Spherical Ellipse

Spherical Ellipse Construction

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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

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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

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spher ellipse with different eccentricies
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spherical ellipse, rendered as tube

Spherical_Ellipse.pdf