3D Transformation Matrix Synthesis in Column Major and Row Major Forms: Applicative Perspective for 3D Object Representation

Abstract

The Transformation of a 2D or 3D objects are the effective means of shifting or changing the dimensions and orientations of images in the most effective way. If we fail to transform the object in terms of displacement ,enlargement, orientation, we may land up in creating something that is distorted and processessing a distorted object is not acceptable in the various critical fields like Medical and Forensics. The usual practice of defining transformations is straight forward. The transformed object can be obtained by coupling original object with the transformation vectors. The main challenge is how to evaluate it. The usual practice is standard Column Vector form. The alternative Row Vector Form is also known approach but what matters is the sequence of operations that make these both approaches worth mentioning.While doing so our analysis on 3D content keeps our  knowledge  flawless  and takes it a step further as far as  Image Processing is concerned. Such analytical study is very vital since most of the content created, acquired, reproduced, and visualized in 3D needs to be mapped on to 3D. This paper describes the transformations(Translation, Scaling and Rotation) in the both Column and Row Vectar Approach. This  paper aims in providing a clear sequence of calculations which differ in both approaches.