public void Test_S2CellId_ParentChildRelationships()
{
S2CellId id = S2CellId.FromFacePosLevel(3, 0x12345678, S2.kMaxCellLevel - 4);
Assert.True(id.IsValid());
Assert.Equal(3UL, id.Face());
Assert.Equal(0x12345700UL, id.Pos());
Assert.Equal(S2.kMaxCellLevel - 4, id.Level());
Assert.False(id.IsLeaf());
Assert.Equal(0x12345610UL, id.ChildBegin(id.Level() + 2).Pos());
Assert.Equal(0x12345640UL, id.ChildBegin().Pos());
Assert.Equal(0x12345400UL, id.Parent().Pos());
Assert.Equal(0x12345000UL, id.Parent(id.Level() - 2).Pos());
// Check ordering of children relative to parents.
Assert.True(id.ChildBegin() < id);
Assert.True(id.ChildEnd() > id);
Assert.Equal(id.ChildEnd(), id.ChildBegin().Next().Next().Next().Next());
Assert.Equal(id.RangeMin(), id.ChildBegin(S2.kMaxCellLevel));
Assert.Equal(id.RangeMax().Next(), id.ChildEnd(S2.kMaxCellLevel));
// Check that cells are represented by the position of their center
// along the Hilbert curve.
Assert.Equal(2 * id.Id, id.RangeMin().Id + id.RangeMax().Id);
}
public void Test_S2CellId_CenterSiTi()
{
S2CellId id = S2CellId.FromFacePosLevel(3, 0x12345678,
S2.kMaxCellLevel);
// Check that the (si, ti) coordinates of the center end in a
// 1 followed by (30 - level) 0s.
// Leaf level, 30.
id.CenterSiTi(out var si, out var ti);
Assert.Equal(1 << 0, si & 1);
Assert.Equal(1 << 0, ti & 1);
// Level 29.
id.Parent(S2.kMaxCellLevel - 1).CenterSiTi(out si, out ti);
Assert.Equal(1 << 1, si & 3);
Assert.Equal(1 << 1, ti & 3);
// Level 28.
id.Parent(S2.kMaxCellLevel - 2).CenterSiTi(out si, out ti);
Assert.Equal(1 << 2, si & 7);
Assert.Equal(1 << 2, ti & 7);
// Level 20.
id.Parent(S2.kMaxCellLevel - 10).CenterSiTi(out si, out ti);
Assert.Equal(1 << 10, si & ((1 << 11) - 1));
Assert.Equal(1 << 10, ti & ((1 << 11) - 1));
// Level 10.
id.Parent(S2.kMaxCellLevel - 20).CenterSiTi(out si, out ti);
Assert.Equal(1 << 20, si & ((1 << 21) - 1));
Assert.Equal(1 << 20, ti & ((1 << 21) - 1));
// Level 0.
id.Parent(0).CenterSiTi(out si, out ti);
Assert.Equal(1 << 30, si & ((1U << 31) - 1));
Assert.Equal(1 << 30, ti & ((1U << 31) - 1));
}
// Computes the smallest S2Cell that covers the S2Cell range (first, last) and
// adds this cell to "cell_ids".
//
// REQUIRES: "first" and "last" have a common ancestor.
private static void CoverRange(S2CellId first, S2CellId last, List <S2CellId> cell_ids)
{
if (first == last)
{
// The range consists of a single index cell.
cell_ids.Add(first);
}
else
{
// Add the lowest common ancestor of the given range.
int level = first.CommonAncestorLevel(last);
System.Diagnostics.Debug.Assert(level >= 0);
cell_ids.Add(first.Parent(level));
}
}
public void Test_S2PaddedCell_ShrinkToFit()
{
const int kIters = 1000;
for (int iter = 0; iter < kIters; ++iter)
{
// Start with the desired result and work backwards.
S2CellId result = S2Testing.GetRandomCellId();
R2Rect result_uv = result.BoundUV();
R2Point size_uv = result_uv.GetSize();
// Find the biggest rectangle that fits in "result" after padding.
// (These calculations ignore numerical errors.)
double max_padding = 0.5 * Math.Min(size_uv[0], size_uv[1]);
double padding = max_padding * S2Testing.Random.RandDouble();
R2Rect max_rect = result_uv.Expanded(-padding);
// Start with a random subset of the maximum rectangle.
R2Point a = new(SampleInterval(max_rect[0]), SampleInterval(max_rect[1]));
R2Point b = new(SampleInterval(max_rect[0]), SampleInterval(max_rect[1]));
if (!result.IsLeaf())
{
// If the result is not a leaf cell, we must ensure that no child of
// "result" also satisfies the conditions of ShrinkToFit(). We do this
// by ensuring that "rect" intersects at least two children of "result"
// (after padding).
int axis = S2Testing.Random.Uniform(2);
double center = result.CenterUV()[axis];
// Find the range of coordinates that are shared between child cells
// along that axis.
R1Interval shared = new(center - padding, center + padding);
double mid = SampleInterval(shared.Intersection(max_rect[axis]));
a = a.SetAxis(axis, SampleInterval(new R1Interval(max_rect[axis].Lo, mid)));
b = b.SetAxis(axis, SampleInterval(new R1Interval(mid, max_rect[axis].Hi)));
}
R2Rect rect = R2Rect.FromPointPair(a, b);
// Choose an arbitrary ancestor as the S2PaddedCell.
S2CellId initial_id = result.Parent(S2Testing.Random.Uniform(result.Level() + 1));
Assert.Equal(result, new S2PaddedCell(initial_id, padding).ShrinkToFit(rect));
}
}
public void Test_CellTarget_VisitContainingShapes()
{
var index = MakeIndexOrDie(
"1:1 # 1:1, 2:2 # 0:0, 0:3, 3:0 | 6:6, 6:9, 9:6 | -1:-1, -1:5, 5:-1");
// Only shapes 2 and 4 should contain a very small cell near 1:1.
var cellid1 = new S2CellId(MakePointOrDie("1:1"));
var target1 = new S2MinDistanceCellTarget(new S2Cell(cellid1));
Assert.True(IsSubsetOfSize(GetContainingShapes(target1, index, 1),
new int[] { 2, 4 }, 1));
Assert.Equal(new int[] { 2, 4 }, GetContainingShapes(target1, index, 5));
// For a larger cell that properly contains one or more index cells, all
// shapes that intersect the first such cell in S2CellId order are returned.
// In the test below, this happens to again be the 1st and 3rd polygons
// (whose shape_ids are 2 and 4).
var cellid2 = cellid1.Parent(5);
var target2 = new S2MinDistanceCellTarget(new S2Cell(cellid2));
Assert.Equal(new int[] { 2, 4 }, GetContainingShapes(target2, index, 5));
}
public void CanonicalizeCovering(List <S2CellId> covering)
{
// We check this on each call because of Options().
System.Diagnostics.Debug.Assert(Options_.MinLevel <= Options_.MaxLevel);
// Note that when the covering parameters have their default values, almost
// all of the code in this function is skipped.
// If any cells are too small, or don't satisfy level_mod(), then replace
// them with ancestors.
if (Options_.MaxLevel < S2.kMaxCellLevel || Options_.LevelMod > 1)
{
for (var i = 0; i < covering.Count; i++)
{
var id = covering[i];
int level = id.Level();
int new_level = AdjustLevel(Math.Min(level, Options_.MaxLevel));
if (new_level != level)
{
covering[i] = id.Parent(new_level);
}
}
}
// Sort the cells and simplify them.
S2CellUnion.Normalize(covering);
// Make sure that the covering satisfies min_level() and level_mod(),
// possibly at the expense of satisfying max_cells().
if (Options_.MinLevel > 0 || Options_.LevelMod > 1)
{
var tmp = new List <S2CellId>();
S2CellUnion.Denormalize(covering, Options_.MinLevel, Options_.LevelMod, tmp);
covering.Clear();
covering.AddRange(tmp);
}
// If there are too many cells and the covering is very large, use the
// S2RegionCoverer to compute a new covering. (This avoids possible O(n^2)
// behavior of the simpler algorithm below.)
var excess = covering.Count - Options_.MaxCells;
if (excess <= 0 || IsCanonical(covering))
{
return;
}
if (excess * covering.Count > 10000)
{
GetCovering(new S2CellUnion(covering), out covering);
}
else
{
// Repeatedly replace two adjacent cells in S2CellId order by their lowest
// common ancestor until the number of cells is acceptable.
while (covering.Count > Options_.MaxCells)
{
int best_index = -1, best_level = -1;
for (int i = 0; i + 1 < covering.Count; ++i)
{
int level = covering[i].CommonAncestorLevel(covering[i + 1]);
level = AdjustLevel(level);
if (level > best_level)
{
best_level = level;
best_index = i;
}
}
if (best_level < Options_.MinLevel)
{
break;
}
// Replace all cells contained by the new ancestor cell.
S2CellId id = covering[best_index].Parent(best_level);
ReplaceCellsWithAncestor(covering, id);
// Now repeatedly check whether all children of the parent cell are
// present, in which case we can replace those cells with their parent.
while (best_level > Options_.MinLevel)
{
best_level -= Options_.LevelMod;
id = id.Parent(best_level);
if (!ContainsAllChildren(covering, id))
{
break;
}
ReplaceCellsWithAncestor(covering, id);
}
}
}
System.Diagnostics.Debug.Assert(IsCanonical(covering));
}
public void Test_S2CellId_Neighbors()
{
// Check the edge neighbors of face 1.
var out_faces = new[] { 5, 3, 2, 0 };
var face_nbrs = new S2CellId[4];
S2CellId.FromFace(1).EdgeNeighbors(face_nbrs);
for (int i = 0; i < 4; ++i)
{
Assert.True(face_nbrs[i].IsFace());
Assert.Equal(out_faces[i], (int)face_nbrs[i].Face());
}
// Check the edge neighbors of the corner cells at all levels. This case is
// trickier because it requires projecting onto adjacent faces.
const int kMaxIJ = S2CellId.kMaxSize - 1;
for (int level = 1; level <= S2.kMaxCellLevel; ++level)
{
S2CellId id2 = S2CellId.FromFaceIJ(1, 0, 0).Parent(level);
var nbrs2 = new S2CellId[4];
id2.EdgeNeighbors(nbrs2);
// These neighbors were determined manually using the face and axis
// relationships defined in s2coords.cc.
int size_ij = S2CellId.SizeIJ(level);
Assert.Equal(S2CellId.FromFaceIJ(5, kMaxIJ, kMaxIJ).Parent(level), nbrs2[0]);
Assert.Equal(S2CellId.FromFaceIJ(1, size_ij, 0).Parent(level), nbrs2[1]);
Assert.Equal(S2CellId.FromFaceIJ(1, 0, size_ij).Parent(level), nbrs2[2]);
Assert.Equal(S2CellId.FromFaceIJ(0, kMaxIJ, 0).Parent(level), nbrs2[3]);
}
// Check the vertex neighbors of the center of face 2 at level 5.
var nbrs = new List <S2CellId>();
new S2CellId(new S2Point(0, 0, 1)).AppendVertexNeighbors(5, nbrs);
nbrs.Sort();
for (int i = 0; i < 4; ++i)
{
Assert.Equal(S2CellId.FromFaceIJ(
2, (1 << 29) - ((i < 2) ? 1 : 0), (1 << 29) - ((i == 0 || i == 3) ? 1 : 0))
.Parent(5), nbrs[i]);
}
nbrs.Clear();
// Check the vertex neighbors of the corner of faces 0, 4, and 5.
S2CellId id1 = S2CellId.FromFacePosLevel(0, 0, S2.kMaxCellLevel);
id1.AppendVertexNeighbors(0, nbrs);
nbrs.Sort();
Assert.Equal(3, nbrs.Count);
Assert.Equal(S2CellId.FromFace(0), nbrs[0]);
Assert.Equal(S2CellId.FromFace(4), nbrs[1]);
Assert.Equal(S2CellId.FromFace(5), nbrs[2]);
// Check that AppendAllNeighbors produces results that are consistent
// with AppendVertexNeighbors for a bunch of random cells.
for (var i = 0; i < 1000; ++i)
{
S2CellId id2 = S2Testing.GetRandomCellId();
if (id2.IsLeaf())
{
id2 = id2.Parent();
}
// TestAllNeighbors computes approximately 2**(2*(diff+1)) cell ids,
// so it's not reasonable to use large values of "diff".
int max_diff = Math.Min(5, S2.kMaxCellLevel - id2.Level() - 1);
int level = id2.Level() + S2Testing.Random.Uniform(max_diff + 1);
TestAllNeighbors(id2, level);
}
}
public void Test_S2Cap_S2CellMethods()
{
// For each cube face, we construct some cells on
// that face and some caps whose positions are relative to that face,
// and then check for the expected intersection/containment results.
for (var face = 0; face < 6; ++face)
{
// The cell consisting of the entire face.
S2Cell root_cell = S2Cell.FromFace(face);
// A leaf cell at the midpoint of the v=1 edge.
S2Cell edge_cell = new(S2.FaceUVtoXYZ(face, 0, 1 - kEps));
// A leaf cell at the u=1, v=1 corner.
S2Cell corner_cell = new(S2.FaceUVtoXYZ(face, 1 - kEps, 1 - kEps));
// Quick check for full and empty caps.
Assert.True(S2Cap.Full.Contains(root_cell));
Assert.False(S2Cap.Empty.MayIntersect(root_cell));
// Check intersections with the bounding caps of the leaf cells that are
// adjacent to 'corner_cell' along the Hilbert curve. Because this corner
// is at (u=1,v=1), the curve stays locally within the same cube face.
S2CellId first = corner_cell.Id.Advance(-3);
S2CellId last = corner_cell.Id.Advance(4);
for (S2CellId id = first; id < last; id = id.Next())
{
S2Cell cell = new(id);
Assert.Equal(id == corner_cell.Id,
cell.GetCapBound().Contains(corner_cell));
Assert.Equal(id.Parent().Contains(corner_cell.Id),
cell.GetCapBound().MayIntersect(corner_cell));
}
var anti_face = (face + 3) % 6; // Opposite face.
for (var cap_face = 0; cap_face < 6; ++cap_face)
{
// A cap that barely contains all of 'cap_face'.
S2Point center = S2.GetNorm(cap_face);
S2Cap covering = new(center, S1Angle.FromRadians(kFaceRadius + kEps));
Assert.Equal(cap_face == face, covering.Contains(root_cell));
Assert.Equal(cap_face != anti_face, covering.MayIntersect(root_cell));
Assert.Equal(center.DotProd(edge_cell.Center()) > 0.1,
covering.Contains(edge_cell));
Assert.Equal(covering.MayIntersect(edge_cell), covering.Contains(edge_cell));
Assert.Equal(cap_face == face, covering.Contains(corner_cell));
Assert.Equal(center.DotProd(corner_cell.Center()) > 0,
covering.MayIntersect(corner_cell));
// A cap that barely intersects the edges of 'cap_face'.
S2Cap bulging = new(center, S1Angle.FromRadians(S2.M_PI_4 + kEps));
Assert.False(bulging.Contains(root_cell));
Assert.Equal(cap_face != anti_face, bulging.MayIntersect(root_cell));
Assert.Equal(cap_face == face, bulging.Contains(edge_cell));
Assert.Equal(center.DotProd(edge_cell.Center()) > 0.1,
bulging.MayIntersect(edge_cell));
Assert.False(bulging.Contains(corner_cell));
Assert.False(bulging.MayIntersect(corner_cell));
// A singleton cap.
S2Cap singleton = new(center, S1Angle.Zero);
Assert.Equal(cap_face == face, singleton.MayIntersect(root_cell));
Assert.False(singleton.MayIntersect(edge_cell));
Assert.False(singleton.MayIntersect(corner_cell));
}
}
}
