private static void TestInterpolate(S2Point a, S2Point b, double t, S2Point expected)
{
a = a.Normalize();
b = b.Normalize();
expected = expected.Normalize();
// We allow a bit more than the usual 1e-15 error tolerance because
// interpolation uses trig functions.
S1Angle kError = S1Angle.FromRadians(3e-15);
Assert.True(new S1Angle(S2.Interpolate(a, b, t), expected) <= kError);
// Now test the other interpolation functions.
S1Angle r = t * new S1Angle(a, b);
Assert.True(new S1Angle(S2.GetPointOnLine(a, b, r), expected) <= kError);
if (a.DotProd(b) == 0)
{ // Common in the test cases below.
Assert.True(new S1Angle(S2.GetPointOnRay(a, b, r), expected) <= kError);
}
if (r.Radians >= 0 && r.Radians < 0.99 * S2.M_PI)
{
S1ChordAngle r_ca = new(r);
Assert.True(new S1Angle(S2.GetPointOnLine(a, b, r_ca), expected) <= kError);
if (a.DotProd(b) == 0)
{
Assert.True(new S1Angle(S2.GetPointOnRay(a, b, r_ca), expected) <= kError);
}
}
}
private static void TestCrossings(S2Point a, S2Point b, S2Point c, S2Point d,
int crossing_sign, int signed_crossing_sign)
{
a = a.Normalize();
b = b.Normalize();
c = c.Normalize();
d = d.Normalize();
TestCrossing(a, b, c, d, crossing_sign, signed_crossing_sign);
TestCrossing(b, a, c, d, crossing_sign, -signed_crossing_sign);
TestCrossing(a, b, d, c, crossing_sign, -signed_crossing_sign);
TestCrossing(b, a, d, c, crossing_sign, signed_crossing_sign);
TestCrossing(a, a, c, d, -1, 0);
TestCrossing(a, b, c, c, -1, 0);
TestCrossing(a, a, c, c, -1, 0);
TestCrossing(a, b, a, b, 0, 1);
if (crossing_sign == 0)
{
// For vertex crossings, if AB crosses CD then CD does not cross AB.
// In order to get the crossing sign right in both cases, all tests are
// specified such that AB crosses CD. The other case is tested here.
Assert.NotEqual(signed_crossing_sign, 0);
TestCrossing(c, d, a, b, crossing_sign, 0);
}
else
{
// TODO(ericv): Document properties of SignedEdgeOrVertexCrossing.
TestCrossing(c, d, a, b, crossing_sign, -signed_crossing_sign);
}
}
private void assertCrossing(S2Point a,
S2Point b,
S2Point c,
S2Point d,
int robust,
bool edgeOrVertex,
bool simple)
{
a = S2Point.Normalize(a);
b = S2Point.Normalize(b);
c = S2Point.Normalize(c);
d = S2Point.Normalize(d);
compareResult(S2EdgeUtil.RobustCrossing(a, b, c, d), robust);
if (simple)
{
assertEquals(robust > 0, S2EdgeUtil.SimpleCrossing(a, b, c, d));
}
var crosser = new EdgeCrosser(a, b, c);
compareResult(crosser.RobustCrossing(d), robust);
compareResult(crosser.RobustCrossing(c), robust);
assertEquals(S2EdgeUtil.EdgeOrVertexCrossing(a, b, c, d), edgeOrVertex);
assertEquals(edgeOrVertex, crosser.EdgeOrVertexCrossing(d));
assertEquals(edgeOrVertex, crosser.EdgeOrVertexCrossing(c));
}
// Given a point X and an edge AB, check that the distance from X to AB is
// "distance_radians" and the closest point on AB is "expected_closest".
private static void CheckDistance(S2Point x, S2Point a, S2Point b, double distance_radians, S2Point expected_closest)
{
x = x.Normalize();
a = a.Normalize();
b = b.Normalize();
expected_closest = expected_closest.Normalize();
Assert2.Near(distance_radians, S2.GetDistance(x, a, b).Radians, S2.DoubleError);
S2Point closest = S2.Project(x, a, b);
Assert.True(S2Pred.CompareEdgeDistance(
closest, a, b, new S1ChordAngle(S2.kProjectPerpendicularErrorS1Angle)) < 0);
// If X is perpendicular to AB then there is nothing further we can expect.
if (distance_radians != S2.M_PI_2)
{
if (expected_closest == new S2Point())
{
// This special value says that the result should be A or B.
Assert.True(closest == a || closest == b);
}
else
{
Assert.True(S2.ApproxEquals(closest, expected_closest));
}
}
S1ChordAngle min_distance = S1ChordAngle.Zero;
Assert.False(S2.UpdateMinDistance(x, a, b, ref min_distance));
min_distance = S1ChordAngle.Infinity;
Assert.True(S2.UpdateMinDistance(x, a, b, ref min_distance));
Assert2.Near(distance_radians, min_distance.ToAngle().Radians, S2.DoubleError);
}
public void testGetLengthCentroid()
{
// Construct random great circles and divide them randomly into segments.
// Then make sure that the length and centroid are correct. Note that
// because of the way the centroid is computed, it does not matter how
// we split the great circle into segments.
for (var i = 0; i < 100; ++i)
{
// Choose a coordinate frame for the great circle.
var x = randomPoint();
var y = S2Point.Normalize(S2Point.CrossProd(x, randomPoint()));
var z = S2Point.Normalize(S2Point.CrossProd(x, y));
var vertices = new List <S2Point>();
for (double theta = 0; theta < 2 * S2.Pi; theta += Math.Pow(rand.NextDouble(), 10))
{
var p = (x * Math.Cos(theta)) + (y * Math.Sin(theta));
if (vertices.Count == 0 || !p.Equals(vertices[vertices.Count - 1]))
{
vertices.Add(p);
}
}
// Close the circle.
vertices.Add(vertices[0]);
var line = new S2Polyline(vertices);
var length = line.ArcLengthAngle;
assertTrue(Math.Abs(length.Radians - 2 * S2.Pi) < 2e-14);
}
}
public void testEqualsAndHashCode()
{
var vertices = new List <S2Point>();
vertices.Add(new S2Point(1, 0, 0));
vertices.Add(new S2Point(0, 1, 0));
vertices.Add(S2Point.Normalize(new S2Point(0, 1, 1)));
vertices.Add(new S2Point(0, 0, 1));
var line1 = new S2Polyline(vertices);
var line2 = new S2Polyline(vertices);
checkEqualsAndHashCodeMethods(line1, line2, true);
var moreVertices = new List <S2Point>(vertices);
moreVertices.RemoveAt(0);
var line3 = new S2Polyline(moreVertices);
checkEqualsAndHashCodeMethods(line1, line3, false);
checkEqualsAndHashCodeMethods(line1, null, false);
checkEqualsAndHashCodeMethods(line1, "", false);
}
// maybe these should be put in a special testing util class
/** Return a random unit-length vector. */
public S2Point randomPoint()
{
return(S2Point.Normalize(new S2Point(
2 * rand.NextDouble() - 1,
2 * rand.NextDouble() - 1,
2 * rand.NextDouble() - 1)));
}
/**
* Return a right-handed coordinate frame (three orthonormal vectors). Returns
* an array of three points: x,y,z
*/
public IReadOnlyList <S2Point> getRandomFrame()
{
var p0 = randomPoint();
var p1 = S2Point.Normalize(S2Point.CrossProd(p0, randomPoint()));
var p2 = S2Point.Normalize(S2Point.CrossProd(p0, p1));
return(new List <S2Point>(new[] { p0, p1, p2 }));
}
public void testIntersectionTolerance()
{
// We repeatedly construct two edges that cross near a random point "p",
// and measure the distance from the actual intersection point "x" to the
// the expected intersection point "p" and also to the edges that cross
// near "p".
//
// Note that getIntersection() does not guarantee that "x" and "p" will be
// close together (since the intersection point is numerically unstable
// when the edges cross at a very small angle), but it does guarantee that
// "x" will be close to both of the edges that cross.
var maxPointDist = new S1Angle();
var maxEdgeDist = new S1Angle();
for (var i = 0; i < 1000; ++i)
{
// We construct two edges AB and CD that intersect near "p". The angle
// between AB and CD (expressed as a slope) is chosen randomly between
// 1e-15 and 1.0 such that its logarithm is uniformly distributed. This
// implies that small values are much more likely to be chosen.
//
// Once the slope is chosen, the four points ABCD must be offset from P
// by at least (1e-15 / slope) so that the points are guaranteed to have
// the correct circular ordering around P. This is the distance from P
// at which the two edges are separated by about 1e-15, which is
// approximately the minimum distance at which we can expect computed
// points on the two lines to be distinct and have the correct ordering.
//
// The actual offset distance from P is chosen randomly in the range
// [1e-15 / slope, 1.0], again uniformly distributing the logarithm.
// This ensures that we test both long and very short segments that
// intersect at both large and very small angles.
var points = getRandomFrame();
var p = points[0];
var d1 = points[1];
var d2 = points[2];
var slope = Math.Pow(1e-15, rand.NextDouble());
d2 = d1 + (d2 * slope);
var a = S2Point.Normalize(p + (d1 * Math.Pow(1e-15 / slope, rand.NextDouble())));
var b = S2Point.Normalize(p - (d1 * Math.Pow(1e-15 / slope, rand.NextDouble())));
var c = S2Point.Normalize(p + (d2 * Math.Pow(1e-15 / slope, rand.NextDouble())));
var d = S2Point.Normalize(p - (d2 * Math.Pow(1e-15 / slope, rand.NextDouble())));
var x = S2EdgeUtil.GetIntersection(a, b, c, d);
var distAb = S2EdgeUtil.GetDistance(x, a, b);
var distCd = S2EdgeUtil.GetDistance(x, c, d);
assertTrue(distAb < S2EdgeUtil.DefaultIntersectionTolerance);
assertTrue(distCd < S2EdgeUtil.DefaultIntersectionTolerance);
// test getIntersection() post conditions
assertTrue(S2.OrderedCcw(a, x, b, S2Point.Normalize(S2.RobustCrossProd(a, b))));
assertTrue(S2.OrderedCcw(c, x, d, S2Point.Normalize(S2.RobustCrossProd(c, d))));
maxEdgeDist = S1Angle.Max(maxEdgeDist, S1Angle.Max(distAb, distCd));
maxPointDist = S1Angle.Max(maxPointDist, new S1Angle(p, x));
}
}
private static S2LatLngRect getEdgeBound(double x1,
double y1,
double z1,
double x2,
double y2,
double z2)
{
return(S2LatLngRect.FromEdge(
S2Point.Normalize(new S2Point(x1, y1, z1)), S2Point.Normalize(new S2Point(x2, y2, z2))));
}
private static void TestWedge(S2Point a0, S2Point ab1, S2Point a2, S2Point b0, S2Point b2, bool contains, bool intersects, WedgeRelation wedgeRelation)
{
a0 = a0.Normalize();
ab1 = ab1.Normalize();
a2 = a2.Normalize();
b0 = b0.Normalize();
b2 = b2.Normalize();
Assert.True(contains == S2WedgeRelations.WedgeContains(a0, ab1, a2, b0, b2));
Assert.True(intersects == S2WedgeRelations.WedgeIntersects(a0, ab1, a2, b0, b2));
Assert.True(wedgeRelation == S2WedgeRelations.GetWedgeRelation(a0, ab1, a2, b0, b2));
}
public void testFaces()
{
IDictionary <S2Point, int> edgeCounts = new Dictionary <S2Point, int>();
IDictionary <S2Point, int> vertexCounts = new Dictionary <S2Point, int>();
for (var face = 0; face < 6; ++face)
{
var id = S2CellId.FromFacePosLevel(face, 0, 0);
var cell = new S2Cell(id);
JavaAssert.Equal(cell.Id, id);
JavaAssert.Equal(cell.Face, face);
JavaAssert.Equal(cell.Level, 0);
// Top-level faces have alternating orientations to get RHS coordinates.
JavaAssert.Equal(cell.Orientation, face & S2.SwapMask);
Assert.True(!cell.IsLeaf);
for (var k = 0; k < 4; ++k)
{
if (edgeCounts.ContainsKey(cell.GetEdgeRaw(k)))
{
edgeCounts[cell.GetEdgeRaw(k)] = edgeCounts[cell
.GetEdgeRaw(k)] + 1;
}
else
{
edgeCounts[cell.GetEdgeRaw(k)] = 1;
}
if (vertexCounts.ContainsKey(cell.GetVertexRaw(k)))
{
vertexCounts[cell.GetVertexRaw(k)] = vertexCounts[cell
.GetVertexRaw(k)] + 1;
}
else
{
vertexCounts[cell.GetVertexRaw(k)] = 1;
}
assertDoubleNear(cell.GetVertexRaw(k).DotProd(cell.GetEdgeRaw(k)), 0);
assertDoubleNear(cell.GetVertexRaw((k + 1) & 3).DotProd(
cell.GetEdgeRaw(k)), 0);
assertDoubleNear(S2Point.Normalize(
S2Point.CrossProd(cell.GetVertexRaw(k), cell
.GetVertexRaw((k + 1) & 3))).DotProd(cell.GetEdge(k)), 1.0);
}
}
// Check that edges have multiplicity 2 and vertices have multiplicity 3.
foreach (var i in edgeCounts.Values)
{
JavaAssert.Equal(i, 2);
}
foreach (var i in vertexCounts.Values)
{
JavaAssert.Equal(i, 3);
}
}
public void Test_EdgeTrueCentroid_SemiEquator()
{
// Test the centroid of polyline ABC that follows the equator and consists
// of two 90 degree edges (i.e., C = -A). The centroid (multiplied by
// length) should point toward B and have a norm of 2.0. (The centroid
// itself has a norm of 2/Pi, and the total edge length is Pi.)
S2Point a = new(0, -1, 0), b = new(1, 0, 0), c = new(0, 1, 0);
S2Point centroid = S2Centroid.TrueCentroid(a, b) + S2Centroid.TrueCentroid(b, c);
Assert.True(S2.ApproxEquals(b, centroid.Normalize()));
Assert2.DoubleEqual(2.0, centroid.Norm());
}
private static void CheckMaxDistance(S2Point x, S2Point a, S2Point b, double distance_radians)
{
x = x.Normalize();
a = a.Normalize();
b = b.Normalize();
S1ChordAngle max_distance = S1ChordAngle.Straight;
Assert.False(S2.UpdateMaxDistance(x, a, b, ref max_distance));
max_distance = S1ChordAngle.Negative;
Assert.True(S2.UpdateMaxDistance(x, a, b, ref max_distance));
Assert2.Near(distance_radians, max_distance.Radians(), S2.DoubleError);
}
public void testMayIntersect()
{
var vertices = new List <S2Point>();
vertices.Add(S2Point.Normalize(new S2Point(1, -1.1, 0.8)));
vertices.Add(S2Point.Normalize(new S2Point(1, -0.8, 1.1)));
var line = new S2Polyline(vertices);
for (var face = 0; face < 6; ++face)
{
var cell = S2Cell.FromFacePosLevel(face, (byte)0, 0);
assertEquals(line.MayIntersect(cell), (face & 1) == 0);
}
}
// Given two edges a0a1 and b0b1, check that the maximum distance between them
// is "distance_radians". Parameters are passed by value so that this
// function can normalize them.
private static void CheckEdgePairMaxDistance(S2Point a0, S2Point a1, S2Point b0, S2Point b1, double distance_radians)
{
a0 = a0.Normalize();
a1 = a1.Normalize();
b0 = b0.Normalize();
b1 = b1.Normalize();
S1ChordAngle max_distance = S1ChordAngle.Straight;
Assert.False(S2.UpdateEdgePairMaxDistance(a0, a1, b0, b1, ref max_distance));
max_distance = S1ChordAngle.Negative;
Assert.True(S2.UpdateEdgePairMaxDistance(a0, a1, b0, b1, ref max_distance));
Assert2.Near(distance_radians, max_distance.Radians(), S2.DoubleError);
}
private static S2Point PerturbAtDistance(S1Angle distance, S2Point a0, S2Point b0)
{
S2Point x = S2.InterpolateAtDistance(distance, a0, b0);
if (S2Testing.Random.OneIn(2))
{
for (int i = 0; i < 3; ++i)
{
x = x.SetAxis(i, MathUtils.NextAfter(x[i], S2Testing.Random.OneIn(2) ? 1 : -1));
}
x = x.Normalize();
}
return(x);
}
public void testRectBound()
{
// Empty and full caps.
Assert.True(S2Cap.Empty.RectBound.IsEmpty);
Assert.True(S2Cap.Full.RectBound.IsFull);
var kDegreeEps = 1e-13;
// Maximum allowable error for latitudes and longitudes measured in
// degrees. (assertDoubleNear uses a fixed tolerance that is too small.)
// Cap that includes the south pole.
var rect =
S2Cap.FromAxisAngle(getLatLngPoint(-45, 57), S1Angle.FromDegrees(50)).RectBound;
assertDoubleNear(rect.LatLo.Degrees, -90, kDegreeEps);
assertDoubleNear(rect.LatHi.Degrees, 5, kDegreeEps);
Assert.True(rect.Lng.IsFull);
// Cap that is tangent to the north pole.
rect = S2Cap.FromAxisAngle(S2Point.Normalize(new S2Point(1, 0, 1)), S1Angle.FromRadians(S2.PiOver4)).RectBound;
assertDoubleNear(rect.Lat.Lo, 0);
assertDoubleNear(rect.Lat.Hi, S2.PiOver2);
Assert.True(rect.Lng.IsFull);
rect = S2Cap
.FromAxisAngle(S2Point.Normalize(new S2Point(1, 0, 1)), S1Angle.FromDegrees(45)).RectBound;
assertDoubleNear(rect.LatLo.Degrees, 0, kDegreeEps);
assertDoubleNear(rect.LatHi.Degrees, 90, kDegreeEps);
Assert.True(rect.Lng.IsFull);
// The eastern hemisphere.
rect = S2Cap
.FromAxisAngle(new S2Point(0, 1, 0), S1Angle.FromRadians(S2.PiOver2 + 5e-16)).RectBound;
assertDoubleNear(rect.LatLo.Degrees, -90, kDegreeEps);
assertDoubleNear(rect.LatHi.Degrees, 90, kDegreeEps);
Assert.True(rect.Lng.IsFull);
// A cap centered on the equator.
rect = S2Cap.FromAxisAngle(getLatLngPoint(0, 50), S1Angle.FromDegrees(20)).RectBound;
assertDoubleNear(rect.LatLo.Degrees, -20, kDegreeEps);
assertDoubleNear(rect.LatHi.Degrees, 20, kDegreeEps);
assertDoubleNear(rect.LngLo.Degrees, 30, kDegreeEps);
assertDoubleNear(rect.LngHi.Degrees, 70, kDegreeEps);
// A cap centered on the north pole.
rect = S2Cap.FromAxisAngle(getLatLngPoint(90, 123), S1Angle.FromDegrees(10)).RectBound;
assertDoubleNear(rect.LatLo.Degrees, 80, kDegreeEps);
assertDoubleNear(rect.LatHi.Degrees, 90, kDegreeEps);
Assert.True(rect.Lng.IsFull);
}
private S2LatLngRect getEdgeBound(double x1,
double y1,
double z1,
double x2,
double y2,
double z2)
{
var bounder = new RectBounder();
var p1 = S2Point.Normalize(new S2Point(x1, y1, z1));
var p2 = S2Point.Normalize(new S2Point(x2, y2, z2));
bounder.AddPoint(p1);
bounder.AddPoint(p2);
return(bounder.Bound);
}
public void testInterpolate()
{
var vertices = new List <S2Point>();
vertices.Add(new S2Point(1, 0, 0));
vertices.Add(new S2Point(0, 1, 0));
vertices.Add(S2Point.Normalize(new S2Point(0, 1, 1)));
vertices.Add(new S2Point(0, 0, 1));
var line = new S2Polyline(vertices);
assertEquals(line.Interpolate(-0.1), vertices[0]);
assertTrue(S2.ApproxEquals(
line.Interpolate(0.1), S2Point.Normalize(new S2Point(1, Math.Tan(0.2 * S2.Pi / 2), 0))));
assertTrue(S2.ApproxEquals(line.Interpolate(0.25), S2Point.Normalize(new S2Point(1, 1, 0))));
assertTrue(S2.ApproxEquals(line.Interpolate(0.5), vertices[1]));
assertTrue(S2.ApproxEquals(line.Interpolate(0.75), vertices[2]));
assertTrue(S2.ApproxEquals(line.Interpolate(1.1), vertices[3]));
}
protected S2Point samplePoint(S2Cap cap)
{
// We consider the cap axis to be the "z" axis. We choose two other axes to
// complete the coordinate frame.
var z = cap.Axis;
var x = z.Ortho;
var y = S2Point.CrossProd(z, x);
// The surface area of a spherical cap is directly proportional to its
// height. First we choose a random height, and then we choose a random
// point along the circle at that height.
var h = rand.NextDouble() * cap.Height;
var theta = 2 * S2.Pi * rand.NextDouble();
var r = Math.Sqrt(h * (2 - h)); // Radius of circle.
// (cos(theta)*r*x + sin(theta)*r*y + (1-h)*z).Normalize()
return(S2Point.Normalize(((x * Math.Cos(theta) * r) + (y * Math.Sin(theta) * r)) + (z * (1 - h))));
}
private void getVertices(String str,
S2Point x,
S2Point y,
S2Point z,
double maxPerturbation,
List <S2Point> vertices)
{
// Parse the vertices, perturb them if desired, and transform them into the
// given frame.
var line = makePolyline(str);
for (var i = 0; i < line.NumVertices; ++i)
{
var p = line.Vertex(i);
// (p[0]*x + p[1]*y + p[2]*z).Normalize()
var axis = S2Point.Normalize(((x * p.X) + (y * p.Y)) + (z * p.Z));
var cap = S2Cap.FromAxisAngle(axis, S1Angle.FromRadians(maxPerturbation));
vertices.Add(samplePoint(cap));
}
}
// A slightly more efficient version of Project() 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. Requires that x, a, and b have unit length.
public static S2Point Project(S2Point x, S2Point a, S2Point b, S2Point a_cross_b)
{
System.Diagnostics.Debug.Assert(a.IsUnitLength());
System.Diagnostics.Debug.Assert(b.IsUnitLength());
System.Diagnostics.Debug.Assert(x.IsUnitLength());
// TODO(ericv): When X is nearly perpendicular to the plane containing AB,
// the result is guaranteed to be close to the edge AB but may be far from
// the true projected result. This could be fixed by computing the product
// (A x B) x X x (A x B) using methods similar to S2::RobustCrossProd() and
// S2::GetIntersection(). However note that the error tolerance would need
// to be significantly larger in order for this calculation to succeed in
// double precision most of the time. For example to avoid higher precision
// when X is within 60 degrees of AB the minimum error would be 18 * DBL_ERR,
// and to avoid higher precision when X is within 87 degrees of AB the
// minimum error would be 120 * DBL_ERR.
// The following is not necessary to meet accuracy guarantees but helps
// to avoid unexpected results in unit tests.
if (x == a || x == b)
{
return(x);
}
// Find the closest point to X along the great circle through AB. Note that
// we use "n" rather than a_cross_b in the final cross product in order to
// avoid the possibility of underflow.
S2Point n = a_cross_b.Normalize();
S2Point p = S2.RobustCrossProd(n, x).CrossProd(n).Normalize();
// If this point is on the edge AB, then it's the closest point.
S2Point pn = p.CrossProd(n);
if (S2Pred.Sign(p, n, a, pn) > 0 && S2Pred.Sign(p, n, b, pn) < 0)
{
return(p);
}
// Otherwise, the closest point is either A or B.
return(((x - a).Norm2() <= (x - b).Norm2()) ? a : b);
}
public void Test_S2_GoodFastHashSpreads()
{
int kTestPoints = 1 << 16;
var set = new List <int>();
var points = new SortedSet <S2Point>();
var base_ = new S2Point(1, 1, 1);
for (var i = 0; i < kTestPoints; ++i)
{
// All points in a tiny cap to test avalanche property of hash
// function (the cap would be of radius 1mm on Earth (4*10^9/2^35).
S2Point perturbed = base_ + S2Testing.RandomPoint() / (1UL << 35);
perturbed = perturbed.Normalize();
set.Add(perturbed.GetHashCode());
points.Add(perturbed);
}
// A real collision is extremely unlikely.
Assert.Equal(0, kTestPoints - points.Count);
// Allow a few for the hash.
Assert.True(10 >= kTestPoints - set.Count);
}
private void assertWedge(S2Point a0,
S2Point ab1,
S2Point a2,
S2Point b0,
S2Point b2,
bool contains,
bool intersects,
bool crosses)
{
a0 = S2Point.Normalize(a0);
ab1 = S2Point.Normalize(ab1);
a2 = S2Point.Normalize(a2);
b0 = S2Point.Normalize(b0);
b2 = S2Point.Normalize(b2);
assertEquals(new WedgeContains().Test(a0, ab1, a2, b0, b2), contains ? 1 : 0);
assertEquals(new WedgeIntersects().Test(a0, ab1, a2, b0, b2), intersects ? -1 : 0);
assertEquals(new WedgeContainsOrIntersects().Test(a0, ab1, a2, b0, b2),
contains ? 1 : intersects ? -1 : 0);
assertEquals(new WedgeContainsOrCrosses().Test(a0, ab1, a2, b0, b2),
contains ? 1 : crosses ? -1 : 0);
}
public void testGetDistance()
{
// Error margin since we're doing numerical computations
var epsilon = 1e-15;
// A rectangle with (lat,lng) vertices (3,1), (3,-1), (-3,-1) and (-3,1)
var inner = "3:1, 3:-1, -3:-1, -3:1;";
// A larger rectangle with (lat,lng) vertices (4,2), (4,-2), (-4,-2) and
// (-4,s)
var outer = "4:2, 4:-2, -4:-2, -4:2;";
var rect = makePolygon(inner);
var shell = makePolygon(inner + outer);
// All of the vertices of a polygon should be distance 0
for (var i = 0; i < shell.NumLoops; i++)
{
for (var j = 0; j < shell.Loop(i).NumVertices; j++)
{
assertEquals(0d, shell.GetDistance(shell.Loop(i).Vertex(j)).Radians, epsilon);
}
}
// A non-vertex point on an edge should be distance 0
assertEquals(0d, rect.GetDistance(
S2Point.Normalize(rect.Loop(0).Vertex(0) + rect.Loop(0).Vertex(1))).Radians,
epsilon);
var origin = S2LatLng.FromDegrees(0, 0).ToPoint();
// rect contains the origin
assertEquals(0d, rect.GetDistance(origin).Radians, epsilon);
// shell does NOT contain the origin, since it has a hole. The shortest
// distance is to (1,0) or (-1,0), and should be 1 degree
assertEquals(1d, shell.GetDistance(origin).Degrees, epsilon);
}
// Given two edges a0a1 and b0b1, check that the minimum distance between them
// is "distance_radians", and that GetEdgePairClosestPoints() returns
// "expected_a" and "expected_b" as the points that achieve this distance.
// S2Point.Empty may be passed for "expected_a" or "expected_b" to indicate
// that both endpoints of the corresponding edge are equally distant, and
// therefore either one might be returned.
//
// Parameters are passed by value so that this function can normalize them.
private static void CheckEdgePairMinDistance(S2Point a0, S2Point a1, S2Point b0, S2Point b1, double distance_radians, S2Point expected_a, S2Point expected_b)
{
a0 = a0.Normalize();
a1 = a1.Normalize();
b0 = b0.Normalize();
b1 = b1.Normalize();
expected_a = expected_a.Normalize();
expected_b = expected_b.Normalize();
var closest = S2.GetEdgePairClosestPoints(a0, a1, b0, b1);
S2Point actual_a = closest.Item1;
S2Point actual_b = closest.Item2;
if (expected_a == S2Point.Empty)
{
// This special value says that the result should be a0 or a1.
Assert.True(actual_a == a0 || actual_a == a1);
}
else
{
Assert.True(S2.ApproxEquals(expected_a, actual_a));
}
if (expected_b == S2Point.Empty)
{
// This special value says that the result should be b0 or b1.
Assert.True(actual_b == b0 || actual_b == b1);
}
else
{
Assert.True(S2.ApproxEquals(expected_b, actual_b));
}
S1ChordAngle min_distance = S1ChordAngle.Zero;
Assert.False(S2.UpdateEdgePairMinDistance(a0, a1, b0, b1, ref min_distance));
min_distance = S1ChordAngle.Infinity;
Assert.True(S2.UpdateEdgePairMinDistance(a0, a1, b0, b1, ref min_distance));
Assert2.Near(distance_radians, min_distance.Radians(), S2.DoubleError);
}
// Given a point X and an edge AB, check that the distance from X to AB is
// "distanceRadians" and the closest point on AB is "expectedClosest".
private static void checkDistance(
S2Point x, S2Point a, S2Point b, double distanceRadians, S2Point expectedClosest)
{
var kEpsilon = 1e-10;
x = S2Point.Normalize(x);
a = S2Point.Normalize(a);
b = S2Point.Normalize(b);
expectedClosest = S2Point.Normalize(expectedClosest);
assertEquals(distanceRadians, S2EdgeUtil.GetDistance(x, a, b).Radians, kEpsilon);
var closest = S2EdgeUtil.GetClosestPoint(x, a, b);
if (expectedClosest.Equals(new S2Point(0, 0, 0)))
{
// This special value says that the result should be A or B.
assertTrue(closest == a || closest == b);
}
else
{
assertTrue(S2.ApproxEquals(closest, expectedClosest));
}
}
public void Test_RectBounder_MaxLatitudeRandom()
{
// Check that the maximum latitude of edges is computed accurately to within
// 3 * S2Constants.DoubleEpsilon (the expected maximum error). We concentrate on maximum
// latitudes near the equator and north pole since these are the extremes.
const int kIters = 100;
for (int iter = 0; iter < kIters; ++iter)
{
// Construct a right-handed coordinate frame (U,V,W) such that U points
// slightly above the equator, V points at the equator, and W is slightly
// offset from the north pole.
S2Point u = S2Testing.RandomPoint();
u = new S2Point(u.X, u.Y, S2.DoubleEpsilon * 1e-6 * Math.Pow(1e12, S2Testing.Random.RandDouble())); // log is uniform
u = u.Normalize();
S2Point v = S2.RobustCrossProd(new S2Point(0, 0, 1), u).Normalize();
S2Point w = S2.RobustCrossProd(u, v).Normalize();
// Construct a line segment AB that passes through U, and check that the
// maximum latitude of this segment matches the latitude of U.
S2Point a = (u - S2Testing.Random.RandDouble() * v).Normalize();
S2Point b = (u + S2Testing.Random.RandDouble() * v).Normalize();
S2LatLngRect ab_bound = GetEdgeBound(a, b);
Assert2.Near(S2LatLng.Latitude(u).Radians,
ab_bound.Lat.Hi, kRectError.LatRadians);
// Construct a line segment CD that passes through W, and check that the
// maximum latitude of this segment matches the latitude of W.
S2Point c = (w - S2Testing.Random.RandDouble() * v).Normalize();
S2Point d = (w + S2Testing.Random.RandDouble() * v).Normalize();
S2LatLngRect cd_bound = GetEdgeBound(c, d);
Assert2.Near(S2LatLng.Latitude(w).Radians,
cd_bound.Lat.Hi, kRectError.LatRadians);
}
}
public void S2CapBasicTest()
{
// Test basic properties of empty and full caps.
var empty = S2Cap.Empty;
var full = S2Cap.Full;
Assert.True(empty.IsValid);
Assert.True(empty.IsEmpty);
Assert.True(empty.Complement.IsFull);
Assert.True(full.IsValid);
Assert.True(full.IsFull);
Assert.True(full.Complement.IsEmpty);
JavaAssert.Equal(full.Height, 2.0);
assertDoubleNear(full.Angle.Degrees, 180);
// Containment and intersection of empty and full caps.
Assert.True(empty.Contains(empty));
Assert.True(full.Contains(empty));
Assert.True(full.Contains(full));
Assert.True(!empty.InteriorIntersects(empty));
Assert.True(full.InteriorIntersects(full));
Assert.True(!full.InteriorIntersects(empty));
// Singleton cap containing the x-axis.
var xaxis = S2Cap.FromAxisHeight(new S2Point(1, 0, 0), 0);
Assert.True(xaxis.Contains(new S2Point(1, 0, 0)));
Assert.True(!xaxis.Contains(new S2Point(1, 1e-20, 0)));
JavaAssert.Equal(xaxis.Angle.Radians, 0.0);
// Singleton cap containing the y-axis.
var yaxis = S2Cap.FromAxisAngle(new S2Point(0, 1, 0), S1Angle.FromRadians(0));
Assert.True(!yaxis.Contains(xaxis.Axis));
JavaAssert.Equal(xaxis.Height, 0.0);
// Check that the complement of a singleton cap is the full cap.
var xcomp = xaxis.Complement;
Assert.True(xcomp.IsValid);
Assert.True(xcomp.IsFull);
Assert.True(xcomp.Contains(xaxis.Axis));
// Check that the complement of the complement is *not* the original.
Assert.True(xcomp.Complement.IsValid);
Assert.True(xcomp.Complement.IsEmpty);
Assert.True(!xcomp.Complement.Contains(xaxis.Axis));
// Check that very small caps can be represented accurately.
// Here "kTinyRad" is small enough that unit vectors perturbed by this
// amount along a tangent do not need to be renormalized.
var kTinyRad = 1e-10;
var tiny =
S2Cap.FromAxisAngle(S2Point.Normalize(new S2Point(1, 2, 3)), S1Angle.FromRadians(kTinyRad));
var tangent = S2Point.Normalize(S2Point.CrossProd(tiny.Axis, new S2Point(3, 2, 1)));
Assert.True(tiny.Contains(tiny.Axis + (tangent * 0.99 * kTinyRad)));
Assert.True(!tiny.Contains(tiny.Axis + (tangent * 1.01 * kTinyRad)));
// Basic tests on a hemispherical cap.
var hemi = S2Cap.FromAxisHeight(S2Point.Normalize(new S2Point(1, 0, 1)), 1);
JavaAssert.Equal(hemi.Complement.Axis, -hemi.Axis);
JavaAssert.Equal(hemi.Complement.Height, 1.0);
Assert.True(hemi.Contains(new S2Point(1, 0, 0)));
Assert.True(!hemi.Complement.Contains(new S2Point(1, 0, 0)));
Assert.True(hemi.Contains(S2Point.Normalize(new S2Point(1, 0, -(1 - EPS)))));
Assert.True(!hemi.InteriorContains(S2Point.Normalize(new S2Point(1, 0, -(1 + EPS)))));
// A concave cap.
var concave = S2Cap.FromAxisAngle(getLatLngPoint(80, 10), S1Angle.FromDegrees(150));
Assert.True(concave.Contains(getLatLngPoint(-70 * (1 - EPS), 10)));
Assert.True(!concave.Contains(getLatLngPoint(-70 * (1 + EPS), 10)));
Assert.True(concave.Contains(getLatLngPoint(-50 * (1 - EPS), -170)));
Assert.True(!concave.Contains(getLatLngPoint(-50 * (1 + EPS), -170)));
// Cap containment tests.
Assert.True(!empty.Contains(xaxis));
Assert.True(!empty.InteriorIntersects(xaxis));
Assert.True(full.Contains(xaxis));
Assert.True(full.InteriorIntersects(xaxis));
Assert.True(!xaxis.Contains(full));
Assert.True(!xaxis.InteriorIntersects(full));
Assert.True(xaxis.Contains(xaxis));
Assert.True(!xaxis.InteriorIntersects(xaxis));
Assert.True(xaxis.Contains(empty));
Assert.True(!xaxis.InteriorIntersects(empty));
Assert.True(hemi.Contains(tiny));
Assert.True(hemi.Contains(
S2Cap.FromAxisAngle(new S2Point(1, 0, 0), S1Angle.FromRadians(S2.PiOver4 - EPS))));
Assert.True(!hemi.Contains(
S2Cap.FromAxisAngle(new S2Point(1, 0, 0), S1Angle.FromRadians(S2.PiOver4 + EPS))));
Assert.True(concave.Contains(hemi));
Assert.True(concave.InteriorIntersects(hemi.Complement));
Assert.True(!concave.Contains(S2Cap.FromAxisHeight(-concave.Axis, 0.1)));
}