ellipsoid 1sphere morph 001
The ellipsoid is a linear deformation of the sphere.
ellipsoid 2focus wa 001
The rotationally symmetric ellipsoid has an interesting focussing property, called “wisper room”. If some pub has a ceiling of this shape and a table is placed at one focal point then a spy can hear from a safe distance the conversations at the table.
ellipsoid 3focus ellipsoid 4focus
The focal rays again.
ellipsoid 5geodesic ana
The coordinate planes are symmetry planes of the ellipsoid and therefore they intersect it in closed geodesics. These are ellipses. All other closed geodesics are much more complicated. Here is one in anaglyph.
ellipsoid 6geodesic ray
Another closed geodesic on a raytraced ellipsoid. Note that the pieces behind the ellipsoid are in darker color.
ellipsoid 7anaglyph
Anaglyph ellipsoid.

Conic Section Surfaces

  1. Ellipsoid
  2. Paraboloid
  3. Hyperbolic Paraboloid
  4. Hyperboloid of One Sheet
  5. Hyperboloid of Two Sheet

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