The Enneper-Weierstrass parameterization is a parameterization of a minimal surface in terms of two functions 
and 
as
![[x(r,phi); y(r,phi); z(r,phi)]=Reint[f(1-g^2); if(1+g^2); 2fg]dz,](/images/equations/Enneper-WeierstrassParameterization/NumberedEquation1.svg) |
where 
and ![Re[z]](/images/equations/Enneper-WeierstrassParameterization/Inline4.svg)
is the real part of 
. Examples are given in the following table.
| surface |  |  |
| order-three Bour surfaces member | 1 |  |
| Enneper surface | 1 |  |
| Henneberg surface |  |  |
| Scherk's second surface |  |  |
| trinoid |  |  |
The notation above specifies the Weierstrass data by two functions 
and 
,
with 
representing the Gauss map
by stereographic projection. Another
common notation uses the Gauss map together with the
height differential 
,
taking the data to be 
(Meeks and Pérez 2011). In the normalization
above, 
, so the same surface
is written
 |
The apparent singular factors cancel where the data extend regularly. For a globally single-valued surface, the real parts of the periods of the three differentials must vanish (Meeks and Pérez 2011).
Multiplication of 
by a constant phase gives locally isometric associated
minimal surfaces. The Schwarz
D surface, Schwarz P surface, and gyroid
arise this way from 
and 
(Gandy and Klinowski 2000).
Wolfram Research, Inc. "Weierstrass Surfaces."