/// <summary>
/// Surface area in radians^2 of spherical triangle on unit sphere.
///
/// For the math, see:
/// https://en.wikipedia.org/wiki/Spherical_trigonometry#Area_and_spherical_excess
/// </summary>
/// <param name="a">length of triangle side A in radians</param>
/// <param name="b">length of triangle side B in radians</param>
/// <param name="c">length of triangle side C in radians</param>
/// <returns>area in radians^2 of triangle on unit sphere</returns>
/// <!--
/// geoCoord.c
/// double triangleEdgeLengthsToArea
/// -->
private static decimal TriangleEdgeLengthToArea(decimal a, decimal b, decimal c)
{
decimal s = (a + b + c) / 2;
a = (s - a) / 2;
b = (s - b) / 2;
c = (s - c) / 2;
s /= 2;
return(4 * DecimalEx.ATan
(DecimalEx.Sqrt(DecimalEx.Tan(s) *
DecimalEx.Tan(a) *
DecimalEx.Tan(b) *
DecimalEx.Tan(c))));
}
/// <summary>
/// Determines the center point in spherical coordinates of a cell given by 2D
/// hex coordinates on a particular icosahedral face.
/// </summary>
/// <param name="v">The 2D hex coordinates of the cell</param>
/// <param name="face">The icosahedral face upon which the 2D hex coordinate system is centered</param>
/// <param name="res">The H3 resolution of the cell</param>
/// <param name="substrate">
/// Indicates whether or not this grid is actually a substrate
/// grid relative to the specified resolution.
/// </param>
/// <returns>The spherical coordinates of the cell center point</returns>
/// <!--
/// faceIjk.c
/// void _hex2dToGeo
/// -->
public static GeoCoord ToGeoCoord(this Vec2d v, int face, int res, int substrate)
{
// calculate (r, theta) in hex2d
decimal r = v.Magnitude;
bool bSubstrate = substrate != 0;
if (r < Constants.H3.EPSILON)
{
return(Constants.FaceIjk.FaceCenterGeo[face]);
}
decimal theta = DecimalEx.ATan2(v.Y, v.X);
// scale for current resolution length u
for (var i = 0; i < res; i++)
{
r /= Constants.FaceIjk.MSqrt7;
}
// scale accordingly if this is a substrate grid
if (substrate != 0)
{
r /= 3.0m;
if (res.IsResClassIii())
{
r /= Constants.FaceIjk.MSqrt7;
}
}
r *= Constants.H3.RES0_U_GNOMONIC;
// perform inverse gnomonic scaling of r
r = DecimalEx.ATan(r);
// adjust theta for Class III
// if a substrate grid, then it's already been adjusted for Class III
if (!bSubstrate && res.IsResClassIii())
{
theta = (theta + Constants.H3.M_AP7_ROT_RADS).NormalizeRadians();
}
// find theta as an azimuth
theta = (Constants.FaceIjk.FaceAxesAzRadsCii[face, 0] - theta).NormalizeRadians();
// now find the point at (r,theta) from the face center
return(Constants.FaceIjk.FaceCenterGeo[face]
.GetAzimuthDistancePoint(theta, r));
}
public void Test(decimal d, decimal expected, decimal tolerance)
{
tolerance = Helper.GetScaledTolerance(expected, (int)tolerance, true);
Assert.That(DecimalEx.ATan(d), Is.EqualTo(expected).Within(tolerance));
}