Here is the shortest possible way of generating quick parametric curves in Rhino Python. So, you may change the f, g, and h functions to test any function curve. In this Python code, the list comprehension [(f(t), g(t), h(t)) for t in [t0 + i*dt for i in range(int((t1-t0)/dt)+1)]] works by first generating a list of t values from t0 to t1 with an increment of dt using the inner comprehension. The outer comprehension then iterates over these t values,…

Modeling a rhombicosidodecahedron requires exploding and extending the faces of a dodecahedron and an icosahedron of the same edge length. We begin with both polyhedra centered at the same point. Then, we explode the faces of the dodecahedron and icosahedron outward from the center. We extend their planes while maintaining their orientation and shape. As these faces extend, they intersect and form new polygonal regions. Triangular and pentagonal faces emerge naturally from the extended faces of the dodecahedron and icosahedron,…

Today’s polyhedra are the famous Archimedean Solids! I created a simple Grasshopper script to generate pendants from these beautiful solids. I call this Archimedean Pendants. However, you can implement other polyhedra to the same code. I hardcoded the vertex coordinates so you won’t need an extra add-on to generate the polyhedra. Thanks to the new SubD component Multipipe, it makes life much easier to produce 3dprint-ready results. To make this definition more useful, you can add scale operations in all…

Urban Atölye, led by architect Nilüfer Kozikoğlu initiated the development of this Grasshopper code. The concept was to create a random relief pattern on a surface to be carved out using CNC technology. In Turkish, this technique is referred to as “kaşıklama,” as the resulting shapes resemble those carved out by a spoon. Consequently, I named this Grasshopper definition “spooning.” The definition employs the Populate Geometry component to achieve a random distribution. However, you can further refine it to allow…

The Image Sampler has always been a very effective Grasshopper component. Once again, I had the opportunity to use this component for a professional job. As you can see, with the help of a straightforward and short script, we can create a relief of an image to fit the desired panel dimensions on the screen. We can process this onto a suitable material using a CNC mill, laser cutter, or water jet. For the beginners, here are the image sampler…

Here is a wave generator code I developed using Grasshopper and Python. While searching for a solution to the realistic water simulations, I came up with the Gerstner Waves. I tried to implement it. However, I came up with this final result, which is not a Gerstner Wave generator, but a much simpler one. It combines many user-fed wave components and calculates the resulting single wave. I played with this code for hours with different components. So, it is worth…

A Penrose tiling exemplifies a type of tiling known as aperiodic. In this context, tiling involves covering a plane with non-overlapping polygons or shapes. Aperiodic means the tiling lacks arbitrarily large repeating sections. These tilings derive their name from mathematician and physicist Roger Penrose, who extensively studied them during the 1970s. Despite their absence of translational symmetry, Penrose tilings can exhibit both reflection symmetry and fivefold rotational symmetry. I created a simple Penrose Tiling Generator in Grasshopper. I used the…

It is not possible to cover a double curvature surface with planar quads. Here is one method that overcomes quad tiling on double curvature by pulling one vertex of the quads to the plane defined by the other three. This method was used in architecture on several occasions such as the exterior facade of The Yas Hotel, designed by Asymptote Architecture in 2009. The same approach is also evident in the roof design covering the central courtyard of the Smithsonian…

Today’s beautiful curve is the spherical cycloid. It is a cycloid, rolling on a 3d circular path rather than a straight and 2d one. There are algebraic explanations of this curve. Therefore, I find it interesting to experiment with them, since it is more interesting than the regular planar cycloids, epicycloids, and hypocycloids. This curve is believed to have been studied first by Jean Bernoulli in 1732. The interesting and playful part of this is the resulting curve is always…

Gyroid is a popular triply-periodic minimal surface. Although it is a mathematical entity, designers and architects like its approximations very much. We used an interpretation of Gyroid in the rammed-earth structure: “Common-action Wall” in 2017. In that project, we utilized its spatial quality of dividing the space into two intertwining and symmetrical volumes. By making one of these volumes solid, I left the other void. So, in this tutorial, I am going to explain modeling the Gyroid Solid by utilizing…