Realistic
Visualization of 3D and 4D Mathematical
Objects
Dr. Mirek Majewski
PNG University of Technology
Department of Mathematics &
Computer Science
Papua New Guinea
Email 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 finitepoint
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
raytracing language POVRay. 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 POVRay 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
