Visualizing and Investigating Multidimensional Functions

Abstract

This paper addresses the problem of visualizing multidimensional scalar functions. These functions are often encountered in fields such as Engineering, Mathematics, and Physics to understand and model complex phenomena. We propose a novel method based on the dimension reduction philosophy called HyperCell. Its basic concept is to represent the function by means of dynamic orthogonal low (ID, 2D, or 3D) dimensional subspaces, called Cells. Firstly the user defines a N-dimensional region of interest, in which the data can be visualized. Then the user interactively creates cells by selecting up to three dimensions from the function domain. A cell can be visualized using a standard visualization algorithm such as isosurfacing or volume rendering. The analysis of the function is done by investigating several cells, which can be sampled simultaneously at different regions of interest in N-Space. The HyperCell method allows several useful operations to help the exploratory process such as navigation and rotation in N-Space, and brushing.