Algorithms

Creating and handling new types of grid configurations might be an important topic, as Grasshopper is not supporting them natively (yet). I tried to create some semi-regular tessellations based on regular grids. It is actually truncated versions of regular grids, but it slowly becomes interesting as I realized that I may further truncate emerging grids to create Level 2 and Level 3 grids with more complex tessellations. Here are two examples of Level 1, truncating regular tessellations of squares and…

Playing with the 2D Metaball component in Grasshopper. I was curious about why there are no Metaballs in 3D in Grasshopper. Then, I realized that in fact, the 2D Metaball component is creating a section of a 3D Metaball computation. I think it is a topic worth studying even 10 years after this original post to develop an easy way to create the metaball surfaces. In 2012, thanks to the Grasshopper’s easy interface, I was able to create a series…

Basic Design Studio at Bilgi University is coming to semester’s big final. Nowadays, students are trying to build their final projects. Oğuz and Gupse’s group has a truss structure with nearly 800 segments. They attempt to build it by taking length values from their own Rhino model by hand. And this itself had brought a difficulty, because one person of the group should be assigned only to do this measurement, reducing their workforce. They asked me if there is an…

Galapagos was a great improvement when it became available natively within Grasshopper as an Evolutionary Solver. However, I couldn’t find time to examine it until recently. This examination gave me an idea of algorithmic thinking, tool making, and tool using. The first experiment shown below tries to solve equilateral triangulation, based on the Delaunay method. Galapagos has two different solvers, named “simulated annealing solver” and “evolutionary solver” shown respectively below. Both of them are trying to reach a fitness value…

Experimenting with various plug-ins for solar calculations, I found Daniel Da Rocha’s robust implementation of the solar position algorithm in vb.net. It calculates the solar angle of any place and time. Although it’s written in the old vb.net component, it still works great. I’m trying to create a fast and easy workflow to optimize Grasshopper models based on solar directions. This is done by projecting faces to the solar planes and checking how much of their area is included in…

This is the continuation of my scripting experiment within Grasshopper. Like the minimum spanning tree algorithm, this is also a famous problem of computational geometry; the shortest path problem. I’m now coding faster and understanding the namespace more easily in Grasshopper. This time, the challenge was implementing Dijkstra’s algorithm for the Shortest Path Generator. Again, it’s a quite powerful algorithm, I even plan to use it in my current project. Although there is a faster alternative, Shortest Walk-in Food4Rhino and it…

This is the basic form of a surface division, based on curvature. As each point on the surface has a curvature value, this might be used to dispatch those values and see the points at flat and curved parts of the surface. I used my favourite surface equation definition (here) as implemented equation of cos(x)+cos(y) in the animation below.

This is the updated version of my MST code from 2012. After over a hundred hours of Rhinocommon and Grasshopper SDK studies, and lots of dead ends, I was finally able to calculate the minimum spanning tree of any given curve network in Grasshopper. Problems like these are interesting to me because of their clear logic and diverse areas of applications in design. I tried to simulate Dijkstra’s, Kruskal’s, and Prim’s algorithms, but no chance. There are similar solutions such…

Trying to further improve my experience in parametric modeling, I’m mixing and joining old definitions to reveal different potentials. I’m experiencing spatial mapping or morphing in Grasshopper. This is an equivalent form of the “flow along surface” command in Rhinoceros. It re-builds a geometric composition over another space (from world XY coordinates onto a surface with UV coordinates here) This is especially useful in creating surface compositions from famous tessellations such as Voronoi. There are lots of things I can…

Another famous shape of architectural geometry is a set of definitions creating minimal surfaces. I’ve found the trigonometric equation of the Gyroid and created a simple logic for approximating it as points in Grasshopper. However, when I searched the net for similar solutions, I found lots of them including the same approach as mine (Wynstan Wu’s definition). I was planning to develop a script in Grasshopper to take these estimated points and pull them to the Gyroid surface. Then, I…