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A transformation structure for animated 3-D computer graphics

This paper discusses a means of describing in a generalized manner a transformation structure that will accommodate varying orders and levels of transformations on sets and subsets of points describing objects. These structures were designed specifically for animation of multiple set objects.A solar system, a multiple gimbaled gyro and a butterfly consist of such sets of points and subsets of points, each requiring different orders of translations and rotations.For this initial version, a binary tree structure is used to describe either a rotation, a translation or object description at each node. A more general n-ary tree structure could have been used, but resources are limited and the quickest implementation was generated to test the ideas for this paper.For generality and ease of description, 4 x 4 matrices are used. Each matrix type is discussed and fully displayed to minimize confusion between conventional arrays and those used in this paper. Transformation methods and parsing methods are discussed.The scope of this paper is to discuss a technique and not its implementation; thus printouts are omitted. Also, this paper is intended as an informal means of communicating one of many methods which will do the same thing.