/Proj4/PJ_robin.c
C | 108 lines | 102 code | 2 blank | 4 comment | 15 complexity | c682333968ce57df501c64420025f135 MD5 | raw file
1#ifndef lint 2static const char SCCSID[]="@(#)PJ_robin.c 4.1 94/02/15 GIE REL"; 3#endif 4#define PJ_LIB__ 5#include "projects.h" 6PROJ_HEAD(robin, "Robinson") "\n\tPCyl., Sph."; 7#define V(C,z) (C.c0 + z * (C.c1 + z * (C.c2 + z * C.c3))) 8#define DV(C,z) (C.c1 + z * (C.c2 + C.c2 + z * 3. * C.c3)) 9/* note: following terms based upon 5 deg. intervals in degrees. */ 10static struct COEFS { 11 float c0, c1, c2, c3; 12} X[] = { 131, -5.67239e-12, -7.15511e-05, 3.11028e-06, 140.9986, -0.000482241, -2.4897e-05, -1.33094e-06, 150.9954, -0.000831031, -4.4861e-05, -9.86588e-07, 160.99, -0.00135363, -5.96598e-05, 3.67749e-06, 170.9822, -0.00167442, -4.4975e-06, -5.72394e-06, 180.973, -0.00214869, -9.03565e-05, 1.88767e-08, 190.96, -0.00305084, -9.00732e-05, 1.64869e-06, 200.9427, -0.00382792, -6.53428e-05, -2.61493e-06, 210.9216, -0.00467747, -0.000104566, 4.8122e-06, 220.8962, -0.00536222, -3.23834e-05, -5.43445e-06, 230.8679, -0.00609364, -0.0001139, 3.32521e-06, 240.835, -0.00698325, -6.40219e-05, 9.34582e-07, 250.7986, -0.00755337, -5.00038e-05, 9.35532e-07, 260.7597, -0.00798325, -3.59716e-05, -2.27604e-06, 270.7186, -0.00851366, -7.0112e-05, -8.63072e-06, 280.6732, -0.00986209, -0.000199572, 1.91978e-05, 290.6213, -0.010418, 8.83948e-05, 6.24031e-06, 300.5722, -0.00906601, 0.000181999, 6.24033e-06, 310.5322, 0.,0.,0. }, 32Y[] = { 330, 0.0124, 3.72529e-10, 1.15484e-09, 340.062, 0.0124001, 1.76951e-08, -5.92321e-09, 350.124, 0.0123998, -7.09668e-08, 2.25753e-08, 360.186, 0.0124008, 2.66917e-07, -8.44523e-08, 370.248, 0.0123971, -9.99682e-07, 3.15569e-07, 380.31, 0.0124108, 3.73349e-06, -1.1779e-06, 390.372, 0.0123598, -1.3935e-05, 4.39588e-06, 400.434, 0.0125501, 5.20034e-05, -1.00051e-05, 410.4968, 0.0123198, -9.80735e-05, 9.22397e-06, 420.5571, 0.0120308, 4.02857e-05, -5.2901e-06, 430.6176, 0.0120369, -3.90662e-05, 7.36117e-07, 440.6769, 0.0117015, -2.80246e-05, -8.54283e-07, 450.7346, 0.0113572, -4.08389e-05, -5.18524e-07, 460.7903, 0.0109099, -4.86169e-05, -1.0718e-06, 470.8435, 0.0103433, -6.46934e-05, 5.36384e-09, 480.8936, 0.00969679, -6.46129e-05, -8.54894e-06, 490.9394, 0.00840949, -0.000192847, -4.21023e-06, 500.9761, 0.00616525, -0.000256001, -4.21021e-06, 511., 0.,0.,0 }; 52#define FXC 0.8487 53#define FYC 1.3523 54#define C1 11.45915590261646417544 55#define RC1 0.08726646259971647884 56#define NODES 18 57#define ONEEPS 1.000001 58#define EPS 1e-8 59FORWARD(s_forward); /* spheroid */ 60 int i; 61 double dphi; 62 63 i = floor((dphi = fabs(lp.phi)) * C1); 64 if (i >= NODES) i = NODES - 1; 65 dphi = RAD_TO_DEG * (dphi - RC1 * i); 66 xy.x = V(X[i], dphi) * FXC * lp.lam; 67 xy.y = V(Y[i], dphi) * FYC; 68 if (lp.phi < 0.) xy.y = -xy.y; 69 return (xy); 70} 71INVERSE(s_inverse); /* spheroid */ 72 int i; 73 double t, t1; 74 struct COEFS T; 75 76 lp.lam = xy.x / FXC; 77 lp.phi = fabs(xy.y / FYC); 78 if (lp.phi >= 1.) { /* simple pathologic cases */ 79 if (lp.phi > ONEEPS) I_ERROR 80 else { 81 lp.phi = xy.y < 0. ? -HALFPI : HALFPI; 82 lp.lam /= X[NODES].c0; 83 } 84 } else { /* general problem */ 85 /* in Y space, reduce to table interval */ 86 for (i = floor(lp.phi * NODES);;) { 87 if (Y[i].c0 > lp.phi) --i; 88 else if (Y[i+1].c0 <= lp.phi) ++i; 89 else break; 90 } 91 T = Y[i]; 92 /* first guess, linear interp */ 93 t = 5. * (lp.phi - T.c0)/(Y[i+1].c0 - T.c0); 94 /* make into root */ 95 T.c0 -= lp.phi; 96 for (;;) { /* Newton-Raphson reduction */ 97 t -= t1 = V(T,t) / DV(T,t); 98 if (fabs(t1) < EPS) 99 break; 100 } 101 lp.phi = (5 * i + t) * DEG_TO_RAD; 102 if (xy.y < 0.) lp.phi = -lp.phi; 103 lp.lam /= V(X[i], t); 104 } 105 return (lp); 106} 107FREEUP; if (P) pj_dalloc(P); } 108ENTRY0(robin) P->es = 0.; P->inv = s_inverse; P->fwd = s_forward; ENDENTRY(P)