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 Rn.

A a surface in R3 can locally be parametrized by a map

F(u,v) = (x(u, v),y(u, v),z(u, v)) : D ->  R3

of a domain D in R2 where x, y, z are the coordinate functions.


  1. Manfredo P. do Carmo: Differential Geometry of Curves and Surfaces, Prentice-Hall Englewood Cliffs, NJ (1976).
  2. Gerd Fischer: Mathematical Models, Vieweg Verlag (1986).
  3. George Francis: A Topological Picture Book, Springer Verlag (1987).
  4. Alfred Gray: Modern Differential Geometry of Curves and Surfaces, CRC Press (1994).
  5. 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.