3D-visualisation of complex functions
Michael Oberguggenberger
Alexander Ostermann
Lukas Einkemmer
Markus Unterweger
Content: This page contains a Java applet illustrating the 3D-visualisation of complex functions and instruction for its use.
Applet
Theory
Analysis for Computer Scientists, Chapter 4
Help
Visualisation of a complex function
With this applet the real part, imaginary part, and absolute value (modulus) of a complex function can be visualised. As can be seen from the screenshot, the complex function is entered into the field f(z)=. The tab Choice of surface allows one to specify whether the real part, the imaginary part, or the absolute value is displayed. The slider Number of grid points determines the number of points that are used to construct the surface on the screen. The fields Re z and Im z specify the domain in the complex plane. When constructing the grid the applet tries to automatically detect singularities so that the grid points are connected correctly. In the screenshot the imaginary part of the logarithm is shown.
Surface options
In addition to the number of grid points, the tab Surface options allows you to adjust the image. The selection box Surface determines whether the surface is drawn as a (transparent) wireframe or with texture (a mixed option is also available). The Filling options determine how the triangles from which the surface is constructed are coloured. The option Simple fills the entire triangle with the colour of one of its vertices. If the option Interpolate is selected the colour is interpolated between the colours of the vertices. The option Colour admits additional modifications that influence the colour of the surface. If the option z is selected the colour changes only in z-direction. With the option xy the colour changes only in x- and y-directions. The option xyz changes the colour in all directions. The option Front and Back has the effect of drawing the surface with only two colours, one for the front side and one for the back. In addition, the field Rendering options allows one to choose between high image quality or fast display.
Projection
The tab Projection allows you to choose the type of projection. With the options Perspective and Parallel projection you can select between these two types of projection. If Perspective is selected the distance of the camera from the surface can be adjusted by the minus and plus buttons. The selection box Projection plane allows one to specify a parallel projection onto one of the coordinate planes. The button Reset restores the default values.
Surface rotation
By moving the mouse while pressing the left mouse button the surface can be rotated.
Scaling the axes, boxes, and labels
The tab Axes allows one to control the scaling of the axes. Depending on the chosen option, the axes can be scaled jointly or independently. In the selection box Axes model it can be specified whether a box with or without labels is displayed.
Questions
If you have further questions or comments, or if you found a bug, please send us an e-mail.
Financially supported by
University of Innsbruck: New Media and Learning Technologies
Austrian Federal Ministry of Education, Science and Research