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_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));
}
}