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Precision Measurements and Parametric Models of Vertebral Endplates

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Inclined toroidal surface that fits an off-axis conic section.

O Cardona-Nuñez, A Cornejo-Rodriguez, A Cordero-Davila

|November 25, 2010

Summary

This summary is machine-generated.

Researchers created a method to find the best-fitting inclined toroidal surface for off-axis conic sections. This technique uses a known curvature toroid to derive an equation for axis inclination, aiding in geometric analysis.

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Area of Science:

Geometry
Computational Mathematics
Surface Fitting

Background:

Off-axis conic sections present challenges in precise geometric description.
Determining fitting surfaces for complex curves requires robust mathematical formulations.

Purpose of the Study:

To develop a formulation for determining an inclined toroidal surface that best fits an off-axis conic section.
To derive an analytic equation for the angle of inclination of the toroid's axis.

Main Methods:

Utilized the continuous least-squares method for surface fitting.
Employed a toroid with known curvature to establish geometric relationships.

Main Results:

Successfully determined the inclined toroidal surface that best fits the off-axis conic section.
Obtained an analytic equation for the angle of inclination relative to the section's normal.

Conclusions:

The developed formulation provides an effective method for fitting inclined toroids to off-axis conic sections.
The derived analytic equation simplifies the determination of axis inclination in geometric modeling.