Winged edge

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The winged edge data structure is a data representation used to describe polygon models in computer graphics. It explicitly describes the geometry and topology of faces, edges, and vertices when three or more surfaces come together and meet at a common edge. Adjacency information is used in algorithms like Subdivision surface. The ordering is such that the surfaces are ordered counter-clockwise with respect to the innate orientation of the intersection edge. Moreover the representation allows numerically unstable situations like that depicted below.

The winged edge data structure allows for quick traversal between faces, edges, and vertices due to the explicitly linked structure of the network. It serves adjacency queries in constant time with little storage overhead. This rich form of specifying an unstructured grid is in contrast to simpler specifications of polygon meshes such as a node and element list, or the implied connectivity of a regular grid. An alternative to the winged edge data structure is the Half-edge data structure.

Point on edge.png


Here is a data structure suitable for representing a winged edge. The abbreviation "WE" stands for "Winged Edge".

class WE_Edge {
  WE_Vertex vert1, vert2;
  WE_Face aFace, bFace;
  WE_Edge aPrev, aNext, bPrev, bNext; // clockwise ordering
  WE_EdgeDataObject data;
class WE_Vertex {
  float x, y, z;
  List<WE_Edge> edges;
  WE_VertexDataObject data;
class WE_Face {
  List<WE_Edge> edges;
  WE_FaceDataObject data;

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