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/*
* Copyright (c) 2014 Bojan Savric
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/*
* The Patterson Cylindrical projection was designed by Tom Patterson, US National
* Park Service, in 2014, using Flex Projector. The polynomial equations for the
* projection were developed by Bojan Savric, Oregon State University, in
* collaboration with Tom Patterson and Bernhard Jenny, Oregon State University.
*
* Java reference algorithm implemented by Bojan Savric in Java Map Projection
* Library (a Java port of PROJ.4) in the file PattersonProjection.java.
*
* References:
* Java Map Projection Library
* https://github.com/OSUCartography/JMapProjLib
*
* Patterson Cylindrical Projection
* http://shadedrelief.com/patterson/
*
* Patterson, T., Savric, B., and Jenny, B. (2015). Cartographic Perspectives
* (No.78). Describes the projection design and characteristics, and
* developing the equations. doi:10.14714/CP78.1270
* http://dx.doi.org/10.14714/CP78.1270
*
* Port to PROJ.4 by Micah Cochran, 26 March 2016
*/
#define PJ_LIB__
#include <projects.h>
PROJ_HEAD(patterson, "Patterson Cylindrical") "\n\tCyl.";
#define K1 1.0148
#define K2 0.23185
#define K3 -0.14499
#define K4 0.02406
#define C1 K1
#define C2 (5.0 * K2)
#define C3 (7.0 * K3)
#define C4 (9.0 * K4)
#define EPS11 1.0e-11
#define MAX_Y 1.790857183
static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
XY xy = {0.0,0.0};
double phi2;
(void) P;
phi2 = lp.phi * lp.phi;
xy.x = lp.lam;
xy.y = lp.phi * (K1 + phi2 * phi2 * (K2 + phi2 * (K3 + K4 * phi2)));
return xy;
}
static LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
LP lp = {0.0,0.0};
double yc, tol, y2, f, fder;
(void) P;
yc = xy.y;
/* make sure y is inside valid range */
if (xy.y > MAX_Y) {
xy.y = MAX_Y;
} else if (xy.y < -MAX_Y) {
xy.y = -MAX_Y;
}
for (;;) { /* Newton-Raphson */
y2 = yc * yc;
f = (yc * (K1 + y2 * y2 * (K2 + y2 * (K3 + K4 * y2)))) - xy.y;
fder = C1 + y2 * y2 * (C2 + y2 * (C3 + C4 * y2));
yc -= tol = f / fder;
if (fabs(tol) < EPS11) {
break;
}
}
lp.phi = yc;
/* longitude */
lp.lam = xy.x;
return lp;
}
static void *freeup_new (PJ *P) { /* Destructor */
if (0==P)
return 0;
return pj_dealloc(P);
}
static void freeup (PJ *P) {
freeup_new (P);
return;
}
PJ *PROJECTION(patterson) {
P->es = 0.;
P->inv = s_inverse;
P->fwd = s_forward;
return P;
}
#ifndef PJ_SELFTEST
int pj_patterson_selftest (void) {return 0;}
#else
int pj_patterson_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char s_args[] = {"+proj=patterson +a=6400000 +lat_1=0.5 +lat_2=2"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY s_fwd_expect[] = {
{223402.144255274179, 113354.250397779804},
{223402.144255274179, -113354.250397779804},
{-223402.144255274179, 113354.250397779804},
{-223402.144255274179, -113354.250397779804},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP s_inv_expect[] = {
{0.00179049310978382265, 0.000882190140807953657},
{0.00179049310978382265, -0.000882190140807953657},
{-0.00179049310978382265, 0.000882190140807953657},
{-0.00179049310978382265, -0.000882190140807953657},
};
return pj_generic_selftest (0, s_args, tolerance_xy, tolerance_lp, 4, 4, fwd_in, 0, s_fwd_expect, inv_in, 0, s_inv_expect);
}
#endif
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