Computer graphics processing and selective visual display system – Computer graphics processing – Graph generating
Reexamination Certificate
1999-06-25
2002-03-26
Luu, Matthew (Department: 2672)
Computer graphics processing and selective visual display system
Computer graphics processing
Graph generating
C345S419000, C345S421000, C345S441000
Reexamination Certificate
active
06362823
ABSTRACT:
BACKGROUND
1. The Field of the Invention
This invention relates generally to the organization and understanding of data generated in multi-dimensional space. More specifically, a data system of multi-dimensional data points is visualized in a parallel coordinate system. An area of interest is then identified, and the n point representations of conventional parallel coordinates are brought back into a single point representation that is the single point vector resultant of n dimensional spaces viewable in familiar three dimensional display space.
2. The State of the Art
Problem solving in multi-dimensional (or multi-variate) space is an increasingly important field of research. This is particularly true because data sets (systems) are becoming increasingly complex and large. The number of systems that require analysis is growing faster than the existing systems can be analyzed. Furthermore, the existing tools are proving to be inadequate for the large systems.
Statistical methods are the classical means used to derive meaning from data defined systems. Such methods typically apply their analyses to whole regions of data. For example, conventional software analysis tools combine statistical analysis methods in conjunction with conventional visualization techniques. A second class of methods are known as data mining. A typical product employing such techniques is SGI's Mine Set product line.
Visualization of data can at least enable identification of a domain of relevance to which statistical analyses should be directed. These visualization techniques include the method developed by A. Inselberg, Parallel Coordinates, A Tool for Visualizing Multi-variate Relations. A. Klinger, in Human Machine Interactive Systems which exemplifies the use of one approach to visualization of multi-dimensional spaces. Another is the work of nDimensional Visualization (the nDV method) which is explained in the parent case. These visualization techniques may reveal other relationships that conventional statistical tools might miss. The visualizations may also identify possible rotations and rejuxtapositions of coordinates that can be relevant to developing new understandings of relationships. A helpful summary of the state of the art in visualization can be found in the recently published book
Readings in Information Visualization: Using Vision to Think,
by S. Card, J. Mackinlay and B. Shneiderman.
It is also known in the art to map from parallel or concurrent multi-dimensional spaces back into classical orthogonal three dimensional space in order to display the effect of the selected three dimensions upon each other. However, those using this method do not teach, suggest, or otherwise contemplate displaying data in anything other than classical orthogonal three dimensional (or two dimensional) relationships.
Insight to data-defined relationships is provided by nDimensional Visualizations's technique (the nDV method) for viewing data within a parallel coordinate system. This unique directrix-based-geometry maps classical familiar geometric shapes in orthogonal space into the corresponding shapes in parallel coordinates. The nDV method provides the basic understanding of what to look for while examining data models in their parallel coordinate data spaces. These new understandings of the geometry of parallel coordinates reveal possible curve-fitable waveforms that can now be more readily recognized, but which have not been previously considered for curve fittings because they could not be seen in classical parallel coordinate mapping.
Classical geometries that are mapped using the original generatrix mapping of the nDV method include straight lines, intersecting straight lines, circles, squares, polygons, cylinders, cones, spheres, cubes, and polyhedra. These classic shapes are mapped from familiar two dimensional and three dimensional shapes into parallel coordinate models using line-generatrices. Line-generatrices are important because these are the shapes typically encountered in data-defined space models. Knowledge about the meanings of the line structures encountered in parallel coordinate data defined spaces is vital when synthesizing the cumulative effect or meaning of those structures.
Most prominent of these new waveforms are those generated as products of sin/cos functions. For example, Fourier analyses typically look only for the sums of sin/cos functions. Such sin/cos product functions can be decomposed by classic trigonometric identities into the sum and difference frequencies represented by these product functions. Knowledge of the meaning of sum and difference frequencies allows usage of these trigonometric identities to reveal the spherical relationships between those coordinates that could not be otherwise recognized.
It was a concept of the parent case that animated data space models using the nDV method are the basis for being able to see, recognize for their significance, and then use structures and relationships within the data. What is now needed is a new method of deriving more information about, or identifying new relationships within, the data space models created using the nDV method.
It would be an advantage over the prior art to be able to select any number of coordinates that are observed in the parallel coordinates generated by using the nDV method, and map them back into three dimensional orthogonal (but not necessarily 90 degree orthogonal) space.
It would be another advantage to apply curve-fitable waveforms to these transformed coordinates to thereby identify portions of the data that is mapped in parallel coordinate space which correspond to recognizable waveforms.
OBJECTS AND SUMMARY OF THE INVENTION
It is an object of the present invention to provide a method for transforming multi-variate data shown in a parallel coordinate system to Single-point representations of n-dimensional points using Broken-line Parallel coordinates (or SBP space).
It is another object to transform multi-variate data shown in SBP space to a parallel coordinate system.
It is another object to facilitate recognition of structure, patterns and trends within data plotted in parallel coordinate space or SBP space.
It is another object to facilitate identification of structures or relationships generated along, across and among the coordinates of multi-dimensional data.
It is another object to facilitate quantification of these relationships.
It is another object to facilitate understanding of how these structures are descriptive of relationships among or between the variables within a system.
It is another object to facilitate learning the behavior of a system through observation of the data in SBP space.
It is another object to facilitate the understanding of multi-variate data from observation in SBP space such that further experiments using the system can be implemented to thereby obtain more useful data.
It is another object to facilitate the understanding of multi-variate data from observation of the data in SBP space such that further observations of other portions of the multi-variate data can be selected based on a previous observation.
The presently preferred embodiment of the present invention is realized in a method for utilizing an intellectual structure for visualizing a system of multi-variate data points in a parallel coordinate system, identifying an area of interest within the system, and then transforming a selected portion of the system for visualization in single-point representations of n-dimensional points using broken-line parallel coordinates.
In a first aspect of the invention, the n point representations of conventional parallel coordinates are brought back into a single point representation that is the single point vector resultant of n dimensional spaces viewable in familiar three dimensional display space.
In a second aspect of the invention, coordinates are grouped in pairs, and the angle of inclination of the planes between the coordinate pairs in the presently preferred embodiment is chosen to be 180
degrees, thereby resulting in evenly distributed
Johnson Robert R.
Millar Rodney D.
Palmer Eric
Palmer Marc
Havan Thu-Thao
Luu Matthew
Morriss Bateman O'Bryant & Compagni
N-Dimensional Visualization
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