// This function is designed to choose line segment endpoints that are difficult
// to handle correctly. Given two adjacent cube vertices P and Q, it returns
// either an edge midpoint, face midpoint, or corner vertex along the edge PQ
// and then perturbs it slightly. It also sometimes returns a random point from
// anywhere on the sphere.
private S2Point PerturbedCornerOrMidpoint(S2Point p, S2Point q)
{
S2Point a = (S2Testing.Random.Uniform(3) - 1) * p + (S2Testing.Random.Uniform(3) - 1) * q;
if (S2Testing.Random.OneIn(10))
{
// This perturbation often has no effect except on coordinates that are
// zero, in which case the perturbed value is so small that operations on
// it often result in underflow.
a += Math.Pow(1e-300, S2Testing.Random.RandDouble()) * S2Testing.RandomPoint();
}
else if (S2Testing.Random.OneIn(2))
{
// For coordinates near 1 (say > 0.5), this perturbation yields values
// that are only a few representable values away from the initial value.
a += 4 * S2.DoubleEpsilon * S2Testing.RandomPoint();
}
else
{
// A perturbation whose magnitude is in the range [1e-25, 1e-10].
a += 1e-10 * Math.Pow(S2.DoubleError, S2Testing.Random.RandDouble()) * S2Testing.RandomPoint();
}
if (a.Norm2() < S2.DoubleMinNorm)
{
// If a.Norm2 is denormalized, Normalize() loses too much precision.
return(PerturbedCornerOrMidpoint(p, q));
}
return(a);
}