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;
}
}
// The implementation is approximate but conservative; it always returns
// "false" if the cell is not contained by the buffered region, but it may
// also return false in some cases where "cell" is in fact contained.
public bool Contains(S2Cell cell)
{
// Return true if the buffered region is guaranteed to cover whole globe.
if (radius_successor_ > S1ChordAngle.Straight)
{
return(true);
}
// To implement this method perfectly would require computing the directed
// Hausdorff distance, which is expensive (and not currently implemented).
// However the following heuristic is almost as good in practice and much
// cheaper to compute.
// Return true if the unbuffered region contains this cell.
if (Index().MakeS2ShapeIndexRegion().Contains(cell))
{
return(true);
}
// Otherwise approximate the cell by its bounding cap.
//
// NOTE(ericv): It would be slightly more accurate to first find the closest
// point in the indexed geometry to the cell, and then measure the actual
// maximum distance from that point to the cell (a poor man's Hausdorff
// distance). But based on actual tests this is not worthwhile.
S2Cap cap = cell.GetCapBound();
if (Radius < cap.Radius)
{
return(false);
}
// Return true if the distance to the cell center plus the radius of the
// cell's bounding cap is less than or equal to "radius_".
var target = new S2ClosestEdgeQuery.PointTarget(cell.Center());
return(query_.IsDistanceLess(target, radius_successor_ - cap.Radius));
}
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))));
}