Watermarking three-dimensional polygonal models through geometric and topological modifications

This paper discusses techniques for embedding data into three-dimensional (3-D) polygonal models of geometry. Given objects consisting of points, lines, (connected) polygons, or curved surfaces, the algorithms described in produce polygonal models with data embedded into either their vertex coordinates, their vertex topology (connectivity), or both. Such data embedding can be used, for example, for copyright notification, copyright protection, theft deterrence, and inventory of 3-D polygonal models. A description of the background and requirements is followed by a discussion of where, and by what fundamental methods, data can be embedded into 3-D polygonal models. The paper then presents several data embedding algorithms, with examples, based on these fundamental methods. By means of these algorithms and examples, we show that the embedding of data into 3-D polygonal models is a practicable technique.