# VisuMath (version 3.0)

## Author: Ignace Van de Woestyne

### Introduction

In several scientific disciplines, one makes use of functions to describe phenomena or processes. For these, mathematics offers a number of utilities. For instance, with the use of different coordinate systems, these functions can be described efficiently. To see which objects these functions represent, VisuMath is developed. Evidently, the objects that can be visualized live in a 2- or 3-dimensional space. So VisuMath visualizes only curves and surfaces.

Consequently VisuMath is a visualization tool. In this respect, it corresponds to the goal that the author is aiming for to develop visualization techniques. We are convinced that, influenced by an "image culture" with which we all are confronted, people learn more effectively and more efficiently when knowledge is transferred in a visual way. This is done at the moment only in a rather limited way. This is perhaps a consequence of the lack of knowledge of several domains that one needs to control in order to achieve this (interdisciplinarity because of the knowledge of mathematics, computer programming and visualization techniques), and the cost of using existing commercial software.

The program VisuMath combines high quality visual output with ease of use. It is developed especially for research and education and is therefore free of charge for these purposes. Within the program, one can switch between English and Dutch but other languages can be added if one is willing to do some effort. Click here for an explanation on how this can be achieved.

### Structure of the program

VisuMath 3.0 contains three main parts that can be activated using the corresponding buttons in the upper toolbar:
• 2D

This part is used to draw graphics of curves in a plane. The curves can be described using a function of one variable, a parameter equation, a polar equation or an implicit equation. Also for functions of one variable the first and second derivative, the mean function and the Taylor expansion can be computed and visualized. Furthermore, there is the possibility to calculate integrals of continuous functions and to visualize the area, the upper sum, the lower sum and the Riemann sum.

• 3D

This part is used to draw graphics of surfaces in a 3-dimensional space. The surfaces can be described by means of a function of two variables, a parameter equation, an implicit equation or using cylindrical or spherical coordinates. Also, there is the possibility to draw tubular shaped surfaces.

• Conics

With this option, it is possible to find the general equation of a non-degenerate conic, after entering the necessary data. Also, the conic is drawn including the corresponding transformed axes.

Three additional options are available when working in 3D. Especially, the new OpenGL option becomes available by default as soon as one swithes to 3D. If one prefers to work with the limited 3d-design environment by disactivating the OpenGL option, the buttons Output 3D and VRML-environment become active.
• Open GL

With this option, it is possible to observe 3D-objects dynamically and also to change options on the fly.

• Output 3D

With this option, it is possible to store the 3d-model in different interesting formats for export to other packages (such as graphical editors and 3d-authoring software).

• VRML-environment / Design-environment

With this button, one switches between the design environment and the VRML-environment. To see the model as VRML-model however in the VRML-environment, it must first be saved as VRML-file. This is done with the option Output 3D. Furthermore, the PC on which VisuMath is installed must be equipped with a VRML viewer, for example the Cortona VRML client (can be downloaded from the Internet from the coordinates www.parallelgraphics.com/products/cortona/).