/**
* If this method returns false, the region does not intersect the given cell.
* Otherwise, either region intersects the cell, or the intersection
* relationship could not be determined.
*/
public bool MayIntersect(S2Cell cell)
{
if (NumVertices == 0)
{
return(false);
}
// We only need to check whether the cell contains vertex 0 for correctness,
// but these tests are cheap compared to edge crossings so we might as well
// check all the vertices.
for (var i = 0; i < NumVertices; ++i)
{
if (cell.Contains(Vertex(i)))
{
return(true);
}
}
var cellVertices = new S2Point[4];
for (var i = 0; i < 4; ++i)
{
cellVertices[i] = cell.GetVertex(i);
}
for (var j = 0; j < 4; ++j)
{
var crosser =
new EdgeCrosser(cellVertices[j], cellVertices[(j + 1) & 3], Vertex(0));
for (var i = 1; i < NumVertices; ++i)
{
if (crosser.RobustCrossing(Vertex(i)) >= 0)
{
// There is a proper crossing, or two vertices were the same.
return(true);
}
}
}
return(false);
}
/**
* Returns true if this rectangle intersects the given cell. (This is an exact
* test and may be fairly expensive, see also MayIntersect below.)
*/
public bool Intersects(S2Cell cell)
{
// First we eliminate the cases where one region completely contains the
// other. Once these are disposed of, then the regions will intersect
// if and only if their boundaries intersect.
if (IsEmpty)
{
return(false);
}
if (Contains(cell.Center))
{
return(true);
}
if (cell.Contains(Center.ToPoint()))
{
return(true);
}
// Quick rejection test (not required for correctness).
if (!Intersects(cell.RectBound))
{
return(false);
}
// Now check whether the boundaries intersect. Unfortunately, a
// latitude-longitude rectangle does not have straight edges -- two edges
// are curved, and at least one of them is concave.
// Precompute the cell vertices as points and latitude-longitudes.
var cellV = new S2Point[4];
var cellLl = new S2LatLng[4];
for (var i = 0; i < 4; ++i)
{
cellV[i] = cell.GetVertex(i); // Must be normalized.
cellLl[i] = new S2LatLng(cellV[i]);
if (Contains(cellLl[i]))
{
return(true); // Quick acceptance test.
}
}
for (var i = 0; i < 4; ++i)
{
var edgeLng = S1Interval.FromPointPair(
cellLl[i].Lng.Radians, cellLl[(i + 1) & 3].Lng.Radians);
if (!_lng.Intersects(edgeLng))
{
continue;
}
var a = cellV[i];
var b = cellV[(i + 1) & 3];
if (edgeLng.Contains(_lng.Lo))
{
if (IntersectsLngEdge(a, b, _lat, _lng.Lo))
{
return(true);
}
}
if (edgeLng.Contains(_lng.Hi))
{
if (IntersectsLngEdge(a, b, _lat, _lng.Hi))
{
return(true);
}
}
if (IntersectsLatEdge(a, b, _lat.Lo, _lng))
{
return(true);
}
if (IntersectsLatEdge(a, b, _lat.Hi, _lng))
{
return(true);
}
}
return(false);
}
// //////////////////////////////////////////////////////////////////////
// S2Region interface (see {@code S2Region} for details):
/**
* Return true if the cap intersects 'cell', given that the cap vertices have
* alrady been checked.
*/
public bool Intersects(S2Cell cell, IReadOnlyList <S2Point> vertices)
{
// Return true if this cap intersects any point of 'cell' excluding its
// vertices (which are assumed to already have been checked).
// If the cap is a hemisphere or larger, the cell and the complement of the
// cap are both convex. Therefore since no vertex of the cell is contained,
// no other interior point of the cell is contained either.
if (_height >= 1)
{
return(false);
}
// We need to check for empty caps due to the axis check just below.
if (IsEmpty)
{
return(false);
}
// Optimization: return true if the cell contains the cap axis. (This
// allows half of the edge checks below to be skipped.)
if (cell.Contains(_axis))
{
return(true);
}
// At this point we know that the cell does not contain the cap axis,
// and the cap does not contain any cell vertex. The only way that they
// can intersect is if the cap intersects the interior of some edge.
var sin2Angle = _height * (2 - _height); // sin^2(capAngle)
for (var k = 0; k < 4; ++k)
{
var edge = cell.GetEdgeRaw(k);
var dot = _axis.DotProd(edge);
if (dot > 0)
{
// The axis is in the interior half-space defined by the edge. We don't
// need to consider these edges, since if the cap intersects this edge
// then it also intersects the edge on the opposite side of the cell
// (because we know the axis is not contained with the cell).
continue;
}
// The Norm2() factor is necessary because "edge" is not normalized.
if (dot * dot > sin2Angle * edge.Norm2)
{
return(false); // Entire cap is on the exterior side of this edge.
}
// Otherwise, the great circle containing this edge intersects
// the interior of the cap. We just need to check whether the point
// of closest approach occurs between the two edge endpoints.
var dir = S2Point.CrossProd(edge, _axis);
if (dir.DotProd(vertices[k]) < 0 &&
dir.DotProd(vertices[(k + 1) & 3]) > 0)
{
return(true);
}
}
return(false);
}
