From a Mathematical Formula to the Kuen Spaceship: an Introduction to Interactive 3D Mathematical Art

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.