A pattern description language—PADEL

摘要

This paper describes an artificial language, called PADEL, which may be used to describe line drawings. The descriptions consist of strings of concatenated symbols denoting vertices and branches of the picture or line drawing. These picture elements are formally defined followed by a description of the grammar which generates the language. The actual construction of the descriptive strings from a given picture is then discussed. The language is then analyzed and noted to be phrase structured, finite, context free language. The regular expression which describes all strings in the language is then derived.Using the language just described, a set of topological manipulations of the picture are defined by operations on the descriptive strings. Manipulations such as rotations, reflections and scaling are defined on two dimensional picture descriptions. A nonuniform scale change, which may be termed “rubber sheet warping,” is also described.The pattern description language is next extended to the description of three dimensional objects by representing the branch labels as three tuples which are the direction angles of the branch unit vectors. Rotations of such pictures about the coordinate axis are then described. It is then shown that the angular relationships among the branches of the picture remain invariant under these transformations and, thus, the “shape” of the object remains invariant. An inverse rotation is next introduced. Finally projections of the picture onto the principal planes and more generally onto an arbitrary plane is described.