Non-orthogonal Co-ordinates in Computer Graphics

Abstract

There are many applications that are not naturally based on the orthogonal co-ordinate systems, like ultrasound imaging, astronomy, mechanical computations etc. In many cases it is necessary to transform the problem formulation to the orthogonal co-ordinate system, where the problem is solved, transform the solution back and visualize the solution. The polar, spherical or cylindrical co-ordinate systems are natural to many problems and sometime also used for computations. It will be shown that the polar systems in E2 can be used for the visualization pipeline and some properties of such system will be discussed including geometric transformation in the polar system.