The Calculus of the Non-Exact Perspective Projection - Scene-Shifting for Computer Animation

Abstract

This paper shows the principle way to apply the, scene-shiftin technique of the classical film to computer animation. calculus is presented which is a modification of the well-known classical calculus of the perspective projection. However,, a given perspective view (which may be a frame in a computer animated film) of a three-dunensiona! scene does not change homogenous1 when the position of the viewer (i.e. the eyepoint, the location of the camera ... ) changes. So the subject of this paper is to ask for these parts of the frame with only little changes within a tolerance E. Based on the theorems of the presented calculus, a computer animated film as a sequence of single frames may no longer be computed frame by frame, one frame independent from another, and every frame passing through the whole visualization pipeline of the rendering system. In any frame, parts of the preceeding frame may be inserted, if necessary with two-dimensional modifications: scaling, shifting. This will decrease the computing costs for that frame significantly, since for these arts of the frame no new perspective transformahon and rendering is required. It is a shortening of the visualization pipeline. For the sake of the compactness of this paper we will give no detailed proofs of the theorems presented in here. The interested readers may obtain these information directly from the author.