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);
}
}
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 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 void Test_BoundaryIntersects_RectCrossingAntiMeridian()
{
S2LatLngRect rect = RectFromDegrees(20, 170, 40, -170);
Assert.True(rect.Contains(MakePointOrDie("30:180")));
// Check that crossings of all four sides are detected.
Assert.True(rect.BoundaryIntersects(
MakePointOrDie("25:160"), MakePointOrDie("25:180")));
Assert.True(rect.BoundaryIntersects(
MakePointOrDie("25:-160"), MakePointOrDie("25:-180")));
Assert.True(rect.BoundaryIntersects(
MakePointOrDie("15:175"), MakePointOrDie("30:175")));
Assert.True(rect.BoundaryIntersects(
MakePointOrDie("45:175"), MakePointOrDie("30:175")));
// Check that the edges on the opposite side of the sphere but at the same
// latitude do not intersect the rectangle boundary.
Assert.False(rect.BoundaryIntersects(
MakePointOrDie("25:-20"), MakePointOrDie("25:0")));
Assert.False(rect.BoundaryIntersects(
MakePointOrDie("25:20"), MakePointOrDie("25:0")));
Assert.False(rect.BoundaryIntersects(
MakePointOrDie("15:-5"), MakePointOrDie("30:-5")));
Assert.False(rect.BoundaryIntersects(
MakePointOrDie("45:-5"), MakePointOrDie("30:-5")));
}
public void testCellOps(S2LatLngRect r, S2Cell cell, int level)
{
// Test the relationship between the given rectangle and cell:
// 0 == no intersection, 1 == MayIntersect, 2 == Intersects,
// 3 == Vertex Containment, 4 == Contains
var vertexContained = false;
for (var i = 0; i < 4; ++i)
{
if (r.Contains(cell.GetVertexRaw(i))
|| (!r.IsEmpty && cell.Contains(r.GetVertex(i).ToPoint())))
{
vertexContained = true;
}
}
assertEquals(r.MayIntersect(cell), level >= 1);
assertEquals(r.Intersects(cell), level >= 2);
assertEquals(vertexContained, level >= 3);
assertEquals(r.Contains(cell), level >= 4);
}
private static void TestCellOps(S2LatLngRect r, S2Cell cell, int level)
{
// Test the relationship between the given rectangle and cell:
// 0 == no intersection, 1 == MayIntersect, 2 == Intersects,
// 3 == Vertex Containment, 4 == Contains
bool vertex_contained = false;
for (int i = 0; i < 4; ++i)
{
if (r.Contains(cell.VertexRaw(i)) ||
(!r.IsEmpty() && cell.Contains(r.Vertex(i).ToPoint())))
{
vertex_contained = true;
}
}
Assert.Equal(r.MayIntersect(cell), level >= 1);
Assert.Equal(r.Intersects(cell), level >= 2);
Assert.Equal(vertex_contained, level >= 3);
Assert.Equal(r.Contains(cell), level >= 4);
}
public void testCellOps(S2LatLngRect r, S2Cell cell, int level)
{
// Test the relationship between the given rectangle and cell:
// 0 == no intersection, 1 == MayIntersect, 2 == Intersects,
// 3 == Vertex Containment, 4 == Contains
var vertexContained = false;
for (var i = 0; i < 4; ++i)
{
if (r.Contains(cell.GetVertexRaw(i)) ||
(!r.IsEmpty && cell.Contains(r.GetVertex(i).ToPoint())))
{
vertexContained = true;
}
}
assertEquals(r.MayIntersect(cell), level >= 1);
assertEquals(r.Intersects(cell), level >= 2);
assertEquals(vertexContained, level >= 3);
assertEquals(r.Contains(cell), level >= 4);
}
private static S1Angle BruteForceRectPointDistance(S2LatLngRect a, S2LatLng b)
{
if (a.Contains(b))
{
return(S1Angle.FromRadians(0));
}
S1Angle b_to_lo_lat = GetDistance(b, a.LatLo(), a.Lng);
S1Angle b_to_hi_lat = GetDistance(b, a.LatHi(), a.Lng);
S1Angle b_to_lo_lng = S2.GetDistance(b.ToPoint(), new S2LatLng(a.LatLo(), a.LngLo()).ToPoint(), new S2LatLng(a.LatHi(), a.LngLo()).ToPoint());
S1Angle b_to_hi_lng = S2.GetDistance(b.ToPoint(), new S2LatLng(a.LatLo(), a.LngHi()).ToPoint(), new S2LatLng(a.LatHi(), a.LngHi()).ToPoint());
return(new[] { b_to_lo_lat, b_to_hi_lat, b_to_lo_lng, b_to_hi_lng }.Min());
}
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 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);
}
}
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 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);
}
}
static void TestSubdivide(S2Cell cell)
{
GatherStats(cell);
if (cell.IsLeaf())
{
return;
}
var children = new S2Cell[4];
Assert.True(cell.Subdivide(children));
S2CellId child_id = cell.Id.ChildBegin();
double exact_area = 0;
double approx_area = 0;
double average_area = 0;
for (int i = 0; i < 4; ++i, child_id = child_id.Next())
{
exact_area += children[i].ExactArea();
approx_area += children[i].ApproxArea();
average_area += children[i].AverageArea();
// Check that the child geometry is consistent with its cell ID.
Assert.Equal(child_id, children[i].Id);
Assert.True(S2.ApproxEquals(children[i].Center(), child_id.ToPoint()));
S2Cell direct = new(child_id);
Assert.Equal(direct.Face, children[i].Face);
Assert.Equal(direct.Level, children[i].Level);
Assert.Equal(direct.Orientation, children[i].Orientation);
Assert.Equal(direct.CenterRaw(), children[i].CenterRaw());
for (int k = 0; k < 4; ++k)
{
Assert.Equal(direct.VertexRaw(k), children[i].VertexRaw(k));
Assert.Equal(direct.EdgeRaw(k), children[i].EdgeRaw(k));
}
// Test Contains() and MayIntersect().
Assert.True(cell.Contains(children[i]));
Assert.True(cell.MayIntersect(children[i]));
Assert.False(children[i].Contains(cell));
Assert.True(cell.Contains(children[i].CenterRaw()));
for (int j = 0; j < 4; ++j)
{
Assert.True(cell.Contains(children[i].VertexRaw(j)));
if (j != i)
{
Assert.False(children[i].Contains(children[j].CenterRaw()));
Assert.False(children[i].MayIntersect(children[j]));
}
}
// Test GetCapBound and GetRectBound.
S2Cap parent_cap = cell.GetCapBound();
S2LatLngRect parent_rect = cell.GetRectBound();
if (cell.Contains(new S2Point(0, 0, 1)) || cell.Contains(new S2Point(0, 0, -1)))
{
Assert.True(parent_rect.Lng.IsFull());
}
S2Cap child_cap = children[i].GetCapBound();
S2LatLngRect child_rect = children[i].GetRectBound();
Assert.True(child_cap.Contains(children[i].Center()));
Assert.True(child_rect.Contains(children[i].CenterRaw()));
Assert.True(parent_cap.Contains(children[i].Center()));
Assert.True(parent_rect.Contains(children[i].CenterRaw()));
for (int j = 0; j < 4; ++j)
{
Assert.True(child_cap.Contains(children[i].Vertex(j)));
Assert.True(child_rect.Contains(children[i].Vertex(j)));
Assert.True(child_rect.Contains(children[i].VertexRaw(j)));
Assert.True(parent_cap.Contains(children[i].Vertex(j)));
Assert.True(parent_rect.Contains(children[i].Vertex(j)));
Assert.True(parent_rect.Contains(children[i].VertexRaw(j)));
if (j != i)
{
// The bounding caps and rectangles should be tight enough so that
// they exclude at least two vertices of each adjacent cell.
int cap_count = 0;
int rect_count = 0;
for (int k = 0; k < 4; ++k)
{
if (child_cap.Contains(children[j].Vertex(k)))
{
++cap_count;
}
if (child_rect.Contains(children[j].VertexRaw(k)))
{
++rect_count;
}
}
Assert.True(cap_count <= 2);
if (child_rect.LatLo().Radians > -S2.M_PI_2 &&
child_rect.LatHi().Radians < S2.M_PI_2)
{
// Bounding rectangles may be too large at the poles because the
// pole itself has an arbitrary fixed longitude.
Assert.True(rect_count <= 2);
}
}
}
// Check all children for the first few levels, and then sample randomly.
// We also always subdivide the cells containing a few chosen points so
// that we have a better chance of sampling the minimum and maximum metric
// values. kMaxSizeUV is the absolute value of the u- and v-coordinate
// where the cell size at a given level is maximal.
double kMaxSizeUV = 0.3964182625366691;
R2Point[] special_uv =
{
new R2Point(S2.DoubleEpsilon, S2.DoubleEpsilon), // Face center
new R2Point(S2.DoubleEpsilon, 1), // Edge midpoint
new R2Point(1, 1), // Face corner
new R2Point(kMaxSizeUV, kMaxSizeUV), // Largest cell area
new R2Point(S2.DoubleEpsilon, kMaxSizeUV), // Longest edge/diagonal
};
bool force_subdivide = false;
foreach (R2Point uv in special_uv)
{
if (children[i].BoundUV.Contains(uv))
{
force_subdivide = true;
}
}
var debugFlag =
#if s2debug
true;
#else
false;
#endif
if (force_subdivide ||
cell.Level < (debugFlag ? 5 : 6) ||
S2Testing.Random.OneIn(debugFlag ? 5 : 4))
{
TestSubdivide(children[i]);
}
}
// Check sum of child areas equals parent area.
//
// For ExactArea(), the best relative error we can expect is about 1e-6
// because the precision of the unit vector coordinates is only about 1e-15
// and the edge length of a leaf cell is about 1e-9.
//
// For ApproxArea(), the areas are accurate to within a few percent.
//
// For AverageArea(), the areas themselves are not very accurate, but
// the average area of a parent is exactly 4 times the area of a child.
Assert.True(Math.Abs(Math.Log(exact_area / cell.ExactArea())) <= Math.Abs(Math.Log((1 + 1e-6))));
Assert.True(Math.Abs(Math.Log((approx_area / cell.ApproxArea()))) <= Math.Abs(Math.Log((1.03))));
Assert.True(Math.Abs(Math.Log((average_area / cell.AverageArea()))) <= Math.Abs(Math.Log((1 + 1e-15))));
}
