/// <summary>
/// Generates the cell boundary in spherical coordinates for a pentagonal cell
/// given by a FaceIJK address at a specified resolution.
/// </summary>
/// <param name="h">The FaceIJK address of the pentagonal cell.</param>
/// <param name="res">The H3 resolution of the cell.</param>
/// <param name="g">The spherical coordinates of the cell boundary.</param>
/// <!-- Based off 3.1.1 -->
public static void _faceIjkPentToGeoBoundary(ref FaceIJK h, int res, ref GeoBoundary g)
{
// 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
CoordIJK[] vertsCII =
{
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
CoordIJK[] vertsCIII =
{
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
List <CoordIJK> verts = new List <CoordIJK>();
verts = H3Index.isResClassIII(res)
? vertsCIII.ToList()
: vertsCII.ToList();
// adjust the center point to be in an aperture 33r substrate grid
// these should be composed for speed
FaceIJK centerIJK = new FaceIJK();
centerIJK.face = h.face;
centerIJK.coord = new CoordIJK(h.coord.i, h.coord.j, h.coord.k);
CoordIJK._downAp3(ref centerIJK.coord);
CoordIJK._downAp3r(ref centerIJK.coord);
// 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))
{
CoordIJK._downAp7r(ref centerIJK.coord);
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[Constants.NUM_PENT_VERTS];
for (int v = 0; v < Constants.NUM_PENT_VERTS; v++)
{
fijkVerts[v] = new FaceIJK();
fijkVerts[v].face = centerIJK.face;
CoordIJK._ijkAdd(centerIJK.coord, verts[v], ref fijkVerts[v].coord);
CoordIJK._ijkNormalize(ref fijkVerts[v].coord);
}
// convert each vertex to lat/lon
// adjust the face of each vertex as appropriate and introduce
// edge-crossing vertices as needed
g.numVerts = 0;
for (int i = 0; i < g.verts.Count; i++)
{
g.verts[i] = new GeoCoord();
}
FaceIJK lastFijk = new FaceIJK();
for (int vert = 0; vert < Constants.NUM_PENT_VERTS + 1; vert++)
{
int v = vert % Constants.NUM_PENT_VERTS;
FaceIJK fijk = fijkVerts[v];
int pentLeading4 = 0;
int overage = _adjustOverageClassII(ref fijk, adjRes, pentLeading4, 1);
if (overage == 2) // in a different triangle
{
while (true)
{
overage = _adjustOverageClassII(ref fijk, adjRes, pentLeading4, 1);
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 = new FaceIJK(fijk.face, new CoordIJK(fijk.coord.i, fijk.coord.j, fijk.coord.k));
Vec2d orig2d0 = new Vec2d();
CoordIJK._ijkToHex2d(lastFijk.coord, ref orig2d0);
int currentToLastDir = adjacentFaceDir[tmpFijk.face, lastFijk.face];
FaceOrientIJK fijkOrient =
new FaceOrientIJK(
faceNeighbors[tmpFijk.face, currentToLastDir].face,
faceNeighbors[tmpFijk.face, currentToLastDir].translate.i,
faceNeighbors[tmpFijk.face, currentToLastDir].translate.j,
faceNeighbors[tmpFijk.face, currentToLastDir].translate.k,
faceNeighbors[tmpFijk.face, currentToLastDir].ccwRot60
);
// faceNeighbors[tmpFijk.face,currentToLastDir];
tmpFijk.face = fijkOrient.face;
//CoordIJK ijk = tmpFijk.coord;
CoordIJK ijk = new CoordIJK(tmpFijk.coord.i, tmpFijk.coord.j, tmpFijk.coord.k);
// rotate and translate for adjacent face
for (int i = 0; i < fijkOrient.ccwRot60; i++)
{
CoordIJK._ijkRotate60ccw(ref ijk);
}
CoordIJK transVec = fijkOrient.translate;
CoordIJK._ijkScale(ref transVec, unitScaleByCIIres[adjRes] * 3);
CoordIJK._ijkAdd(ijk, transVec, ref ijk);
CoordIJK._ijkNormalize(ref ijk);
Vec2d orig2d1 = new Vec2d();
CoordIJK._ijkToHex2d(ijk, ref orig2d1);
// find the appropriate icosa face edge vertexes
int maxDim = maxDimByCIIres[adjRes];
Vec2d v0 = new Vec2d(3.0 * maxDim, 0.0);
Vec2d v1 = new Vec2d(-1.5 * maxDim, 3.0 * Constants.M_SQRT3_2 * maxDim);
Vec2d v2 = new Vec2d(-1.5 * maxDim, -3.0 * Constants.M_SQRT3_2 * maxDim);
Vec2d edge0 = new Vec2d();
Vec2d edge1 = new Vec2d();
switch (adjacentFaceDir[tmpFijk.face, fijk.face])
{
case IJ:
edge0 = v0;
edge1 = v1;
break;
case JK:
edge0 = v1;
edge1 = v2;
break;
case KI:
default:
if (adjacentFaceDir[tmpFijk.face, fijk.face] != KI)
{
throw new Exception("assert(adjacentFaceDir[tmpFijk.face][fijk.face] == KI);");
}
edge0 = v2;
edge1 = v0;
break;
}
// find the intersection and add the lat/lon point to the result
Vec2d inter = new Vec2d();
Vec2d._v2dIntersect(orig2d0, orig2d1, edge0, edge1, ref inter);
var gnv = g.verts[g.numVerts];
_hex2dToGeo(ref inter, tmpFijk.face, adjRes, 1, ref gnv);
g.verts[g.numVerts] = gnv;
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 < Constants.NUM_PENT_VERTS)
{
Vec2d vec = new Vec2d();
CoordIJK._ijkToHex2d(fijk.coord, ref vec);
var gnv = g.verts[g.numVerts];
_hex2dToGeo(ref vec, fijk.face, adjRes, 1, ref gnv);
g.verts[g.numVerts] = gnv;
g.numVerts++;
}
lastFijk = fijk;
}
}
/// <summary>
/// Adjusts a FaceIJK address in place so that the resulting cell address is
/// relative to the correct icosahedral face.
/// </summary>
/// <param name="fijk">The FaceIJK address of the cell.</param>
/// <param name="res">The H3 resolution of the cell.</param>
/// <param name="pentLeading4">Whether or not the cell is a pentagon with a leading digit 4</param>
/// <param name="substrate">Whether or not the cell is in a substrate grid.</param>
/// <returns>
/// 0 if on original face (no overage); 1 if on face edge (only occurs
/// on substrate grids); 2 if overage on new face interior
/// </returns>
/// <!-- Based off 3.1.1 -->
public static int _adjustOverageClassII(ref FaceIJK fijk, int res, int pentLeading4, int substrate)
{
int overage = 0;
CoordIJK ijk = new CoordIJK(fijk.coord.i, fijk.coord.j, fijk.coord.k);
// get the maximum dimension value; scale if a substrate grid
int maxDim = maxDimByCIIres[res];
if (substrate != 0)
{
maxDim *= 3;
}
// check for overage
if ((substrate != 0) && ijk.i + ijk.j + ijk.k == maxDim) // on edge
{
overage = 1;
}
else if (ijk.i + ijk.j + ijk.k > maxDim) // overage
{
overage = 2;
FaceOrientIJK fijkOrient = new FaceOrientIJK();
if (ijk.k > 0)
{
if (ijk.j > 0) // jk "quadrant"
{
//fijkOrient = faceNeighbors[fijk.face,JK];
fijkOrient = new FaceOrientIJK(
faceNeighbors[fijk.face, JK].face,
faceNeighbors[fijk.face, JK].translate.i,
faceNeighbors[fijk.face, JK].translate.j,
faceNeighbors[fijk.face, JK].translate.k,
faceNeighbors[fijk.face, JK].ccwRot60);
}
else // ik "quadrant"
{
//fijkOrient = faceNeighbors[fijk.face,KI];
fijkOrient = new FaceOrientIJK(
faceNeighbors[fijk.face, KI].face,
faceNeighbors[fijk.face, KI].translate.i,
faceNeighbors[fijk.face, KI].translate.j,
faceNeighbors[fijk.face, KI].translate.k,
faceNeighbors[fijk.face, KI].ccwRot60);
// adjust for the pentagonal missing sequence
if (pentLeading4 != 0)
{
// translate origin to center of pentagon
CoordIJK origin = new CoordIJK();
CoordIJK._setIJK(ref origin, maxDim, 0, 0);
CoordIJK tmp = new CoordIJK();
CoordIJK._ijkSub(ref ijk, ref origin, ref tmp);
// rotate to adjust for the missing sequence
CoordIJK._ijkRotate60cw(ref tmp);
// translate the origin back to the center of the triangle
CoordIJK._ijkAdd(tmp, origin, ref ijk);
}
}
}
else // ij "quadrant"
{
// fijkOrient = faceNeighbors[fijk.face,IJ];
fijkOrient = new FaceOrientIJK(
faceNeighbors[fijk.face, IJ].face,
faceNeighbors[fijk.face, IJ].translate.i,
faceNeighbors[fijk.face, IJ].translate.j,
faceNeighbors[fijk.face, IJ].translate.k,
faceNeighbors[fijk.face, IJ].ccwRot60);
}
fijk.face = fijkOrient.face;
// rotate and translate for adjacent face
for (int i = 0; i < fijkOrient.ccwRot60; i++)
{
CoordIJK._ijkRotate60ccw(ref ijk);
}
// CoordIJK transVec = fijkOrient.translate;
CoordIJK transVec = new CoordIJK
(
fijkOrient.translate.i,
fijkOrient.translate.j,
fijkOrient.translate.k
);
int unitScale = unitScaleByCIIres[res];
if (substrate != 0)
{
unitScale *= 3;
}
CoordIJK._ijkScale(ref transVec, unitScale);
CoordIJK._ijkAdd(ijk, transVec, ref ijk);
CoordIJK._ijkNormalize(ref ijk);
// overage points on pentagon boundaries can end up on edges
if ((substrate != 0) && ijk.i + ijk.j + ijk.k == maxDim) // on edge
{
overage = 1;
}
}
fijk.coord = ijk;
return(overage);
}