/// <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="res">The desired H3 resolution for the encoding.</param>
/// <param name="face">The icosahedral face containing the spherical coordinates.</param>
/// <returns>The 2D hex coordinates of the cell containing the point.</returns>
public Vec2d ToHex2d(int res, int face)
{
var v = new Vec2d();
var v3d = this.ToVec3d();
// determine the icosahedron face
face = 0;
double sqd = Vec3d._pointSquareDist(FaceIJK.faceCenterPoint[0], v3d);
for (int f = 1; f < NUM_ICOSA_FACES; f++)
{
double sqdT = Vec3d._pointSquareDist(FaceIJK.faceCenterPoint[f], v3d);
if (sqdT < sqd)
{
face = f;
sqd = sqdT;
}
}
// cos(r) = 1 - 2 * sin^2(r/2) = 1 - 2 * (sqd / 4) = 1 - sqd/2
double r = Math.Acos(1 - sqd / 2);
if (r < EPSILON)
{
v.x = v.y = 0.0;
return(v);
}
// now have face and r, now find CCW theta from CII i-axis
double theta = PositiveAngleRadians(FaceIJK.faceAxesAzRadsCII[face][0] - PositiveAngleRadians(GeoCoord._geoAzimuthRads(FaceIJK.faceCenterGeo[face], this)));
// adjust theta for Class III (odd resolutions)
if (H3Index.isResClassIII(res))
{
theta = PositiveAngleRadians(theta - M_AP7_ROT_RADS);
}
// perform gnomonic scaling of r
r = Math.Tan(r);
// scale for current resolution length u
r /= RES0_U_GNOMONIC;
for (int i = 0; i < res; i++)
{
r *= M_SQRT7;
}
// we now have (r, theta) in hex2d with theta ccw from x-axes
// convert to local x,y
v.x = r * Math.Cos(theta);
v.y = r * Math.Sin(theta);
return(v);
}
