Curves

One-dimensional curves from algebra, differential geometry and topology. Classic curves as well as new examples and counter-examples. Immersed curves and curves on surfaces. A parametrized curve c in a euclidean 3-space is a map

c : [a, b] -> R3

from an interval [a, b] of the real line into R3, which may have self-intersections or be knotted.

The curves in this model server are often specified as a polygon immersed in a euclidean space Rn.

References

  1. Egbert Brieskorn, Horst Knörrer Plane Algebraic Curves Birkhäuser Verlag, Basel-Boston 1986
  2. J.D. Lawrence A Catalog of Special Plane Curves Dover Publications, New York 1972.
  3. R.J. Walker Algebraic Curves Springer Verlag, Berlin-New York 1978.
  4. Alfred Gray Modern Differential Geometry of Curves and Surfaces CRC Press 1994.
  5. V. Kommerell, K. Kommerell Theorie der Raumkurven und krummen Flächen Walter de Gruyter, Berlin 1931.
  6. MacTutor Famous Curves Index University of St. Andrews

Technical Note

As a guide, polygons should be connected, no degenerate edges, no duplicate vertices.