Differential geometry is a mathematical discipline that uses the methods of differential and integral calculus to study problems in geometry. The theory of plane and space curves and of surfaces in the three-dimensional Euclidean space formed the basis for its initial development in the eighteenth and nineteenth century. Since the late nineteenth century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. It is closely related with differential topology and with the geometric aspects of the theory of differential equations.
Enneper surface :In mathematics, in the fields of differential geometry and algebraic geometry, the Enneper surface is a surface that can be described parametrically by:
x= u(1-u2 / 3 + v3) /3
It was introduced by Alfred Enneper in connection with minimal surface theory
Mathematica 6 enneper suface original code
Mathematica 6 prametrically modified surface
Exported geometry to rhino
First render sketch more to come . . .
In an attemp of doing design in a more rationalized way I am currenttly exploring form using diferential geometry I´ve noticed that many architects use this matematical discipline to develop their projects, thing that doesnt happens to often in design , thats why i decided to get into this fourtunately for me there are some softwares like Mathematica 6 and Rhino math plug-in that help people to develop complex surfaces once you have a basic undertanding of parametric functions.
The goal of this project was to explore different surface ecuations by changing their parametric values to develop forms wich may be used in the design of a functional object.
The result was the Enneper stool by using the enneper surface ecuations and exploring different parametric values i develop a form wich can be used as an stool , achieving a functional object with a very interesting ahestetic. There is some more work to do finish compltely this project wich i hope to finish and post soon.