This is a new series aimed at beginners in Grasshopper. The design method pioneered by Grasshopper with the way he defines geometric relationships is becoming increasingly popular today. Its interactive interface, which looks like a game or a puzzle at first glance may seem easy and its impressive geometric results are a little dazzling. But when you enter the world of Grasshopper, it is understood that it is not a simple toy at all. It is very difficult to get…

This is my first experiment with the Fourier Series in Grasshopper using Python. This is a technique to decompose functions into their frequency components. Fourier series have a wide range of applications in physics and engineering. What makes it especially fascinating, however, is the visual intuition it offers. It looks like a kind of mathematical “magic” that emerges from the geometry of frequency. I explored several excellent visual explanations online, including those by Coding Train, 3Blue1Brown, and Mathologer, each offering…

This is the new paper with Meryem Nurefşan Yabanigül, published at Automation in Construction. It is also Meryem’s master’s thesis. This study is about testing the production of curved surfaces with non-linear robotic hotwire cutting and shape memory alloys. Below is the abstract of it: Robotic arms are being used by construction firms and schools of architecture around the world in design/build research and material studies. Some of these studies utilize robotic hot wire cutting (RHC) as an efficient production…

In this session, I will add two new methods to the Vector class. I think this will finish the basics for the vectors. In the future, we are going to need several new methods like adding multiple vectors and interpolation. But for now, I think this would be sufficient to further advance into parametric curves and surfaces. These new methods will be based on the dot product method we created in the last post. I will add the vector projection…

This is the continuation of the Vector class we started here, and further advanced here, here, and here. This new Rhino Python implementation is mostly educational and partially a hobby. Before this session, we have developed display, magnitude, add, multiply, reverse, and subtract methods. This time, I am adding the vector normalization and dot product methods and seeing the utilizations of the dot product. Line Explanation 1-26 Already explained in the previous posts. 27 Define a new method called “normalize”….

This is the continuation of the previous post on parametric curve equations. In this new version, the script picks a NURBS curve from the user. Then, it analyses the curve’s degree and control points. Unfortunately, only the curves with degree+1 number of control points can be processed. In the future, I hope that I will be able to extend this script to include multi-span curves with more than degree +1 control points. Finally, the script creates the three functions for…

Today, I am going to make only one addition to the Vector class we recently started in Rhino Python. The magnitude of a vector can be easily calculated by assuming that the axes (2 or 3 axes) of it are perpendicular to each other. This gives us an opportunity to assume a right triangle visually, and calculate the magnitude (length) of a vector by using the Pythagorean Theorem. In short, if you square and add the components of a vector,…

The parametric curve equations are good examples to demonstrate the bridge between computer-aided design and mathematics. Although useless and pointless, it is a good exercise to extract the curve equations. In this Rhino Python code, I present a generalized equation extractor for Rhino. Rhino curves are good examples de Casteljau and Bézier curves. You can see the mathematical underpinnings of Rhino curves with this exercise: This code asks the user the degree of the curve. By default, Rhino’s curves are…

The SpaceChase plugin for Grasshopper focuses on initiating dynamic capabilities to Space Syntax theory by introducing the “Dynamic Canvas” model along with real-time editing capabilities in an interactive physics-based environment. SpaceChase is a software development project for “Mekan Dizimi Tasarım Uygulaması” under the ARDEB 1001 program of TÜBİTAK. It is a collaborative research project between İstanbul Technical University, İstanbul Bilgi University, and Tuşpa Design Studio. You can find more information about the project here. In SpaceChase, a Kangaroo-based dynamic graph is introduced along with contextual node and…

This is a new paper published in Nexus Network Journal. I tried to implement euclidean constructions by compass in the approximation of famous parametric curves; Bézier curves, and B-Splines. Then, I created the algorithms to calculate the number of steps on a compass-only construction of Bézier curves. I developed a simple Python script to simulate the geometric constructions. However, I have been studying this topic for nearly four years. In the future, I wish that it would be a good…