public void testContainment()
{
Trace.WriteLine("TestContainment");
IDictionary <S2CellId, S2CellId> parentMap = new Dictionary <S2CellId, S2CellId>();
var cells = new List <S2CellId>();
for (var face = 0; face < 6; ++face)
{
expandCell(S2CellId.FromFacePosLevel(face, 0, 0), cells, parentMap);
}
for (var i = 0; i < cells.Count; ++i)
{
for (var j = 0; j < cells.Count; ++j)
{
var contained = true;
for (var id = cells[j]; id != cells[i]; id = parentMap[id])
{
if (!parentMap.ContainsKey(id))
{
contained = false;
break;
}
}
JavaAssert.Equal(cells[i].Contains(cells[j]), contained);
JavaAssert.Equal(cells[j] >= cells[i].RangeMin &&
cells[j] <= cells[i].RangeMax, contained);
JavaAssert.Equal(cells[i].Intersects(cells[j]),
cells[i].Contains(cells[j]) || cells[j].Contains(cells[i]));
}
}
}
private void expandCell(
S2CellId parent, List <S2CellId> cells, IDictionary <S2CellId, S2CellId> parentMap)
{
cells.Add(parent);
if (parent.Level == kMaxExpandLevel)
{
return;
}
var i = 0;
var j = 0;
int?orientation = 0;
var face = parent.ToFaceIjOrientation(ref i, ref j, ref orientation);
JavaAssert.Equal(face, parent.Face);
var pos = 0;
for (var child = parent.ChildBegin; !child.Equals(parent.ChildEnd);
child = child.Next)
{
// Do some basic checks on the children
JavaAssert.Equal(child.Level, parent.Level + 1);
Assert.True(!child.IsLeaf);
int?childOrientation = 0;
JavaAssert.Equal(child.ToFaceIjOrientation(ref i, ref j, ref childOrientation), face);
JavaAssert.Equal(
childOrientation.Value, orientation.Value ^ S2.PosToOrientation(pos));
parentMap.Add(child, parent);
expandCell(child, cells, parentMap);
++pos;
}
}
public void testNeighbors()
{
Trace.WriteLine("TestNeighbors");
// Check the edge neighbors of face 1.
int[] outFaces = { 5, 3, 2, 0 };
var faceNbrs = S2CellId.FromFacePosLevel(1, 0, 0).GetEdgeNeighbors();
for (var i = 0; i < 4; ++i)
{
Assert.True(faceNbrs[i].IsFace);
JavaAssert.Equal(faceNbrs[i].Face, outFaces[i]);
}
// Check the vertex neighbors of the center of face 2 at level 5.
var nbrs = new List <S2CellId>();
S2CellId.FromPoint(new S2Point(0, 0, 1)).GetVertexNeighbors(5, nbrs);
nbrs.Sort();
for (var i = 0; i < 4; ++i)
{
JavaAssert.Equal(nbrs[i], S2CellId.FromFaceIj(
2, (1 << 29) - (i < 2 ? 1 : 0), (1 << 29) - ((i == 0 || i == 3) ? 1 : 0)).ParentForLevel(5));
}
nbrs.Clear();
// Check the vertex neighbors of the corner of faces 0, 4, and 5.
var id = S2CellId.FromFacePosLevel(0, 0, S2CellId.MaxLevel);
id.GetVertexNeighbors(0, nbrs);
nbrs.Sort();
JavaAssert.Equal(nbrs.Count, 3);
JavaAssert.Equal(nbrs[0], S2CellId.FromFacePosLevel(0, 0, 0));
JavaAssert.Equal(nbrs[1], S2CellId.FromFacePosLevel(4, 0, 0));
JavaAssert.Equal(nbrs[2], S2CellId.FromFacePosLevel(5, 0, 0));
// Check that GetAllNeighbors produces results that are consistent
// with GetVertexNeighbors for a bunch of random cells.
for (var i = 0; i < 1000; ++i)
{
var id1 = getRandomCellId();
var toTest = id1;
if (id1.IsLeaf)
{
toTest = id1.Parent;
}
// TestAllNeighbors computes approximately 2**(2*(diff+1)) cell id1s,
// so it's not reasonable to use large values of "diff".
var maxDiff = Math.Min(6, S2CellId.MaxLevel - toTest.Level - 1);
var level = toTest.Level + random(maxDiff);
testAllNeighbors(toTest, level);
}
}
public void S2CellIdTestBasic()
{
Trace.WriteLine("TestBasic");
// Check default constructor.
var id = new S2CellId();
//JavaAssert.Equal(id.id(), 0);
//Assert.True(!id.isValid());
// Check basic accessor methods.
id = S2CellId.FromFacePosLevel(3, 0x12345678, S2CellId.MaxLevel - 4);
//Assert.True(id.isValid());
//JavaAssert.Equal(id.face(), 3);
// JavaAssert.Equal(id.pos(), 0x12345700);
//JavaAssert.Equal(id.level(), S2CellId.MAX_LEVEL - 4);
//Assert.True(!id.isLeaf());
//// Check face definitions
//JavaAssert.Equal(getCellId(0, 0).face(), 0);
//JavaAssert.Equal(getCellId(0, 90).face(), 1);
//JavaAssert.Equal(getCellId(90, 0).face(), 2);
//JavaAssert.Equal(getCellId(0, 180).face(), 3);
//JavaAssert.Equal(getCellId(0, -90).face(), 4);
//JavaAssert.Equal(getCellId(-90, 0).face(), 5);
//// Check parent/child relationships.
//JavaAssert.Equal(id.childBegin(id.level() + 2).pos(), 0x12345610);
//JavaAssert.Equal(id.childBegin().pos(), 0x12345640);
//JavaAssert.Equal(id.parent().pos(), 0x12345400);
//JavaAssert.Equal(id.parent(id.level() - 2).pos(), 0x12345000);
//// Check ordering of children relative to parents.
//Assert.True(id.childBegin().lessThan(id));
//var childEnd = id.childEnd();
//var childId = childEnd.id();
//var id1 = id.id();
//Assert.True(id.childEnd().greaterThan(id));
//JavaAssert.Equal(id.childBegin().next().next().next().next(), id.childEnd());
//JavaAssert.Equal(id.childBegin(S2CellId.MAX_LEVEL), id.rangeMin());
//JavaAssert.Equal(id.childEnd(S2CellId.MAX_LEVEL), id.rangeMax().next());
// Check wrapping from beginning of Hilbert curve to end and vice versa.
// JavaAssert.Equal(S2CellId.begin(0).prevWrap(), S2CellId.end(0).prev());
JavaAssert.Equal(S2CellId.Begin(S2CellId.MaxLevel).PreviousWithWrap,
S2CellId.FromFacePosLevel(5, ~0UL >> S2CellId.FaceBits, S2CellId.MaxLevel));
JavaAssert.Equal(S2CellId.End(4).Previous.NextWithWrap, S2CellId.Begin(4));
JavaAssert.Equal(S2CellId.End(S2CellId.MaxLevel).Previous.NextWithWrap,
S2CellId.FromFacePosLevel(0, 0, S2CellId.MaxLevel));
// Check that cells are represented by the position of their center
// along the Hilbert curve.
JavaAssert.Equal(id.RangeMin.Id + id.RangeMax.Id, 2 * id.Id);
}
/**
* Test all of the interval operations on the given pair of intervals.
* "expected_relation" is a sequence of "T" and "F" characters corresponding
* to the expected results of contains(), interiorContains(), Intersects(),
* and InteriorIntersects() respectively.
*/
private void testIntervalOps(R1Interval x, R1Interval y, String expectedRelation)
{
JavaAssert.Equal(x.Contains(y), expectedRelation[0] == 'T');
JavaAssert.Equal(x.InteriorContains(y), expectedRelation[1] == 'T');
JavaAssert.Equal(x.Intersects(y), expectedRelation[2] == 'T');
JavaAssert.Equal(x.InteriorIntersects(y), expectedRelation[3] == 'T');
JavaAssert.Equal(x.Contains(y), x.Union(y).Equals(x));
JavaAssert.Equal(x.Intersects(y), !x.Intersection(y).IsEmpty);
}
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 testInverses()
{
Trace.WriteLine("TestInverses");
// Check the conversion of random leaf cells to S2LatLngs and back.
for (var i = 0; i < 200000; ++i)
{
var id = getRandomCellId(S2CellId.MaxLevel);
Assert.True(id.IsLeaf && id.Level == S2CellId.MaxLevel);
var center = id.ToLatLng();
JavaAssert.Equal(S2CellId.FromLatLng(center).Id, id.Id);
}
}
public void testTokens()
{
Trace.WriteLine("TestTokens");
// Test random cell ids at all levels.
for (var i = 0; i < 10000; ++i)
{
var id = getRandomCellId();
if (!id.IsValid)
{
continue;
}
var token = id.ToToken();
Assert.True(token.Length <= 16);
JavaAssert.Equal(S2CellId.FromToken(token), id);
}
// Check that invalid cell ids can be encoded.
var token1 = S2CellId.None.ToToken();
JavaAssert.Equal(S2CellId.FromToken(token1), S2CellId.None);
}
public void S1AngleBasicTest()
{
// Check that the conversion between Pi radians and 180 degrees is exact.
JavaAssert.Equal(S1Angle.FromRadians(Math.PI).Radians, Math.PI);
JavaAssert.Equal(S1Angle.FromRadians(Math.PI).Degrees, 180.0);
JavaAssert.Equal(S1Angle.FromDegrees(180).Radians, Math.PI);
JavaAssert.Equal(S1Angle.FromDegrees(180).Degrees, 180.0);
JavaAssert.Equal(S1Angle.FromRadians(Math.PI / 2).Degrees, 90.0);
// Check negative angles.
JavaAssert.Equal(S1Angle.FromRadians(-Math.PI / 2).Degrees, -90.0);
JavaAssert.Equal(S1Angle.FromDegrees(-45).Radians, -Math.PI / 4);
// Check that E5/E6/E7 representations work as expected.
JavaAssert.Equal(S1Angle.E5(2000000), S1Angle.FromDegrees(20));
JavaAssert.Equal(S1Angle.E6(-60000000), S1Angle.FromDegrees(-60));
JavaAssert.Equal(S1Angle.E7(750000000), S1Angle.FromDegrees(75));
JavaAssert.Equal(S1Angle.FromDegrees(12.34567).E5(), 1234567);
JavaAssert.Equal(S1Angle.FromDegrees(12.345678).E6(), 12345678);
JavaAssert.Equal(S1Angle.FromDegrees(-12.3456789).E7(), -123456789);
}
public void testCells()
{
// 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.
// The distance from the center of a face to one of its vertices.
var kFaceRadius = Math.Atan(S2.Sqrt2);
for (var face = 0; face < 6; ++face)
{
// The cell consisting of the entire face.
var rootCell = S2Cell.FromFacePosLevel(face, (byte)0, 0);
// A leaf cell at the midpoint of the v=1 edge.
var edgeCell = new S2Cell(S2Projections.FaceUvToXyz(face, 0, 1 - EPS));
// A leaf cell at the u=1, v=1 corner.
var cornerCell = new S2Cell(S2Projections.FaceUvToXyz(face, 1 - EPS, 1 - EPS));
// Quick check for full and empty caps.
Assert.True(S2Cap.Full.Contains(rootCell));
Assert.True(!S2Cap.Empty.MayIntersect(rootCell));
// 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.
var first = cornerCell.Id.Previous.Previous.Previous;
var last = cornerCell.Id.Next.Next.Next.Next;
for (var id = first; id < last; id = id.Next)
{
var cell = new S2Cell(id);
JavaAssert.Equal(cell.CapBound.Contains(cornerCell), id.Equals(cornerCell.Id));
JavaAssert.Equal(
cell.CapBound.MayIntersect(cornerCell), id.Parent.Contains(cornerCell.Id));
}
var antiFace = (face + 3) % 6; // Opposite face.
for (var capFace = 0; capFace < 6; ++capFace)
{
// A cap that barely contains all of 'cap_face'.
var center = S2Projections.GetNorm(capFace);
var covering = S2Cap.FromAxisAngle(center, S1Angle.FromRadians(kFaceRadius + EPS));
JavaAssert.Equal(covering.Contains(rootCell), capFace == face);
JavaAssert.Equal(covering.MayIntersect(rootCell), capFace != antiFace);
JavaAssert.Equal(covering.Contains(edgeCell), center.DotProd(edgeCell.Center) > 0.1);
JavaAssert.Equal(covering.Contains(edgeCell), covering.MayIntersect(edgeCell));
JavaAssert.Equal(covering.Contains(cornerCell), capFace == face);
JavaAssert.Equal(
covering.MayIntersect(cornerCell), center.DotProd(cornerCell.Center) > 0);
// A cap that barely intersects the edges of 'cap_face'.
var bulging = S2Cap.FromAxisAngle(center, S1Angle.FromRadians(S2.PiOver4 + EPS));
Assert.True(!bulging.Contains(rootCell));
JavaAssert.Equal(bulging.MayIntersect(rootCell), capFace != antiFace);
JavaAssert.Equal(bulging.Contains(edgeCell), capFace == face);
JavaAssert.Equal(bulging.MayIntersect(edgeCell), center.DotProd(edgeCell.Center) > 0.1);
Assert.True(!bulging.Contains(cornerCell));
Assert.True(!bulging.MayIntersect(cornerCell));
// A singleton cap.
var singleton = S2Cap.FromAxisAngle(center, S1Angle.FromRadians(0));
JavaAssert.Equal(singleton.MayIntersect(rootCell), capFace == face);
Assert.True(!singleton.MayIntersect(edgeCell));
Assert.True(!singleton.MayIntersect(cornerCell));
}
}
}
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)));
}
protected static void assertEquals(object actual, object expected)
{
JavaAssert.Equal(actual, expected);
}
public void testToToken()
{
JavaAssert.Equal("000000000000010a", new S2CellId(266).ToToken());
JavaAssert.Equal("80855c", new S2CellId(unchecked ((ulong)-9185834709882503168L)).ToToken());
}
public void testSubdivide(S2Cell cell)
{
gatherStats(cell);
if (cell.IsLeaf)
{
return;
}
var children = new S2Cell[4];
for (var i = 0; i < children.Length; ++i)
{
children[i] = new S2Cell();
}
Assert.True(cell.Subdivide(children));
var childId = cell.Id.ChildBegin;
double exactArea = 0;
double approxArea = 0;
double averageArea = 0;
for (var i = 0; i < 4; ++i, childId = childId.Next)
{
exactArea += children[i].ExactArea();
approxArea += children[i].ApproxArea();
averageArea += children[i].AverageArea();
// Check that the child geometry is consistent with its cell id.
JavaAssert.Equal(children[i].Id, childId);
Assert.True(children[i].Center.ApproxEquals(childId.ToPoint(), 1e-15));
var direct = new S2Cell(childId);
JavaAssert.Equal(children[i].Face, direct.Face);
JavaAssert.Equal(children[i].Level, direct.Level);
JavaAssert.Equal(children[i].Orientation, direct.Orientation);
JavaAssert.Equal(children[i].CenterRaw, direct.CenterRaw);
for (var k = 0; k < 4; ++k)
{
JavaAssert.Equal(children[i].GetVertexRaw(k), direct.GetVertexRaw(k));
JavaAssert.Equal(children[i].GetEdgeRaw(k), direct.GetEdgeRaw(k));
}
// Test Contains() and MayIntersect().
Assert.True(cell.Contains(children[i]));
Assert.True(cell.MayIntersect(children[i]));
Assert.True(!children[i].Contains(cell));
Assert.True(cell.Contains(children[i].CenterRaw));
for (var j = 0; j < 4; ++j)
{
Assert.True(cell.Contains(children[i].GetVertexRaw(j)));
if (j != i)
{
Assert.True(!children[i].Contains(children[j].CenterRaw));
Assert.True(!children[i].MayIntersect(children[j]));
}
}
// Test GetCapBound and GetRectBound.
var parentCap = cell.CapBound;
var parentRect = cell.RectBound;
if (cell.Contains(new S2Point(0, 0, 1)) ||
cell.Contains(new S2Point(0, 0, -1)))
{
Assert.True(parentRect.Lng.IsFull);
}
var childCap = children[i].CapBound;
var childRect = children[i].RectBound;
Assert.True(childCap.Contains(children[i].Center));
Assert.True(childRect.Contains(children[i].CenterRaw));
Assert.True(parentCap.Contains(children[i].Center));
Assert.True(parentRect.Contains(children[i].CenterRaw));
for (var j = 0; j < 4; ++j)
{
Assert.True(childCap.Contains(children[i].GetVertex(j)));
Assert.True(childRect.Contains(children[i].GetVertex(j)));
Assert.True(childRect.Contains(children[i].GetVertexRaw(j)));
Assert.True(parentCap.Contains(children[i].GetVertex(j)));
if (!parentRect.Contains(children[i].GetVertex(j)))
{
Console.WriteLine("cell: " + cell + " i: " + i + " j: " + j);
Console.WriteLine("Children " + i + ": " + children[i]);
Console.WriteLine("Parent rect: " + parentRect);
Console.WriteLine("Vertex raw(j) " + children[i].GetVertex(j));
Console.WriteLine("Latlng of vertex: " + new S2LatLng(children[i].GetVertex(j)));
Console.WriteLine("RectBound: " + cell.RectBound);
}
Assert.True(parentRect.Contains(children[i].GetVertex(j)));
if (!parentRect.Contains(children[i].GetVertexRaw(j)))
{
Console.WriteLine("cell: " + cell + " i: " + i + " j: " + j);
Console.WriteLine("Children " + i + ": " + children[i]);
Console.WriteLine("Parent rect: " + parentRect);
Console.WriteLine("Vertex raw(j) " + children[i].GetVertexRaw(j));
Console.WriteLine("Latlng of vertex: " + new S2LatLng(children[i].GetVertexRaw(j)));
Console.WriteLine("RectBound: " + cell.RectBound);
}
Assert.True(parentRect.Contains(children[i].GetVertexRaw(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.
var capCount = 0;
var rectCount = 0;
for (var k = 0; k < 4; ++k)
{
if (childCap.Contains(children[j].GetVertex(k)))
{
++capCount;
}
if (childRect.Contains(children[j].GetVertexRaw(k)))
{
++rectCount;
}
}
Assert.True(capCount <= 2);
if (childRect.LatLo.Radians > -S2.PiOver2 &&
childRect.LatHi.Radians < S2.PiOver2)
{
// Bounding rectangles may be too large at the poles because the
// pole itself has an arbitrary fixed longitude.
Assert.True(rectCount <= 2);
}
}
}
// Check all children for the first few levels, and then sample randomly.
// Also subdivide one corner cell, one edge cell, and one center cell
// so that we have a better chance of sample the minimum metric values.
var forceSubdivide = false;
var center = S2Projections.GetNorm(children[i].Face);
var edge = center + S2Projections.GetUAxis(children[i].Face);
var corner = edge + S2Projections.GetVAxis(children[i].Face);
for (var j = 0; j < 4; ++j)
{
var p = children[i].GetVertexRaw(j);
if (p.Equals(center) || p.Equals(edge) || p.Equals(corner))
{
forceSubdivide = true;
}
}
if (forceSubdivide || cell.Level < (DEBUG_MODE ? 5 : 6) ||
random(DEBUG_MODE ? 10 : 4) == 0)
{
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(exactArea / cell.ExactArea())) <= Math
.Abs(Math.Log(1 + 1e-6)));
Assert.True(Math.Abs(Math.Log(approxArea / cell.ApproxArea())) <= Math
.Abs(Math.Log(1.03)));
Assert.True(Math.Abs(Math.Log(averageArea / cell.AverageArea())) <= Math
.Abs(Math.Log(1 + 1e-15)));
}
public void R1IntervalBasicTest()
{
// Constructors and accessors.
var unit = new R1Interval(0, 1);
var negunit = new R1Interval(-1, 0);
JavaAssert.Equal(unit.Lo, 0.0);
JavaAssert.Equal(unit.Hi, 1.0);
JavaAssert.Equal(negunit.Lo, -1.0);
JavaAssert.Equal(negunit.Hi, 0.0);
// is_empty()
var half = new R1Interval(0.5, 0.5);
Assert.True(!unit.IsEmpty);
Assert.True(!half.IsEmpty);
var empty = R1Interval.Empty;
Assert.True(empty.IsEmpty);
// GetCenter(), GetLength()
JavaAssert.Equal(unit.Center, 0.5);
JavaAssert.Equal(half.Center, 0.5);
JavaAssert.Equal(negunit.Length, 1.0);
JavaAssert.Equal(half.Length, 0.0);
Assert.True(empty.Length < 0);
// contains(double), interiorContains(double)
Assert.True(unit.Contains(0.5));
Assert.True(unit.InteriorContains(0.5));
Assert.True(unit.Contains(0));
Assert.True(!unit.InteriorContains(0));
Assert.True(unit.Contains(1));
Assert.True(!unit.InteriorContains(1));
// contains(R1Interval), interiorContains(R1Interval)
// Intersects(R1Interval), InteriorIntersects(R1Interval)
testIntervalOps(empty, empty, "TTFF");
testIntervalOps(empty, unit, "FFFF");
testIntervalOps(unit, half, "TTTT");
testIntervalOps(unit, unit, "TFTT");
testIntervalOps(unit, empty, "TTFF");
testIntervalOps(unit, negunit, "FFTF");
testIntervalOps(unit, new R1Interval(0, 0.5), "TFTT");
testIntervalOps(half, new R1Interval(0, 0.5), "FFTF");
// addPoint()
R1Interval r;
r = empty.AddPoint(5);
Assert.True(r.Lo == 5.0 && r.Hi == 5.0);
r = r.AddPoint(-1);
Assert.True(r.Lo == -1.0 && r.Hi == 5.0);
r = r.AddPoint(0);
Assert.True(r.Lo == -1.0 && r.Hi == 5.0);
// fromPointPair()
JavaAssert.Equal(R1Interval.FromPointPair(4, 4), new R1Interval(4, 4));
JavaAssert.Equal(R1Interval.FromPointPair(-1, -2), new R1Interval(-2, -1));
JavaAssert.Equal(R1Interval.FromPointPair(-5, 3), new R1Interval(-5, 3));
// expanded()
JavaAssert.Equal(empty.Expanded(0.45), empty);
JavaAssert.Equal(unit.Expanded(0.5), new R1Interval(-0.5, 1.5));
// union(), intersection()
Assert.True(new R1Interval(99, 100).Union(empty).Equals(new R1Interval(99, 100)));
Assert.True(empty.Union(new R1Interval(99, 100)).Equals(new R1Interval(99, 100)));
Assert.True(new R1Interval(5, 3).Union(new R1Interval(0, -2)).IsEmpty);
Assert.True(new R1Interval(0, -2).Union(new R1Interval(5, 3)).IsEmpty);
Assert.True(unit.Union(unit).Equals(unit));
Assert.True(unit.Union(negunit).Equals(new R1Interval(-1, 1)));
Assert.True(negunit.Union(unit).Equals(new R1Interval(-1, 1)));
Assert.True(half.Union(unit).Equals(unit));
Assert.True(unit.Intersection(half).Equals(half));
Assert.True(unit.Intersection(negunit).Equals(new R1Interval(0, 0)));
Assert.True(negunit.Intersection(half).IsEmpty);
Assert.True(unit.Intersection(empty).IsEmpty);
Assert.True(empty.Intersection(unit).IsEmpty);
}
