Algorithms Complexity and Non-linear Co-ordinates Theoretical Fiction or Practical Use?

Abstract

There are some applications, where the polar, cylindrical or spherical co-ordinate systems can be used for finding a solution of given problem. Especially some technical problems [Lio97a], like sonar and radar applications, where the distance from an object is measured under known angles, flow computation, radiation, medical imaging and ultrasound imaging etc. could benefit from their use. It is a usual practice that all the data from those applications are transformed to the cartesian orthogonal co-ordinate system, where all data are processed. The data are than displayed directly or transform back to the original co-ordinate system. Nevertheless it is well known that representation of a point in E2 is different drom a line representation and therefore the processing pipeline have to respect this fact. The polar, cylindrical and spherical co-ordinate systems offer some possibilities how to handle graphical information in an unambiguous way and also make an effective processing. On the other hand, it is necessary to say that in usual practical graphical applications the direct use of non-linear co-ordinates can be quite complicated can hopefully lead to new understanding of some fundamental algorithms and developing of new more effective methods.