Curiously Recurring Template Pattern and generics constraints (C#)

Question

I would like to create a method in a base generic class to return a specialized collection of derived objects and perform some operations on them, like in the following exam

Answer 1

I have used the following to create not a linked list, but a generecic linked tree. It works wonderfully nicely.

public class Tree where T : Tree
{
    T parent;
    List children;

    public Tree(T parent)
    {
        this.parent = parent;
        this.children = new List();
        if( parent!=null ) { parent.children.Add(this as T); }
    }
    public bool IsRoot { get { return parent == null; } }
    public bool IsLeaf { get { return children.Count == 0; } }
}

Example usage from Mechanics (Coordinate System Hierarchy)

class Coord3 : Tree
{
    Vector3 position;
    Matrix3 rotation;
    private Coord3() : this(Vector3.Zero, Matrix3.Identity) { }
    private Coord3(Vector3 position, Matrix3 rotation) : base(null) 
    {  
       this.position = position;
       this.rotation = rotation;
    }
    public Coord3(Coord3 parent, Vector3 position, Matrix3 rotation) 
       : base(parent)
    {
       this.position = position;
       this.rotation = rotation;
    }
    public static readonly Coord3 World = new Coord3();

    public Coord3 ToGlobalCoordinate()
    {
       if( IsRoot )
       { 
            return this;
       } else {
            Coord3 base_cs = parent.ToGlobalCoordinate();
            Vector3 global_pos = 
                      base_cs.position + base_cs.rotation * this.position;
            Matrix3 global_rot = base_cs.rotation * this.rotation;
            return new Coord3(global_pos, global_ori );
       }
    }
}

The trick is to initialize the root object with null parent. Remember you cannot do Coord3() : base(this) { }.