private static void gatherStats(S2Cell cell)
{
var s = levelStats[cell.Level];
var exactArea = cell.ExactArea();
var approxArea = cell.ApproxArea();
double minEdge = 100, maxEdge = 0, avgEdge = 0;
double minDiag = 100, maxDiag = 0;
double minWidth = 100, maxWidth = 0;
double minAngleSpan = 100, maxAngleSpan = 0;
for (var i = 0; i < 4; ++i)
{
var edge = cell.GetVertexRaw(i).Angle(cell.GetVertexRaw((i + 1) & 3));
minEdge = Math.Min(edge, minEdge);
maxEdge = Math.Max(edge, maxEdge);
avgEdge += 0.25 * edge;
var mid = cell.GetVertexRaw(i) + cell.GetVertexRaw((i + 1) & 3);
var width = S2.PiOver2 - mid.Angle(cell.GetEdgeRaw(i ^ 2));
minWidth = Math.Min(width, minWidth);
maxWidth = Math.Max(width, maxWidth);
if (i < 2)
{
var diag = cell.GetVertexRaw(i).Angle(cell.GetVertexRaw(i ^ 2));
minDiag = Math.Min(diag, minDiag);
maxDiag = Math.Max(diag, maxDiag);
var angleSpan = cell.GetEdgeRaw(i).Angle(
-cell.GetEdgeRaw(i ^ 2));
minAngleSpan = Math.Min(angleSpan, minAngleSpan);
maxAngleSpan = Math.Max(angleSpan, maxAngleSpan);
}
}
s.count += 1;
s.minArea = Math.Min(exactArea, s.minArea);
s.maxArea = Math.Max(exactArea, s.maxArea);
s.avgArea += exactArea;
s.minWidth = Math.Min(minWidth, s.minWidth);
s.maxWidth = Math.Max(maxWidth, s.maxWidth);
s.avgWidth += 0.5 * (minWidth + maxWidth);
s.minEdge = Math.Min(minEdge, s.minEdge);
s.maxEdge = Math.Max(maxEdge, s.maxEdge);
s.avgEdge += avgEdge;
s.maxEdgeAspect = Math.Max(maxEdge / minEdge, s.maxEdgeAspect);
s.minDiag = Math.Min(minDiag, s.minDiag);
s.maxDiag = Math.Max(maxDiag, s.maxDiag);
s.avgDiag += 0.5 * (minDiag + maxDiag);
s.maxDiagAspect = Math.Max(maxDiag / minDiag, s.maxDiagAspect);
s.minAngleSpan = Math.Min(minAngleSpan, s.minAngleSpan);
s.maxAngleSpan = Math.Max(maxAngleSpan, s.maxAngleSpan);
s.avgAngleSpan += 0.5 * (minAngleSpan + maxAngleSpan);
var approxRatio = approxArea / exactArea;
s.minApproxRatio = Math.Min(approxRatio, s.minApproxRatio);
s.maxApproxRatio = Math.Max(approxRatio, s.maxApproxRatio);
}
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 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)));
}
private static void gatherStats(S2Cell cell)
{
var s = levelStats[cell.Level];
var exactArea = cell.ExactArea();
var approxArea = cell.ApproxArea();
double minEdge = 100, maxEdge = 0, avgEdge = 0;
double minDiag = 100, maxDiag = 0;
double minWidth = 100, maxWidth = 0;
double minAngleSpan = 100, maxAngleSpan = 0;
for (var i = 0; i < 4; ++i)
{
var edge = cell.GetVertexRaw(i).Angle(cell.GetVertexRaw((i + 1) & 3));
minEdge = Math.Min(edge, minEdge);
maxEdge = Math.Max(edge, maxEdge);
avgEdge += 0.25*edge;
var mid = cell.GetVertexRaw(i) + cell.GetVertexRaw((i + 1) & 3);
var width = S2.PiOver2 - mid.Angle(cell.GetEdgeRaw(i ^ 2));
minWidth = Math.Min(width, minWidth);
maxWidth = Math.Max(width, maxWidth);
if (i < 2)
{
var diag = cell.GetVertexRaw(i).Angle(cell.GetVertexRaw(i ^ 2));
minDiag = Math.Min(diag, minDiag);
maxDiag = Math.Max(diag, maxDiag);
var angleSpan = cell.GetEdgeRaw(i).Angle(
-cell.GetEdgeRaw(i ^ 2));
minAngleSpan = Math.Min(angleSpan, minAngleSpan);
maxAngleSpan = Math.Max(angleSpan, maxAngleSpan);
}
}
s.count += 1;
s.minArea = Math.Min(exactArea, s.minArea);
s.maxArea = Math.Max(exactArea, s.maxArea);
s.avgArea += exactArea;
s.minWidth = Math.Min(minWidth, s.minWidth);
s.maxWidth = Math.Max(maxWidth, s.maxWidth);
s.avgWidth += 0.5*(minWidth + maxWidth);
s.minEdge = Math.Min(minEdge, s.minEdge);
s.maxEdge = Math.Max(maxEdge, s.maxEdge);
s.avgEdge += avgEdge;
s.maxEdgeAspect = Math.Max(maxEdge/minEdge, s.maxEdgeAspect);
s.minDiag = Math.Min(minDiag, s.minDiag);
s.maxDiag = Math.Max(maxDiag, s.maxDiag);
s.avgDiag += 0.5*(minDiag + maxDiag);
s.maxDiagAspect = Math.Max(maxDiag/minDiag, s.maxDiagAspect);
s.minAngleSpan = Math.Min(minAngleSpan, s.minAngleSpan);
s.maxAngleSpan = Math.Max(maxAngleSpan, s.maxAngleSpan);
s.avgAngleSpan += 0.5*(minAngleSpan + maxAngleSpan);
var approxRatio = approxArea/exactArea;
s.minApproxRatio = Math.Min(approxRatio, s.minApproxRatio);
s.maxApproxRatio = Math.Max(approxRatio, s.maxApproxRatio);
}
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 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)));
}
