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9 June 2003 Visual identification of structure in four-dimensional data
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Abstract
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.
© (2003) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Robert R. Johnson, Rodney Millar, and Isaac Ben "Visual identification of structure in four-dimensional data", Proc. SPIE 5009, Visualization and Data Analysis 2003, (9 June 2003); https://doi.org/10.1117/12.473902
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