public void Test_S2CellUnion_FromMinMax()
{
// Check the very first leaf cell and face cell.
S2CellId face1_id = S2CellId.FromFace(0);
TestFromMinMax(face1_id.RangeMin(), face1_id.RangeMin());
TestFromMinMax(face1_id.RangeMin(), face1_id.RangeMax());
// Check the very last leaf cell and face cell.
S2CellId face5_id = S2CellId.FromFace(5);
TestFromMinMax(face5_id.RangeMin(), face5_id.RangeMax());
TestFromMinMax(face5_id.RangeMax(), face5_id.RangeMax());
// Check random ranges of leaf cells.
for (int iter = 0; iter < 100; ++iter)
{
S2CellId x = S2Testing.GetRandomCellId(S2.kMaxCellLevel);
S2CellId y = S2Testing.GetRandomCellId(S2.kMaxCellLevel);
if (x > y)
{
var tmp = x; x = y; y = tmp;
}
TestFromMinMax(x, y);
}
}
public void Test_S2PaddedCell_GetEntryExitVertices()
{
int kIters = 1000;
for (int iter = 0; iter < kIters; ++iter)
{
S2CellId id = S2Testing.GetRandomCellId();
// Check that entry/exit vertices do not depend on padding.
Assert.Equal(new S2PaddedCell(id, 0).GetEntryVertex(),
new S2PaddedCell(id, 0.5).GetEntryVertex());
Assert.Equal(new S2PaddedCell(id, 0).GetExitVertex(),
new S2PaddedCell(id, 0.5).GetExitVertex());
// Check that the exit vertex of one cell is the same as the entry vertex
// of the immediately following cell. (This also tests wrapping from the
// end to the start of the S2CellId curve with high probability.)
Assert.Equal(new S2PaddedCell(id, 0).GetExitVertex(),
new S2PaddedCell(id.NextWrap(), 0).GetEntryVertex());
// Check that the entry vertex of a cell is the same as the entry vertex
// of its first child, and similarly for the exit vertex.
if (!id.IsLeaf())
{
Assert.Equal(new S2PaddedCell(id, 0).GetEntryVertex(),
new S2PaddedCell(id.Child(0), 0).GetEntryVertex());
Assert.Equal(new S2PaddedCell(id, 0).GetExitVertex(),
new S2PaddedCell(id.Child(3), 0).GetExitVertex());
}
}
}
public void Test_EncodedS2PointVectorTest_SnappedFractalLoops()
{
S2Testing.Random.Reset(S2Testing.Random.RandomSeed);
#if DEBUG
const int kMaxPoints = 3 << 10;
#else
const int kMaxPoints = 3 << 14;
#endif
for (int num_points = 3; num_points <= kMaxPoints; num_points *= 4)
{
int s2polygon_size = 0, lax_polygon_size = 0;
for (int i = 0; i < 10; ++i)
{
S2Testing.Fractal fractal = new();
fractal.SetLevelForApproxMaxEdges(num_points);
var frame = S2Testing.GetRandomFrame();
var loop = fractal.MakeLoop(frame, S2Testing.KmToAngle(10));
List <S2Point> points = new();
for (int j = 0; j < loop.NumVertices; ++j)
{
points.Add(new S2CellId(loop.Vertex(j)).ToPoint());
}
S2Polygon s2polygon = new(new S2Loop(points));
Encoder encoder = new();
s2polygon.Encode(encoder);
s2polygon_size += encoder.Length();
// S2LaxPolygonShape has 2 extra bytes of overhead to encode one loop.
lax_polygon_size +=
TestEncodedS2PointVector(points.ToArray(), CodingHint.COMPACT, -1) + 2;
}
_logger.WriteLine($"n={num_points:d5} s2={s2polygon_size:d9} lax={lax_polygon_size:9}");
}
}
public void Test_S1ChordAngle_GetS2PointConstructorMaxError()
{
// Check that the error bound returned by GetS2PointConstructorMaxError() is
// large enough.
for (var iter = 0; iter < 100000; ++iter)
{
S2Testing.Random.Reset(iter); // Easier to reproduce a specific case.
var x = S2Testing.RandomPoint();
var y = S2Testing.RandomPoint();
if (S2Testing.Random.OneIn(10))
{
// Occasionally test a point pair that is nearly identical or antipodal.
var r = S1Angle.FromRadians(S2.DoubleError * S2Testing.Random.RandDouble());
y = S2.GetPointOnLine(x, y, r);
if (S2Testing.Random.OneIn(2))
{
y = -y;
}
}
S1ChordAngle dist = new(x, y);
var error = dist.GetS2PointConstructorMaxError();
var er1 = S2Pred.CompareDistance(x, y, dist.PlusError(error));
if (er1 > 0)
{
}
Assert.True(er1 <= 0);
var er2 = S2Pred.CompareDistance(x, y, dist.PlusError(-error));
if (er2 < 0)
{
}
Assert.True(er2 >= 0);
}
}
public void Test_S2LatLngRect_GetDirectedHausdorffDistanceRandomPairs()
{
// Test random pairs.
int kIters = 1000;
for (int i = 0; i < kIters; ++i)
{
S2LatLngRect a =
S2LatLngRect.FromPointPair(new S2LatLng(S2Testing.RandomPoint()),
new S2LatLng(S2Testing.RandomPoint()));
S2LatLngRect b =
S2LatLngRect.FromPointPair(new S2LatLng(S2Testing.RandomPoint()),
new S2LatLng(S2Testing.RandomPoint()));
// a and b are *minimum* bounding rectangles of two random points, in
// particular, their Voronoi diagrams are always of the same topology. We
// take the "complements" of a and b for more thorough testing.
S2LatLngRect a2 = new(a.Lat, a.Lng.Complement());
S2LatLngRect b2 = new(b.Lat, b.Lng.Complement());
// Note that "a" and "b" come from the same distribution, so there is no
// need to test pairs such as (b, a), (b, a2), etc.
VerifyGetDirectedHausdorffDistance(a, b);
VerifyGetDirectedHausdorffDistance(a, b2);
VerifyGetDirectedHausdorffDistance(a2, b);
VerifyGetDirectedHausdorffDistance(a2, b2);
}
}
public void Test_S2RegionTermIndexer_MaxLevelSetLoosely()
{
// Test that correct terms are generated even when (max_level - min_level)
// is not a multiple of level_mod.
var options = new S2RegionTermIndexer.Options();
options.MinLevel = (1);
options.LevelMod = (2);
options.MaxLevel = (19);
var indexer1 = new S2RegionTermIndexer(options);
options.MaxLevel = (20);
var indexer2 = new S2RegionTermIndexer(options);
S2Point point = S2Testing.RandomPoint();
Assert.Equal(indexer1.GetIndexTerms(point, ""),
indexer2.GetIndexTerms(point, ""));
Assert.Equal(indexer1.GetQueryTerms(point, ""),
indexer2.GetQueryTerms(point, ""));
S2Cap cap = S2Testing.GetRandomCap(0.0, 1.0); // Area range.
Assert.Equal(indexer1.GetIndexTerms(cap, ""),
indexer2.GetIndexTerms(cap, ""));
Assert.Equal(indexer1.GetQueryTerms(cap, ""),
indexer2.GetQueryTerms(cap, ""));
}
public void Test_S2PointVectorShape_ConstructionAndAccess()
{
const int kNumPoints = 100;
S2Point[] points = new S2Point[kNumPoints];
S2Testing.Random.Reset(S2Testing.Random.RandomSeed);
for (int i = 0; i < kNumPoints; ++i)
{
points[i] = S2Testing.RandomPoint();
}
S2PointVectorShape shape = new(points);
Assert.Equal(kNumPoints, shape.NumEdges());
Assert.Equal(kNumPoints, shape.NumChains());
Assert.Equal(0, shape.Dimension());
Assert.False(shape.IsEmpty());
Assert.False(shape.IsFull());
for (int i = 0; i < kNumPoints; ++i)
{
Assert.Equal(i, shape.GetChain(i).Start);
Assert.Equal(1, shape.GetChain(i).Length);
var edge = shape.GetEdge(i);
S2Point pt = points[i];
Assert.Equal(pt, edge.V0);
Assert.Equal(pt, edge.V1);
}
}
private static void CheckCovering(S2RegionCoverer.Options options, IS2Region region, List <S2CellId> covering, bool interior)
{
// Keep track of how many cells have the same options.min_level() ancestor.
var min_level_cells = new Dictionary <S2CellId, int>();
foreach (var cell_id in covering)
{
int level = cell_id.Level();
Assert.True(level >= options.MinLevel);
Assert.False(level <= options.MaxLevel);
Assert.Equal(0, (level - options.MinLevel) % options.LevelMod);
min_level_cells[cell_id.Parent(options.MinLevel)] += 1;
}
if (covering.Count > options.MaxCells)
{
// If the covering has more than the requested number of cells, then check
// that the cell count cannot be reduced by using the parent of some cell.
foreach (var count in min_level_cells.Values)
{
Assert.Equal(1, count);
}
}
if (interior)
{
foreach (S2CellId cell_id in covering)
{
Assert.True(region.Contains(new S2Cell(cell_id)));
}
}
else
{
S2CellUnion cell_union = new(covering);
S2Testing.CheckCovering(region, cell_union, true);
}
}
public void Test_S2ClosestEdgeQuery_IsConservativeDistanceLessOrEqual()
{
// Test
int num_tested = 0;
int num_conservative_needed = 0;
for (int iter = 0; iter < 1000; ++iter)
{
S2Testing.Random.Reset(iter + 1); // Easier to reproduce a specific case.
S2Point x = S2Testing.RandomPoint();
S2Point dir = S2Testing.RandomPoint();
S1Angle r = S1Angle.FromRadians(Math.PI * Math.Pow(1e-30, S2Testing.Random.RandDouble()));
S2Point y = S2.InterpolateAtDistance(r, x, dir);
Distance limit = new(r);
if (S2Pred.CompareDistance(x, y, limit) <= 0)
{
MutableS2ShapeIndex index = new();
index.Add(new S2PointVectorShape(new S2Point[] { x }));
S2ClosestEdgeQuery query = new(index);
S2ClosestEdgeQuery.PointTarget target = new(y);
Assert.True(query.IsConservativeDistanceLessOrEqual(target, limit));
++num_tested;
if (!query.IsDistanceLess(target, limit))
{
++num_conservative_needed;
}
}
}
// Verify that in most test cases, the distance between the target points
// was close to the desired value. Also verify that at least in some test
// cases, the conservative distance test was actually necessary.
Assert.True(num_tested >= 300);
Assert.True(num_tested <= 700);
Assert.True(num_conservative_needed >= 25);
}
public void Test_S2EdgeVectorShape_EdgeAccess()
{
S2EdgeVectorShape shape = new();
S2Testing.Random.Reset(S2Testing.Random.RandomSeed);
int kNumEdges = 100;
List <(S2Point, S2Point)> edges = new();
for (int i = 0; i < kNumEdges; ++i)
{
S2Point a = S2Testing.RandomPoint(); // Control the evaluation order
edges.Add((a, S2Testing.RandomPoint()));
shape.Add(edges.Last().Item1, edges.Last().Item2);
}
Assert.Equal(kNumEdges, shape.NumEdges());
Assert.Equal(kNumEdges, shape.NumChains());
Assert.Equal(1, shape.Dimension());
Assert.False(shape.IsEmpty());
Assert.False(shape.IsFull());
for (int i = 0; i < kNumEdges; ++i)
{
Assert.Equal(i, shape.GetChain(i).Start);
Assert.Equal(1, shape.GetChain(i).Length);
var edge = shape.GetEdge(i);
Assert.Equal(edges[i].Item1, edge.V0);
Assert.Equal(edges[i].Item2, edge.V1);
}
}
public void Test_S2_Rotate()
{
for (int iter = 0; iter < 1000; ++iter)
{
S2Point axis = S2Testing.RandomPoint();
S2Point target = S2Testing.RandomPoint();
// Choose a distance whose logarithm is uniformly distributed.
double distance = Math.PI * Math.Pow(1e-15, S2Testing.Random.RandDouble());
// Sometimes choose points near the far side of the axis.
if (S2Testing.Random.OneIn(5))
{
distance = Math.PI - distance;
}
S2Point p = S2.InterpolateAtDistance(S1Angle.FromRadians(distance),
axis, target);
// Choose the rotation angle.
double angle = S2.M_2_PI * Math.Pow(1e-15, S2Testing.Random.RandDouble());
if (S2Testing.Random.OneIn(3))
{
angle = -angle;
}
if (S2Testing.Random.OneIn(10))
{
angle = 0;
}
TestRotate(p, axis, S1Angle.FromRadians(angle));
}
}
private static void ChooseEdgeNearCell(S2Cell cell, out S2Point a, out S2Point b)
{
S2Cap cap = cell.GetCapBound();
if (S2Testing.Random.OneIn(5))
{
// Choose a point anywhere on the sphere.
a = S2Testing.RandomPoint();
}
else
{
// Choose a point inside or somewhere near the cell.
a = S2Testing.SamplePoint(new S2Cap(cap.Center, 1.5 * cap.RadiusAngle()));
}
// Now choose a maximum edge length ranging from very short to very long
// relative to the cell size, and choose the other endpoint.
double max_length = Math.Min(100 * Math.Pow(1e-4, S2Testing.Random.RandDouble()) *
cap.Radius.Radians(), S2.M_PI_2);
b = S2Testing.SamplePoint(new S2Cap(a, S1Angle.FromRadians(max_length)));
if (S2Testing.Random.OneIn(20))
{
// Occasionally replace edge with antipodal edge.
a = -a;
b = -b;
}
}
// This function is designed to choose line segment endpoints that are difficult
// to handle correctly. Given two adjacent cube vertices P and Q, it returns
// either an edge midpoint, face midpoint, or corner vertex along the edge PQ
// and then perturbs it slightly. It also sometimes returns a random point from
// anywhere on the sphere.
private S2Point PerturbedCornerOrMidpoint(S2Point p, S2Point q)
{
S2Point a = (S2Testing.Random.Uniform(3) - 1) * p + (S2Testing.Random.Uniform(3) - 1) * q;
if (S2Testing.Random.OneIn(10))
{
// This perturbation often has no effect except on coordinates that are
// zero, in which case the perturbed value is so small that operations on
// it often result in underflow.
a += Math.Pow(1e-300, S2Testing.Random.RandDouble()) * S2Testing.RandomPoint();
}
else if (S2Testing.Random.OneIn(2))
{
// For coordinates near 1 (say > 0.5), this perturbation yields values
// that are only a few representable values away from the initial value.
a += 4 * S2.DoubleEpsilon * S2Testing.RandomPoint();
}
else
{
// A perturbation whose magnitude is in the range [1e-25, 1e-10].
a += 1e-10 * Math.Pow(S2.DoubleError, S2Testing.Random.RandDouble()) * S2Testing.RandomPoint();
}
if (a.Norm2() < S2.DoubleMinNorm)
{
// If a.Norm2 is denormalized, Normalize() loses too much precision.
return(PerturbedCornerOrMidpoint(p, q));
}
return(a);
}
public void AddEdges(S2Cap index_cap, int num_edges, MutableS2ShapeIndex index)
{
var fractal = new S2Testing.Fractal();
fractal.SetLevelForApproxMaxEdges(num_edges);
index.Add(new S2Loop.Shape(
fractal.MakeLoop(S2Testing.GetRandomFrameAt(index_cap.Center),
index_cap.RadiusAngle())));
}
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 void Test_S2ConvexHullQuery_PointsInsideHull()
{
// Repeatedly build the convex hull of a set of points, then add more points
// inside that loop and build the convex hull again. The result should
// always be the same.
int kIters = 1000;
for (int iter = 0; iter < kIters; ++iter)
{
S2Testing.Random.Reset(iter + 1); // Easier to reproduce a specific case.
// Choose points from within a cap of random size, up to but not including
// an entire hemisphere.
S2Cap cap = S2Testing.GetRandomCap(S2.DoubleError, 1.999 * Math.PI);
S2ConvexHullQuery query = new();
int num_points1 = S2Testing.Random.Uniform(100) + 3;
for (int i = 0; i < num_points1; ++i)
{
query.AddPoint(S2Testing.SamplePoint(cap));
}
var hull = query.GetConvexHull();
// When the convex hull is nearly a hemisphere, the algorithm sometimes
// returns a full cap instead. This is because it first computes a
// bounding rectangle for all the input points/edges and then converts it
// to a bounding cap, which sometimes yields a non-convex cap (radius
// larger than 90 degrees). This should not be a problem in practice
// (since most convex hulls are not hemispheres), but in order make this
// test pass reliably it means that we need to reject convex hulls whose
// bounding cap (when computed from a bounding rectangle) is not convex.
//
// TODO(b/203702905): This test can still fail (about 1 iteration in
// 500,000) because the S2LatLngRect::GetCapBound implementation does not
// guarantee that A.Contains(B) implies
// A.GetCapBound().Contains(B.GetCapBound()).
if (hull.GetCapBound().Height() >= 1)
{
continue;
}
// Otherwise, add more points inside the convex hull.
int num_points2 = 1000;
for (int i = 0; i < num_points2; ++i)
{
S2Point p = S2Testing.SamplePoint(cap);
if (hull.Contains(p))
{
query.AddPoint(p);
}
}
// Finally, build a new convex hull and check that it hasn't changed.
var hull2 = (query.GetConvexHull());
_logger.WriteLine("Iteration: " + iter);
Assert.True(hull2.BoundaryEquals(hull));
}
}
public void AddEdges(S2Cap index_cap, int num_edges, MutableS2ShapeIndex index)
{
var points = new List <S2Point>();
for (int i = 0; i < num_edges; ++i)
{
points.Add(S2Testing.SamplePoint(index_cap));
}
index.Add(new S2PointVectorShape(points.ToArray()));
}
public void Test_E7()
{
ExpectMaxDigits(S2LatLng.FromDegrees(0, 0), 7);
for (var i = 0; i < kIters; i++)
{
var ll = S2LatLng.FromPoint(S2Testing.RandomPoint());
var ll_e7 = S2LatLng.FromE7(ll.Lat().E7(), ll.Lng().E7());
ExpectMaxDigits(ll_e7, 7);
}
}
public void Test_GetCrossingCandidates_DegenerateEdgeOnCellVertexIsItsOwnCandidate()
{
for (int i = 0; i < 100; ++i)
{
List <(S2Point, S2Point)> edges = new();
S2Cell cell = new(S2Testing.GetRandomCellId());
edges.Add((cell.Vertex(0), cell.Vertex(0)));
TestAllCrossings(edges);
}
}
public void AddPoints(S2Cap index_cap, int num_points, TestIndex index)
{
var points = S2Testing.MakeRegularPoints(
index_cap.Center, index_cap.RadiusAngle(), num_points);
for (int i = 0; i < points.Length; ++i)
{
index.Add(points[i], i);
}
}
public void Test_S2CellId_ExpandedByDistanceUV()
{
const double max_dist_degrees = 10;
for (var iter = 0; iter < 100; ++iter)
{
S2CellId id = S2Testing.GetRandomCellId();
double dist_degrees = S2Testing.Random.UniformDouble(-max_dist_degrees, max_dist_degrees);
TestExpandedByDistanceUV(id, S1Angle.FromDegrees(dist_degrees));
}
}
public void Test_S2_GetPointToRightS1ChordAngle()
{
S2Point a = S2LatLng.FromDegrees(0, 0).ToPoint();
S2Point b = S2LatLng.FromDegrees(0, 5).ToPoint(); // east
S1Angle kDistance = S2Testing.MetersToAngle(10);
S2Point c = S2.GetPointToRight(a, b, new S1ChordAngle(kDistance));
Assert2.Near(new S1Angle(a, c).Radians, kDistance.Radians, 1e-15);
// CAB must be a right angle with C to the right of AB.
Assert2.Near(S2.TurnAngle(c, a, b), -S2.M_PI_2 /*radians*/, 1e-15);
}
public void Test_S2CellId_Inverses()
{
// Check the conversion of random leaf cells to S2LatLngs and back.
for (int i = 0; i < 200000; ++i)
{
S2CellId id = S2Testing.GetRandomCellId(S2.kMaxCellLevel);
Assert.True(id.IsLeaf());
Assert.Equal(S2.kMaxCellLevel, id.Level());
S2LatLng center = id.ToLatLng();
Assert.Equal(id.Id, new S2CellId(center).Id);
}
}
public void Test_XYZToFaceSiTi()
{
// Check the conversion of random cells to center points and back.
for (int level = 0; level <= S2.kMaxCellLevel; ++level)
{
for (int i = 0; i < 1000; ++i)
{
S2CellId id = S2Testing.GetRandomCellId(level);
int actual_level = S2.XYZtoFaceSiTi(id.ToPoint(), out var face, out var si, out var ti);
Assert.Equal(level, actual_level);
S2CellId actual_id =
S2CellId.FromFaceIJ(face, (int)(si / 2), (int)(ti / 2)).Parent(level);
Assert.Equal(id, actual_id);
// Now test a point near the cell center but not equal to it.
S2Point p_moved = id.ToPoint() + new S2Point(1e-13, 1e-13, 1e-13);
actual_level = S2.XYZtoFaceSiTi(p_moved, out var face_moved, out var si_moved, out var ti_moved);
Assert.Equal(-1, actual_level);
Assert.Equal(face, face_moved);
Assert.Equal(si, si_moved);
Assert.Equal(ti, ti_moved);
// Finally, test some random (si,ti) values that may be at different
// levels, or not at a valid level at all (for example, si == 0).
int face_random = S2Testing.Random.Uniform(S2CellId.kNumFaces);
uint si_random, ti_random;
uint mask = ~0U << (S2.kMaxCellLevel - level);
do
{
si_random = S2Testing.Random.Rand32() & mask;
ti_random = S2Testing.Random.Rand32() & mask;
} while (si_random > S2.kMaxSiTi || ti_random > S2.kMaxSiTi);
S2Point p_random = S2.FaceSiTitoXYZ(face_random, si_random, ti_random);
actual_level = S2.XYZtoFaceSiTi(p_random, out face, out si, out ti);
if (face != face_random)
{
// The chosen point is on the edge of a top-level face cell.
Assert.Equal(-1, actual_level);
Assert.True(si == 0 || si == S2.kMaxSiTi ||
ti == 0 || ti == S2.kMaxSiTi);
}
else
{
Assert.Equal(si_random, si);
Assert.Equal(ti_random, ti);
if (actual_level >= 0)
{
Assert.Equal(p_random, S2CellId.FromFaceIJ(face, (int)(si / 2), (int)(ti / 2)).Parent(actual_level).ToPoint());
}
}
}
}
}
public void Test_S2CellUnion_Expand()
{
// This test generates coverings for caps of random sizes, expands
// the coverings by a random radius, and then make sure that the new
// covering covers the expanded cap. It also makes sure that the
// new covering is not too much larger than expected.
var coverer = new S2RegionCoverer();
for (var i = 0; i < 1000; ++i)
{
_logger.WriteLine($"Iteration {i}");
var cap = S2Testing.GetRandomCap(
S2Cell.AverageArea(S2.kMaxCellLevel), S2.M_4_PI);
// Expand the cap area by a random factor whose log is uniformly
// distributed between 0 and log(1e2).
var expanded_cap = S2Cap.FromCenterHeight(
cap.Center, Math.Min(2.0, Math.Pow(1e2, rnd.RandDouble()) * cap.Height()));
var radius = (expanded_cap.Radius - cap.Radius).Radians();
var max_level_diff = rnd.Uniform(8);
// Generate a covering for the original cap, and measure the maximum
// distance from the cap center to any point in the covering.
coverer.Options_.MaxCells = 1 + rnd.Skewed(10);
var covering = coverer.GetCovering(cap);
S2Testing.CheckCovering(cap, covering, true);
var covering_radius = GetRadius(covering, cap.Center);
// This code duplicates the logic in Expand(min_radius, max_level_diff)
// that figures out an appropriate cell level to use for the expansion.
int min_level = S2.kMaxCellLevel;
foreach (var id in covering)
{
min_level = Math.Min(min_level, id.Level());
}
var expand_level = Math.Min(min_level + max_level_diff,
S2.kMinWidth.GetLevelForMinValue(radius));
// Generate a covering for the expanded cap, and measure the new maximum
// distance from the cap center to any point in the covering.
covering.Expand(S1Angle.FromRadians(radius), max_level_diff);
S2Testing.CheckCovering(expanded_cap, covering, false);
double expanded_covering_radius = GetRadius(covering, cap.Center);
// If the covering includes a tiny cell along the boundary, in theory the
// maximum angle of the covering from the cap center can increase by up to
// twice the maximum length of a cell diagonal.
Assert.True(expanded_covering_radius - covering_radius <=
2 * S2.kMaxDiag.GetValue(expand_level));
}
}
public void Test_GetReferencePoint_PartiallyDegenerateLoops()
{
for (var iter = 0; iter < 100; ++iter)
{
// First we construct a long convoluted edge chain that follows the
// S2CellId Hilbert curve. At some random point along the curve, we
// insert a small triangular loop.
List <List <S2Point> > loops = new(1) { new() };
var loop = loops[0];
int num_vertices = 100;
var start = S2Testing.GetRandomCellId(S2.kMaxCellLevel - 1);
var end = start.AdvanceWrap(num_vertices);
var loop_cellid = start.AdvanceWrap(
S2Testing.Random.Uniform(num_vertices - 2) + 1);
var triangle = new List <S2Point>();
for (var cellid = start; cellid != end; cellid = cellid.NextWrap())
{
if (cellid == loop_cellid)
{
// Insert a small triangular loop. We save the loop so that we can
// test whether it contains the origin later.
triangle.Add(cellid.Child(0).ToPoint());
triangle.Add(cellid.Child(1).ToPoint());
triangle.Add(cellid.Child(2).ToPoint());
loop.AddRange(triangle);
loop.Add(cellid.Child(0).ToPoint());
}
else
{
loop.Add(cellid.ToPoint());
}
}
// Now we retrace our steps, except that we skip the three edges that form
// the triangular loop above.
for (S2CellId cellid = end; cellid != start; cellid = cellid.PrevWrap())
{
if (cellid == loop_cellid)
{
loop.Add(cellid.Child(0).ToPoint());
}
else
{
loop.Add(cellid.ToPoint());
}
}
S2LaxPolygonShape shape = new(loops);
S2Loop triangle_loop = new(triangle);
var rp = shape.GetReferencePoint();
Assert.Equal(triangle_loop.Contains(rp.Point), rp.Contained);
}
}
}
// Chooses a random S2Point that is often near the intersection of one of the
// coodinates planes or coordinate axes with the unit sphere. (It is possible
// to represent very small perturbations near such points.)
private static S2Point ChoosePoint()
{
var x = S2Testing.RandomPoint().ToArray();
for (int i = 0; i < 3; ++i)
{
if (S2Testing.Random.OneIn(3))
{
x[i] *= Math.Pow(1e-50, S2Testing.Random.RandDouble());
}
}
return(new S2Point(x).Normalize());
}
public void Test_VisitIntersectingShapes_Points()
{
List <S2Point> vertices = new();
for (int i = 0; i < 100; ++i)
{
vertices.Add(S2Testing.RandomPoint());
}
MutableS2ShapeIndex index = new();
index.Add(new S2PointVectorShape(vertices.ToArray()));
new VisitIntersectingShapesTest(index).Run();
}
public void Test_S2_ProjectError()
{
for (int iter = 0; iter < 1000; ++iter)
{
S2Testing.Random.Reset(iter + 1); // Easier to reproduce a specific case.
S2Point a = ChoosePoint();
S2Point b = ChoosePoint();
S2Point n = S2.RobustCrossProd(a, b).Normalize();
S2Point x = S2Testing.SamplePoint(new S2Cap(n, S1Angle.FromRadians(1e-15)));
S2Point p = S2.Project(x, a, b);
Assert.True(S2Pred.CompareEdgeDistance(
p, a, b, new S1ChordAngle(S2.kProjectPerpendicularErrorS1Angle)) < 0);
}
}
public void Test_GetCrossings_ShapeIdsAreCorrect()
{
// This tests that when some index cells contain only one shape, the
// intersecting edges are returned with the correct shape id.
MutableS2ShapeIndex index = new();
index.Add(new S2Polyline.OwningShape(
new S2Polyline(S2Testing.MakeRegularPoints(
MakePointOrDie("0:0"), S1Angle.FromDegrees(5), 100))));
index.Add(new S2Polyline.OwningShape(
new S2Polyline(S2Testing.MakeRegularPoints(
MakePointOrDie("0:20"), S1Angle.FromDegrees(5), 100))));
TestPolylineCrossings(index, MakePointOrDie("1:-10"), MakePointOrDie("1:30"));
}