This consists of a list of space curves in three dimensional space, corresponding usually to curvature discontinuities in a solid object. Space curves may be considered therefore as the boundaries between surfaces, but curved surfaces can cause problems. Some wire frame systems may use facet boundaries, as a curved surface can be approximated by planar facets, e.g. Figure 2. If this is not the case, how is a cylinder represented ? In effect there are only two space curves defining curvature boundaries, i.e. the circles at each end of the solid. It is difficult to model extremal edges in a computer vision system, since these are often viewpoint dependent. Furthermore, the wire-frame representation is an ambiguous technique for representing an object, as it does not define explicitly the enclosed surfaces. Usually, there may be more than one possible interpretation of the same wireframe, e.g. Figure 6, below. Wire frames can often be interpreted as different solid objects or as different orientations of the same object.
Figure 6: The ambiguity of a wire frame definition
For a computer vision system, wire frames are used usually to match against edge-derived descriptions, either from a single two dimensional image, or for example from the 3D edge description derived from a passive stereo or a motion tracking system. Ambiguity is avoided, since there is a finite number of possible models, each of which has a unique configuration of space curves in 3D space.
Surface boundary representations
Comments to: Sarah Price at ICBL.