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_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);
}
}
}
public void Test_EncodedS2PointVectorTest_LastTwoPointsAtAllLevels()
{
// Test encoding the last two S2CellIds at each level.
for (int level = 0; level <= S2.kMaxCellLevel; ++level)
{
_logger.WriteLine("Level = " + level);
S2CellId id = S2CellId.End(level).Prev();
// Notice that this costs only 4 bits more than encoding the last S2CellId
// by itself (see LastAtAllLevels). This is because encoding a block of
// size 1 uses 8-bit deltas (which reduces the size of "base" by 4 bits),
// while this test uses two 4-bit deltas.
int expected_size = 6 + (level + 2) / 4;
TestEncodedS2PointVector(new S2Point[] { id.ToPoint(), id.Prev().ToPoint() },
CodingHint.COMPACT, expected_size);
}
}
public void Test_S2ClosestCellQuery_TargetPointInsideIndexedCell()
{
// Tests a target point in the interior of an indexed cell.
S2CellId cell_id = MakeCellIdOrDie("4/012");
S2CellIndex index = new();
index.Add(cell_id, 1);
index.Build();
S2ClosestCellQuery query = new(index);
S2ClosestCellQuery.PointTarget target = new(cell_id.ToPoint());
var result = query.FindClosestCell(target);
Assert.Equal(S1ChordAngle.Zero, result.Distance);
Assert.Equal(cell_id, result.CellId);
Assert.Equal(1, result.Label);
}
public void Test_EncodedS2PointVectorTest_ManyDuplicatePointsAtAllLevels()
{
// Test encoding 32 copies of the last S2CellId at each level. This uses
// between 27 and 38 bytes depending on the level. (Note that the encoding
// can use less than 1 byte per point in this situation.)
for (int level = 0; level <= S2.kMaxCellLevel; ++level)
{
_logger.WriteLine("Level = " + level);
S2CellId id = S2CellId.End(level).Prev();
// Encoding: header (2 bytes), base ((level + 2) / 4 bytes), block count
// (1 byte), block offsets (2 bytes), block headers (2 bytes), 32 deltas
// (16 bytes). At level 30 the encoding size goes up by 1 byte because
// we can't encode an 8 byte "base" value, so instead this case uses a
// base of 7 bytes plus a one-byte offset in each of the 2 blocks.
int expected_size = 23 + (level + 2) / 4;
if (level == 30)
{
expected_size += 1;
}
var points = new S2Point[32].Fill(id.ToPoint());
TestEncodedS2PointVector(points, CodingHint.COMPACT, expected_size);
}
}
public void Test_EncodedS2PointVectorTest_MaxFaceSiTiAtAllLevels()
{
// Similar to the test above, but tests encoding the S2CellId at each level
// whose face, si, and ti values are all maximal. This turns out to be the
// S2CellId whose human-readable form is 5/222...22 (0xb555555555555555),
// however for clarity we construct it using S2CellId.FromFaceIJ.
for (int level = 0; level <= S2.kMaxCellLevel; ++level)
{
_logger.WriteLine("Level = " + level);
S2CellId id = S2CellId.FromFaceIJ(5, S2.kLimitIJ - 1, S2.kLimitIJ - 1)
.Parent(level);
// This encoding is one byte bigger than the previous test at levels 7, 11,
// 15, 19, 23, and 27. This is because in the previous test, the
// odd-numbered value bits are all zero (except for the face number), which
// reduces the number of base bits needed by exactly 1. The encoding size
// at level==3 is unaffected because for singleton blocks, the lowest 8
// value bits are encoded in the delta.
int expected_size = (level < 4) ? 6 : 6 + (level + 1) / 4;
TestEncodedS2PointVector(new S2Point[] { id.ToPoint() },
CodingHint.COMPACT, expected_size);
}
}
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))));
}
