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Visualization of Complex Function Graphs in Augmented Reality
by Robert Liebo
Abstract
Understanding the properties of a function over complex numbers can be much more
difficult than with a function over real numbers. This work provides one approach in
the area of visualization and augmented reality to gain insight into these properties.
The applied visualization techniques use the full palette of a 3D scene graph's
basic elements, the complex function can be seen and understood through the
location, the shape, the color and even the animation of a resulting visual object. The
proper usage of these visual mappings provides an intuitive graphical representation
of the function graph and reveals the important features of a specific function.
Augmented reality (AR) combines the real world with virtual objects
generated by a computer. Using multi user AR for mathematical visualization enables
sophisticated educational solutions for studies dealing with complex functions.
A software framework that has been implemented will be explained in detail,
it is tailored to provide an optimal solution for complex function graph visualization,
but shows as well an approach to visualize general data sets with more than 3
dimensions. The framework can be used in a variety of environments, a desktop
setup and an immersive setup will be shown as examples.
Finally some common tasks involving complex functions will be shown in
connection with this framework as example usage possibilities.
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