private static S2Point PerturbATowardsB(S2Point a, S2Point b)
{
var choice = S2Testing.Random.RandDouble();
if (choice < 0.1)
{
return(a);
}
if (choice < 0.3)
{
// Return a point that is exactly proportional to A and that still
// satisfies S2.IsUnitLength().
for (; ;)
{
var b2 = (2 - a.Norm() + 5 * (S2Testing.Random.RandDouble() - 0.5) * S2.DoubleEpsilon) * a;
if (b2 != a && b2.IsUnitLength())
{
return(b2);
}
}
}
if (choice < 0.5)
{
// Return a point such that the distance squared to A will underflow.
return(S2.InterpolateAtDistance(S1Angle.FromRadians(1e-300), a, b));
}
// Otherwise return a point whose distance from A is near S2Constants.DoubleEpsilon such
// that the log of the pdf is uniformly distributed.
double distance = S2.DoubleEpsilon * 1e-5 * Math.Pow(1e6, S2Testing.Random.RandDouble());
return(S2.InterpolateAtDistance(S1Angle.FromRadians(distance), a, b));
}
public void Test_EdgeTrueCentroid_GreatCircles()
{
// Construct random great circles and divide them randomly into segments.
// Then make sure that the centroid is approximately at the center of the
// sphere. Note that because of the way the centroid is computed, it does
// not matter how we split the great circle into segments.
//
// Note that this is a direct test of the properties that the centroid
// should have, rather than a test that it matches a particular formula.
for (int iter = 0; iter < 100; ++iter)
{
// Choose a coordinate frame for the great circle.
S2Point centroid = S2Point.Empty;
S2Testing.GetRandomFrame(out var x, out var y, out _);
S2Point v0 = x;
for (double theta = 0; theta < S2.M_2_PI;
theta += Math.Pow(S2Testing.Random.RandDouble(), 10))
{
S2Point v1 = Math.Cos(theta) * x + Math.Sin(theta) * y;
centroid += S2Centroid.TrueCentroid(v0, v1);
v0 = v1;
}
// Close the circle.
centroid += S2Centroid.TrueCentroid(v0, x);
Assert.True(centroid.Norm() <= 2e-14);
}
}
public void Test_GetLengthAndCentroid_GreatCircles()
{
// Construct random great circles and divide them randomly into segments.
// Then make sure that the length and centroid are correct. Note that
// because of the way the centroid is computed, it does not matter how
// we split the great circle into segments.
for (int iter = 0; iter < 100; ++iter)
{
// Choose a coordinate frame for the great circle.
S2Testing.GetRandomFrame(out var x, out var y, out _);
var lineList = new List <S2Point>();
double theta = 0;
while (theta < S2.M_2_PI)
{
lineList.Add(Math.Cos(theta) * x + Math.Sin(theta) * y);
theta += S2Testing.Random.RandDouble();
}
// Close the circle.
lineList.Add(lineList[0]);
var line = lineList.ToArray();
S1Angle length = S2PolylineMeasures.GetLength(line);
Assert.True(Math.Abs(length.Radians - S2.M_2_PI) <= 2e-14);
S2Point centroid = S2PolylineMeasures.GetCentroid(line);
Assert.True(centroid.Norm() <= 2e-14);
}
}
public void Test_EdgeTrueCentroid_SemiEquator()
{
// Test the centroid of polyline ABC that follows the equator and consists
// of two 90 degree edges (i.e., C = -A). The centroid (multiplied by
// length) should point toward B and have a norm of 2.0. (The centroid
// itself has a norm of 2/Pi, and the total edge length is Pi.)
S2Point a = new(0, -1, 0), b = new(1, 0, 0), c = new(0, 1, 0);
S2Point centroid = S2Centroid.TrueCentroid(a, b) + S2Centroid.TrueCentroid(b, c);
Assert.True(S2.ApproxEquals(b, centroid.Normalize()));
Assert2.DoubleEqual(2.0, centroid.Norm());
}