Visualization of equations in an interactive environment

Abstract

Tke interactive visualization of equations in 3D is potentially an important tool for both research and education. We describe a method of visualizing equations in their explicit form using 3D fields. Equations are written algebraically, interpreted by an equation parser and then expressed as scalar fields. Fields are represented as isosurfaces making use of an algorithm similar to the method of marching cubes. The implementation allows the real time interaction of equation parameters, isosurface rotations and colouring. A variety of applications from mathematics and physics are given together with examples of the construction of data probes using equations.