#rhino-python

While trying to program the curves produced by Spirograph toys in Grasshopper, I took a slightly different path. The topic eventually led to a broader heading: harmonic motion, and from there, to the Fourier Series we looked at previously. This simple Python code models Fourier Synthesis, driven by circles of different radii in a very straightforward way. The Python component sets up a loop that calculates the effect of each circle to the x and y values, individually. In this…

Hot-wire cutting (HWC) is a cost-effective subtractive fabrication technique used across many industries. The basic idea of HWC is to cut a block of material by melting it with a resistance-heated wire under tension. It is effective for materials with low melting temperatures, such as expanded polystyrene (EPS) and extruded polystyrene (XPS). Generally, HWC is associated with mold production in the architecture, engineering, and construction (AEC) industries. Robotic hot-wire cutting (RHWC) is a subtopic of HWC. In a standard RHWC…

We previously looked at the terrain generator script we used in projects with first-year architecture students over here. Later on, we added a few analysis modules to this tool. You might remember the slope analysis tool from this link. Today’s topic is another type of analysis: flow. The idea for this code wasn’t actually mine; I developed it by looking at an existing script based on Serkan Uysal’s suggestion. Unfortunately, I don’t know who originally wrote it. Keeping track of…

I’m looking forward to teaching Design Mathematics, a compulsory course in Istanbul Bilgi University’s graduate program in Architectural Design. The course was previously offered as an elective in the undergraduate program (here). Over time, I have also shared parts of the course content on the blog, particularly the sections on linear algebra and Rhino Python. Unfortunately, though, I have never quite managed to turn this material into the book project I had envisioned. Perhaps this semester I’ll finally make it…

Exploring dual polyhedra in Grasshopper is an interesting topic. In this post, I try to generate the dual of any polyhedron using Rhino Python and possibly Grasshopper. I developed this code for Rhino Python earlier here, and now I have converted it into a Grasshopper-Python component for better usability. I start the process by breaking the polyhedron into individual faces and gathering the corner points of each face. These points become the vertices of the dual polyhedron. Then, for each…

String art is a cool art technique that combines geometry and aesthetics to recreate images using lines between pins. Here is a good reference to start studying it. In this post, I explored a custom Rhino Python script designed for Rhinoceros 7 and 8. It transforms a grayscale image into a dense web of threads. The algorithm analyzes the darkest areas of the image and connects pins in a circular layout to form compositions. The script begins by converting a…

Differential growth is a process where different parts of a structure grow at different rates, leading to complex forms. After watching this, I decided to try it in Grasshopper. Here, differential growth mimics this behavior by applying rules such as Repulsion to avoid crowding or overlapping, Cohesion to keep parts connected or within a range, and Insertion to add new elements when a part stretches too far. The algorithm I present here simulates a differential growth process starting from a…

The Fourier Transform is a powerful mathematical technique that allows us to analyze the different frequency components within a signal or shape. Its discrete version, the Discrete Fourier Transform (DFT), is used when working with numerical data. I studied the Fourier Series here before. One of the most fascinating aspects of the DFT is that it can represent a signal or shape using rotating circles (or vectors). Each circle corresponds to a specific frequency, amplitude, and phase. When connected in…

Although it appears simple, Goldberg Polyhedra in Grasshopper became a tough challenge, which I like a lot. I spent about 24 hours attempting to generate these polyhedra. I started with Goldberg’s original method. This creates an equilateral triangle using coordinates denoted as m and n on a hexagonal grid. Then, we place this triangle onto the faces of an icosahedron. Finally, we project them onto a concentric sphere. We can create many polyhedra by changing the values of m and…

Below is the first paper of my son, Mete Yazar. It is about a mathematical and geometric exercise of calculating the surface area of an arbitrary shape (a classical guitar’s body panel). He did a good job in utilizing Bezier/de Casteljau curves and generating the parametric equations of the piecewise curve. I helped him to validate the results by using rhinoceros CAD software. Therefore, it seems that his calculations are correct. In this paper, we attempted to calculate a guitar’s…