Realistic Visualization of 3D and 4D Mathematical Objects

Dr. Mirek Majewski
PNG University of Technology
Department of Mathematics & Computer Science
Papua New Guinea

E-mail majewski@maths.unitech.ac.pg

Abstract

Most of the popular mathematical packages like Derive, Mathematica or Maple display 3D graphs as an opaque wire frame object. These graphs are usually a finite-point approximation of the real 3D objects. This means that in many cases such graphs are inaccurate and incomplete. In some of these programs, we have an opportunity to change the display and add some shades, change colors or enlightening, however, it does not improve most of the graphs noticeably.

In my paper, I show how to obtain realistic images of many types of 3D mathematical objects: functions of two variables, implicit functions of three variables, parametric functions, some 3D fractals, etc. For this purpose, I use famous mathematical program Maple V and ray-tracing language POV-Ray. In many cases, I use some basic information taken from Maple: equation of a surface, range of variables, camera position, etc. I transform this information into a POV-Ray program and render it on a PC. I can apply also any kind of texture, light and animation, to show correctly all details of my object.

Full Paper in PDF