/// <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);
}
/// <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="isSubstrate">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>
public static GeoCoord FromHex2d(Vec2d v, int face, int res, bool isSubstrate)
{
var g = new GeoCoord();
// calculate (r, theta) in hex2d
double r = Vec2d._v2dMag(v);
if (r < EPSILON)
{
return(FaceIJK.faceCenterGeo[face]);
}
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 (isSubstrate)
{
r /= 3.0;
if (H3Index.isResClassIII(res))
{
r /= M_SQRT7;
}
}
r *= 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 (!isSubstrate && H3Index.isResClassIII(res))
{
theta = PositiveAngleRadians(theta + M_AP7_ROT_RADS);
}
// find theta as an azimuth
theta = PositiveAngleRadians(FaceIJK.faceAxesAzRadsCII[face][0] - theta);
// now find the point at (r,theta) from the face center
g = GeoCoord._geoAzDistanceRads(FaceIJK.faceCenterGeo[face], theta, r);
return(g);
}
/// <summary>
/// Generates the cell boundary in spherical coordinates for a cell given by a
/// FaceIJK address at a specified resolution.
/// </summary>
/// <param name="res">The H3 resolution of the cell.</param>
/// <param name="isPentagon">Whether or not the cell is a pentagon.</param>
/// <returns>The spherical coordinates of the cell boundary.</returns>
public GeoBoundary ToGeoBoundary(int res, bool isPentagon)
{
if (isPentagon)
{
return(PentagonToGeoBoundary(res));
}
var g = new GeoBoundary();
// the vertexes of an origin-centered cell in a Class II resolution on a
// substrate grid with aperture sequence 33r. The aperture 3 gets us the
// vertices, and the 3r gets us back to Class II.
// vertices listed ccw from the i-axes
var vertsCII = new CoordIJK[NUM_HEX_VERTS]
{
new CoordIJK(2, 1, 0), // 0
new CoordIJK(1, 2, 0), // 1
new CoordIJK(0, 2, 1), // 2
new CoordIJK(0, 1, 2), // 3
new CoordIJK(1, 0, 2), // 4
new CoordIJK(2, 0, 1) // 5
};
// the vertexes of an origin-centered cell in a Class III resolution on a
// substrate grid with aperture sequence 33r7r. The aperture 3 gets us the
// vertices, and the 3r7r gets us to Class II.
// vertices listed ccw from the i-axes
var vertsCIII = new CoordIJK[NUM_HEX_VERTS]
{
new CoordIJK(5, 4, 0), // 0
new CoordIJK(1, 5, 0), // 1
new CoordIJK(0, 5, 4), // 2
new CoordIJK(0, 1, 5), // 3
new CoordIJK(4, 0, 5), // 4
new CoordIJK(5, 0, 1) // 5
};
// get the correct set of substrate vertices for this resolution
var verts = H3Index.isResClassIII(res) ? vertsCIII : vertsCII;
// adjust the center point to be in an aperture 33r substrate grid
// these should be composed for speed
FaceIJK centerIJK = this;
centerIJK.coord = centerIJK.coord._downAp3()._downAp3r();
// if res is Class III we need to add a cw aperture 7 to get to
// icosahedral Class II
int adjRes = res;
if (H3Index.isResClassIII(res))
{
centerIJK.coord = centerIJK.coord._downAp7r();
adjRes++;
}
// The center point is now in the same substrate grid as the origin
// cell vertices. Add the center point substate coordinates
// to each vertex to translate the vertices to that cell.
var fijkVerts = new FaceIJK[NUM_HEX_VERTS];
for (int v = 0; v < NUM_HEX_VERTS; v++)
{
fijkVerts[v].face = centerIJK.face;
fijkVerts[v].coord = (centerIJK.coord + verts[v]).Normalize();
}
// convert each vertex to lat/lon
// adjust the face of each vertex as appropriate and introduce
// edge-crossing vertices as needed
g.numVerts = 0;
int lastFace = -1;
int lastOverage = 0; // 0: none; 1: edge; 2: overage
for (int vert = 0; vert < NUM_HEX_VERTS + 1; vert++)
{
int v = vert % NUM_HEX_VERTS;
FaceIJK fijk = fijkVerts[v];
int overage = AdjustOverageClassII(adjRes, false, true);
/*
* Check for edge-crossing. Each face of the underlying icosahedron is a
* different projection plane. So if an edge of the hexagon crosses an
* icosahedron edge, an additional vertex must be introduced at that
* intersection point. Then each half of the cell edge can be projected
* to geographic coordinates using the appropriate icosahedron face
* projection. Note that Class II cell edges have vertices on the face
* edge, with no edge line intersections.
*/
if (H3Index.isResClassIII(res) && vert > 0 && fijk.face != lastFace && lastOverage != 1)
{
// find hex2d of the two vertexes on original face
int lastV = (v + 5) % NUM_HEX_VERTS;
var orig2d0 = fijkVerts[lastV].coord.ToHex2d();
var orig2d1 = fijkVerts[v].coord.ToHex2d();
// find the appropriate icosa face edge vertexes
int maxDim = maxDimByCIIres[adjRes];
var v0 = new Vec2d(3.0 * maxDim, 0.0);
var v1 = new Vec2d(-1.5 * maxDim, 3.0 * M_SQRT3_2 * maxDim);
var v2 = new Vec2d(-1.5 * maxDim, -3.0 * M_SQRT3_2 * maxDim);
int face2 = (lastFace == centerIJK.face) ? fijk.face : lastFace;
Vec2d edge0;
Vec2d edge1;
switch (adjacentFaceDir[centerIJK.face][face2])
{
case IJ:
edge0 = v0;
edge1 = v1;
break;
case JK:
edge0 = v1;
edge1 = v2;
break;
case KI:
default:
//assert(adjacentFaceDir[centerIJK.face][face2] == KI);
edge0 = v2;
edge1 = v0;
break;
}
// find the intersection and add the lat/lon point to the result
var inter = new Vec2d(0, 0);
Vec2d._v2dIntersect(orig2d0, orig2d1, edge0, edge1, ref inter);
/*
* If a point of intersection occurs at a hexagon vertex, then each
* adjacent hexagon edge will lie completely on a single icosahedron
* face, and no additional vertex is required.
*/
bool isIntersectionAtVertex = Vec2d._v2dEquals(orig2d0, inter) || Vec2d._v2dEquals(orig2d1, inter);
if (!isIntersectionAtVertex)
{
g.verts[g.numVerts] = GeoCoord.FromHex2d(inter, centerIJK.face, adjRes, true);
g.numVerts++;
}
}
// convert vertex to lat/lon and add to the result
// vert == NUM_HEX_VERTS is only used to test for possible intersection
// on last edge
if (vert < NUM_HEX_VERTS)
{
var vec = fijk.coord.ToHex2d();
g.verts[g.numVerts] = GeoCoord.FromHex2d(vec, fijk.face, adjRes, true);
g.numVerts++;
}
lastFace = fijk.face;
lastOverage = overage;
}
return(g);
}
/// <summary>
/// Convert an FaceIJK address to the corresponding H3Index.
/// </summary>
/// <param name="res">The cell resolution.</param>
/// <returns>The encoded H3Index (or 0 on failure).</returns>
public H3Index ToH3Index(int res)
{
// initialize the index
var h = new H3Index(H3Index.H3_INIT);
h.Mode = H3_HEXAGON_MODE;
h.Resolution = res;
// check for res 0/base cell
if (res == 0)
{
if (coord.i > MAX_FACE_COORD || coord.j > MAX_FACE_COORD || coord.k > MAX_FACE_COORD)
{
return(H3Index.H3_INVALID_INDEX); // out of range input
}
// TODO: fix
h.BaseCell = this.ToBaseCell();
return(h);
}
// we need to find the correct base cell FaceIJK for this H3 index;
// start with the passed in face and resolution res ijk coordinates
// in that face's coordinate system
//var fijkBC = new FaceIJK(this);
var fijkBC = new FaceIJK(this);
// build the H3Index from finest res up
// adjust r for the fact that the res 0 base cell offsets the indexing digits
//CoordIJK* ijk = &fijkBC.coord;
var ijk = fijkBC.coord;
for (int r = res - 1; r >= 0; r--)
{
var lastIJK = new CoordIJK(ijk);
CoordIJK lastCenter;
if (H3Index.isResClassIII(r + 1))
{
// rotate ccw
ijk = ijk._upAp7();
lastCenter = ijk._downAp7();
}
else
{
// rotate cw
ijk = ijk._upAp7r();
lastCenter = ijk._downAp7r();
}
var normalDiff = (lastIJK - lastCenter).Normalize();
h.SetIndexDigit(r + 1, normalDiff.UnitIJKToDigit());
}
// fijkBC should now hold the IJK of the base cell in the
// coordinate system of the current face
if (fijkBC.coord.i > MAX_FACE_COORD || fijkBC.coord.j > MAX_FACE_COORD || fijkBC.coord.k > MAX_FACE_COORD)
{
return(H3Index.H3_INVALID_INDEX); // out of range input
}
// TODO: check, added this check for debugging since it leads to invalid negative array indexes
//if (fijkBC.coord.i < 0 || fijkBC.coord.j < 0 || fijkBC.coord.k < 0)
// return H3Index.H3_INVALID_INDEX; // out of range input
// lookup the correct base cell
var baseCell = fijkBC.ToBaseCell();
h.BaseCell = baseCell;
// rotate if necessary to get canonical base cell orientation
// for this base cell
int numRots = _faceIjkToBaseCellCCWrot60(fijkBC);
if (_isBaseCellPentagon(baseCell))
{
// force rotation out of missing k-axes sub-sequence
if ((int)h._h3LeadingNonZeroDigit() == (int)Direction.K_AXES_DIGIT)
{
// check for a cw/ccw offset face; default is ccw
if (_baseCellIsCwOffset(baseCell, fijkBC.face))
{
h = h._h3Rotate60cw();
}
else
{
h = h._h3Rotate60ccw();
}
}
for (int i = 0; i < numRots; i++)
{
h = h._h3RotatePent60ccw();
}
}
else
{
for (int i = 0; i < numRots; i++)
{
h = h._h3Rotate60ccw();
}
}
return(h);
}
/// <summary>
/// Generates the cell boundary in spherical coordinates for a pentagonal cell
/// given by a FaceIJK address at a specified resolution.
/// </summary>
/// <param name="res">The H3 resolution of the cell.</param>
/// <returns>The spherical coordinates of the cell boundary.</returns>
public GeoBoundary PentagonToGeoBoundary(int res)
{
var g = new GeoBoundary();
// the vertexes of an origin-centered pentagon in a Class II resolution on a
// substrate grid with aperture sequence 33r. The aperture 3 gets us the
// vertices, and the 3r gets us back to Class II.
// vertices listed ccw from the i-axes
var vertsCII = new CoordIJK[NUM_PENT_VERTS]
{
new CoordIJK(2, 1, 0), // 0
new CoordIJK(1, 2, 0), // 1
new CoordIJK(0, 2, 1), // 2
new CoordIJK(0, 1, 2), // 3
new CoordIJK(1, 0, 2), // 4
};
// the vertexes of an origin-centered pentagon in a Class III resolution on
// a substrate grid with aperture sequence 33r7r. The aperture 3 gets us the
// vertices, and the 3r7r gets us to Class II. vertices listed ccw from the
// i-axes
var vertsCIII = new CoordIJK[NUM_PENT_VERTS]
{
new CoordIJK(5, 4, 0), // 0
new CoordIJK(1, 5, 0), // 1
new CoordIJK(0, 5, 4), // 2
new CoordIJK(0, 1, 5), // 3
new CoordIJK(4, 0, 5), // 4
};
// get the correct set of substrate vertices for this resolution
CoordIJK[] verts = H3Index.isResClassIII(res) ? vertsCIII : vertsCII;
// adjust the center point to be in an aperture 33r substrate grid
// these should be composed for speed
FaceIJK centerIJK = this;
centerIJK.coord = centerIJK.coord._downAp3()._downAp3r();
// if res is Class III we need to add a cw aperture 7 to get to
// icosahedral Class II
int adjRes = res;
if (H3Index.isResClassIII(res))
{
centerIJK.coord = centerIJK.coord._downAp7r();
adjRes++;
}
// The center point is now in the same substrate grid as the origin
// cell vertices. Add the center point substate coordinates
// to each vertex to translate the vertices to that cell.
FaceIJK[] fijkVerts = new FaceIJK[NUM_PENT_VERTS];
for (int v = 0; v < NUM_PENT_VERTS; v++)
{
fijkVerts[v].face = centerIJK.face;
fijkVerts[v].coord = (centerIJK.coord + verts[v]).Normalize();
}
// convert each vertex to lat/lon
// adjust the face of each vertex as appropriate and introduce
// edge-crossing vertices as needed
g.numVerts = 0;
var lastFijk = new FaceIJK(0, new CoordIJK(0, 0, 0));
for (int vert = 0; vert < NUM_PENT_VERTS + 1; vert++)
{
int v = vert % NUM_PENT_VERTS;
FaceIJK fijk = fijkVerts[v];
var pentLeading4 = false;
int overage = AdjustOverageClassII(adjRes, pentLeading4, true);
if (overage == 2) // in a different triangle
{
while (true)
{
overage = AdjustOverageClassII(adjRes, pentLeading4, true);
if (overage != 2) // not in a different triangle
{
break;
}
}
}
// all Class III pentagon edges cross icosa edges
// note that Class II pentagons have vertices on the edge,
// not edge intersections
if (H3Index.isResClassIII(res) && vert > 0)
{
// find hex2d of the two vertexes on the last face
FaceIJK tmpFijk = fijk;
var orig2d0 = lastFijk.coord.ToHex2d();
int currentToLastDir = adjacentFaceDir[tmpFijk.face][lastFijk.face];
var fijkOrient = faceNeighbors[tmpFijk.face][currentToLastDir];
tmpFijk.face = fijkOrient.face;
CoordIJK ijk = tmpFijk.coord;
// rotate and translate for adjacent face
for (int i = 0; i < fijkOrient.ccwRot60; i++)
{
ijk = ijk._ijkRotate60ccw();
}
CoordIJK transVec = fijkOrient.translate;
transVec *= unitScaleByCIIres[adjRes] * 3;
ijk = (ijk + transVec).Normalize();
var orig2d1 = ijk.ToHex2d();
// find the appropriate icosa face edge vertexes
int maxDim = maxDimByCIIres[adjRes];
var v0 = new Vec2d(3.0 * maxDim, 0.0);
var v1 = new Vec2d(-1.5 * maxDim, 3.0 * M_SQRT3_2 * maxDim);
var v2 = new Vec2d(-1.5 * maxDim, -3.0 * M_SQRT3_2 * maxDim);
Vec2d edge0;
Vec2d edge1;
switch (adjacentFaceDir[tmpFijk.face][fijk.face])
{
case IJ:
edge0 = v0;
edge1 = v1;
break;
case JK:
edge0 = v1;
edge1 = v2;
break;
case KI:
default:
//assert(adjacentFaceDir[tmpFijk.face][fijk.face] == KI);
edge0 = v2;
edge1 = v0;
break;
}
// find the intersection and add the lat/lon point to the result
var inter = new Vec2d(0, 0);
Vec2d._v2dIntersect(orig2d0, orig2d1, edge0, edge1, ref inter);
g.verts[g.numVerts] = GeoCoord.FromHex2d(inter, tmpFijk.face, adjRes, true);
g.numVerts++;
}
// convert vertex to lat/lon and add to the result
// vert == NUM_PENT_VERTS is only used to test for possible intersection
// on last edge
if (vert < NUM_PENT_VERTS)
{
var vec = fijk.coord.ToHex2d();
g.verts[g.numVerts] = GeoCoord.FromHex2d(vec, fijk.face, adjRes, true);
g.numVerts++;
}
lastFijk = fijk;
}
return(g);
}