PolarEyez: A Radial Focus+Context Visualization for Multidimensional Functions


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Virginia Tech


Multi-dimensional functions are characterized by a large number of parameters on which the functional value depends. They are commonly used in engineering problems such as image analysis and system modeling. Multi-dimensional function spaces are very difficult to understand due to their multi-dimensional nature and the presence of a large number of data points in the functional space.

A point called the focal point is selected by the user in the vast multi-dimensional parameter space. Rays called "focal rays" emanate from the focal point in all directions to the boundaries of the functional space. The focal rays contain functional data points. The focal point is mapped onto the center of the visualization with the focal rays arranged radially around it. The degree of detail decreases as we move away from the focal point toward the edges of the visualization in accordance with the focus+context technique. The functional values are mapped onto a color scheme with shades of green representing positive function values, and shades of red representing negative function values. Interactive features such as the ability to change the focal point, highlighting of functional values aid the user in exploring and analyzing the functional space. The algorithm, practical applications of the visualization approach and results of formative evaluation studies are also elaborated in this thesis.

The contributions of this thesis are fourfold, namely, providing an overview of the functional space, equal treatment of all dimensions, improved scalability and a smooth blending of details with the overview.



Visualization, Multi-dimensional functions