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

• 作者: Alicia R. Billington Peter J. Fabri William E. Lee III
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Modeling Response Surfaces ELLIPSOID
• 年，卷（期）: 2014,（2）
• 页码范围: 234-240
• 页数: 7页
• 分类号: O1

摘要

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.