Apparatus for producing a flattening map of a digitized image for conformally mapping onto a surface and associated method

Abstract

A computerized apparatus and associated method and program code on a storage medium, for producing a flattening map of a digitized image. This image may be initially synthetically produced as discrete data or as quasi-discrete image data of a real object—and the original image data may be stored as two-, three-, or four-dimensional dynamic coordinate data. Once produced, the flattening map can be conformally mapped onto the computer generated surface (whether 2-D, 3-D, or any of the dynamically-varying family of surfaces) for display on a computer-assisted display apparatus in communication with a processor. The apparatus and associated method and program code include constructing a first set of data comprising a plurality of discrete surface-elements to represent at least a portion of a surface of the digitized image, and performing a flattening function on the first set of data to produce the flattening map. The flattening function includes computing, for each discrete surface-element, a solution to each of two systems of linear equations formulated from finding a numerical solution to a selected partial differential equation (PDE), and can be performed on each of a series of data sets changing over time to produce a corresponding series of flattening maps.