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));
}
}