/// <summary>
/// Returns the radius of a given hexagon in km.
/// </summary>
/// <param name="h3Index">The index of the hexagon</param>
/// <returns>The radius of the hexagon in km</returns>
public static double _hexRadiusKm(H3Index h3Index)
{
// There is probably a cheaper way to determine the radius of a
// hexagon, but this way is conceptually simple
GeoCoord h3Center = h3Index.ToGeoCoord();
GeoBoundary h3Boundary = h3Index.ToGeoBoundary();
// TODO: double check this logic
return(GeoCoord._geoDistKm(h3Center, h3Boundary.verts[0]));
}
/// <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>
/// 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);
}
