/**

* \file CircularEngine.cpp

* \brief Implementation for GeographicLib::CircularEngine class

*

* Copyright (c) Charles Karney (2011) <charles@karney.com> and licensed under

* the MIT/X11 License. For more information, see

* http://geographiclib.sourceforge.net/

**********************************************************************/

#include <GeographicLib/CircularEngine.hpp>

namespace GeographicLib {

using namespace std;

Math::real CircularEngine::Value(bool gradp, real cl, real sl,

real& gradx, real& grady, real& gradz)

const {

gradp = _gradp && gradp;

const vector<real>& root_( SphericalEngine::root_ );

// 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 = _M; 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