Prof. Robert R. Johnson Profile

Prof. Robert R. Johnson

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Proceedings Article | 9 June 2003 Paper

Visual identification of structure in four-dimensional data

Robert Johnson, Rodney Millar, Isaac Ben

Proceedings Volume 5009, (2003) https://doi.org/10.1117/12.473902

KEYWORDS: 3D modeling, Data modeling, 3D displays, Visualization, Optical spheres, Spherical lenses, Visual process modeling, Clouds, Proteins, Solid modeling

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Structure in 4-D data is visualized with a new modeling algorithm called SBP. The SBP vector fusion algorithm makes 3-D display space models of data having any dimensionality that is input in matrix form. SBP maps points on complete manifolds in 4-D to 3-D to visualize any 4-D data. Starting with familiar shapes in 2-D data, 3-D models are constructed to demonstrate how SBP works. Then 3-D data is modeled in 3-D display space. Finally 4-D data are modeled in 3-D display space. The 3-D display space models are points mapped from collections of points on 4-D manifolds. Two types of SBP models are discussed: the latitude/longitude collection and the helical collection. SBP also maps points on complete manifolds of n-D data to 3-D display space models. The objective of this work is to present what 4-D spheres and tori look like when visualized from 4-D data using the SBP algorithm. This demonstrates the SBP algorithm as a new and useful tool for visualizing and understanding 4-D data, and by implication, n-D geometry. Future uses for SBP could be modeling and studying protein structure and space-time structure in general relativity and string theory.

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