// This method verifies a.GetDistance(b), where b is a S2LatLng, by comparing
// its result against a.GetDistance(c), c being the point rectangle created
// from b.
private static void VerifyGetRectPointDistance(S2LatLngRect a, S2LatLng p)
{
S1Angle distance1 = BruteForceRectPointDistance(a, p.Normalized());
S1Angle distance2 = a.GetDistance(p.Normalized());
Assert2.Near(Math.Abs(distance1.Radians - distance2.Radians), 0, 1e-10);
}
public static ulong[] GetCellIdsForLatLong(double latitude, double longitude)
{
var latLong = S2LatLng.FromDegrees(latitude, longitude);
var cell = S2CellId.FromLatLng(latLong);
var cellId = cell.ParentForLevel(15);
var cells = cellId.GetEdgeNeighbors();
var cellIds = new List <ulong>
{
cellId.Id
};
foreach (var cellEdge1 in cells)
{
if (!cellIds.Contains(cellEdge1.Id))
{
cellIds.Add(cellEdge1.Id);
}
foreach (var cellEdge2 in cellEdge1.GetEdgeNeighbors())
{
if (!cellIds.Contains(cellEdge2.Id))
{
cellIds.Add(cellEdge2.Id);
}
}
}
return(cellIds.ToArray());
}
public void AddUser(Guid uid, double lon, double lat)
{
var lonLat = S2LatLng.FromDegrees(lat, lon);
var cellId = S2CellId.FromLatLng(lonLat);
var cellIdStorageLevel = cellId.ParentForLevel(_level);
var userList = new UserList {
s2CellId = cellIdStorageLevel, list = new List <Guid>()
};
var item = tree.Search(userList.s2CellId);
if (item != null)
{
userList = new UserList {
s2CellId = item.Key, list = item.Pointer
};
tree.Delete(userList.s2CellId);
}
if (userList.list == null)
{
userList.list = new List <Guid>();
}
userList.list.Add(uid);
tree.Insert(userList.s2CellId, userList.list);
}
public void Test_S2LatLngRect_FromPoint()
{
S2LatLng p = S2LatLng.FromDegrees(23, 47);
Assert.Equal(S2LatLngRect.FromPoint(p), new S2LatLngRect(p, p));
Assert.True(S2LatLngRect.FromPoint(p).IsPoint());
}
// Returns the bounding rectangle of the edge chain that connects the
// vertices defined so far. This bound satisfies the guarantee made
// above, i.e. if the edge chain defines a loop, then the bound contains
// the S2LatLng coordinates of all S2Points contained by the loop.
public S2LatLngRect GetBound()
{
// To save time, we ignore numerical errors in the computed S2LatLngs while
// accumulating the bounds and then account for them here.
//
// S2LatLng(S2Point) has a maximum error of 0.955 * S2Constants.DoubleEpsilon in latitude.
// In the worst case, we might have rounded "inwards" when computing the
// bound and "outwards" when computing the latitude of a contained point P,
// therefore we expand the latitude bounds by 2 * S2Constants.DoubleEpsilon in each
// direction. (A more complex analysis shows that 1.5 * S2Constants.DoubleEpsilon is
// enough, but the expansion amount should be a multiple of S2Constants.DoubleEpsilon in
// order to avoid rounding errors during the expansion itself.)
//
// S2LatLng(S2Point) has a maximum error of S2Constants.DoubleEpsilon in longitude, which
// is simply the maximum rounding error for results in the range [-Pi, Pi].
// This is true because the Gnu implementation of atan2() comes from the IBM
// Accurate Mathematical Library, which implements correct rounding for this
// instrinsic (i.e., it returns the infinite precision result rounded to the
// nearest representable value, with ties rounded to even values). This
// implies that we don't need to expand the longitude bounds at all, since
// we only guarantee that the bound contains the *rounded* latitudes of
// contained points. The *true* latitudes of contained points may lie up to
// S2Constants.DoubleEpsilon outside of the returned bound.
S2LatLng kExpansion = S2LatLng.FromRadians(2 * S2.DoubleEpsilon, 0);
return(bound_.Expanded(kExpansion).PolarClosure());
}
private static void TestIntervalOps(S2LatLngRect x, S2LatLngRect y, string expected_relation, S2LatLngRect expected_union, S2LatLngRect expected_intersection)
{
// Test all of the interval operations on the given pair of intervals.
// "expected_relation" is a sequence of "T" and "F" characters corresponding
// to the expected results of Contains(), InteriorContains(), Intersects(),
// and InteriorIntersects() respectively.
Assert.Equal(x.Contains(y), expected_relation[0] == 'T');
Assert.Equal(x.InteriorContains(y), expected_relation[1] == 'T');
Assert.Equal(x.Intersects(y), expected_relation[2] == 'T');
Assert.Equal(x.InteriorIntersects(y), expected_relation[3] == 'T');
Assert.Equal(x.Contains(y), x.Union(y) == x);
Assert.Equal(x.Intersects(y), !x.Intersection(y).IsEmpty());
Assert.Equal(x.Union(y), expected_union);
Assert.Equal(x.Intersection(y), expected_intersection);
if (y.Size() == S2LatLng.FromRadians(0, 0))
{
S2LatLngRect r = x;
r.AddPoint(y.Lo());
Assert.Equal(r, expected_union);
}
}
/// <summary>
/// Filter out any points outside of the queried area from the input list.
/// </summary>
/// <param name="list">List of items return by Amazon DynamoDB. It may contains points outside of the actual area queried.</param>
/// <param name="geoQueryRequest">List of items within the queried area.</param>
/// <returns></returns>
private IEnumerable <IDictionary <string, AttributeValue> > Filter(IEnumerable <IDictionary <string, AttributeValue> > list,
GeoQueryRequest geoQueryRequest)
{
var result = new List <IDictionary <String, AttributeValue> >();
S2LatLngRect?latLngRect = null;
S2LatLng? centerLatLng = null;
double radiusInMeter = 0;
if (geoQueryRequest is QueryRectangleRequest)
{
latLngRect = S2Util.GetBoundingLatLngRect(geoQueryRequest);
}
foreach (var item in list)
{
var geoJson = item[_config.GeoJsonAttributeName].S;
var geoPoint = GeoJsonMapper.GeoPointFromString(geoJson);
var latLng = S2LatLng.FromDegrees(geoPoint.lat, geoPoint.lng);
if (latLngRect != null && latLngRect.Value.Contains(latLng))
{
result.Add(item);
}
else if (centerLatLng != null && radiusInMeter > 0 &&
centerLatLng.Value.GetEarthDistance(latLng) <= radiusInMeter)
{
result.Add(item);
}
}
return(result);
}
public List <S2CellId> GetS2CellIds(ushort level, int maxCells)
{
//var geofence = Geofence.FromMultiPolygon(this);
var bbox = GetBoundingBox();
var regionCoverer = new S2RegionCoverer
{
MinLevel = level,
MaxLevel = level,
MaxCells = maxCells,
};
var region = new S2LatLngRect(
S2LatLng.FromDegrees(bbox.MinimumLatitude, bbox.MinimumLongitude),
S2LatLng.FromDegrees(bbox.MaximumLatitude, bbox.MaximumLongitude)
);
var coverage = new List <S2CellId>();
regionCoverer.GetCovering(region, coverage);
var result = new List <S2CellId>();
foreach (var cellId in coverage)
{
var cell = new S2Cell(cellId);
for (var i = 0; i <= 3; i++)
{
var vertex = cell.GetVertex(i);
var coord = new S2LatLng(new S2Point(vertex.X, vertex.Y, vertex.Z));
//if (geofence.Intersects(coord.LatDegrees, coord.LngDegrees))
if (GeofenceService.InPolygon(this, coord.LatDegrees, coord.LngDegrees))
{
result.Add(cellId);
}
}
}
return(result);
}
/**
* This method verifies a.getDistance(b), where b is a S2LatLng, by comparing
* its result against a.getDistance(c), c being the point rectangle created
* from b.
*/
private static void verifyGetRectPointDistance(S2LatLngRect a, S2LatLng p)
{
var distance1 = bruteForceRectPointDistance(a, p.Normalized);
var distance2 = a.GetDistance(p.Normalized);
assertEquals(distance1.Radians, distance2.Radians, 1e-10);
}
public void Test_MakeLatLngRect_ValidInput()
{
Assert.True(MakeLatLngRect("-10:-10, 10:10", out var rect));
Assert.Equal(rect, new S2LatLngRect(
S2LatLng.FromDegrees(-10, -10),
S2LatLng.FromDegrees(10, 10)));
}
public void Test_S2LatLng_TestDistance()
{
Assert.Equal(0.0, S2LatLng.FromDegrees(90, 0).GetDistance(S2LatLng.FromDegrees(90, 0)).Radians);
Assert2.Near(77.0, S2LatLng.FromDegrees(-37, 25).GetDistance(S2LatLng.FromDegrees(-66, -155)).GetDegrees(), 1e-13);
Assert2.Near(115.0, S2LatLng.FromDegrees(0, 165).GetDistance(S2LatLng.FromDegrees(0, -80)).GetDegrees(), 1e-13);
Assert2.Near(180.0, S2LatLng.FromDegrees(47, -127).GetDistance(S2LatLng.FromDegrees(-47, 53)).GetDegrees(), 2e-6);
}
public void testConversion()
{
// Test special cases: poles, "date line"
assertDoubleNear(
new S2LatLng(S2LatLng.FromDegrees(90.0, 65.0).ToPoint()).Lat.Degrees, 90.0);
assertEquals(
new S2LatLng(S2LatLng.FromRadians(-S2.PiOver2, 1).ToPoint()).Lat.Radians, -S2.PiOver2);
assertDoubleNear(
Math.Abs(new S2LatLng(S2LatLng.FromDegrees(12.2, 180.0).ToPoint()).Lng.Degrees), 180.0);
assertEquals(
Math.Abs(new S2LatLng(S2LatLng.FromRadians(0.1, -S2.Pi).ToPoint()).Lng.Radians),
S2.Pi);
// Test a bunch of random points.
for (var i = 0; i < 100000; ++i)
{
var p = randomPoint();
assertTrue(S2.ApproxEquals(p, new S2LatLng(p).ToPoint()));
}
// Test generation from E5
var test = S2LatLng.FromE5(123456, 98765);
assertDoubleNear(test.Lat.Degrees, 1.23456);
assertDoubleNear(test.Lng.Degrees, 0.98765);
}
public void Test_LoopTestBase_GetAreaConsistentWithOrientation()
{
// Test that GetArea() returns an area near 0 for degenerate loops that
// contain almost no points, and an area near 4*Pi for degenerate loops that
// contain almost all points.
const int kMaxVertices = 6;
for (int i = 0; i < 50; ++i)
{
int num_vertices = 3 + S2Testing.Random.Uniform(kMaxVertices - 3 + 1);
// Repeatedly choose N vertices that are exactly on the equator until we
// find some that form a valid loop.
S2PointLoopSpan loop = new();
do
{
for (int i2 = 0; i2 < num_vertices; ++i2)
{
// We limit longitude to the range [0, 90] to ensure that the loop is
// degenerate (as opposed to following the entire equator).
loop.Add(
S2LatLng.FromRadians(0, S2Testing.Random.RandDouble() * S2.M_PI_2).ToPoint());
}
} while (!new S2Loop(loop, S2Debug.DISABLE).IsValid());
bool ccw = S2.IsNormalized(loop);
// The error bound is sufficient for current tests but not guaranteed.
_ = i + ": " + loop.ToDebugString();
Assert2.Near(ccw ? 0 : S2.M_4_PI, S2.GetArea(loop), 1e-14);
Assert.Equal(!ccw, new S2Loop(loop).Contains(new S2Point(0, 0, 1)));
}
}
private S2CellId getCellId(double latDegrees, double lngDegrees)
{
var id = S2CellId.FromLatLng(S2LatLng.FromDegrees(latDegrees, lngDegrees));
Trace.WriteLine(Convert.ToString(unchecked ((long)id.Id), 16));
return(id);
}
private static List <Coordinate> GetS2Cells(BoundingBox bbox)
{
var regionCoverer = new S2RegionCoverer
{
MinLevel = 15,
MaxLevel = 15,
//MaxCells = 100,
};
var region = new S2LatLngRect(
S2LatLng.FromDegrees(bbox.MinimumLatitude, bbox.MinimumLongitude),
S2LatLng.FromDegrees(bbox.MaximumLatitude, bbox.MaximumLongitude)
);
var cellIds = regionCoverer.GetCovering(region);
var list = new List <Coordinate>();
foreach (var cellId in cellIds)
{
var center = cellId.ToLatLng();
list.Add(new Coordinate(center.LatDegrees, center.LngDegrees));
}
// TODO: Check if point is within geofence
//var filtered = FilterCoordinates(coordinates);
//return filtered;
return(list);
}
/// <summary>
/// Find the cell of the given level that covers the given Geoposition.
/// This method uses the library given S2RegionCoverer to find the leaf cell containing the given Geoposition
/// and uses binary operation on the leaf cell's Id to find the higher level cell containing the leaf.
/// This is somehow more accurate than using the S2RegionCoverer for the higher level cell, where some errors occured.
/// </summary>
/// <param name="pos">Position in the cell</param>
/// <param name="level">Level of the cell</param>
/// <returns>The cell covering the given position that matches the specifications</returns>
private S2Cell FindExactCell(BasicGeoposition pos, int level)
{
var point = S2LatLngRect.FromPoint(S2LatLng.FromDegrees(pos.Latitude, pos.Longitude));
var cells = new List <S2CellId>();
// find leaf cell
var coverer = new S2RegionCoverer()
{
MinLevel = 30,
MaxLevel = 30,
MaxCells = 1
};
coverer.GetCovering(point, cells);
var leaf = new S2Cell(cells[0]);
int shift = 64 - (3 + level * 2 + 1);
ulong id = leaf.Id.Id & ulong.MaxValue << shift;
id |= 0 | ((ulong)1 << shift);
return(new S2Cell(new S2CellId(id)));
}
public static ulong GetPokeCell(ICoordinate poke)
{
var latLng = S2LatLng.FromDegrees((double)poke.Latitude, (double)poke.Longitude);
var hash = S2CellId.FromLatLng(latLng).ParentForLevel(20).Id;
return(hash);
}
// This function assumes that GetDirectedHausdorffDistance() always returns
// a distance from some point in a to b. So the function mainly tests whether
// the returned distance is large enough, and only does a weak test on whether
// it is small enough.
private static void VerifyGetDirectedHausdorffDistance(S2LatLngRect a, S2LatLngRect b)
{
S1Angle hausdorff_distance = a.GetDirectedHausdorffDistance(b);
const double kResolution = 0.1;
S1Angle max_distance = S1Angle.Zero;
int sample_size_on_lat =
(int)(a.Lat.GetLength() / kResolution) + 1;
int sample_size_on_lng =
(int)(a.Lng.GetLength() / kResolution) + 1;
double delta_on_lat = a.Lat.GetLength() / sample_size_on_lat;
double delta_on_lng = a.Lng.GetLength() / sample_size_on_lng;
double lng = a.Lng.Lo;
for (int i = 0; i <= sample_size_on_lng; ++i, lng += delta_on_lng)
{
double lat = a.Lat.Lo;
for (int j = 0; j <= sample_size_on_lat; ++j, lat += delta_on_lat)
{
S2LatLng latlng = S2LatLng.FromRadians(lat, lng).Normalized();
S1Angle distance_to_b = b.GetDistance(latlng);
if (distance_to_b >= max_distance)
{
max_distance = distance_to_b;
}
}
}
Assert.True(max_distance.Radians <= hausdorff_distance.Radians + 1e-10);
Assert.True(max_distance.Radians >= hausdorff_distance.Radians - kResolution);
}
public void Test_S2LatLngRect_GetVertex()
{
S2LatLngRect r1 = new(new R1Interval(0, S2.M_PI_2), new S1Interval(-Math.PI, 0));
Assert.Equal(r1.Vertex(0), S2LatLng.FromRadians(0, Math.PI));
Assert.Equal(r1.Vertex(1), S2LatLng.FromRadians(0, 0));
Assert.Equal(r1.Vertex(2), S2LatLng.FromRadians(S2.M_PI_2, 0));
Assert.Equal(r1.Vertex(3), S2LatLng.FromRadians(S2.M_PI_2, Math.PI));
// Make sure that GetVertex() returns vertices in CCW order.
for (int i = 0; i < 4; ++i)
{
double lat = S2.M_PI_4 * (i - 2);
double lng = S2.M_PI_2 * (i - 2) + 0.2;
S2LatLngRect r = new(
new R1Interval(lat, lat + S2.M_PI_4),
new S1Interval(
Math.IEEERemainder(lng, S2.M_2_PI),
Math.IEEERemainder(lng + S2.M_PI_2, S2.M_2_PI)));
for (int k = 0; k < 4; ++k)
{
Assert.True(S2Pred.Sign(
r.Vertex(k - 1).ToPoint(),
r.Vertex(k).ToPoint(),
r.Vertex(k + 1).ToPoint()) > 0);
}
}
}
public void testGetClosestPoint()
{
var kMargin = 1e-6;
var a = S2LatLng.FromDegrees(-0.5, 0).ToPoint();
var b = S2LatLng.FromDegrees(+0.5, 0).ToPoint();
// On edge at end points.
assertEquals(a, S2EdgeUtil.GetClosestPoint(a, a, b));
assertEquals(b, S2EdgeUtil.GetClosestPoint(b, a, b));
// On edge in between.
var mid = S2LatLng.FromDegrees(0, 0).ToPoint();
assertEquals(mid, S2EdgeUtil.GetClosestPoint(mid, a, b));
// End points are closest
assertEquals(a, S2EdgeUtil.GetClosestPoint(S2LatLng.FromDegrees(-1, 0).ToPoint(), a, b));
assertEquals(b, S2EdgeUtil.GetClosestPoint(S2LatLng.FromDegrees(+1, 0).ToPoint(), a, b));
// Intermediate point is closest.
var x = S2LatLng.FromDegrees(+0.1, 1).ToPoint();
var expectedClosestPoint = S2LatLng.FromDegrees(+0.1, 0).ToPoint();
assertTrue(expectedClosestPoint.ApproxEquals(S2EdgeUtil.GetClosestPoint(x, a, b), kMargin));
}
public void testIntervalOps(S2LatLngRect x, S2LatLngRect y, String expectedRelation,
S2LatLngRect expectedUnion, S2LatLngRect expectedIntersection)
{
// Test all of the interval operations on the given pair of intervals.
// "expected_relation" is a sequence of "T" and "F" characters corresponding
// to the expected results of Contains(), InteriorContains(), Intersects(),
// and InteriorIntersects() respectively.
assertEquals(x.Contains(y), expectedRelation[0] == 'T');
assertEquals(x.InteriorContains(y), expectedRelation[1] == 'T');
assertEquals(x.Intersects(y), expectedRelation[2] == 'T');
assertEquals(x.InteriorIntersects(y), expectedRelation[3] == 'T');
assertEquals(x.Contains(y), x.Union(y).Equals(x));
assertEquals(x.Intersects(y), !x.Intersection(y).IsEmpty);
assertTrue(x.Union(y).Equals(expectedUnion));
assertTrue(x.Intersection(y).Equals(expectedIntersection));
if (y.Size == S2LatLng.FromRadians(0, 0))
{
var r = x.AddPoint(y.Lo);
assertTrue(r == expectedUnion);
}
}
public List <Guid> Search(double lon, double lat, int radius)
{
var latlng = S2LatLng.FromDegrees(lat, lon);
var centerPoint = pointFromLatLng(lat, lon);
var centerAngle = ((double)radius) / EarthRadiusM;
var cap = S2Cap.FromAxisAngle(centerPoint, S1Angle.FromRadians(centerAngle));
var regionCoverer = new S2RegionCoverer();
regionCoverer.MaxLevel = 13;
// regionCoverer.MinLevel = 13;
//regionCoverer.MaxCells = 1000;
// regionCoverer.LevelMod = 0;
var covering = regionCoverer.GetCovering(cap);
var res = new List <Guid>();
foreach (var u in covering)
{
var sell = new S2CellId(u.Id);
if (sell.Level < _level)
{
var begin = sell.ChildBeginForLevel(_level);
var end = sell.ChildEndForLevel(_level);
do
{
var cur = tree.Search(new S2CellId(begin.Id));
if (cur != null)
{
res.AddRange(cur.Pointer);
}
begin = begin.Next;
} while (begin.Id != end.Id);
}
else
{
var item = tree.Search(sell);
if (item != null)
{
res.AddRange(item.Pointer);
}
}
}
return(res);
}
private void assertPointApproximatelyEquals(
S2Loop s2Loop, int vertexIndex, double lat, double lng, double error)
{
var latLng = new S2LatLng(s2Loop.Vertex(vertexIndex));
assertDoubleNear(latLng.LatDegrees, lat, error);
assertDoubleNear(latLng.LngDegrees, lng, error);
}
public static ulong GenerateGeohash(GeoPoint geoPoint)
{
var latLng = S2LatLng.FromDegrees(geoPoint.lat, geoPoint.lng);
var cell = new S2Cell(latLng);
var cellId = cell.Id;
return(cellId.Id);
}
public static ulong GenerateGeohash(double latitude, double longitude)
{
var latLng = S2LatLng.FromDegrees(latitude, longitude);
var cell = new S2Cell(latLng);
var cellId = cell.Id;
return(cellId.Id);
}
public List <Guid> Search(double lon, double lat, int radius)
{
var latlng = S2LatLng.FromDegrees(lat, lon);
var centerPoint = Index.pointFromLatLng(lat, lon);
var centerAngle = ((double)radius) / Index.EarthRadiusM;
var cap = S2Cap.FromAxisAngle(centerPoint, S1Angle.FromRadians(centerAngle));
var regionCoverer = new S2RegionCoverer();
regionCoverer.MaxLevel = 13;
// regionCoverer.MinLevel = 13;
//regionCoverer.MaxCells = 1000;
// regionCoverer.LevelMod = 0;
var covering = regionCoverer.GetCovering(cap);
var res = new List <Guid>();
foreach (var u in covering)
{
var sell = new S2CellId(u.Id);
if (sell.Level < _level)
{
var begin = sell.ChildBeginForLevel(_level);
var end = sell.ChildEndForLevel(_level);
var qres = rtree.Query(new Range <S2CellId>(begin, end));
foreach (var r in qres)
{
res.AddRange(r.Content);
}
}
else
{
var qres = rtree.Query(new Range <S2CellId>(sell));
if (qres.Count > 0)
{
foreach (var r in qres)
{
res.AddRange(r.Content);
}
}
}
}
return(res);
}
private static S2LatLngRect RectFromDegrees(double lat_lo, double lng_lo, double lat_hi, double lng_hi)
{
// Convenience method to construct a rectangle. This method is
// intentionally *not* in the S2LatLngRect interface because the
// argument order is ambiguous, but hopefully it's not too confusing
// within the context of this unit test.
return(new S2LatLngRect(S2LatLng.FromDegrees(lat_lo, lng_lo).Normalized(), S2LatLng.FromDegrees(lat_hi, lng_hi).Normalized()));
}
public override S2LatLng ToLatLng(R2Point p)
{
// This formula is more accurate near zero than the atan(exp()) version.
double x = to_radians_ * Math.IEEERemainder(p.X, x_wrap_);
double k = Math.Exp(2 * to_radians_ * p.Y);
double y = double.IsInfinity(k) ? S2.M_PI_2 : Math.Asin((k - 1) / (k + 1));
return(S2LatLng.FromRadians(y, x));
}
public void Test_E6()
{
for (var i = 0; i < kIters; i++)
{
var ll = S2LatLng.FromPoint(S2Testing.RandomPoint());
var ll_e6 = S2LatLng.FromE6(ll.Lat().E6(), ll.Lng().E6());
ExpectMaxDigits(ll_e6, 6);
}
}
public override R2Point FromLatLng(S2LatLng ll)
{
// This formula is more accurate near zero than the log(tan()) version.
// Note that latitudes of +/- 90 degrees yield "y" values of +/- infinity.
double sin_phi = Math.Sin(ll.LatRadians);
double y = 0.5 * Math.Log((1 + sin_phi) / (1 - sin_phi));
return(new R2Point(from_radians_ * ll.LngRadians, from_radians_ * y));
}
public static void DrawS2Cells(List<ulong> cellsIds, GMapOverlay mapLayer)
{
for (int i=0; i<cellsIds.Count; i++)
{
S2CellId cellId = new S2CellId(cellsIds[i]);
S2Cell cell = new S2Cell(cellId);
List<PointLatLng> points = new List<PointLatLng>();
for (int j=0; j<4; j++)
{
S2LatLng point = new S2LatLng(cell.GetVertex(j));
points.Add(new PointLatLng(point.LatDegrees, point.LngDegrees));
}
GMapPolygon polygon = new GMapPolygon(points, "mypolygon");
polygon.Fill = new SolidBrush(Color.FromArgb(50, Color.Red));
polygon.Stroke = new Pen(Color.Red, 1);
mapLayer.Polygons.Add(polygon);
}
}
public void AddPoint(S2Point b)
{
// assert (S2.isUnitLength(b));
var bLatLng = new S2LatLng(b);
if (bound.IsEmpty)
{
bound = bound.AddPoint(bLatLng);
}
else
{
// We can't just call bound.addPoint(bLatLng) here, since we need to
// ensure that all the longitudes between "a" and "b" are included.
bound = bound.Union(S2LatLngRect.FromPointPair(aLatLng, bLatLng));
// Check whether the Min/Max latitude occurs in the edge interior.
// We find the normal to the plane containing AB, and then a vector
// "dir" in this plane that also passes through the equator. We use
// RobustCrossProd to ensure that the edge normal is accurate even
// when the two points are very close together.
var aCrossB = S2.RobustCrossProd(a, b);
var dir = S2Point.CrossProd(aCrossB, new S2Point(0, 0, 1));
var da = dir.DotProd(a);
var db = dir.DotProd(b);
if (da*db < 0)
{
// Minimum/maximum latitude occurs in the edge interior. This affects
// the latitude bounds but not the longitude bounds.
var absLat = Math.Acos(Math.Abs(aCrossB[2]/aCrossB.Norm));
var lat = bound.Lat;
if (da < 0)
{
// It's possible that absLat < lat.lo() due to numerical errors.
lat = new R1Interval(lat.Lo, Math.Max(absLat, bound.Lat.Hi));
}
else
{
lat = new R1Interval(Math.Min(-absLat, bound.Lat.Lo), lat.Hi);
}
bound = new S2LatLngRect(lat, bound.Lng);
}
}
a = b;
aLatLng = bLatLng;
}
private void assertPointApproximatelyEquals(
S2Loop s2Loop, int vertexIndex, double lat, double lng, double error)
{
var latLng = new S2LatLng(s2Loop.Vertex(vertexIndex));
assertDoubleNear(latLng.LatDegrees, lat, error);
assertDoubleNear(latLng.LngDegrees, lng, error);
}
private static S1Angle bruteForceRectPointDistance(S2LatLngRect a, S2LatLng b)
{
if (a.Contains(b))
{
return S1Angle.FromRadians(0);
}
var bToLoLat = getDistance(b, a.LatLo, a.Lng);
var bToHiLat = getDistance(b, a.LatHi, a.Lng);
var bToLoLng =
S2EdgeUtil.GetDistance(b.ToPoint(), new S2LatLng(a.LatLo, a.LngLo).ToPoint(),
new S2LatLng(a.LatHi, a.LngLo).ToPoint());
var bToHiLng =
S2EdgeUtil.GetDistance(b.ToPoint(), new S2LatLng(a.LatLo, a.LngHi).ToPoint(),
new S2LatLng(a.LatHi, a.LngHi).ToPoint());
return S1Angle.Min(bToLoLat, S1Angle.Min(bToHiLat, S1Angle.Min(bToLoLng, bToHiLng)));
}
public void testGetDistanceRandomPairs()
{
// Test random pairs.
for (var i = 0; i < 10000; ++i)
{
var a =
S2LatLngRect.FromPointPair(new S2LatLng(randomPoint()), new S2LatLng(randomPoint()));
var b =
S2LatLngRect.FromPointPair(new S2LatLng(randomPoint()), new S2LatLng(randomPoint()));
verifyGetDistance(a, b);
var c = new S2LatLng(randomPoint());
verifyGetRectPointDistance(a, c);
verifyGetRectPointDistance(b, c);
}
}
public void testBasic()
{
// Most of the S2LatLngRect methods have trivial implementations that
// use the R1Interval and S1Interval classes, so most of the testing
// is done in those unit tests.
// Test basic properties of empty and full caps.
var empty = S2LatLngRect.Empty;
var full = S2LatLngRect.Full;
assertTrue(empty.IsValid);
assertTrue(empty.IsEmpty);
assertTrue(full.IsValid);
assertTrue(full.IsFull);
// assertTrue various constructors and accessor methods.
var d1 = rectFromDegrees(-90, 0, -45, 180);
assertDoubleNear(d1.LatLo.Degrees, -90);
assertDoubleNear(d1.LatHi.Degrees, -45);
assertDoubleNear(d1.LngLo.Degrees, 0);
assertDoubleNear(d1.LngHi.Degrees, 180);
assertTrue(d1.Lat.Equals(new R1Interval(-S2.PiOver2, -S2.PiOver4)));
assertTrue(d1.Lng.Equals(new S1Interval(0, S2.Pi)));
// FromCenterSize()
assertTrue(
S2LatLngRect.FromCenterSize(S2LatLng.FromDegrees(80, 170), S2LatLng.FromDegrees(40, 60))
.ApproxEquals(rectFromDegrees(60, 140, 90, -160)));
assertTrue(S2LatLngRect
.FromCenterSize(S2LatLng.FromDegrees(10, 40), S2LatLng.FromDegrees(210, 400)).IsFull);
assertTrue(
S2LatLngRect.FromCenterSize(S2LatLng.FromDegrees(-90, 180), S2LatLng.FromDegrees(20, 50))
.ApproxEquals(rectFromDegrees(-90, 155, -80, -155)));
// FromPoint(), FromPointPair()
assertEquals(S2LatLngRect.FromPoint(d1.Lo), new S2LatLngRect(d1.Lo, d1.Lo));
assertEquals(
S2LatLngRect.FromPointPair(S2LatLng.FromDegrees(-35, -140), S2LatLng.FromDegrees(15, 155)),
rectFromDegrees(-35, 155, 15, -140));
assertEquals(
S2LatLngRect.FromPointPair(S2LatLng.FromDegrees(25, -70), S2LatLng.FromDegrees(-90, 80)),
rectFromDegrees(-90, -70, 25, 80));
// GetCenter(), GetVertex(), Contains(S2LatLng), InteriorContains(S2LatLng).
var eqM180 = S2LatLng.FromRadians(0, -S2.Pi);
var northPole = S2LatLng.FromRadians(S2.PiOver2, 0);
var r1 = new S2LatLngRect(eqM180, northPole);
assertEquals(r1.Center, S2LatLng.FromRadians(S2.PiOver4, -S2.PiOver2));
assertEquals(r1.GetVertex(0), S2LatLng.FromRadians(0, S2.Pi));
assertEquals(r1.GetVertex(1), S2LatLng.FromRadians(0, 0));
assertEquals(r1.GetVertex(2), S2LatLng.FromRadians(S2.PiOver2, 0));
assertEquals(r1.GetVertex(3), S2LatLng.FromRadians(S2.PiOver2, S2.Pi));
assertTrue(r1.Contains(S2LatLng.FromDegrees(30, -45)));
assertTrue(!r1.Contains(S2LatLng.FromDegrees(30, 45)));
assertTrue(!r1.InteriorContains(eqM180) && !r1.InteriorContains(northPole));
assertTrue(r1.Contains(new S2Point(0.5, -0.3, 0.1)));
assertTrue(!r1.Contains(new S2Point(0.5, 0.2, 0.1)));
// Make sure that GetVertex() returns vertices in CCW order.
for (var i = 0; i < 4; ++i)
{
var lat = S2.PiOver4*(i - 2);
var lng = S2.PiOver2*(i - 2) + 0.2;
var r = new S2LatLngRect(new R1Interval(lat, lat + S2.PiOver4), new S1Interval(
Math.IEEERemainder(lng, 2*S2.Pi), Math.IEEERemainder(lng + S2.PiOver2, 2*S2.Pi)));
for (var k = 0; k < 4; ++k)
{
assertTrue(
S2.SimpleCcw(r.GetVertex((k - 1) & 3).ToPoint(), r.GetVertex(k).ToPoint(),
r.GetVertex((k + 1) & 3).ToPoint()));
}
}
// Contains(S2LatLngRect), InteriorContains(S2LatLngRect),
// Intersects(), InteriorIntersects(), Union(), Intersection().
//
// Much more testing of these methods is done in s1interval_unittest
// and r1interval_unittest.
var r1Mid = rectFromDegrees(45, -90, 45, -90);
var reqM180 = new S2LatLngRect(eqM180, eqM180);
var rNorthPole = new S2LatLngRect(northPole, northPole);
testIntervalOps(r1, r1Mid, "TTTT", r1, r1Mid);
testIntervalOps(r1, reqM180, "TFTF", r1, reqM180);
testIntervalOps(r1, rNorthPole, "TFTF", r1, rNorthPole);
assertTrue(r1.Equals(rectFromDegrees(0, -180, 90, 0)));
testIntervalOps(r1, rectFromDegrees(-10, -1, 1, 20), "FFTT", rectFromDegrees(-10, -180, 90, 20),
rectFromDegrees(0, -1, 1, 0));
testIntervalOps(r1, rectFromDegrees(-10, -1, 0, 20), "FFTF", rectFromDegrees(-10, -180, 90, 20),
rectFromDegrees(0, -1, 0, 0));
testIntervalOps(r1, rectFromDegrees(-10, 0, 1, 20), "FFTF", rectFromDegrees(-10, -180, 90, 20),
rectFromDegrees(0, 0, 1, 0));
testIntervalOps(rectFromDegrees(-15, -160, -15, -150), rectFromDegrees(20, 145, 25, 155),
"FFFF", rectFromDegrees(-15, 145, 25, -150), empty);
testIntervalOps(rectFromDegrees(70, -10, 90, -140), rectFromDegrees(60, 175, 80, 5), "FFTT",
rectFromDegrees(60, -180, 90, 180), rectFromDegrees(70, 175, 80, 5));
// assertTrue that the intersection of two rectangles that overlap in
// latitude
// but not longitude is valid, and vice versa.
testIntervalOps(rectFromDegrees(12, 30, 60, 60), rectFromDegrees(0, 0, 30, 18), "FFFF",
rectFromDegrees(0, 0, 60, 60), empty);
testIntervalOps(rectFromDegrees(0, 0, 18, 42), rectFromDegrees(30, 12, 42, 60), "FFFF",
rectFromDegrees(0, 0, 42, 60), empty);
// AddPoint()
var p = S2LatLngRect.Empty;
p = p.AddPoint(S2LatLng.FromDegrees(0, 0));
p = p.AddPoint(S2LatLng.FromRadians(0, -S2.PiOver2));
p = p.AddPoint(S2LatLng.FromRadians(S2.PiOver4, -S2.Pi));
p = p.AddPoint(new S2Point(0, 0, 1));
assertTrue(p.Equals(r1));
// Expanded()
assertTrue(
rectFromDegrees(70, 150, 80, 170).Expanded(S2LatLng.FromDegrees(20, 30)).ApproxEquals(
rectFromDegrees(50, 120, 90, -160)));
assertTrue(S2LatLngRect.Empty.Expanded(S2LatLng.FromDegrees(20, 30)).IsEmpty);
assertTrue(S2LatLngRect.Full.Expanded(S2LatLng.FromDegrees(20, 30)).IsFull);
assertTrue(
rectFromDegrees(-90, 170, 10, 20).Expanded(S2LatLng.FromDegrees(30, 80)).ApproxEquals(
rectFromDegrees(-90, -180, 40, 180)));
// ConvolveWithCap()
var llr1 =
new S2LatLngRect(S2LatLng.FromDegrees(0, 170), S2LatLng.FromDegrees(0, -170))
.ConvolveWithCap(S1Angle.FromDegrees(15));
var llr2 =
new S2LatLngRect(S2LatLng.FromDegrees(-15, 155), S2LatLng.FromDegrees(15, -155));
assertTrue(llr1.ApproxEquals(llr2));
llr1 = new S2LatLngRect(S2LatLng.FromDegrees(60, 150), S2LatLng.FromDegrees(80, 10))
.ConvolveWithCap(S1Angle.FromDegrees(15));
llr2 = new S2LatLngRect(S2LatLng.FromDegrees(45, -180), S2LatLng.FromDegrees(90, 180));
assertTrue(llr1.ApproxEquals(llr2));
// GetCapBound(), bounding cap at center is smaller:
assertTrue(new S2LatLngRect(S2LatLng.FromDegrees(-45, -45), S2LatLng.FromDegrees(45, 45)).CapBound.ApproxEquals(S2Cap.FromAxisHeight(new S2Point(1, 0, 0), 0.5)));
// GetCapBound(), bounding cap at north pole is smaller:
assertTrue(new S2LatLngRect(S2LatLng.FromDegrees(88, -80), S2LatLng.FromDegrees(89, 80)).CapBound.ApproxEquals(S2Cap.FromAxisAngle(new S2Point(0, 0, 1), S1Angle.FromDegrees(2))));
// GetCapBound(), longitude span > 180 degrees:
assertTrue(
new S2LatLngRect(S2LatLng.FromDegrees(-30, -150), S2LatLng.FromDegrees(-10, 50)).CapBound
.ApproxEquals(S2Cap.FromAxisAngle(new S2Point(0, 0, -1), S1Angle.FromDegrees(80))));
// Contains(S2Cell), MayIntersect(S2Cell), Intersects(S2Cell)
// Special cases.
testCellOps(empty, S2Cell.FromFacePosLevel(3, (byte)0, 0), 0);
testCellOps(full, S2Cell.FromFacePosLevel(2, (byte)0, 0), 4);
testCellOps(full, S2Cell.FromFacePosLevel(5, (byte)0, 25), 4);
// This rectangle includes the first quadrant of face 0. It's expanded
// slightly because cell bounding rectangles are slightly conservative.
var r4 = rectFromDegrees(-45.1, -45.1, 0.1, 0.1);
testCellOps(r4, S2Cell.FromFacePosLevel(0, (byte)0, 0), 3);
testCellOps(r4, S2Cell.FromFacePosLevel(0, (byte)0, 1), 4);
testCellOps(r4, S2Cell.FromFacePosLevel(1, (byte)0, 1), 0);
// This rectangle intersects the first quadrant of face 0.
var r5 = rectFromDegrees(-10, -45, 10, 0);
testCellOps(r5, S2Cell.FromFacePosLevel(0, (byte)0, 0), 3);
testCellOps(r5, S2Cell.FromFacePosLevel(0, (byte)0, 1), 3);
testCellOps(r5, S2Cell.FromFacePosLevel(1, (byte)0, 1), 0);
// Rectangle consisting of a single point.
testCellOps(rectFromDegrees(4, 4, 4, 4), S2Cell.FromFacePosLevel(0, (byte)0, 0), 3);
// Rectangles that intersect the bounding rectangle of a face
// but not the face itself.
testCellOps(rectFromDegrees(41, -87, 42, -79), S2Cell.FromFacePosLevel(2, (byte)0, 0), 1);
testCellOps(rectFromDegrees(-41, 160, -40, -160), S2Cell.FromFacePosLevel(5, (byte)0, 0), 1);
{
// This is the leaf cell at the top right hand corner of face 0.
// It has two angles of 60 degrees and two of 120 degrees.
var cell0tr = new S2Cell(new S2Point(1 + 1e-12, 1, 1));
var bound0tr = cell0tr.RectBound;
var v0 = new S2LatLng(cell0tr.GetVertexRaw(0));
testCellOps(
rectFromDegrees(v0.Lat.Degrees - 1e-8, v0.Lng.Degrees - 1e-8,
v0.Lat.Degrees - 2e-10, v0.Lng.Degrees + 1e-10), cell0tr, 1);
}
// Rectangles that intersect a face but where no vertex of one region
// is contained by the other region. The first one passes through
// a corner of one of the face cells.
testCellOps(rectFromDegrees(-37, -70, -36, -20), S2Cell.FromFacePosLevel(5, (byte)0, 0), 2);
{
// These two intersect like a diamond and a square.
var cell202 = S2Cell.FromFacePosLevel(2, (byte)0, 2);
var bound202 = cell202.RectBound;
testCellOps(
rectFromDegrees(bound202.Lo.Lat.Degrees + 3, bound202.Lo.Lng.Degrees + 3,
bound202.Hi.Lat.Degrees - 3, bound202.Hi.Lng.Degrees - 3), cell202, 2);
}
}
/**
* This method verifies a.getDistance(b), where b is a S2LatLng, by comparing
* its result against a.getDistance(c), c being the point rectangle created
* from b.
*/
private static void verifyGetRectPointDistance(S2LatLngRect a, S2LatLng p)
{
var distance1 = bruteForceRectPointDistance(a, p.Normalized);
var distance2 = a.GetDistance(p.Normalized);
assertEquals(distance1.Radians, distance2.Radians, 1e-10);
}
/**
* Returns the minimum distance from X to the latitude line segment defined by
* the given latitude and longitude interval.
*/
private static S1Angle getDistance(S2LatLng x, S1Angle lat, S1Interval interval)
{
assertTrue(x.IsValid);
assertTrue(interval.IsValid);
// Is X inside the longitude interval?
if (interval.Contains(x.Lng.Radians))
return S1Angle.FromRadians(Math.Abs(x.Lat.Radians - lat.Radians));
// Return the distance to the closer endpoint.
return S1Angle.Min(x.GetDistance(new S2LatLng(lat, S1Angle.FromRadians(interval.Lo))),
x.GetDistance(new S2LatLng(lat, S1Angle.FromRadians(interval.Hi))));
}