/// <summary>
/// Encodes a coordinate on the sphere to the corresponding icosahedral face and
/// containing 2D hex coordinates relative to that face center.
/// </summary>
/// <param name="g">The spherical coordinates to encode.</param>
/// <param name="res">The desired H3 resolution for the encoding.</param>
/// <returns>
/// Tuple
/// Item1: The resulting face
/// Item2: The 2D hex coordinates of the cell containing the point.
/// </returns>
/// <!--
/// faceijk.c
/// void _geoToHex2d
/// -->
public static (int, Vec2d) ToHex2d(this GeoCoord g, int res)
{
var v3d = g.ToVec3d();
var newFace = 0;
// determine the icosahedron face
decimal sqd = v3d.PointSquareDistance(Constants.FaceIjk.FaceCenterPoint[0]);
for (var f = 1; f < Constants.H3.NUM_ICOSA_FACES; f++)
{
decimal sqdT = v3d.PointSquareDistance(Constants.FaceIjk.FaceCenterPoint[f]);
if (!(sqdT < sqd))
{
continue;
}
newFace = f;
sqd = sqdT;
}
// cos(r) = 1 - 2 * sin^2(r/2) = 1 - 2 * (sqd / 4) = 1 - sqd/2
decimal r = DecimalEx.ACos(1 - sqd / 2.0m);
if (r < Constants.H3.EPSILON)
{
return(newFace, new Vec2d());
}
// now have face and r, now find CCW theta from CII i-axis
decimal theta =
(
Constants.FaceIjk.FaceAxesAzRadsCii[newFace, 0] -
Constants.FaceIjk.FaceCenterGeo[newFace].AzimuthRadiansTo(g)
.NormalizeRadians()
).NormalizeRadians();
// adjust theta for Class III (odd resolutions)
if (res.IsResClassIii())
{
theta = (theta - Constants.H3.M_AP7_ROT_RADS).NormalizeRadians();
}
// perform gnomonic scaling of r
r = DecimalEx.Tan(r);
// scale for current resolution length u
r /= Constants.H3.RES0_U_GNOMONIC;
for (var i = 0; i < res; i++)
{
r *= Constants.FaceIjk.MSqrt7;
}
// we now have (r, theta) in hex2d with theta ccw from x-axes
// convert to local x,y
return(newFace,
new Vec2d
(
r * DecimalEx.Cos(theta),
r * DecimalEx.Sin(theta)
));
}
/// <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))));
}
public void findTan()
{
Console.Write("Enter the number:\n");
string stringConversions = Console.ReadLine();
if (stringConversions.Contains("/"))
{
Fract.Fraction(stringConversions);
FractionConverted = Fract.Fraction(stringConversions);
Answer = DecimalEx.Tan(decimalConverted);
Console.WriteLine($"Your answer is {Answer}.\n");
}
else
{
decimalConverted = Decimal.Parse(stringConversions);
Answer = DecimalEx.Tan(decimalConverted);
Console.WriteLine($"Your answer is {Answer}.\n");
}
}