The intersection topic is quite popular at an interdisciplinary level. It can be the friends of geometry, geodesy, satellite orbits in space, all sorts of elliptical motions (e.g., planetary motions), curvature of surfaces and concerning eye-related radio-therapy treatment, for example the anterior surface of the cornea is often represented as ellipsoidal in form.
We have developed an algorithm for intersection of an ellipsoid and a plane with a closed form solution. To do this, we rotate the ellipsoid and the plane until inclined plane moves parallel to the XY plane. In this situation, the intersection ellipse and its projection will be the same.
This study aims to show how to obtain the center, the semi-axis and orientation of the intersection ellipse.
Ellipsoid, normal section curve, 3D reverse transformation, intersection ellipsoid and a plane
