TITLE:
An Automated Model for Fitting a Hemi-Ellipsoid and Calculating Eigenvalues Using Matrices
AUTHORS:
Alicia R. Billington, Peter J. Fabri, William E. Lee III
KEYWORDS:
Modeling; Response Surfaces; Ellipsoid
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.2,
January
17,
2014
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.