## Surfaces

Two-dimensional surfaces from algebra, differential geometry and topology.
Classic surfaces as well as new examples and counter-examples. Immersed
surfaces, implicit surfaces, topological shapes. The surfaces are specified as
a simplicial mesh immersed in an Euclidean space R^{n}.
A a surface in R^{3} can locally be parametrized by a map

F(u,v) = (x(u, v),y(u, v),z(u, v)) : D -> R^{3}

of a domain D in R^{2} where x, y, z are the coordinate functions.

#### References

- Manfredo P. do Carmo:
*Differential Geometry of Curves and Surfaces*,
Prentice-Hall Englewood Cliffs, NJ (1976).
- Gerd Fischer:
*Mathematical Models*, Vieweg Verlag (1986).
- George Francis:
*A Topological Picture Book*, Springer Verlag (1987).
- Alfred Gray:
*Modern Differential Geometry of Curves and Surfaces*,
CRC Press (1994).
- M. Schilling:
*Catalog Mathematischer Modelle für den höheren
mathematischen Unterricht*, Leipzig (1911).

#### Technical Note

As a guide, meshes should have no holes, no degenerate triangles and
elements, no duplicate vertices. Surfaces should have meshes with an adjacency
relation.