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CircularEngine.cpp
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/**
* \file CircularEngine.cpp
* \brief Implementation for GeographicLib::CircularEngine class
*
* Copyright (c) Charles Karney (2011) <karney@alum.mit.edu> and licensed under
* the MIT/X11 License. For more information, see
* https://geographiclib.sourceforge.io/
**********************************************************************/
#include <GeographicLib/CircularEngine.hpp>
namespace GeographicLib {
using namespace std;
Math::real CircularEngine::Value(bool gradp, real sl, real cl,
real& gradx, real& grady, real& gradz) const
{
gradp = _gradp && gradp;
const vector<real>& root( SphericalEngine::sqrttable() );
// Initialize outer sum
real vc = 0, vc2 = 0, vs = 0, vs2 = 0; // v [N + 1], v [N + 2]
// vr, vt, vl and similar w variable accumulate the sums for the
// derivatives wrt r, theta, and lambda, respectively.
real vrc = 0, vrc2 = 0, vrs = 0, vrs2 = 0; // vr[N + 1], vr[N + 2]
real vtc = 0, vtc2 = 0, vts = 0, vts2 = 0; // vt[N + 1], vt[N + 2]
real vlc = 0, vlc2 = 0, vls = 0, vls2 = 0; // vl[N + 1], vl[N + 2]
for (int m = _mM; m >= 0; --m) { // m = M .. 0
// Now Sc[m] = wc, Ss[m] = ws
// Sc'[m] = wtc, Ss'[m] = wtc
if (m) {
real v, A, B; // alpha[m], beta[m + 1]
switch (_norm) {
case FULL:
v = root[2] * root[2 * m + 3] / root[m + 1];
A = cl * v * _uq;
B = - v * root[2 * m + 5] / (root[8] * root[m + 2]) * _uq2;
break;
case SCHMIDT:
v = root[2] * root[2 * m + 1] / root[m + 1];
A = cl * v * _uq;
B = - v * root[2 * m + 3] / (root[8] * root[m + 2]) * _uq2;
break;
default:
A = B = 0;
}
v = A * vc + B * vc2 + _wc[m] ; vc2 = vc ; vc = v;
v = A * vs + B * vs2 + _ws[m] ; vs2 = vs ; vs = v;
if (gradp) {
v = A * vrc + B * vrc2 + _wrc[m]; vrc2 = vrc; vrc = v;
v = A * vrs + B * vrs2 + _wrs[m]; vrs2 = vrs; vrs = v;
v = A * vtc + B * vtc2 + _wtc[m]; vtc2 = vtc; vtc = v;
v = A * vts + B * vts2 + _wts[m]; vts2 = vts; vts = v;
v = A * vlc + B * vlc2 + m*_ws[m]; vlc2 = vlc; vlc = v;
v = A * vls + B * vls2 - m*_wc[m]; vls2 = vls; vls = v;
}
} else {
real A, B, qs;
switch (_norm) {
case FULL:
A = root[3] * _uq; // F[1]/(q*cl) or F[1]/(q*sl)
B = - root[15]/2 * _uq2; // beta[1]/q
break;
case SCHMIDT:
A = _uq;
B = - root[3]/2 * _uq2;
break;
default:
A = B = 0;
}
qs = _q / SphericalEngine::scale();
vc = qs * (_wc[m] + A * (cl * vc + sl * vs ) + B * vc2);
if (gradp) {
qs /= _r;
// The components of the gradient in circular coordinates are
// r: dV/dr
// theta: 1/r * dV/dtheta
// lambda: 1/(r*u) * dV/dlambda
vrc = - qs * (_wrc[m] + A * (cl * vrc + sl * vrs) + B * vrc2);
vtc = qs * (_wtc[m] + A * (cl * vtc + sl * vts) + B * vtc2);
vlc = qs / _u * ( A * (cl * vlc + sl * vls) + B * vlc2);
}
}
}
if (gradp) {
// Rotate into cartesian (geocentric) coordinates
gradx = cl * (_u * vrc + _t * vtc) - sl * vlc;
grady = sl * (_u * vrc + _t * vtc) + cl * vlc;
gradz = _t * vrc - _u * vtc ;
}
return vc;
}
} // namespace GeographicLib
CircularEngine.hpp
Header for GeographicLib::CircularEngine class.
real
GeographicLib::Math::real real
Definition GeodSolve.cpp:28
GeographicLib::Math::real
double real
Definition Math.hpp:115
GeographicLib
Namespace for GeographicLib.
Definition Accumulator.cpp:12
std
Definition NearestNeighbor.hpp:806