Virtual edges and viewing faces are viewing-direction-dependent features of 3D objects with curved surfaces. The appearance of virtual edges causes ambiguity in relating and interpreting the 2D line segments to the 3D attributes of the objects. Explicit identification of the virtual edges and the viewing faces helps to represent and manipulate the projections of these 3D objects in 2D line drawings. Concepts about real edges and virtual edges, real faces and viewing faces, real vertices and virtual vertices, are discussed. Properties of virtual edges and viewing faces from various 3D curved surfaces are illustrated. A projection-dependent viewing face data structure serves as a bridge to interconnect the representation of 3D objects to their 2D line drawings under certain viewing projection. A boundary traversal method takes advantage of the data representation and is applied for generating visible-line-only display of the objects.