Algorithms

“Strange Start Startling Stop” was designed by Mary Purdy at the State University of New York in 1985. The composition is based on a hexagonal lattice (above figure). There are four prototiles, marking the four key moments in the shape-shifting process. The first prototile is a regular hexagon, which is also the first tile of the composition. This prototile morphs into a shape that is a composition of four smaller hexagons, creating the second prototile. This morphing process finishes at…

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…

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…

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,…

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…