WorkGroup: Leonidas Paterakis, Gianluca Santosuosso , Svetlana Nesterushkina, Viraj Kataria

Tutor: Marine Bagneris – Ecole Nationale Supérieure d’Architecture de Montpellier

In this experiment we tried to build a physical model of a free form surface, using the technique of the geodesic curves of the surface.

The general definition of the geodesic curves is: “the shortes path between points on a surface” but an other definition, describes them on a more efficient way : “being γ(s) a geodesic on a surface X, and A a point on γ(s), the curvature of γ(s) in A is the minimum possible curvature among all curves passing through A and having the same tangent line of γ(s) in A”(Hilbert/Cohn-Vossen).

With few words, this means that in every point of the geodesic curve, the normal vector of the surface on that point is perpendicular also with the curve. Fact that simplifies a lot the joints, wich result all the same and very simple.

We started from choosing the type of surface to use and we decided to try a complex surface wich would include multiple curvatures.

This would permit us to verify the potential of this technique on surfaces that present positive and negative curvature.

With the help of Grasshopper plugin for Rhino we created a definition that made possible testing different situations and see the result of the geodesic curves generated immediatelly.

Initial Surface

Trimmed Surface

Parallel points geodesic curves 1

Parallel points geodesic curves 2

Diagonal points geodesic curves 1

Diagonal points geodesic curves 2

Connecting Hole1 with Points

Connecting Hole2 with Points

Connecting Hole1 & Hole2

Intersecting Geodesic Curves

Extracting Geodesic Curves

Naming and organizing the different Geodesics

Rendering

Laser cut File

Assembly phase

Finished model