public void Test_FaceUVtoXYZ()
{
// Check that each face appears exactly once.
S2Point sum = S2Point.Empty;
for (int face = 0; face < 6; ++face)
{
S2Point center = S2.FaceUVtoXYZ(face, 0, 0);
Assert.Equal(S2.GetNorm(face), center);
Assert.Equal(1, Math.Abs(center[center.LargestAbsComponent()]));
sum += center.Fabs();
}
Assert.Equal(sum, new S2Point(2, 2, 2));
// Check that each face has a right-handed coordinate system.
for (int face = 0; face < 6; ++face)
{
Assert.Equal(1, S2.GetUAxis(face).CrossProd(S2.GetVAxis(face))
.DotProd(S2.FaceUVtoXYZ(face, 0, 0)));
}
// Check that the Hilbert curves on each face combine to form a
// continuous curve over the entire cube.
for (int face = 0; face < 6; ++face)
{
// The Hilbert curve on each face starts at (-1,-1) and terminates
// at either (1,-1) (if axes not swapped) or (-1,1) (if swapped).
int sign = ((face & S2.kSwapMask) != 0) ? -1 : 1;
Assert.Equal(S2.FaceUVtoXYZ(face, sign, -sign),
S2.FaceUVtoXYZ((face + 1) % 6, -1, -1));
}
}
public void Test_FaceXYZtoUVW()
{
for (int face = 0; face < 6; ++face)
{
Assert.Equal(new S2Point(0, 0, 0), S2.FaceXYZtoUVW(face, S2Point.Empty));
Assert.Equal(new S2Point(1, 0, 0), S2.FaceXYZtoUVW(face, S2.GetUAxis(face)));
Assert.Equal(new S2Point(-1, 0, 0), S2.FaceXYZtoUVW(face, -S2.GetUAxis(face)));
Assert.Equal(new S2Point(0, 1, 0), S2.FaceXYZtoUVW(face, S2.GetVAxis(face)));
Assert.Equal(new S2Point(0, -1, 0), S2.FaceXYZtoUVW(face, -S2.GetVAxis(face)));
Assert.Equal(new S2Point(0, 0, 1), S2.FaceXYZtoUVW(face, S2.GetNorm(face)));
Assert.Equal(new S2Point(0, 0, -1), S2.FaceXYZtoUVW(face, -S2.GetNorm(face)));
}
}
public void Test_GetCrossingCandidates_PerturbedCubeFaceAxes()
{
List <(S2Point, S2Point)> edges = new();
for (int iter = 0; iter < 5; ++iter)
{
int face = S2Testing.Random.Uniform(6);
double scale = Math.Pow(S2.DoubleError, S2Testing.Random.RandDouble());
S2Point axis = S2.GetUVWAxis(face, S2Testing.Random.Uniform(2));
S2Point a0 = scale * axis + S2.GetNorm(face);
S2Point b0 = scale * axis - S2.GetNorm(face);
GetPerturbedSubEdges(a0, b0, 30, edges);
TestAllCrossings(edges);
}
}
public void Test_GetCrossingCandidates_PerturbedCubeEdges()
{
List <(S2Point, S2Point)> edges = new();
for (int iter = 0; iter < 10; ++iter)
{
int face = S2Testing.Random.Uniform(6);
double scale = Math.Pow(S2.DoubleError, S2Testing.Random.RandDouble());
R2Point uv = new(2 * S2Testing.Random.Uniform(2) - 1, 2 * S2Testing.Random.Uniform(2) - 1); // vertex
S2Point a0 = S2.FaceUVtoXYZ(face, scale * uv);
S2Point b0 = a0 - 2 * S2.GetNorm(face);
// TODO(ericv): This test is currently slow because *every* crossing test
// needs to invoke S2Pred.ExpensiveSign().
GetPerturbedSubEdges(a0, b0, 30, edges);
TestAllCrossings(edges);
}
}
public void Test_UVWAxis()
{
for (int face = 0; face < 6; ++face)
{
// Check that axes are consistent with FaceUVtoXYZ.
Assert.Equal(S2.FaceUVtoXYZ(face, 1, 0) - S2.FaceUVtoXYZ(face, 0, 0),
S2.GetUAxis(face));
Assert.Equal(S2.FaceUVtoXYZ(face, 0, 1) - S2.FaceUVtoXYZ(face, 0, 0),
S2.GetVAxis(face));
Assert.Equal(S2.FaceUVtoXYZ(face, 0, 0), S2.GetNorm(face));
// Check that every face coordinate frame is right-handed.
Assert.Equal(1, S2.GetUAxis(face).CrossProd(S2.GetVAxis(face))
.DotProd(S2.GetNorm(face)));
// Check that GetUVWAxis is consistent with GetUAxis, GetVAxis, GetNorm.
Assert.Equal(S2.GetUAxis(face), S2.GetUVWAxis(face, 0));
Assert.Equal(S2.GetVAxis(face), S2.GetUVWAxis(face, 1));
Assert.Equal(S2.GetNorm(face), S2.GetUVWAxis(face, 2));
}
}
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));
}
}
}