/**
* Return the center of the rectangle in latitude-longitude space (in general
* this is not the center of the region on the sphere).
*/
/**
* Return the minimum distance (measured along the surface of the sphere)
* from a given point to the rectangle (both its boundary and its interior).
* The latLng must be valid.
*/
public S1Angle GetDistance(S2LatLng p)
{
// The algorithm here is the same as in getDistance(S2LagLngRect), only
// with simplified calculations.
var a = this;
Preconditions.CheckState(!a.IsEmpty);
Preconditions.CheckArgument(p.IsValid);
if (a.Lng.Contains(p.Lng.Radians))
{
return(S1Angle.FromRadians(Math.Max(0.0, Math.Max(p.Lat.Radians - a.Lat.Hi,
a.Lat.Lo - p.Lat.Radians))));
}
var interval = new S1Interval(a.Lng.Hi, a.Lng.Complement.Center);
var aLng = a.Lng.Lo;
if (interval.Contains(p.Lng.Radians))
{
aLng = a.Lng.Hi;
}
var lo = S2LatLng.FromRadians(a.Lat.Lo, aLng).ToPoint();
var hi = S2LatLng.FromRadians(a.Lat.Hi, aLng).ToPoint();
var loCrossHi =
S2LatLng.FromRadians(0, aLng - S2.PiOver2).Normalized.ToPoint();
return(S2EdgeUtil.GetDistance(p.ToPoint(), lo, hi, loCrossHi));
}
/**
* Return true if the edge AB intersects the given edge of constant latitude.
*/
private static bool IntersectsLatEdge(S2Point a, S2Point b, double lat,
S1Interval lng)
{
// Return true if the segment AB intersects the given edge of constant
// latitude. Unfortunately, lines of constant latitude are curves on
// the sphere. They can intersect a straight edge in 0, 1, or 2 points.
// assert (S2.isUnitLength(a) && S2.isUnitLength(b));
// First, compute the normal to the plane AB that points vaguely north.
var z = S2Point.Normalize(S2.RobustCrossProd(a, b));
if (z.Z < 0)
{
z = -z;
}
// Extend this to an orthonormal frame (x,y,z) where x is the direction
// where the great circle through AB achieves its maximium latitude.
var y = S2Point.Normalize(S2.RobustCrossProd(z, new S2Point(0, 0, 1)));
var x = S2Point.CrossProd(y, z);
// assert (S2.isUnitLength(x) && x.z >= 0);
// Compute the angle "theta" from the x-axis (in the x-y plane defined
// above) where the great circle intersects the given line of latitude.
var sinLat = Math.Sin(lat);
if (Math.Abs(sinLat) >= x.Z)
{
return(false); // The great circle does not reach the given latitude.
}
// assert (x.z > 0);
var cosTheta = sinLat / x.Z;
var sinTheta = Math.Sqrt(1 - cosTheta * cosTheta);
var theta = Math.Atan2(sinTheta, cosTheta);
// The candidate intersection points are located +/- theta in the x-y
// plane. For an intersection to be valid, we need to check that the
// intersection point is contained in the interior of the edge AB and
// also that it is contained within the given longitude interval "lng".
// Compute the range of theta values spanned by the edge AB.
var abTheta = S1Interval.FromPointPair(Math.Atan2(
a.DotProd(y), a.DotProd(x)), Math.Atan2(b.DotProd(y), b.DotProd(x)));
if (abTheta.Contains(theta))
{
// Check if the intersection point is also in the given "lng" interval.
var isect = (x * cosTheta) + (y * sinTheta);
if (lng.Contains(Math.Atan2(isect.Y, isect.X)))
{
return(true);
}
}
if (abTheta.Contains(-theta))
{
// Check if the intersection point is also in the given "lng" interval.
var intersection = (x * cosTheta) - (y * sinTheta);
if (lng.Contains(Math.Atan2(intersection.Y, intersection.X)))
{
return(true);
}
}
return(false);
}
/**
* Return the width and height of this rectangle in latitude-longitude space.
* Empty rectangles have a negative width and height.
*/
/**
* More efficient version of Contains() that accepts a S2LatLng rather than an
* S2Point.
*/
public bool Contains(S2LatLng ll)
{
// assert (ll.isValid());
return(_lat.Contains(ll.Lat.Radians) && _lng.Contains(ll.Lng.Radians));
}
