public void TestUniformity_InUnitCircle()
{
var rng = new StatelessRng(kSeed);
// Parametrization based on polar coords
Func <Vector2, Vector2?> Parametrize = cartesian => {
float radius = cartesian.magnitude;
if (radius == 0)
{
return(null);
}
// cdf = cumulative distribution function ~= "area under"
// area of cirle of radius "mag" relative to area of entire circle
// to make uniform, compute cdf(var) / cdf (total) = mag^2 / 1^2
float radiusUniform = radius * radius;
// area increases linearly with angle01, so just need to rescale to [0,1)
float angle = Mathf.Atan2(cartesian.y, cartesian.x);
float angleUniform = ToAngle01(angle);
return(new Vector2(angleUniform, radiusUniform));
};
S.CheckUniformity(new[] { "theta", "rr" },
Gen(i => Parametrize(rng.InUnitCircle(i))));
}
public void TestUniformity_InIntRangeSmall()
{
var rng = new StatelessRng(kSeed);
int kMin = -10, kMax = 40;
S.CheckUniformity("u", Gen(i => (rng.InIntRange(i, kMin, kMax) - kMin + .5f) / (kMax - kMin)));
}
public void TestCheckUniformity()
{
var rng = new StatelessRng(kSeed);
Func <Vector2, Vector2?> Parametrize = v => new Vector2((v.x + 1) / 2, (v.y + 1) / 2);
Assert.Throws <AssertionException>(() =>
S.CheckUniformity(new[] { "x", "y" },
Gen(i => Parametrize(rng.InUnitCircle(i)))));
}
public void TestUniformity_OnUnitCircle()
{
var rng = new StatelessRng(kSeed);
Func <int, float?> distribution = i => {
Vector2 v = rng.OnUnitCircle(i);
return(ToAngle01(Mathf.Atan2(v.y, v.x)));
};
S.CheckUniformity("theta", Gen(distribution));
}
public void TestUniformity_OnUnitSphere()
{
var rng = new StatelessRng(kSeed);
Vector3[] vals = Gen(i => rng.OnUnitSphere(i)).ToArray();
S.CheckUniformity(new[] { "theta", "z" }, vals.Select(ParametrizeSphereSurfaceThetaZ));
// Try along another axis
S.CheckUniformity(
new[] { "theta", "y" },
vals.Select(v => new Vector3(v.x, v.z, v.y))
.Select(ParametrizeSphereSurfaceThetaZ));
}
public void TestUniformity_InUnitSphere()
{
var rng = new StatelessRng(kSeed);
Vector3[] vals = Gen(i => rng.InUnitSphere(i)).ToArray();
Func <Vector3, Vector3> ThetaRrrZr = v3 => {
float r = v3.magnitude;
if (r == 0)
{
return(Vector3.zero);
}
float angle01 = ToAngle01(Mathf.Atan2(v3.y, v3.x));
return(new Vector3(angle01, r * r * r, ((v3.z / r) + 1f) / 2f));
};
S.CheckUniformity(new[] { "theta", "rrr", "z/r" }, vals.Select(ThetaRrrZr));
}
public void TestUniformity_Rotation()
{
var rng = new StatelessRng(kSeed);
Quaternion[] vals = Gen(i => rng.Rotation(i)).ToArray();
Func <Quaternion, Vector2> ParametrizeAxisAndAngle = q => {
Vector3 axis; // a unit vector
float angleRad;
q.ToAngleAxis(out angleRad, out axis);
Vector2 param01 = ParametrizeSphereSurfaceThetaZ(axis);
float param2 = ToAngle01(angleRad);
return(new Vector3(param01.x, param01.y, param2));
};
S.CheckUniformity(
new[] { "axis theta", "axis z", "angle" },
vals.Select(ParametrizeAxisAndAngle));
}
public void TestUniformity_InRange()
{
var rng = new StatelessRng(kSeed);
S.CheckUniformity("u", Gen(i => (rng.InRange(i, -10, 20) + 10f) / 30f));
}
public void TestUniformity_In01()
{
var rng = new StatelessRng(kSeed);
S.CheckUniformity("u", Gen(i => rng.In01(i)));
}