From a Mathematical Formula to the Kuen Spaceship: an Introduction to Interactive 3D Mathematical Art
Miroslaw Majewski majewski@mupad.com
College of Information Systems Zayed University United Arab Emirates
Abstract
For centuries shapes of mathematical objects were inspiration
for mathematically inclined artists. We can find mathematical art in
architecture of ancient Greece, Alhambra, Taj Mahal or Isfahan, in
works of Escher or Mandelbrot, and in many other places. We can look
also at various patterns derived from the nature and recognize in them
mathematical shapes.
In this paper we will look into 3D shapes obtained from mathematical
formulae. We will investigate how such formulae can be used to create
3D shapes with the help of computer programs like MuPAD, Maple or
Mathematica. We will investigate how the obtained shape can be
transformed into live interactive 3D objects that can be manipulated on
a local computer or in a web page using JavaView. We will discuss a
number of technical problems that developers face while producing such
objects and we will show how these problems can be solved. We will
discuss selected technical aspects of such models: constrained and
unconstrained scaling, using the right lighting systems, setting up
camera, using transparency, optimizing the file size and enhancing
quality of the model.
In the second part of this paper we will show how one can create a
mathematical model with realistic attributes and environment, and then
rendered it into a high quality image or video using a graphical
package like Strata 3D, Maya or 3D Studio.
