Spherical Ellipse

Spherical Ellipse Construction

spherellipse construct 001
Spherical Ellipse Construction, with Tangent
  1. Let there be a fixed circle C with center F1 on a sphere.
  2. Let there be a fixed point F2 inside the circle, not coincide with F1.
  3. Let P be a point on C.
  4. Let t be a line perpendicular to line[P, F2] and intersect midpoint[P, F2]
  5. Let Q be the intersection[line[F1,P], line[t]]
  6. As Q move about, Q traces out an ellipse, and t is its tagent at Q.

Note: t forms a great circle. F1 and F2 are the foci.

spherical ellipse gray crp spherical ellipse thick
spherical ellipse construction with tangent
Spherical Ellipse 001

Spherical Ellipse with Osculating Circles

spher ellipse osculatin 001
Spherical Ellipse with osculating circles, the locus of their center is its evolute
Spherical ellipse normals 82801
Spherical ellipse normals in red

Spherical Ellipse with Different Eccentricies

spher ellipse expanding 001
spher ellipse with different eccentricies
spherical ellipse tube 07608
spherical ellipse, rendered as tube