/// <summary>
/// Construct a group of 4 edges {e[0], e[1], e[2], e[3]} where e[0] represent the canonical
/// representative to which edge e belongs. This allows to represent and edge
/// by dividing it into 4 edges.
/// For more See 2.2 Duality (Definition 2.1.) and 5.BASIC TOPOLOGICAL OPERATORS in the article.
/// </summary>
public static QuadEdge <T> MakeEdge(Vec3 origin, Vec3 destination)
{
// Primal
QuadEdge <T> qE0 = new QuadEdge <T>(null, null, origin);
// Dual
QuadEdge <T> qE1 = new QuadEdge <T>(null, null, null);
// Primal
QuadEdge <T> qE2 = new QuadEdge <T>(null, null, destination);
// Dual
QuadEdge <T> qE3 = new QuadEdge <T>(null, null, null);
// Onext ring of the primal (delaunay)
// See Fig.5 (c)
qE0._oNext = qE0;
qE2._oNext = qE2;
// Onext ring of the Dual (Voronoi)
// See Fig.5 (c)
qE1._oNext = qE3;
qE3._oNext = qE1;
// Create connection between subdivision (allow to access Primal and Dual)
// Implicitly set qE0.Destination = qE2.Origin (Destination == Rot.Rot.Origin)
qE0._rot = qE1;
qE1._rot = qE2;
qE2._rot = qE3;
qE3._rot = qE0;
// Return the canonical representative.
return(qE0);
}
/// <summary>
/// Construct a face abstraction based on a <paramref name="primal"/> edge.
/// </summary>
/// <param name="primal">Delaunay edge with Origin as face center.</param>
/// <param name="onBounds">Mark face as a face on the faces bounds.</param>
/// <param name="reconstructed">Must be true if face has a site at infinity.</param>
public Face(QuadEdge <TEdge> primal, bool onBounds, bool reconstructed)
{
this._primal = primal;
this._onBounds = onBounds;
this._reconstructed = reconstructed;
this._id = nextID++;
}
/// <summary>
/// This operation affects the two edge rings a.Origin and b.Origin and, independently,
/// the two edge rings a.Left and b.Left. In each case,
/// - (a) if the two rings are distinct, Splice will combine them into one
/// - (b) if the two are exactly the same ring, Splice will break it in two separate pieces
/// - (c) if the two are the same ring taken with opposite orientations, Splice will Flip (and reverse the order)
/// of a segment of that ring
/// </summary>
/// <remarks>
/// Splice is its own inverse and calling twice in a row revert it back to origin.
/// Splice does not affect Rot neither Origin and Destination that have no topological meaning.
/// </remarks>
/// <param name="a">First QuadEdge<T></param>
/// <param name="b">Second QuadEdge<T></param>
public static void Splice(QuadEdge <T> a, QuadEdge <T> b)
{
QuadEdge <T> alpha = a._oNext._rot;
QuadEdge <T> beta = b._oNext._rot;
// Swap them all !
Helper.Swap <QuadEdge <T> >(ref a._oNext, ref b._oNext);
Helper.Swap <QuadEdge <T> >(ref alpha._oNext, ref beta._oNext);
}
/// <summary>
/// Construct an edge.
/// </summary>
public QuadEdge(QuadEdge <T> oNext, QuadEdge <T> rot, Vec3 origin)
{
this._oNext = oNext;
this._rot = rot;
this._origin = origin;
this.Tag = false;
_id = QuadEdge <T> .nextID++;
}
/// <summary>
/// Iterate over every edge destination sharing the same origin (default to CW order)
/// </summary>
/// <param name="CCW">Select in which order vertices should be returned.</param>
public IEnumerable <Vec3> DestinationsFrom(bool CCW = false)
{
QuadEdge <T> current = this;
do
{
yield return(current.Destination);
current = CCW ? current.Onext : current.Oprev;
} while (current != this);
}
/// <summary>
/// Iterate over every edges sharing the same origin (default to CW order)
/// </summary>
/// <param name="CCW">Select in which order edges should be returned.</param>
public IEnumerable <QuadEdge <T> > EdgesFrom(bool CCW = false)
{
QuadEdge <T> current = this;
do
{
yield return(current);
current = CCW ? current.Onext : current.Oprev;
} while (current != this);
}
/// <summary>
/// Iterate over edges with same LEFT face (default to CW order)
/// starting from this and return their origin.
/// </summary>
/// <param name="CCW">Select in which order vertices should be returned.</param>
public IEnumerable <Vec3> LeftVertices(bool CCW = false)
{
QuadEdge <T> current = this;
do
{
yield return(current.Origin);
current = CCW ? current.Lnext : current.Lprev;
} while (current != this);
}
// Helpers enumerables used to abstract structure complexity
/// <summary>
/// Iterate over edges with same RIGHT face (default to CW order)
/// starting from this.
/// </summary>
/// <param name="CCW">Select in which order vertices should be returned.</param>
public IEnumerable <QuadEdge <T> > RightEdges(bool CCW = false)
{
QuadEdge <T> current = this;
do
{
yield return(current);
current = CCW ? current.Rnext : current.Rprev;
} while (current != this);
}
/// <summary>
/// Connect two edges together leading to a.Destination --> b.Origin
/// </summary>
public static QuadEdge <T> Connect(QuadEdge <T> a, QuadEdge <T> b)
{
// Connect a to b
QuadEdge <T> edge = MakeEdge(a.Destination, b.Origin);
// See 6. TOPOLOGICAL OPERATORS FOR DELAUNAY DIAGRAMS
Splice(edge, a.Lnext);
Splice(edge.Sym, b);
return(edge);
}
/// <summary>
/// Iterate over every vertices forming a face around this edge origin
/// (default to CW order) assuming each edge face share the same left face.
/// Edge between two sites at infinity does not exists (occurs for a face
/// on the convex hull) and then a site will be missing.
/// </summary>
/// <remarks>
/// In case of CCW == false missing edge Origin can be found by first taking
/// left most edge (in primal graph) and then its Destination.
/// </remarks>
/// <param name="CCW">Select in which order vertices should be returned.</param>
public IEnumerable <Vec3> FaceLeftVertices(bool CCW = false)
{
QuadEdge <T> current = this.Rot;
var first = current;
do
{
yield return(current.Origin);
current = CCW ? current.Lnext : current.Lprev;
} while (current != first);
}
/// <summary>
/// Swap common segment between two triangles. Can be used to transform
/// a two non delaunay triangles to a pair of triangle respecting this constraint.
/// </summary>
/// <remarks>
///
/// /|\ / \
/// / | \ / \
/// / | \ / \
/// \ | / ---> \-----/
/// \ | / \ /
/// \|/ \ /
///
///
/// </remarks>
public static void Swap(QuadEdge <T> edge)
{
QuadEdge <T> a = edge.Oprev;
QuadEdge <T> b = edge.Sym.Oprev;
// Disconnect edge
Splice(edge, a);
Splice(edge.Sym, b);
// Reconnect edge
Splice(edge, a.Lnext);
Splice(edge.Sym, b.Lnext);
// Update pointers
edge._origin = a.Destination;
edge.Destination = b.Destination;
}
/// <summary>
/// Disconnect edge from the structure. Opposite operation of Connect.
/// </summary>
public static void Delete(QuadEdge <T> edge)
{
Splice(edge, edge.Oprev);
Splice(edge.Sym, edge.Sym.Oprev);
}
