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…

This is the continuation of my new project of re-creating the parametric curve and surface methods of Rhino via Python scripting. If you remember, I started with the building block of vector operations, here and here. Then, I defined vector addition and multiplication, before going deeper into the geometric calculations. In fact, they are using the previously defined addition and multiplication methods. New Vector Operations: Subtraction and Reversing In the future, we are going to need to reverse a vector,…

Together with Sevde Dinçer, we published a new study on the digital reconstruction of muqarnas. This is also Sevde’s ongoing Ph.D. topic. Previously, she started studying muqarnas geometry in her master thesis under the supervision of Togan Tong. Then, she advanced her studies in this field. Eventually, my contribution to this study was about redefining and comparing the three major modeling approaches. Apart from that, the case study, literature research, and all the rest were done by her. This paper…

Today, I am going to advance the Vector class a bit more. Firstly, I will improve the display method I introduced recently. Then, I will add two new methods which handle the fundamental vector arithmetics in Rhino Python. Improving the Display Method In the previous attempt, I displayed vectors on the origin of the Rhino viewport. The coordinates of the tail of a vector are not stored within the object attributes. Normally, I can store two coordinates, one for the…

Let’s continue from the Vector class that started yesterday. Previously, I defined this class to store three numbers (coordinates), named as “components”. I defined a method named __init__ for this. Similarly, I am adding a display method to the Vector class today. Note that I am using Rhino 6 in this code, but it should also work in Rhino 5 or 7. The code Below is the line-by-line explanation of the method: Line Explanation 1-4 Already explained before. 5 Start…

In this new series, I will be using Rhino Python to create some of the fundamental mathematical objects in Rhino. We will learn how to code in Python, and also try to get deeper into the intuition behind some of the fundamental concepts we use every day in Rhino and Grasshopper. The Vector class in Rhino Python is the starting point of this journey. Just like vectors, most of the topics are already built-in object classes in RhinoPython. But I…

Hydrophilic Structures is the 2018-2019 Spring Semester Graduate Studio of the Architectural Design Program. The studio aims to increase the public interaction with water, while being sensitive to the ecological and historical context of the shores of İstanbul. Students will be encouraged to design sustainable, floating modules and structures, which can be integrated into semi-open architectural programmes. A full-scale prototype will be fabricated and tested at the Santral Campus coast to Haliç. The main conceptual framework of the studio consists…

This is a simple inverse kinematics solution developed by Andreas Aristidou and Joan Lasenby in 2011. They call it Forwards and Backwards Reaching Inverse Kinematics (FABRIK in short). It was quite interesting the learn this technique because it is a fast and accurate approximation of a kinematic chain. There are very interesting potentials of this technique in terms of architectural simulations. I tried to develop a Rhino Python script in Rhino 6. It seems to be working properly. Here is…