## 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] -> R^{3}

from an interval [a, b] of the real line into R^{3}, 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 R^{n}.

#### References

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

#### Technical
Note

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