An important key to reconstructing a three-dimensional object depicted by a two-dimensional line drawing projection is face identification. Identification of edge circuits in a 2D projection corresponding to actual faces of a 3D object becomes complex when the projected object is in wireframe representation. This representation is commonly encountered in drawings made during the conceptual design stage of mechanical parts. When nonmanifold objects are considered, the situation becomes even more complex. This paper discusses the principles underlying face identification and presents an algorithm capable of performing this identification. Face-edge-vertex relationships applicable to nonmanifold objects are also proposed. Examples from a working implementation are given.

A general algorithm for identification of deterministic rapidly time-varying parameters is introduced. The new algorithm is based upon applying a linear combination of the equations determined by the ordinary least-squares method. With this algorithm there is no need to modify the covariance matrix or to use forgetting factors in order to accurately follow the time-varying parameters.