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 }
// 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 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 }