/** * 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 longitude. */ private static bool IntersectsLngEdge(S2Point a, S2Point b, R1Interval lat, double lng) { // Return true if the segment AB intersects the given edge of constant // longitude. The nice thing about edges of constant longitude is that // they are straight lines on the sphere (geodesics). return(S2.SimpleCrossing(a, b, S2LatLng.FromRadians(lat.Lo, lng) .ToPoint(), S2LatLng.FromRadians(lat.Hi, lng).ToPoint())); }
/** * Return true if the rectangle is valid, which essentially just means that * the latitude bounds do not exceed Pi/2 in absolute value and the longitude * bounds do not exceed Pi in absolute value. * */ /** Return the k-th vertex of the rectangle (k = 0,1,2,3) in CCW order. */ public S2LatLng GetVertex(int k) { // Return the points in CCW order (SW, SE, NE, NW). switch (k) { case 0: return(S2LatLng.FromRadians(_lat.Lo, _lng.Lo)); case 1: return(S2LatLng.FromRadians(_lat.Lo, _lng.Hi)); case 2: return(S2LatLng.FromRadians(_lat.Hi, _lng.Hi)); case 3: return(S2LatLng.FromRadians(_lat.Hi, _lng.Lo)); default: throw new ArgumentException("Invalid vertex index."); } }
/** * 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))))); }