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


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.

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A. Billington, P. Fabri and W. Lee III, "An Automated Model for Fitting a Hemi-Ellipsoid and Calculating Eigenvalues Using Matrices," Applied Mathematics, Vol. 5 No. 2, 2014, pp. 234-240. doi: 10.4236/am.2014.52025.

Conflicts of Interest

The authors declare no conflicts of interest.


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