * cosphi * cos(lam); | ||
| xyz.y = (N + h) * cosphi * sin(lam); | ||
| xyz.z = (N * (1 - P->es) + h) * sin(phi); | ||
|
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| /*********************************************************************/ | ||
| /* */ | ||
| /* For historical reasons, in proj, plane coordinates are measured */ | ||
| /* in units of the semimajor axis. Since 3D handling is grafted on */ | ||
| /* later, this is not the case for heights. And even though this */ | ||
| /* coordinate really is 3D cartesian, the z-part looks like a height */ | ||
| /* to proj. Hence, we have the somewhat unusual situation of having */ | ||
| /* a point coordinate with differing units between dimensions. */ | ||
| /* */ | ||
| /* The scaling and descaling is handled by the pj_fwd/inv functions. */ | ||
| /* */ | ||
| /*********************************************************************/ | ||
| xyz.x /= P->a; | ||
| xyz.y /= P->a; | ||
|
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| return xyz; | ||
| } | ||
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|
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| /*********************************************************************/ | ||
| static LPZ geodetic (XYZ cartesian, PJ *P) { | ||
| /*********************************************************************/ | ||
| double N, b, p, theta, c, s, e2s; | ||
| LPZ lpz; | ||
|
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| cartesian.x *= P->a; | ||
| cartesian.y *= P->a; | ||
|
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| /* Perpendicular distance from point to Z-axis (HM eq. 5-28) */ | ||
| p = hypot (cartesian.x, cartesian.y); | ||
|
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| /* Ancillary ellipsoidal parameters */ | ||
| b = semiminor_axis (P->a, P->es); | ||
| e2s = second_eccentricity_squared (P->a, P->es); | ||
|
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| /* HM eq. (5-37) */ | ||
| theta = atan2 (cartesian.z * P->a, p * b); | ||
|
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| /* HM eq. (5-36) (from BB, 1976) */ | ||
| c = cos(theta); | ||
| s = sin(theta); | ||
| lpz.phi = atan2 (cartesian.z + e2s*b*s*s*s, p - P->es*P->a*c*c*c); | ||
| lpz.lam = atan2 (cartesian.y, cartesian.x); | ||
| N = normal_radius_of_curvature (P->a, P->es, lpz.phi); | ||
|
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|
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| c = cos(lpz.phi); | ||
| if (fabs(c) < 1e-3) { | ||
| /* poleward of 89.9427 deg, we avoid division by zero */ | ||
| /* by computing the height as the cartesian z value */ | ||
| /* minus the semiminor axis length */ | ||
| lpz.z = cartesian.z - (cartesian.z > 0? b: -b); | ||
| } | ||
| else | ||
| lpz.z = p / c - N; | ||
|
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| return lpz; | ||
| } | ||
|
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|
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| /* Rather pointless, but... */ | ||
| static XY cart_forward (LP lp, PJ *P) { | ||
| TRIPLET point; | ||
| point.lp = lp; | ||
| point.lpz.z = 0; | ||
|
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| point.xyz = cartesian (point.lpz, P); | ||
| return point.xy; | ||
| } | ||
|
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| /* Rather pointless, but... */ | ||
| static LP cart_reverse (XY xy, PJ *P) { | ||
| TRIPLET point; | ||
| point.xy = xy; | ||
| point.xyz.z = 0; | ||
|
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| point.lpz = geodetic (point.xyz, P); | ||
| return point.lp; | ||
| } | ||
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| /*********************************************************************/ | ||
| PJ *PROJECTION(cart) { | ||
| /*********************************************************************/ | ||
| P->fwd3d = cartesian; /* or use cart_forward_3d, but add scaling */ | ||
| P->inv3d = geodetic; /* or use cart_reverse_3d, but add scaling */ | ||
| P->fwd = cart_forward; | ||
| P->inv = cart_reverse; | ||
| return P; | ||
| } | ||
|
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| /* selftest stub */ | ||
| int pj_cart_selftest (void) {return 0;} |
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