A boundary representation technique for three-dimensional objects

The marching cubes algorithm of W.E. Lorensen and H.E. Cline (1987) is a method that is used frequently in 3D object visualisation. The underlying concept of the technique is to form piecewise planar approximations to surfaces, for which pre-determined normals are used for shading purposes. It should be noted that these approximations are precisely as accurate as the data given; there is no loss in quality or error introduced. The approach of using these cubes to represent data can also be used to fully describe the piecewise planar approximation to the surface. Problems arise however, in terms of the storage space required for the representation of large objects, and it is this issue that is addressed in this paper. We present an algorithm that transforms pixel-wise data into a boundary representation that has potential for large reductions in storage. The algorithm does not involve any further approximation of the surface of the object than that given as input. The algorithm also provides a structure that makes surface analysis and matching very simple