/// <summary>
/// Splices two edges together or apart.
/// Splice affects the two edge rings around the origins of a and b, and, independently, the two
/// edge rings around the left faces of <tt>a</tt> and <tt>b</tt>.
/// In each case, (i) if the two rings are distinct,
/// Splice will combine them into one, or (ii) if the two are the same ring, Splice will break it
/// into two separate pieces. Thus, Splice can be used both to attach the two edges together, and
/// to break them apart.
/// </summary>
/// <param name="a">an edge to splice</param>
/// <param name="b">an edge to splice</param>
public static void Splice(QuadEdge a, QuadEdge b)
{
var alpha = a.ONext.Rot;
var beta = b.ONext.Rot;
var t1 = b.ONext;
var t2 = a.ONext;
var t3 = beta.ONext;
var t4 = alpha.ONext;
a.SetNext(t1);
b.SetNext(t2);
alpha.SetNext(t3);
beta.SetNext(t4);
}
/// <summary>
/// Creates a new QuadEdge quartet from <see cref="Vertex"/>o to <see cref="Vertex"/> d.
/// </summary>
/// <param name="o">the origin Vertex</param>
/// <param name="d">the destination Vertex</param>
/// <returns>the new QuadEdge quartet</returns>
public static QuadEdge MakeEdge(Vertex o, Vertex d)
{
var q0 = new QuadEdge();
var q1 = new QuadEdge();
var q2 = new QuadEdge();
var q3 = new QuadEdge();
q0.Rot = q1;
q1.Rot = q2;
q2.Rot = q3;
q3.Rot = q0;
q0.SetNext(q0);
q1.SetNext(q3);
q2.SetNext(q2);
q3.SetNext(q1);
var baseQE = q0;
baseQE.Orig = o;
baseQE.Dest = d;
return(baseQE);
}