The Truncated Icosahedron (5,6,6) is an Archimedean Solid we often recognize as the iconic soccer ball. This geometric structure, also affectionately known as the “Buckyball” in honor of the visionary architect Buckminster Fuller, has gained significant popularity and recognition both within the realms of mathematics and everyday life. It is composed of twelve regular pentagons and twenty regular hexagons, meticulously arranged to achieve a harmonious balance. This symmetrical nature makes […]

Truncated hexagonal tessellation (or named 3-12-12) is represented in hyperbolic space (as far as I understood it). The idea is simple if you don’t mix it with complex equations. Below is the 2-dimensional representation of hyperbolic projection. Paper space is defined by the thick line there. Projection is based on a two-sheet hyperboloid surface. Euclidean version of this tessellation is described here. Here is the Grasshopper3D file containing the above […]

[GHX: 0.8.0066] This is my second attempt on getting into non-euclidean representations of space. Althouth it seems easy at first sight, this represents a close point of theory between mathematics and contemporary computational design geometry. As always, architects tend to use mathematical terms such as “non-euclidean geometries” but as far as I saw, most of them have no idea about what it is. So, I’m trying to learn and understand this […]

This is my first attempt at representing a non-euclidean space. There are several representations of a non-euclidean space in euclidean means such as Beltrami-Klein or Klein, Poincare, Poincare half-plane, and Weierstrass. Here, I tried to understand Poincare’s approach. Random straight lines are drawn on a hypothetical hyperbolic space using a simulation of Poincare’s famous disk representation. Although there is a precise description of the disk and its construction, I used a ready-made […]

Using SPM Vector Components developed by two talented people, Daniel Hambleton and Chris Walsh (website here), I’ve studied ways of displaying dynamic diagrams of form. I’ve modified an example file and found myself in a surprising formal exploration. It’s like watching the clouds, giving them meaning like a sheep, a flower, a baby… Here is a link to the Grasshopper file. Right-click and save it to your computer (don’t left-click it) [GHX: 0.8.0066: SPM […]

I’ve worked a little more about the Solar Position definition I’ve started here. The definition uses Danel da Rocha’s beautiful solar position script and utilizes it with other components. It creates visual output for any given surface, divided into quads (with side faces of course) and coloring according to their orientation to the sun. This time (file here: [GHX: 0.8.0066]) I added an occlusion part to calculate the surface’s own shadow. Now, […]

Here I am testing the nesting. RhinoNest is a plug-in for Rhino and a set of components for Grasshopper. I tested it using my old interlocking fabrication definition (here) and (here). I downloaded RhinoNest from this website and installed it. However, I sounded a little complicated at first sight. Then I found a sample definition (here) and modified it a little bit to meet my purposes. First of all, I added orientation components […]

I have come across several high school topics I was afraid of. While I was searching for a geodesic dome definition in Grasshopper, it was quite surprising that I found an easier way of modeling an approximation of icosahedron, the famous platonic solid. Icosahedron was a research topic of this website at various posts before (here, here, and here). In order to generate geodesic spheres, first I had to solve […]

Yesterday, Kağan asked me about the isovist component in Grasshopper and how it works. In fact, it is a long story, I said because once upon a time, I was curious about Space Syntax theory as my old friend Ela Çil introduced it. So, here is an original definition of Michael Benedikt; “The environment is defined as a collection of visible actual surfaces in space. An isovist is the set […]

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 […]

Not all of them, but when you get the idea, you’ll see there are lots of different alternatives for creating Fuller’s famous Geodesic Domes (Although in fact, he is not the inventor of it). I was playing with Platonic Solids in Rhino and realized that the “Pull” command is very useful in subdividing objects. I modeled this in Rhino 4. First, take a regular Icosahedron and divide it. Because, this […]

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 […]

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, […]

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. […]

The tetrahedron is a popular platonic solid for designers. We’ve explained how to draw them using equilateral triangles here before. Recently I’ve found (sorry, lost the web address) a much quicker way of modeling a Tetrahedron using a cube. It’s very simple, just connecting the three opposite corners of the cube automatically makes them equal, resulting in the four equal faces. Of course this time you’ll have to calculate the […]

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 […]

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 […]

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. Here is the Grasshopper definition [GHX: 0.8.0066] (Please use right click + save target as to download ghx definitions in this site. Otherwise your browser may try to execute them […]

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 […]

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 […]