Intersections of ellipsoids and planes of arbitrary orientation and position

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


This paper considers an ellipse, produced by the intersection of a triaxial ellipsoid and a plane (both arbitrarily oriented), and derives explicit expressions for its axis ratio and orientation. The relationship between central and noncentral sections, and the problem of intersection probability, are discussed. The resulting equations have obvious applications in structural geology and optical mineralogy, and in stereological modeling of grain-size and grain-shape distributions.