// Create children that fill a single orbit, equally spaced
// https://en.wikipedia.org/wiki/Klemperer_rosette
public void ExpandRosette(ref Random random, int vertices)
{
//Debug.Log("Expanding Rosette");
// Rosette children replace the parent, parent orbital node is left empty
Empty = true;
// Masses in a rosette alternate, so every sequential pair has the same shared mass
var sharedMass = Mass / vertices * 2;
// Proportion of the masses of sequential pairs is random, but only for even vertex counts
var proportion = vertices % 2 == 0 ? random.NextFloat(.5f, .95f) : .5f;
// Place children at a fixed distance in the center of the range
var dist = (ChildDistanceMinimum + ChildDistanceMaximum) / 2;
// Position of first child
var p0 = new float2(0, dist);
// Position of second child
var p1 = OrbitData.Evaluate(1.0f / vertices) * dist;
// Maximum child distance is half the distance to the neighbor minus the neighbor's radius
var p0ChildDist = (distance(p0, p1) * proportion - Settings.PlanetSafetyRadius.Evaluate(sharedMass * (1 - proportion))) * .75f;
var p1ChildDist = (distance(p0, p1) * (1 - proportion) - Settings.PlanetSafetyRadius.Evaluate(sharedMass * proportion)) * .75f;
for (int i = 0; i < vertices; i++)
{
var child = new GeneratorPlanet
{
Settings = Settings,
Parent = this,
Mass = sharedMass * (i % 2 == 0 ? proportion : 1 - proportion), // Masses alternate
Distance = dist,
Phase = (float)i / vertices,
ChildDistanceMaximum = (i % 2 == 0 ? p0ChildDist : p1ChildDist)
};
child.ChildDistanceMinimum = Settings.PlanetSafetyRadius.Evaluate(child.Mass) * 2;
//child.Period = Settings..Evaluate(child.Distance);
Children.Add(child);
}
ChildDistanceMinimum = dist + p0ChildDist;
}