/// <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>
/// <param name="face">The icosahedral face containing the spherical coordinates.</param>
/// <param name="v">The 2D hex coordinates of the cell containing the point.</param>
/// <!-- Based off 3.1.1 -->
public static void _geoToHex2d(GeoCoord g, int res, ref int face, ref Vec2d v)
{
Vec3d v3d = new Vec3d();
Vec3d._geoToVec3d(g, ref v3d);
// determine the icosahedron face
face = 0;
double sqd = Vec3d._pointSquareDist(faceCenterPoint[0], v3d);
for (int f = 1; f < Constants.NUM_ICOSA_FACES; f++)
{
double sqdT = Vec3d._pointSquareDist(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 < Constants.EPSILON)
{
v.x = 0.0;
v.y = 0.0;
return;
}
// now have face and r, now find CCW theta from CII i-axis
double theta =
GeoCoord._posAngleRads(faceAxesAzRadsCII[face, 0] -
GeoCoord._posAngleRads(GeoCoord._geoAzimuthRads(faceCenterGeo[face], g)));
// adjust theta for Class III (odd resolutions)
if (H3Index.isResClassIII(res))
{
theta = GeoCoord._posAngleRads(theta - Constants.M_AP7_ROT_RADS);
}
// perform gnomonic scaling of r
r = Math.Tan(r);
// scale for current resolution length u
r /= Constants.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);
}
/// <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>
/// <param name="g">The spherical coordinates of the cell center point.</param>
/// <!-- Based off 3.1.1 -->
public static void _hex2dToGeo(ref Vec2d v, int face, int res, int substrate, ref GeoCoord g)
{
// calculate (r, theta) in hex2d
double r = Vec2d._v2dMag(v);
if (r < Constants.EPSILON)
{
g = faceCenterGeo[face];
return;
}
double theta = Math.Atan2(v.y, v.x);
// scale for current resolution length u
for (int i = 0; i < res; i++)
{
r /= M_SQRT7;
}
// scale accordingly if this is a substrate grid
if (substrate > 0)
{
r /= 3.0;
if (H3Index.isResClassIII(res))
{
r /= M_SQRT7;
}
}
r *= Constants.RES0_U_GNOMONIC;
// perform inverse gnomonic scaling of r
r = Math.Atan(r);
// adjust theta for Class III
// if a substrate grid, then it's already been adjusted for Class III
if (substrate == 0 && H3Index.isResClassIII(res))
{
theta = GeoCoord._posAngleRads(theta + Constants.M_AP7_ROT_RADS);
}
// find theta as an azimuth
theta = GeoCoord._posAngleRads(faceAxesAzRadsCII[face, 0] - theta);
// now find the point at (r,theta) from the face center
GeoCoord._geoAzDistanceRads(ref faceCenterGeo[face], theta, r, ref g);
}