private void TestEllipsoidInOctant(EllipsoidClosestPoint_t func)
{
using (var unused = new WithRandomSeed(4))
{
Vector3 abc = new Vector3(4, 3, 2);
for (int theta = 0; theta < 360; theta += 7)
{
for (int phi = 0; phi < 180; phi += 7)
{
for (float bump = -1; bump <= 4f; bump += .32f)
{
// Find a spot on the ellipsoid, bump it out by its normal
Vector3 pointOnEllipse = EllipsoidSphericalToCartesian(abc, new Vector2(theta, phi));
Vector3 normal = NormalAtEllipsoid(abc, pointOnEllipse);
Vector3 bumped = pointOnEllipse + normal * bump;
// pointOnEllipse is guaranteed to be the closest point to "bumped" as long as we
// haven't bumped the point into a different octant.
if (GetOctant(bumped) != GetOctant(pointOnEllipse))
{
continue;
}
AssertAlmostEqual(pointOnEllipse, func(abc, bumped), message: (theta, phi, bump));
}
}
}
}
}
// Tests random points both inside and outside the ellipsoid
private void TestEllipsoidRandomPoints(EllipsoidClosestPoint_t func)
{
Vector3 he = new Vector3(4, 3, 2);
for (int i = 0; i < 100; ++i)
{
Vector3 point = CMul(he, Random.onUnitSphere * 2);
Vector3 cp = func(he, point);
Vector3 surfaceNormal = NormalAtEllipsoid(he, cp);
// We don't have ground truth, so instead we verify this invariant:
// The normal at cp is parallel to (point - cp).
Vector3 delta = (point - cp);
Vector3 err = delta - (Vector3.Dot(surfaceNormal, delta) * surfaceNormal);
AssertAlmostEqual(err, Vector3.zero, message: point);
}
}
