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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
* https://doi.org/10.14714/CP78.1270
*
* Port to PROJ.4 by Micah Cochran, 26 March 2016
*/
#define PJ_LIB__
#include <math.h>
#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
/* Not sure at all of the appropriate number for MAX_ITER... */
#define MAX_ITER 100
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;
int i;
(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 (i = MAX_ITER; i ; --i) { /* 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;
}
}
if( i == 0 )
pj_ctx_set_errno( P->ctx, PJD_ERR_NON_CONVERGENT );
lp.phi = yc;
/* longitude */
lp.lam = xy.x;
return lp;
}
PJ *PROJECTION(patterson) {
P->es = 0.;
P->inv = s_inverse;
P->fwd = s_forward;
return P;
}
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