/// <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);
}
/// <summary>
/// Produces an index for ijk+ coordinates anchored by an origin.
///
/// The coordinate space used by this function may have deleted
/// regions or warping due to pentagonal distortion.
///
/// Failure may occur if the coordinates are too far away from the origin
/// or if the index is on the other side of a pentagon.
/// </summary>
/// <param name="origin">An anchoring index for the ijk+ coordinate system.</param>
/// <param name="ijk">IJK+ Coordinates to find the index of</param>
/// <param name="out_h3">The index will be placed here on success</param>
/// <returns>0 on success, or another value on failure</returns>
/// <!-- Based off 3.2.0 -->
internal static int localIjkToH3(H3Index origin, CoordIJK ijk, ref H3Index out_h3)
{
int res = H3Index.H3_GET_RESOLUTION(origin);
int originBaseCell = H3Index.H3_GET_BASE_CELL(origin);
int originOnPent = BaseCells._isBaseCellPentagon(originBaseCell)
? 1
: 0;
// This logic is very similar to faceIjkToH3
// initialize the index
out_h3 = H3Index.H3_INIT;
H3Index.H3_SET_MODE(ref out_h3, Constants.H3_HEXAGON_MODE);
H3Index.H3_SET_RESOLUTION(ref out_h3, res);
Direction dir;
// check for res 0/base cell
if (res == 0)
{
if (ijk.i > 1 || ijk.j > 1 || ijk.k > 1)
{
// out of range input
return(1);
}
dir = CoordIJK._unitIjkToDigit(ref ijk);
int newBaseCell = BaseCells._getBaseCellNeighbor(originBaseCell, dir);
if (newBaseCell == BaseCells.INVALID_BASE_CELL)
{
// Moving in an invalid direction off a pentagon.
return(1);
}
H3Index.H3_SET_BASE_CELL(ref out_h3, newBaseCell);
return(0);
}
// we need to find the correct base cell offset (if any) for this H3 index;
// start with the passed in base cell and resolution res ijk coordinates
// in that base cell's coordinate system
CoordIJK ijkCopy = new CoordIJK(ijk.i, ijk.j, ijk.k);
// build the H3Index from finest res up
// adjust r for the fact that the res 0 base cell offsets the indexing
// digits
for (int r = res - 1; r >= 0; r--)
{
CoordIJK lastIJK = ijkCopy;
CoordIJK lastCenter;
if (H3Index.isResClassIII(r + 1))
{
// rotate ccw
CoordIJK._upAp7(ref ijkCopy);
lastCenter = ijkCopy;
CoordIJK._downAp7(ref lastCenter);
}
else
{
// rotate cw
CoordIJK._upAp7r(ref ijkCopy);
lastCenter = ijkCopy;
CoordIJK._downAp7r(ref lastCenter);
}
CoordIJK diff = new CoordIJK();
CoordIJK._ijkSub(ref lastIJK, ref lastCenter, ref diff);
CoordIJK._ijkNormalize(ref diff);
H3Index.H3_SET_INDEX_DIGIT(ref out_h3, r + 1, (ulong)CoordIJK._unitIjkToDigit(ref diff));
}
// ijkCopy should now hold the IJK of the base cell in the
// coordinate system of the current base cell
if (ijkCopy.i > 1 || ijkCopy.j > 1 || ijkCopy.k > 1)
{
// out of range input
return(2);
}
// lookup the correct base cell
dir = CoordIJK._unitIjkToDigit(ref ijkCopy);
int baseCell = BaseCells._getBaseCellNeighbor(originBaseCell, dir);
// If baseCell is invalid, it must be because the origin base cell is a
// pentagon, and because pentagon base cells do not border each other,
// baseCell must not be a pentagon.
int indexOnPent =
(baseCell == BaseCells.INVALID_BASE_CELL
? 0
: BaseCells._isBaseCellPentagon(baseCell)
? 1
: 0);
if (dir != (int)Direction.CENTER_DIGIT)
{
// If the index is in a warped direction, we need to unwarp the base
// cell direction. There may be further need to rotate the index digits.
int pentagonRotations = 0;
if (originOnPent != 0)
{
Direction originLeadingDigit = H3Index._h3LeadingNonZeroDigit(origin);
pentagonRotations =
PENTAGON_ROTATIONS_REVERSE[(int)originLeadingDigit, (int)dir];
for (int i = 0; i < pentagonRotations; i++)
{
dir = CoordIJK._rotate60ccw(dir);
}
// The pentagon rotations are being chosen so that dir is not the
// deleted direction. If it still happens, it means we're moving
// into a deleted subsequence, so there is no index here.
if (dir == Direction.K_AXES_DIGIT)
{
return(3);
}
baseCell = BaseCells._getBaseCellNeighbor(originBaseCell, dir);
// indexOnPent does not need to be checked again since no pentagon
// base cells border each other.
if (baseCell == BaseCells.INVALID_BASE_CELL)
{
throw new Exception("assert(baseCell != BaseCells.INVALID_BASE_CELL);");
}
if (BaseCells._isBaseCellPolarPentagon(baseCell))
{
throw new Exception("assert(!BaseCells._isBaseCellPentagon(baseCell));");
}
}
// Now we can determine the relation between the origin and target base
// cell.
int baseCellRotations =
BaseCells.baseCellNeighbor60CCWRots[originBaseCell, (int)dir];
if (baseCellRotations < 0)
{
throw new Exception("assert(baseCellRotations >= 0);");
}
// Adjust for pentagon warping within the base cell. The base cell
// should be in the right location, so now we need to rotate the index
// back. We might not need to check for errors since we would just be
// double mapping.
if (indexOnPent != 0)
{
Direction revDir =
BaseCells._getBaseCellDirection(baseCell, originBaseCell);
if (revDir == Direction.INVALID_DIGIT)
{
throw new Exception("assert(revDir != Direction.INVALID_DIGIT);");
}
// Adjust for the different coordinate space in the two base cells.
// This is done first because we need to do the pentagon rotations
// based on the leading digit in the pentagon's coordinate system.
for (int i = 0; i < baseCellRotations; i++)
{
out_h3 = H3Index._h3Rotate60ccw(ref out_h3);
}
Direction indexLeadingDigit = H3Index._h3LeadingNonZeroDigit(out_h3);
if (BaseCells._isBaseCellPolarPentagon(baseCell))
{
pentagonRotations =
PENTAGON_ROTATIONS_REVERSE_POLAR[(int)revDir, (int)indexLeadingDigit];
}
else
{
pentagonRotations =
PENTAGON_ROTATIONS_REVERSE_NONPOLAR[(int)revDir, (int)indexLeadingDigit];
}
if (pentagonRotations < 0)
{
throw new Exception("assert(pentagonRotations >= 0);");
}
for (int i = 0; i < pentagonRotations; i++)
{
out_h3 = H3Index._h3RotatePent60ccw(ref out_h3);
}
}
else
{
if (pentagonRotations < 0)
{
throw new Exception("assert(pentagonRotations >= 0);");
}
for (int i = 0; i < pentagonRotations; i++)
{
out_h3 = H3Index._h3Rotate60ccw(ref out_h3);
}
// Adjust for the different coordinate space in the two base cells.
for (int i = 0; i < baseCellRotations; i++)
{
out_h3 = H3Index._h3Rotate60ccw(ref out_h3);
}
}
}
else if (originOnPent != 0 && indexOnPent != 0)
{
int originLeadingDigit = (int)H3Index._h3LeadingNonZeroDigit(origin);
int indexLeadingDigit = (int)H3Index._h3LeadingNonZeroDigit(out_h3);
int withinPentagonRotations =
PENTAGON_ROTATIONS_REVERSE[originLeadingDigit, indexLeadingDigit];
if (withinPentagonRotations < 0)
{
throw new Exception("assert(withinPentagonRotations >= 0);");
}
for (int i = 0; i < withinPentagonRotations; i++)
{
out_h3 = H3Index._h3Rotate60ccw(ref out_h3);
}
}
if (indexOnPent != 0)
{
// TODO: There are cases in h3ToLocalIjk which are failed but not
// accounted for here - instead just fail if the recovered index is
// invalid.
if (H3Index._h3LeadingNonZeroDigit(out_h3) == Direction.K_AXES_DIGIT)
{
return(4);
}
}
H3Index.H3_SET_BASE_CELL(ref out_h3, baseCell);
return(0);
}
/// <summary>
/// Produces ijk+ coordinates for an index anchored by an origin.
///
/// The coordinate space used by this function may have deleted
/// regions or warping due to pentagonal distortion.
///
/// Coordinates are only comparable if they come from the same
/// origin index.
///
/// Failure may occur if the index is too far away from the origin
/// or if the index is on the other side of a pentagon.
/// </summary>
/// <param name="origin">An anchoring index for the ijk+ coordinate system</param>
/// <param name="h3">Index to find the coordinates of</param>
/// <param name="out_coord">ijk+ coordinates of the index will be placed here on success</param>
/// <returns>0 on success, or another value on failure.</returns>
/// <!-- Based off 3.2.0 -->
static int h3ToLocalIjk(H3Index origin, H3Index h3, ref CoordIJK out_coord)
{
int res = H3Index.H3_GET_RESOLUTION(origin);
if (res != H3Index.H3_GET_RESOLUTION(h3))
{
return(1);
}
int originBaseCell = H3Index.H3_GET_BASE_CELL(origin);
int baseCell = H3Index.H3_GET_BASE_CELL(h3);
// Direction from origin base cell to index base cell
Direction dir = 0;
Direction revDir = 0;
if (originBaseCell != baseCell)
{
dir = BaseCells._getBaseCellDirection(originBaseCell, baseCell);
if (dir == Direction.INVALID_DIGIT)
{
// Base cells are not neighbors, can't unfold.
return(2);
}
revDir = BaseCells._getBaseCellDirection(baseCell, originBaseCell);
if (revDir == Direction.INVALID_DIGIT)
{
throw new Exception("assert(revDir != INVALID_DIGIT)");
}
}
int originOnPent = (BaseCells._isBaseCellPentagon(originBaseCell)
? 1
: 0);
int indexOnPent = (BaseCells._isBaseCellPentagon(baseCell)
? 1
: 0);
FaceIJK indexFijk = new FaceIJK();
if (dir != Direction.CENTER_DIGIT)
{
// Rotate index into the orientation of the origin base cell.
// cw because we are undoing the rotation into that base cell.
int baseCellRotations = BaseCells.baseCellNeighbor60CCWRots[originBaseCell, (int)dir];
if (indexOnPent != 0)
{
for (int i = 0; i < baseCellRotations; i++)
{
h3 = H3Index._h3RotatePent60cw(h3);
revDir = CoordIJK._rotate60cw(revDir);
if (revDir == Direction.K_AXES_DIGIT)
{
revDir = CoordIJK._rotate60cw(revDir);
}
}
}
else
{
for (int i = 0; i < baseCellRotations; i++)
{
h3 = H3Index._h3Rotate60cw(ref h3);
revDir = CoordIJK._rotate60cw(revDir);
}
}
}
// Face is unused. This produces coordinates in base cell coordinate space.
H3Index._h3ToFaceIjkWithInitializedFijk(h3, ref indexFijk);
if (dir != Direction.CENTER_DIGIT)
{
if (baseCell == originBaseCell)
{
throw new Exception("assert(baseCell != originBaseCell);");
}
if ((originOnPent != 0) && (indexOnPent != 0))
{
throw new Exception("assert(!(originOnPent && indexOnPent));");
}
int pentagonRotations = 0;
int directionRotations = 0;
if (originOnPent != 0)
{
int originLeadingDigit = (int)H3Index._h3LeadingNonZeroDigit(origin);
if ((H3Index.isResClassIII(res) &&
FAILED_DIRECTIONS_III[originLeadingDigit, (int)dir]) ||
(!H3Index.isResClassIII(res) &&
FAILED_DIRECTIONS_II[originLeadingDigit, (int)dir]))
{
// TODO this part of the pentagon might not be unfolded
// correctly.
return(3);
}
directionRotations = PENTAGON_ROTATIONS[originLeadingDigit, (int)dir];
pentagonRotations = directionRotations;
}
else if (indexOnPent != 0)
{
int indexLeadingDigit = (int)H3Index._h3LeadingNonZeroDigit(h3);
if ((H3Index.isResClassIII(res) &&
FAILED_DIRECTIONS_III[indexLeadingDigit, (int)revDir]) ||
(!H3Index.isResClassIII(res) &&
FAILED_DIRECTIONS_II[indexLeadingDigit, (int)revDir]))
{
// TODO this part of the pentagon might not be unfolded
// correctly.
return(4);
}
pentagonRotations = PENTAGON_ROTATIONS[(int)revDir, indexLeadingDigit];
}
if (pentagonRotations < 0)
{
throw new Exception("assert(pentagonRotations >= 0);");
}
if (directionRotations < 0)
{
throw new Exception("assert(directionRotations >= 0);");
}
for (int i = 0; i < pentagonRotations; i++)
{
CoordIJK._ijkRotate60cw(ref indexFijk.coord);
}
CoordIJK offset = new CoordIJK();
CoordIJK._neighbor(ref offset, dir);
// Scale offset based on resolution
for (int r = res - 1; r >= 0; r--)
{
if (H3Index.isResClassIII(r + 1))
{
// rotate ccw
CoordIJK._downAp7(ref offset);
}
else
{
// rotate cw
CoordIJK._downAp7r(ref offset);
}
}
for (int i = 0; i < directionRotations; i++)
{
CoordIJK._ijkRotate60cw(ref offset);
}
// Perform necessary translation
CoordIJK._ijkAdd(indexFijk.coord, offset, ref indexFijk.coord);
CoordIJK._ijkNormalize(ref indexFijk.coord);
}
else if (originOnPent != 0 && indexOnPent != 0)
{
// If the origin and index are on pentagon, and we checked that the base
// cells are the same or neighboring, then they must be the same base
// cell.
if (baseCell != originBaseCell)
{
throw new Exception("assert(baseCell == originBaseCell);");
}
int originLeadingDigit = (int)H3Index._h3LeadingNonZeroDigit(origin);
int indexLeadingDigit = (int)H3Index._h3LeadingNonZeroDigit(h3);
if (FAILED_DIRECTIONS_III[originLeadingDigit, indexLeadingDigit] ||
FAILED_DIRECTIONS_II[originLeadingDigit, indexLeadingDigit])
{
// TODO this part of the pentagon might not be unfolded
// correctly.
return(5);
}
int withinPentagonRotations =
PENTAGON_ROTATIONS[originLeadingDigit, indexLeadingDigit];
for (int i = 0; i < withinPentagonRotations; i++)
{
CoordIJK._ijkRotate60cw(ref indexFijk.coord);
}
}
out_coord = indexFijk.coord;
return(0);
}
/// <summary>
/// Generates the cell boundary in spherical coordinates for a cell given by a
/// FaceIJK address at a specified resolution.
/// </summary>
/// <param name="h">The FaceIJK address of the cell.</param>
/// <param name="res">The H3 resolution of the cell.</param>
/// <param name="isPentagon">Whether or not the cell is a pentagon.</param>
/// <param name="g">The spherical coordinates of the cell boundary.</param>
/// <!-- Based off 3.1.1 -->
public static void _faceIjkToGeoBoundary(ref FaceIJK h, int res, int isPentagon, ref GeoBoundary g)
{
if (isPentagon > 0)
{
_faceIjkPentToGeoBoundary(ref h, res, ref g);
return;
}
// 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
CoordIJK[] vertsCII =
{
new CoordIJK {
i = 2, j = 1, k = 0
}, // 0
new CoordIJK {
i = 1, j = 2, k = 0
}, // 1
new CoordIJK {
i = 0, j = 2, k = 1
}, // 2
new CoordIJK {
i = 0, j = 1, k = 2
}, // 3
new CoordIJK {
i = 1, j = 0, k = 2
}, // 4
new CoordIJK {
i = 2, j = 0, k = 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
CoordIJK[] vertsCIII =
{
new CoordIJK {
i = 5, j = 4, k = 0
}, // 0
new CoordIJK {
i = 1, j = 5, k = 0
}, // 1
new CoordIJK {
i = 0, j = 5, k = 4
}, // 2
new CoordIJK {
i = 0, j = 1, k = 5
}, // 3
new CoordIJK {
i = 4, j = 0, k = 5
}, // 4
new CoordIJK {
i = 5, j = 0, k = 1
} // 5
};
// get the correct set of substrate vertices for this resolution
CoordIJK[] verts;
if (H3Index.isResClassIII(res))
{
verts = vertsCIII;
}
else
{
verts = vertsCII;
}
// adjust the center point to be in an aperture 33r substrate grid
// these should be composed for speed
FaceIJK centerIJK = new FaceIJK(h.face, 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_HEX_VERTS];
for (int v = 0; v < Constants.NUM_HEX_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;
int lastFace = -1;
int lastOverage = 0; // 0: none; 1: edge; 2: overage
for (int vert = 0; vert < Constants.NUM_HEX_VERTS + 1; vert++)
{
int v = vert % Constants.NUM_HEX_VERTS;
FaceIJK fijk = new FaceIJK
(
fijkVerts[v].face,
new CoordIJK(fijkVerts[v].coord.i, fijkVerts[v].coord.j, fijkVerts[v].coord.k)
);
int pentLeading4 = 0;
int overage = _adjustOverageClassII(ref fijk, adjRes, pentLeading4, 1);
/*
* 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) % Constants.NUM_HEX_VERTS;
Vec2d orig2d0 = new Vec2d();
CoordIJK._ijkToHex2d(fijkVerts[lastV].coord, ref orig2d0);
Vec2d orig2d1 = new Vec2d();
CoordIJK._ijkToHex2d(fijkVerts[v].coord, 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);
int face2 = lastFace == centerIJK.face ? fijk.face : lastFace;
Vec2d edge0 = new Vec2d();
Vec2d edge1 = new Vec2d();
switch (adjacentFaceDir[centerIJK.face, face2])
{
case IJ:
edge0 = v0;
edge1 = v1;
break;
case JK:
edge0 = v1;
edge1 = v2;
break;
case KI:
default:
if (adjacentFaceDir[centerIJK.face, face2] != KI)
{
throw new Exception("Default failure in _faceIjkToGeoBoundary");
}
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);
/*
* 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)
{
var temp_verts = g.verts[g.numVerts];
_hex2dToGeo(ref inter, centerIJK.face, adjRes, 1, ref temp_verts);
g.verts[g.numVerts] = temp_verts;
g.numVerts++;
Debug.WriteLine(string.Format("!IsIntersection {0}", 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 < Constants.NUM_HEX_VERTS)
{
Vec2d vec = new Vec2d();
CoordIJK._ijkToHex2d(fijk.coord, ref vec);
var temp_verts = g.verts[g.numVerts];
_hex2dToGeo(ref vec, fijk.face, adjRes, 1, ref temp_verts);
g.verts[g.numVerts] = temp_verts;
g.numVerts++;
}
lastFace = fijk.face;
lastOverage = overage;
}
}
/// <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>
/// Returns the hexagon index neighboring the origin, in the direction dir.
///
/// Implementation note: The only reachable case where this returns 0 is if the
/// origin is a pentagon and the translation is in the k direction. Thus,
/// 0 can only be returned if origin is a pentagon.
/// </summary>
/// <param name="origin">Origin index</param>
/// <param name="dir">Direction to move in</param>
/// <param name="rotations">
/// Number of ccw rotations to perform to reorient the translation vector.
/// Will be modified to the new number of rotations to perform (such as
/// when crossing a face edge.)
/// </param>
/// <returns>H3Index of the specified neighbor or 0 if deleted k-subsequence distortion is encountered.</returns>
/// <!-- Based off 3.2.0 -->
internal static ulong h3NeighborRotations(H3Index origin, Direction dir, ref int rotations)
{
H3Index out_hex = origin;
for (int i = 0; i < rotations; i++)
{
dir = CoordIJK._rotate60ccw(dir);
}
int newRotations = 0;
int oldBaseCell = H3Index.H3_GET_BASE_CELL(out_hex);
Direction oldLeadingDigit = H3Index._h3LeadingNonZeroDigit(out_hex);
// Adjust the indexing digits and, if needed, the base cell.
int r = H3Index.H3_GET_RESOLUTION(out_hex) - 1;
while (true)
{
if (r == -1)
{
H3Index.H3_SET_BASE_CELL(ref out_hex, BaseCells.baseCellNeighbors[oldBaseCell, (int)dir]);
newRotations = BaseCells.baseCellNeighbor60CCWRots[oldBaseCell, (int)dir];
if (H3Index.H3_GET_BASE_CELL(out_hex) == BaseCells.INVALID_BASE_CELL)
{
// Adjust for the deleted k vertex at the base cell level.
// This edge actually borders a different neighbor.
H3Index.H3_SET_BASE_CELL(ref out_hex,
BaseCells.baseCellNeighbors[oldBaseCell, (int)Direction.IK_AXES_DIGIT]);
newRotations =
BaseCells.baseCellNeighbor60CCWRots[oldBaseCell, (int)Direction.IK_AXES_DIGIT];
// perform the adjustment for the k-subsequence we're skipping
// over.
out_hex = H3Index._h3Rotate60ccw(ref out_hex);
rotations++;
}
break;
}
Direction oldDigit = H3Index.H3_GET_INDEX_DIGIT(out_hex, r + 1);
Direction nextDir;
if (H3Index.isResClassIII(r + 1))
{
H3Index.H3_SET_INDEX_DIGIT(ref out_hex, r + 1, (ulong)NEW_DIGIT_II[(int)oldDigit, (int)dir]);
nextDir = NEW_ADJUSTMENT_II[(int)oldDigit, (int)dir];
}
else
{
H3Index.H3_SET_INDEX_DIGIT(ref out_hex, r + 1,
(ulong)NEW_DIGIT_III[(int)oldDigit, (int)dir]);
nextDir = NEW_ADJUSTMENT_III[(int)oldDigit, (int)dir];
}
if (nextDir != Direction.CENTER_DIGIT)
{
dir = nextDir;
r--;
}
else
{
// No more adjustment to perform
break;
}
}
int newBaseCell = H3Index.H3_GET_BASE_CELL(out_hex);
if (BaseCells._isBaseCellPentagon(newBaseCell))
{
int alreadyAdjustedKSubsequence = 0;
// force rotation out of missing k-axes sub-sequence
if (H3Index._h3LeadingNonZeroDigit(out_hex) == Direction.K_AXES_DIGIT)
{
if (oldBaseCell != newBaseCell)
{
// in this case, we traversed into the deleted
// k subsequence of a pentagon base cell.
// We need to rotate out of that case depending
// on how we got here.
// check for a cw/ccw offset face; default is ccw
if (BaseCells._baseCellIsCwOffset(
newBaseCell, BaseCells.baseCellData[oldBaseCell].homeFijk.face))
{
out_hex = H3Index._h3Rotate60cw(ref out_hex);
}
else
{
out_hex = H3Index._h3Rotate60ccw(ref out_hex); // LCOV_EXCL_LINE
}
// See cwOffsetPent in testKRing.c for why this is
// unreachable.
alreadyAdjustedKSubsequence = 1;
}
else
{
// In this case, we traversed into the deleted
// k subsequence from within the same pentagon
// base cell.
if (oldLeadingDigit == Direction.CENTER_DIGIT)
{
// Undefined: the k direction is deleted from here
return(H3Index.H3_INVALID_INDEX);
}
switch (oldLeadingDigit)
{
case Direction.JK_AXES_DIGIT:
// Rotate out of the deleted k subsequence
// We also need an additional change to the direction we're
// moving in
out_hex = H3Index._h3Rotate60ccw(ref out_hex);
rotations++;
break;
case Direction.IK_AXES_DIGIT:
// Rotate out of the deleted k subsequence
// We also need an additional change to the direction we're
// moving in
out_hex = H3Index._h3Rotate60cw(ref out_hex);
rotations += 5;
break;
default:
// Should never occur
return(H3Index.H3_INVALID_INDEX); // LCOV_EXCL_LINE
}
}
}
for (int i = 0; i < newRotations; i++)
{
out_hex = H3Index._h3RotatePent60ccw(ref out_hex);
}
// Account for differing orientation of the base cells (this edge
// might not follow properties of some other edges.)
if (oldBaseCell != newBaseCell)
{
if (BaseCells._isBaseCellPolarPentagon(newBaseCell))
{
// 'polar' base cells behave differently because they have all
// i neighbors.
if (oldBaseCell != 118 && oldBaseCell != 8 &&
H3Index._h3LeadingNonZeroDigit(out_hex) != Direction.JK_AXES_DIGIT)
{
rotations++;
}
}
else if (H3Index._h3LeadingNonZeroDigit(out_hex) == Direction.IK_AXES_DIGIT &&
alreadyAdjustedKSubsequence == 0)
{
// account for distortion introduced to the 5 neighbor by the
// deleted k subsequence.
rotations++;
}
}
}
else
{
for (int i = 0; i < newRotations; i++)
{
out_hex = H3Index._h3Rotate60ccw(ref out_hex);
}
}
rotations = (rotations + newRotations) % 6;
return(out_hex);
}
