// longitude0, latitude0, parallel1, parallel2
public AlbersEqualAreaProjection(IDictionary <string, double> parameters)
: base(parameters)
{
var latitude0Rad = InputLatitude("latitude0");
var parallel1Rad = InputLatitude("parallel1");
var parallel2Rad = InputLatitude("parallel2");
var cosParallel1 = Math.Cos(parallel1Rad);
var sinParallel1 = Math.Sin(parallel1Rad);
_n2 = sinParallel1 + Math.Sin(parallel2Rad);
if (Math.Abs(_n2) <= MathX.Tolerance)
{
throw new ArgumentOutOfRangeException();
}
_n = _n2 / 2;
_nHalf = _n2 / 4;
var invN2 = 1 / _n2;
_invN = 2 / _n2;
_c = MathX.Square(cosParallel1) + sinParallel1 * _n2;
_cOverN2 = _c * invN2;
var a = _c - Math.Sin(latitude0Rad) * _n2;
if (a < 0)
{
throw new ArgumentOutOfRangeException();
}
_ro0 = Math.Sqrt(a) * _invN;
}
protected internal override void Unproject(double x, double y, out double latitude, out double longitude)
{
var ro = Math.Sign(_n) * Math.Sqrt(x * x + MathX.Square(_ro0 - y));
// If ro is zero or very small then latitude will be +-Pi/2 depending on the sign of f.
latitude = 2 * Math.Atan(Math.Pow(_f / ro, _nInv)) - Math.PI / 2;
longitude = MathX.Clamp(Math.PI, Math.Atan2(x, _ro0 - y) * _nInv);
}
protected internal override void Unproject(double x, double y, out double latitude, out double longitude)
{
var ros = x * x + (_ro0 - y) * (_ro0 - y);
var a = _cOverN2 - ros * _nHalf;
if (double.IsNaN(a) || Math.Abs(a) > 1 + MathX.Tolerance)
{
throw new ArgumentOutOfRangeException(paramName: string.Join(",", new [] { nameof(x), nameof(y) }));
}
latitude = Math.Asin(MathX.Clamp(1, a));
longitude = MathX.Clamp(Math.PI, MathX.Atan2(x, _ro0 - y, "x, y") * _invN);
}
protected internal override void Project(double latitude, double longitude, out double x, out double y)
{
var sinLatitude = Math.Sin(latitude);
var cosLatitude = Math.Cos(latitude);
var sinLongitude = Math.Sin(longitude);
var cosLongitude = Math.Cos(longitude);
var a = _sinFiP * sinLatitude - _cosFiP * cosLatitude * sinLongitude; // sin_fi_p
if (double.IsNaN(a) || Math.Abs(a) > 1)
{
throw new ArgumentOutOfRangeException(string.Join(",", new[] { nameof(latitude), nameof(longitude) }));
}
x = MathX.Atan2(sinLatitude / cosLatitude * _cosFiP + sinLongitude * _sinFiP, cosLongitude, "latitude, longitude");
y = MathX.Clamp(MaxY, Math.Log((1 + a) / (1 - a)) / 2); // protect against +-Infinity
}
protected internal override void Unproject(double x, double y, out double latitude, out double longitude)
{
var sinX = Math.Sin(x);
var cosX = Math.Cos(x);
var sinhY = Math.Sinh(y);
var coshY = Math.Cosh(y);
// cosh_y >= 1 by definition
var a = (_sinFiP * sinhY + _cosFiP * sinX) / coshY;
if (Math.Abs(a) > 1)
{
throw new ArgumentOutOfRangeException(string.Join(",", new [] { nameof(x), nameof(y) }));
}
latitude = Math.Asin(a);
longitude = MathX.Atan2(_sinFiP * sinX - _cosFiP * sinhY, cosX, "x, y");
}
protected internal override void Unproject(double x, double y, out double latitude, out double longitude)
{
if (x >= MaxX)
{
latitude = 0;
longitude = Math.PI / 2;
}
else if (x <= -MaxX)
{
latitude = 0;
longitude = -Math.PI / 2;
}
else
{
// 1 <= cosh(x) <= cosh(MaxX)
latitude = Math.Asin(Math.Sin(y) / Math.Cosh(x));
// In case of x=0 and y=+-Pi/2: latitude will be +-90 and longitude will be 0
longitude = MathX.Atan2(Math.Sinh(x), Math.Cos(y));
}
}
// x will be in range [-MaxX, MaxX]
// y will be in range [-Pi, Pi]
protected internal override void Project(double latitude, double longitude, out double x, out double y)
{
// North pole
if (latitude >= Math.PI / 2 - MathX.Tolerance)
{
x = 0;
y = Math.PI / 2;
return;
}
// South pole
if (latitude <= -Math.PI / 2 + MathX.Tolerance)
{
x = 0;
y = -Math.PI / 2;
return;
}
if (Math.Abs(latitude) <= MathX.Tolerance)
{
// East of India
if (Math.Abs(longitude - Math.PI / 2) <= MathX.Tolerance)
{
x = MaxX;
y = 0;
return;
}
// West of South America
if (Math.Abs(longitude + Math.PI / 2) <= MathX.Tolerance)
{
x = -MaxX;
y = 0;
return;
}
}
double b = Math.Cos(latitude) * Math.Sin(longitude);
x = MathX.Clamp(MaxX, Math.Log((1 + b) / (1 - b)) / 2);
y = Math.Atan2(Math.Tan(latitude), Math.Cos(longitude));
}
protected internal double InputLongitude(string name, double max)
{
return(MathX.InputLong(_parameters[name], max, name));
}
protected internal override void Project(double latitude, double longitude, out double x, out double y)
{
x = longitude;
y = MathX.Clamp(_maxY, Math.Log(Math.Tan(Math.PI / 4 + latitude / 2))); // protect against +-Infinity
}
