ARCHITECTURE + RESEARCH




Hypar Surface Approximation2019Research
Grasshopper + Galapagos
@DFL

The 9 hyperbolic paraboloid surfaces of Le Corbusier’s and Jannis Xenaquis’ Philips Pavilion can be devided in 2 families: four-sided and 3 sided ones. The four-sided hypars are easily modelled using their straight edges ( which are also rulings in 2 directions) as inputs for sweep commands. The 3-sided hypar sections are the result of regular 4-sided hypars, which were sectioned by a ground plane, resulting in the characteristic curved plan of the pavilion. In these cases, if we sweep an edge ruling line along the curve, we will get a surface similar to the hypar, but not actually one, which can have undesirable effects for instance, in robotic hot-wire cutting. Therefore, a simple method was developed to approximate hypar surfaces, using the evolutionary solver in Grasshopper, Galapagos to:  

  1. use as input, the existing lateral ruling edges;
  2. create a 4th random point with variable coordinates;
  3. Generate a hypar surface and intersect it with the ground plane, creating the ground curve;
  4. Find the average distance of this curve to the desired curve in plan;
  5. Minimize this distance as a fitness function
ARCHITECTURE + RESEARCH   

RESEARCH             TEACHING            OTHER            ABOUT                








Hypar Surface Approximation2019Research
Grasshopper + Galapagos
@DFL

The 9 hyperbolic paraboloid surfaces of Le Corbusier’s and Jannis Xenaquis’ Philips Pavilion can be devided in 2 families: four-sided and 3 sided ones. The four-sided hypars are easily modelled using their straight edges ( which are also rulings in 2 directions) as inputs for sweep commands. The 3-sided hypar sections are the result of regular 4-sided hypars, which were sectioned by a ground plane, resulting in the characteristic curved plan of the pavilion. In these cases, if we sweep an edge ruling line along the curve, we will get a surface similar to the hypar, but not actually one, which can have undesirable effects for instance, in robotic hot-wire cutting. Therefore, a simple method was developed to approximate hypar surfaces, using the evolutionary solver in Grasshopper, Galapagos to:  

  1. use as input, the existing lateral ruling edges;
  2. create a 4th random point with variable coordinates;
  3. Generate a hypar surface and intersect it with the ground plane, creating the ground curve;
  4. Find the average distance of this curve to the desired curve in plan;
  5. Minimize this distance as a fitness function