Identifying faces in a 2D line drawing representing a manifold object

A straightforward way to illustrate a 3D model is to use a line drawing. Faces in a 2D line drawing provide important information for reconstructing its 3D geometry. Manifold objects belong to a class of common solids and most solid systems are based on manifold geometry. In this paper, a new method is proposed for finding faces from single 2D line drawings representing manifolds. The face identification is formulated based on a property of manifolds: each edge of a manifold is shared exactly by two faces. The two main steps in our method are 1) searching for cycles from a line drawing and 2) searching for faces from the cycles. In order to speed up the face identification procedure, a number of properties, most of which relate to planar manifold geometry in line drawings, are presented to identify most of the cycles that are or are not real faces in a drawing, thus reducing the number of unknown cycles in the second searching. Schemes to deal with manifolds with curved faces and manifolds each represented by two or more disjoint graphs are also proposed. The experimental results show that our method can handle manifolds previous methods can handle, as well as those they cannot. Index Terms--3D models, face identification, geometry, graphs, line drawings, manifolds.