inline
void
Spherical::Set( )
{
m_longitude.Set( 0. );
m_latitude.Set( 0. );
m_distance = 0.;
}
void
Geodetic::Set( const Point3D & rectangular )
{
//Explanatory Supplement (4.22-11 to 4.22-24)
double X = rectangular.X();
double Y = rectangular.Y();
double Z = rectangular.Z();
double a = radius;
double b = a - flattening * a;
if ( Z < 0.)
b = -b;
if ( (X == 0.) && (Y == 0.) )
{
m_longitude.Set( 0. );
m_latitude.Set( 0. );
m_height = Z - b;
if ( m_height < 0. )
m_height = - m_height;
return;
}
else
m_longitude = ArcTan( Y, X );
if ( Z == 0.)
{
m_latitude.Set( 0. );
m_height.Set( r - radius );
return;
}
double r = std::sqrt( X * X + Y * Y );
double aSqr = a * a;
double bSqr = b * b;
double E = (b * Z - (aSqr - bSqr)) / (a * r);
double ESqr = E * E;
double F = (b * Z + (aSqr + bSqr)) / (a * r);
double P = (4./3.) * (E * F + 1.);
double Q = 2. * (ESqr - F * F);
double D = P * P * P + Q * Q;
double sqrtD = std::sqrt( D );
double v = std::pow( (sqrtD - Q), (1./3.) )
- std::pow( (sqrtD + Q), (1./3.) );
const double epsilon = 1.0;
if ( (std::fabs( Z ) < epsilon ) || (std::fabs( r ) < epsilon) )
v = - (v * v * v + 2. * Q) / (3. * P);
double G = 0.5 * (std::sqrt( ESqr + v ) + E);
double t = std::sqrt( G * G + (F - v * G) / (G + G - E) ) - G;
m_latitude = ArcTan( (a * (1. - t * t)), (2. * b * t) );
m_height = (r - a * t) * m_latitude.Cos( )
+ (Z - b) * m_latitude.Sin( );
}
inline
void
Polar::Set( )
{
m_bearing.Set( );
m_distance = 0.;
}