Taenia Solium

When thinking about serious and specific topics, I suddenly find myself looking back at the basics again. Catenary curves, are not the most beautiful one among those mathematical forms found in nature. However, it still tells us a lot about structures. The name apparently comes from catenaria, the Latin word for “chain”. This Grasshopper code was actually an example from our book 10 years ago (link here). It seems catenary curves could potentially be used in a type of dome…

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…

Lissajous curves, named after the French physicist Jules Antoine Lissajous are a family of curves that emerge from the interaction between two harmonic oscillations. They have applications in various fields including physics, engineering, and signal processing. They are commonly used in electronic devices such as oscilloscopes to visualize the phase relationship between two oscillating signals. Similarly, they are also useful in mechanical engineering for analyzing and designing mechanisms that involve harmonic motion. Lissajous curve functions can help in understanding the…

I have been studying the Bezier-De Casteljau algorithm for several years. Last week, I finally managed to understand and implement B-Spline Construction in Rhino and Grasshopper Python code, using the Cox-De Boor algorithm. This algorithm calculates the effect of control points on a B-Spline with many control points. After this, I am not limited to the degree+1 control points. This animation shows both algorithms working together. This Rhino Python code in a Grasshopper definition can handle three tasks. The first…

This is a Cycloid-like family of curves, generated by its classical description: a rolling circle. I had several other studies on similar topics before. In this cycloid experiment, I used Grasshopper in which, we don’t need to roll the circle. Instead, we can divide a parametric curve, utilizing data lists to simply rotate a circle around it. Finally, evaluating the circle repeatedly creates a Cycloid-like result. I found this as the most simplistic way of showing and studying these special…