// S2Region interface (see {@code S2Region} for details):
/** Return a bounding spherical cap. */
/**
* Given a point, returns the index of the start point of the (first) edge on
* the polyline that is closest to the given point. The polyline must have at
* least one vertex. Throws IllegalStateException if this is not the case.
*/
public int GetNearestEdgeIndex(S2Point point)
{
Preconditions.CheckState(NumVertices > 0, "Empty polyline");
if (NumVertices == 1)
{
// If there is only one vertex, the "edge" is trivial, and it's the only one
return(0);
}
// Initial value larger than any possible distance on the unit sphere.
var minDistance = S1Angle.FromRadians(10);
var minIndex = -1;
// Find the line segment in the polyline that is closest to the point given.
for (var i = 0; i < NumVertices - 1; ++i)
{
var distanceToSegment = S2EdgeUtil.GetDistance(point, Vertex(i), Vertex(i + 1));
if (distanceToSegment < minDistance)
{
minDistance = distanceToSegment;
minIndex = i;
}
}
return(minIndex);
}
/**
* A slightly more efficient version of getDistance() where the cross product
* of the two endpoints has been precomputed. The cross product does not need
* to be normalized, but should be computed using S2.robustCrossProd() for the
* most accurate results.
*/
public static S1Angle GetDistance(S2Point x, S2Point a, S2Point b, S2Point aCrossB)
{
Preconditions.CheckArgument(S2.IsUnitLength(x));
Preconditions.CheckArgument(S2.IsUnitLength(a));
Preconditions.CheckArgument(S2.IsUnitLength(b));
// There are three cases. If X is located in the spherical wedge defined by
// A, B, and the axis A x B, then the closest point is on the segment AB.
// Otherwise the closest point is either A or B; the dividing line between
// these two cases is the great circle passing through (A x B) and the
// midpoint of AB.
if (S2.SimpleCcw(aCrossB, a, x) && S2.SimpleCcw(x, b, aCrossB))
{
// The closest point to X lies on the segment AB. We compute the distance
// to the corresponding great circle. The result is accurate for small
// distances but not necessarily for large distances (approaching Pi/2).
var sinDist = Math.Abs(x.DotProd(aCrossB)) / aCrossB.Norm;
return(S1Angle.FromRadians(Math.Asin(Math.Min(1.0, sinDist))));
}
// Otherwise, the closest point is either A or B. The cheapest method is
// just to compute the minimum of the two linear (as opposed to spherical)
// distances and convert the result to an angle. Again, this method is
// accurate for small but not large distances (approaching Pi).
var linearDist2 = Math.Min((x - a).Norm2, (x - b).Norm2);
return(S1Angle.FromRadians(2 * Math.Asin(Math.Min(1.0, 0.5 * Math.Sqrt(linearDist2)))));
}
public void InitToIntersectionSloppy(
S2Polygon a, S2Polygon b, S1Angle vertexMergeRadius)
{
Preconditions.CheckState(NumLoops == 0);
if (!a._bound.Intersects(b._bound))
{
return;
}
// We want the boundary of A clipped to the interior of B,
// plus the boundary of B clipped to the interior of A,
// plus one copy of any directed edges that are in both boundaries.
var options = S2PolygonBuilderOptions.DirectedXor;
options.MergeDistance = vertexMergeRadius;
var builder = new S2PolygonBuilder(options);
ClipBoundary(a, false, b, false, false, true, builder);
ClipBoundary(b, false, a, false, false, false, builder);
if (!builder.AssemblePolygon(this, null))
{
// TODO (andriy): do something more meaningful here.
Debug.WriteLine("Bad directed edges");
}
}
public static S1Angle Latitude(S2Point p)
{
// We use atan2 rather than asin because the input vector is not necessarily
// unit length, and atan2 is much more accurate than asin near the poles.
return(S1Angle.FromRadians(
Math.Atan2(p[2], Math.Sqrt(p[0] * p[0] + p[1] * p[1]))));
}
/**
* Return the distance (measured along the surface of the sphere) to the given
* point.
*/
public S1Angle GetDistance(S2LatLng o)
{
// This implements the Haversine formula, which is numerically stable for
// small distances but only gets about 8 digits of precision for very large
// distances (e.g. antipodal points). Note that 8 digits is still accurate
// to within about 10cm for a sphere the size of the Earth.
//
// This could be fixed with another sin() and cos() below, but at that point
// you might as well just convert both arguments to S2Points and compute the
// distance that way (which gives about 15 digits of accuracy for all
// distances).
var lat1 = Lat.Radians;
var lat2 = o.Lat.Radians;
var lng1 = Lng.Radians;
var lng2 = o.Lng.Radians;
var dlat = Math.Sin(0.5 * (lat2 - lat1));
var dlng = Math.Sin(0.5 * (lng2 - lng1));
var x = dlat * dlat + dlng * dlng * Math.Cos(lat1) * Math.Cos(lat2);
return(S1Angle.FromRadians(2 * Math.Atan2(Math.Sqrt(x), Math.Sqrt(Math.Max(0.0, 1.0 - x)))));
// Return the distance (measured along the surface of the sphere) to the
// given S2LatLng. This is mathematically equivalent to:
//
// S1Angle::FromRadians(ToPoint().Angle(o.ToPoint())
//
// but this implementation is slightly more efficient.
}
/**
* 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));
}
private S2PolygonBuilderOptions(bool undirectedEdges, bool xorEdges)
{
UndirectedEdges = undirectedEdges;
XorEdges = xorEdges;
Validate = false;
_mergeDistance = S1Angle.FromRadians(0);
}
/**
* Create a cap given its axis and the cap opening angle, i.e. maximum angle
* between the axis and a point on the cap. 'axis' should be a unit-length
* vector, and 'angle' should be between 0 and 180 degrees.
*/
public static S2Cap FromAxisAngle(S2Point axis, S1Angle angle)
{
// The height of the cap can be computed as 1-cos(angle), but this isn't
// very accurate for angles close to zero (where cos(angle) is almost 1).
// Computing it as 2*(sin(angle/2)**2) gives much better precision.
// assert (S2.isUnitLength(axis));
var d = Math.Sin(0.5 * angle.Radians);
return(new S2Cap(axis, 2 * d * d));
}
/**
* 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 a rectangle that contains the convolution of this rectangle with a
* cap of the given angle. This expands the rectangle by a fixed distance (as
* opposed to growing the rectangle in latitude-longitude space). The returned
* rectangle includes all points whose minimum distance to the original
* rectangle is at most the given angle.
*/
public S2LatLngRect ConvolveWithCap(S1Angle angle)
{
// The most straightforward approach is to build a cap centered on each
// vertex and take the union of all the bounding rectangles (including the
// original rectangle; this is necessary for very large rectangles).
// Optimization: convert the angle to a height exactly once.
var cap = S2Cap.FromAxisAngle(new S2Point(1, 0, 0), angle);
var r = this;
for (var k = 0; k < 4; ++k)
{
var vertexCap = S2Cap.FromAxisHeight(GetVertex(k).ToPoint(), cap.Height);
r = r.Union(vertexCap.RectBound);
}
return(r);
}
/**
* 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);
}
/**
* Expand the cell union such that it contains all points whose distance to
* the cell union is at most minRadius, but do not use cells that are more
* than maxLevelDiff levels higher than the largest cell in the input. The
* second parameter controls the tradeoff between accuracy and output size
* when a large region is being expanded by a small amount (e.g. expanding
* Canada by 1km).
*
* For example, if maxLevelDiff == 4, the region will always be expanded by
* approximately 1/16 the width of its largest cell. Note that in the worst
* case, the number of cells in the output can be up to 4 * (1 + 2 **
* maxLevelDiff) times larger than the number of cells in the input.
*/
public void Expand(S1Angle minRadius, int maxLevelDiff)
{
var minLevel = S2CellId.MaxLevel;
foreach (var id in this)
{
minLevel = Math.Min(minLevel, id.Level);
}
// Find the maximum level such that all cells are at least "min_radius"
// wide.
var radiusLevel = S2Projections.MinWidth.GetMaxLevel(minRadius.Radians);
if (radiusLevel == 0 && minRadius.Radians > S2Projections.MinWidth.GetValue(0))
{
// The requested expansion is greater than the width of a face cell.
// The easiest way to handle this is to expand twice.
Expand(0);
}
Expand(Math.Min(minLevel + maxLevelDiff, radiusLevel));
}
public static S2LatLng FromDegrees(double latDegrees, double lngDegrees)
{
return(new S2LatLng(S1Angle.FromDegrees(latDegrees), S1Angle.FromDegrees(lngDegrees)));
}
/**
* 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)))));
}
public static S2LatLng FromE6(long latE6, long lngE6)
{
return(new S2LatLng(S1Angle.E6(latE6), S1Angle.E6(lngE6)));
}
public static S2LatLng FromE7(long latE7, long lngE7)
{
return(new S2LatLng(S1Angle.E7(latE7), S1Angle.E7(lngE7)));
}
public static S1Angle Longitude(S2Point p)
{
// Note that atan2(0, 0) is defined to be zero.
return(S1Angle.FromRadians(Math.Atan2(p[1], p[0])));
}
/**
* Return a polygon which is the union of the given polygons; combines
* vertices that form edges that are almost identical, as defined by
* vertexMergeRadius. Note: clears the List!
*/
public static S2Polygon DestructiveUnionSloppy(System.Collections.Generic.ICollection <S2Polygon> polygons, S1Angle vertexMergeRadius)
{
// Effectively create a priority queue of polygons in order of number of
// vertices. Repeatedly union the two smallest polygons and add the result
// to the queue until we have a single polygon to return.
// map: # of vertices -> polygon
//TreeMultimap<Integer, S2Polygon> queue = TreeMultimap.create();
var queue = new MultiMap <int, S2Polygon>();
foreach (var polygon in polygons)
{
queue.Add(polygon.NumVertices, polygon);
}
polygons.Clear();
// Java uses a live-view that maps to the underlying structure
//Set<Map.Entry<Integer, S2Polygon>> queueSet = queue.entries();
var enumer = queue.SortedValues;
while (queue.CountIsAtLeast(2))
{
// Pop two simplest polygons from queue.
// queueSet = queue.entries();
//Iterator<Map.Entry<Integer, S2Polygon>> smallestIter = queueSet.iterator();
var smallestTwo = enumer.Take(2).ToList();
//Map.Entry<Integer, S2Polygon> smallest = smallestIter.next();
//int aSize = smallest.getKey().intValue();
//S2Polygon aPolygon = smallest.getValue();
//smallestIter.remove();
//smallest = smallestIter.next();
//int bSize = smallest.getKey().intValue();
//S2Polygon bPolygon = smallest.getValue();
//smallestIter.remove();
foreach (var item in smallestTwo)
{
queue.Remove(item);
}
// Union and add result back to queue.
var unionPolygon = new S2Polygon();
unionPolygon.InitToUnionSloppy(smallestTwo[0].Value, smallestTwo[1].Value, vertexMergeRadius);
var unionSize = smallestTwo[0].Key + smallestTwo[1].Key;
queue.Add(unionSize, unionPolygon);
// We assume that the number of vertices in the union polygon is the
// sum of the number of vertices in the original polygons, which is not
// always true, but will almost always be a decent approximation, and
// faster than recomputing.
}
if (queue.Count == 0)
{
return(new S2Polygon());
}
else
{
//return queue.get(queue.asMap().firstKey()).first();
return(queue.SortedValues.First().Value);
}
}
/**
* Basic constructor. The latitude and longitude must be within the ranges
* allowed by is_valid() below.
*
* TODO(dbeaumont): Make this a static factory method (fromLatLng() ?).
*/
public S2LatLng(S1Angle lat, S1Angle lng) : this(lat.Radians, lng.Radians)
{
}
public static S2LatLng FromE5(long latE5, long lngE5)
{
return(new S2LatLng(S1Angle.E5(latE5), S1Angle.E5(lngE5)));
}
