/**
* Returns the smallest cell containing both points, or Sentinel if they are
* not all on the same face. The points don't need to be normalized.
*/
private static S2CellId ContainingCell(S2Point pa, S2Point pb)
{
var a = S2CellId.FromPoint(pa);
var b = S2CellId.FromPoint(pb);
if (a.Face != b.Face)
{
return(S2CellId.Sentinel);
}
while (!a.Equals(b))
{
a = a.Parent;
b = b.Parent;
}
return(a);
}
/**
* Returns the smallest cell containing all four points, or
* {@link S2CellId#sentinel()} if they are not all on the same face. The
* points don't need to be normalized.
*/
private static S2CellId ContainingCell(S2Point pa, S2Point pb, S2Point pc, S2Point pd)
{
var a = S2CellId.FromPoint(pa);
var b = S2CellId.FromPoint(pb);
var c = S2CellId.FromPoint(pc);
var d = S2CellId.FromPoint(pd);
if (a.Face != b.Face || a.Face != c.Face || a.Face != d.Face)
{
return(S2CellId.Sentinel);
}
while (!a.Equals(b) || !a.Equals(c) || !a.Equals(d))
{
a = a.Parent;
b = b.Parent;
c = c.Parent;
d = d.Parent;
}
return(a);
}
/** Computes a set of initial candidates that cover the given region. */
private void GetInitialCandidates()
{
// Optimization: if at least 4 cells are desired (the normal case),
// start with a 4-cell covering of the region's bounding cap. This
// lets us skip quite a few levels of refinement when the region to
// be covered is relatively small.
if (_maxCells >= 4)
{
// Find the maximum level such that the bounding cap contains at most one
// cell vertex at that level.
var cap = _region.CapBound;
var level = Math.Min(S2Projections.MinWidth.GetMaxLevel(2 * cap.Angle.Radians),
Math.Min(MaxLevel, S2CellId.MaxLevel - 1));
if (LevelMod > 1 && level > MinLevel)
{
level -= (level - MinLevel) % LevelMod;
}
// We don't bother trying to optimize the level == 0 case, since more than
// four face cells may be required.
if (level > 0)
{
// Find the leaf cell containing the cap axis, and determine which
// subcell of the parent cell contains it.
var @base = new List <S2CellId>(4);
var id = S2CellId.FromPoint(cap.Axis);
id.GetVertexNeighbors(level, @base);
for (var i = 0; i < @base.Count; ++i)
{
AddCandidate(NewCandidate(new S2Cell(@base[i])));
}
return;
}
}
// Default: start with all six cube faces.
for (var face = 0; face < 6; ++face)
{
AddCandidate(NewCandidate(FaceCells[face]));
}
}
// This is a static method in order to provide named parameters.
// Convenience methods.
public S2Cell(S2Point p)
{
Init(S2CellId.FromPoint(p));
}
/**
* Computes a cell covering of an edge. Clears edgeCovering and returns the
* level of the s2 cells used in the covering (only one level is ever used for
* each call).
*
* If thickenEdge is true, the edge is thickened and extended by 1% of its
* length.
*
* It is guaranteed that no child of a covering cell will fully contain the
* covered edge.
*/
private int GetCovering(
S2Point a, S2Point b, bool thickenEdge, List <S2CellId> edgeCovering)
{
edgeCovering.Clear();
// Selects the ideal s2 level at which to cover the edge, this will be the
// level whose S2 cells have a width roughly commensurate to the length of
// the edge. We multiply the edge length by 2*THICKENING to guarantee the
// thickening is honored (it's not a big deal if we honor it when we don't
// request it) when doing the covering-by-cap trick.
var edgeLength = a.Angle(b);
var idealLevel = S2Projections.MinWidth.GetMaxLevel(edgeLength * (1 + 2 * Thickening));
S2CellId containingCellId;
if (!thickenEdge)
{
containingCellId = ContainingCell(a, b);
}
else
{
if (idealLevel == S2CellId.MaxLevel)
{
// If the edge is tiny, instabilities are more likely, so we
// want to limit the number of operations.
// We pretend we are in a cell much larger so as to trigger the
// 'needs covering' case, so we won't try to thicken the edge.
containingCellId = (new S2CellId(0xFFF0)).ParentForLevel(3);
}
else
{
var pq = (b - a) * Thickening;
var ortho = (S2Point.Normalize(S2Point.CrossProd(pq, a))) * edgeLength * Thickening;
var p = a - pq;
var q = b + pq;
// If p and q were antipodal, the edge wouldn't be lengthened,
// and it could even flip! This is not a problem because
// idealLevel != 0 here. The farther p and q can be is roughly
// a quarter Earth away from each other, so we remain
// Theta(THICKENING).
containingCellId = ContainingCell(p - ortho, p + ortho, q - ortho, q + ortho);
}
}
// Best case: edge is fully contained in a cell that's not too big.
if (!containingCellId.Equals(S2CellId.Sentinel) &&
containingCellId.Level >= idealLevel - 2)
{
edgeCovering.Add(containingCellId);
return(containingCellId.Level);
}
if (idealLevel == 0)
{
// Edge is very long, maybe even longer than a face width, so the
// trick below doesn't work. For now, we will add the whole S2 sphere.
// TODO(user): Do something a tad smarter (and beware of the
// antipodal case).
for (var cellid = S2CellId.Begin(0); !cellid.Equals(S2CellId.End(0));
cellid = cellid.Next)
{
edgeCovering.Add(cellid);
}
return(0);
}
// TODO(user): Check trick below works even when vertex is at
// interface
// between three faces.
// Use trick as in S2PolygonBuilder.PointIndex.findNearbyPoint:
// Cover the edge by a cap centered at the edge midpoint, then cover
// the cap by four big-enough cells around the cell vertex closest to the
// cap center.
var middle = S2Point.Normalize((a + b) / 2);
var actualLevel = Math.Min(idealLevel, S2CellId.MaxLevel - 1);
S2CellId.FromPoint(middle).GetVertexNeighbors(actualLevel, edgeCovering);
return(actualLevel);
}
/**
* Given a connected region and a starting point, return a set of cells at the
* given level that cover the region.
*/
public static void GetSimpleCovering(
IS2Region region, S2Point start, int level, List <S2CellId> output)
{
FloodFill(region, S2CellId.FromPoint(start).ParentForLevel(level), output);
}