/**
* Returns the shortest distance from a point P to this loop, given as the
* angle formed between P, the origin and the nearest point on the loop to P.
* This angle in radians is equivalent to the arclength along the unit sphere.
*/
public S1Angle GetDistance(S2Point p)
{
var normalized = S2Point.Normalize(p);
// The furthest point from p on the sphere is its antipode, which is an
// angle of PI radians. This is an upper bound on the angle.
var minDistance = S1Angle.FromRadians(Math.PI);
for (var i = 0; i < NumVertices; i++)
{
minDistance =
S1Angle.Min(minDistance, S2EdgeUtil.GetDistance(normalized, Vertex(i), Vertex(i + 1)));
}
return(minDistance);
}
/**
* Return the area of the polygon interior, i.e. the region on the left side
* of an odd number of loops (this value return value is between 0 and 4*Pi)
* and the true centroid of the polygon multiplied by the area of the polygon
* (see s2.h for details on centroids). Note that the centroid may not be
* contained by the polygon.
*/
/**
* Returns the shortest distance from a point P to this polygon, given as the
* angle formed between P, the origin and the nearest point on the polygon to
* P. This angle in radians is equivalent to the arclength along the unit
* sphere.
*
* If the point is contained inside the polygon, the distance returned is 0.
*/
public S1Angle GetDistance(S2Point p)
{
if (Contains(p))
{
return(S1Angle.FromRadians(0));
}
// The furthest point from p on the sphere is its antipode, which is an
// angle of PI radians. This is an upper bound on the angle.
var minDistance = S1Angle.FromRadians(Math.PI);
for (var i = 0; i < NumLoops; i++)
{
minDistance = S1Angle.Min(minDistance, Loop(i).GetDistance(p));
}
return(minDistance);
}
/**
* Return the minimum distance (measured along the surface of the sphere) to
* the given S2LatLngRect. Both S2LatLngRects must be non-empty.
*/
public S1Angle GetDistance(S2LatLngRect other)
{
var a = this;
var b = other;
Preconditions.CheckState(!a.IsEmpty);
Preconditions.CheckArgument(!b.IsEmpty);
// First, handle the trivial cases where the longitude intervals overlap.
if (a.Lng.Intersects(b.Lng))
{
if (a.Lat.Intersects(b.Lat))
{
return(S1Angle.FromRadians(0)); // Intersection between a and b.
}
// We found an overlap in the longitude interval, but not in the latitude
// interval. This means the shortest path travels along some line of
// longitude connecting the high-latitude of the lower rect with the
// low-latitude of the higher rect.
S1Angle lo, hi;
if (a.Lat.Lo > b.Lat.Hi)
{
lo = b.LatHi;
hi = a.LatLo;
}
else
{
lo = a.LatHi;
hi = b.LatLo;
}
return(S1Angle.FromRadians(hi.Radians - lo.Radians));
}
// The longitude intervals don't overlap. In this case, the closest points
// occur somewhere on the pair of longitudinal edges which are nearest in
// longitude-space.
S1Angle aLng, bLng;
var loHi = S1Interval.FromPointPair(a.Lng.Lo, b.Lng.Hi);
var hiLo = S1Interval.FromPointPair(a.Lng.Hi, b.Lng.Lo);
if (loHi.Length < hiLo.Length)
{
aLng = a.LngLo;
bLng = b.LngHi;
}
else
{
aLng = a.LngHi;
bLng = b.LngLo;
}
// The shortest distance between the two longitudinal segments will include
// at least one segment endpoint. We could probably narrow this down further
// to a single point-edge distance by comparing the relative latitudes of the
// endpoints, but for the sake of clarity, we'll do all four point-edge
// distance tests.
var aLo = new S2LatLng(a.LatLo, aLng).ToPoint();
var aHi = new S2LatLng(a.LatHi, aLng).ToPoint();
var aLoCrossHi =
S2LatLng.FromRadians(0, aLng.Radians - S2.PiOver2).Normalized.ToPoint();
var bLo = new S2LatLng(b.LatLo, bLng).ToPoint();
var bHi = new S2LatLng(b.LatHi, bLng).ToPoint();
var bLoCrossHi =
S2LatLng.FromRadians(0, bLng.Radians - S2.PiOver2).Normalized.ToPoint();
return(S1Angle.Min(S2EdgeUtil.GetDistance(aLo, bLo, bHi, bLoCrossHi),
S1Angle.Min(S2EdgeUtil.GetDistance(aHi, bLo, bHi, bLoCrossHi),
S1Angle.Min(S2EdgeUtil.GetDistance(bLo, aLo, aHi, aLoCrossHi),
S2EdgeUtil.GetDistance(bHi, aLo, aHi, aLoCrossHi)))));
}
