The winged edge against half-christianity

Question

I am trying to understand Boundary Representation (B-rep), and I cannot find what are the advantages of a half-edge data structure over a winged edge. I found in this book that winged edges cannot represent a state in which a vertex, but without edges, exists in space. But there is no sample.

Another book says that in the regional direction there is ambiguity.

And finally, on this webpage , performance reasons are invoked.

Answer 1

I found a solution in this article .

:

# :

public class WingedEdge
{
    public Curve3d Curve { get; set; }

    /// <summary>
    /// Edge of the left loop starting on the end vertex of this edge.
    /// </summary>
    public Edge EndLeftEdge { get; set; }

    /// <summary>
    /// Edge of the right loop starting on the end vertex of this edge.
    /// </summary>
    public Edge EndRightEdge { get; set; }

    /// <summary>
    /// Vertex on the end point of the edge.
    /// </summary>
    public Vertex EndVertex { get; set; }

    /// <summary>
    /// Face on the left side of the edge.
    /// </summary>
    public Face LeftFace { get; set; }

    /// <summary>
    /// Face on the right side of the edge.
    /// </summary>
    public Face RightFace { get; set; }

    /// <summary>
    /// Edge of the left loop ending on the start vertex of this edge.
    /// </summary>
    public Edge StartLeftEdge { get; set; }

    /// <summary>
    /// Edge of the right loop ending on the start vertex of this edge.
    /// </summary>
    public Edge StartRightEdge { get; set; }

    /// <summary>
    /// Vertex on the start point of the edge.
    /// </summary>
    public Vertex StartVertex { get; set; }
}

, , :

public class Face
{
    /// <summary>
    /// One of the edges bounding this face.
    /// </summary>
    public WingedEdge FirstEdge { get; set; }
}

, :

WingedEdge edge = face.FirstEdge;
do {
  // Do something with the edge
  WingedEdge edge = edge.LeftFace == face ? edge.LeftNextEdge : edge.RightNextEdge;
} while (edge != face.FirstEdge)

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