An Automated Model for Fitting a Hemi-Ellipsoid and Calculating Eigenvalues Using Matrices

Alicia R. Billington, Peter J. Fabri, William E. Lee III

College of Engineering, University of South Florida, Tampa, USA.
College of Engineering, University of South Florida, Tampa, USA;USF Health Morsani College of Medicine, University of South Florida, Tampa, USA.

DOI: 10.4236/am.2014.52025                

Abstract

Ellipsoid modeling is essential in a variety of fields, ranging from astronomy to medicine. Many response surfaces can be approximated by a hemi-ellipsoid, allowing estimation of shape, magnitude, and orientation via orthogonal vectors. If the shape of the ellipsoid under investigation changes over time, serial estimates of the orthogonal vectors allow time-sequence mapping of these complex response surfaces. We have developed a quantitative, analytic method that evaluates the dynamic changes of a hemi-ellipsoid over time that takes data points from a surface and transforms the data using a kernel function to matrix form. A least square analysis minimizes the difference between actual and calculated values and constructs the corresponding eigenvectors. With this method, it is possible to quantify the shape of a dynamic hemi-ellipsoid over time. Potential applications include modeling pressure surfaces in a variety of applications including medical.

Keywords

Modeling; Response Surfaces; Ellipsoid

Conflicts of Interest

The authors declare no conflicts of interest.

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