# Degenerate Edges

(citing an ansert by Roman Lygin from http://www.opencascade.org/org/forum/thread_14761/?forum=3)

As you know some surfaces has so called singularities - parts of its 2D parametric space (U,V) which corresponds to a single point in 3D space (X,Y,Z). The classic example is a sphere which 2D space is [0, 2*Pi] x [-Pi/2, Pi/2]. The south and north pole in 3D space are represented by V-isolines in 2D space as follows:

- south pole: V = -R (any U)

- north pole: V = R (any U)

Consider the Earth - there is no longitude for South and North Poles, they are marked as latitudes 90 South and 90 North respectively.

Open CASCADE requires that a face's wire represents a closed contour both in 2D parametric space and in 3D space. To achieve that, edges with parametric curves (pcurves) lying in surface singularities are marked as degenerated (i.e. have special flag IsDegenerated and has no 3D curve).

Consider the face that is created when using BRepPrimAPI_MakeSphere. It has a wire of 4 edges, 2 of which have pcurves going along U=-R and U=R and have no 3D curve.