Algorithms

Anemone components are still working great, extending the abilities of Grasshopper. Here, I studied a space-filling (or plane-filling) fractal called the Gosper-Peano Curve. You should be very careful about the number of iterations (the N input). Because it can crash your Rhino if you change it to more significant numbers. Also, you should have Anemone components installed in order to run this definition. The generator curve is a special one. This website explains the generation of the curve from the…

Studied earlier in Grasshopper here, creating a cycloid-like curve actually mimics the physical process of rotating disks on a path. Below is a test in Rhino Python (I know the variable names are not conventional).

According to Wolfram, By the duality principle, for every polyhedron, another polyhedron exists in which faces and polyhedron vertices occupy complementary locations. This polyhedron is known as the dual, or reciprocal”. We can use this method to generate new polyhedra from known ones. I tried to develop a Dual Polyhedra Generator in this Rhino Python script. First, the script asks a user to select a closed polysurface object. Then, it attempts to identify the area centroids of the faces. By…

We will see a simple Rhino Python exercise here. I called these Polygon Fractals (or Pentaflakes sometimes). It is both educational and fun to play with them. In Rhino, it can be a good exercise for basic CAD commands and transformations such as move, copy, and scale, and precision drawing operations such as object snapping. Also, in Grasshopper, it can be a good challenge for looping. In Rhino Python, it is already a good exercise for understanding Python and the…

A simple Rhino Python script that generates fractal curves. An example is a test with the Gosper-Peano curve. However the script is not supporting segment directions, which is why the result is not the intended curve. Curve directions could be implemented in the future.

As studied earlier in Grasshopper here, the sunflower spiral, or Phyllotaxis, or Fibonacci’s spiral, could be drawn as an exercise of looping in Rhino Python. Phyllotaxis is the arrangement or patterning of leaves, flowers, or other plant parts around a stem or axis. Thus, it refers to the specific geometric arrangement of these structures in plants. The term “phyllotaxis” comes from the Greek words “phyllon” (meaning “leaf”) and “taxis” (meaning “arrangement” or “order”). Phyllotaxis can vary widely among different plant…

This Rhino Python code calculates the cross-product determinant used to determine the orientation of three points (current, next_point, and point) to see if they form a left turn or a right turn. This is a well-known technique in computational geometry to check the relative orientation of points. In this script, the direction is the cross-product determinant that determines the relative orientation of the points. If the result is negative, the point is to the right of the line from current…

Boris Nikolayevich Delaunay was a Russian mathematician and mountain climber. He developed the Delaunay triangulation, which is a method in computational geometry. It is a triangulation of a set of points such that no point is inside the circumcircle of any triangle formed by the points. It’s widely used in computer graphics and mesh generation. In 2013, I made the brute force code in Rhino Python which is a slow solution to this problem. It used to be a nice…

This python code proves how much effort it takes to create a simple hexagonal tessellation. There are, of course, much easier and faster methods than this. But here you see a code that introduces students to Rhino Python. Using this code, a new Rhino command can be generated, and for the first time in Rhino, we can have a command that creates a hexagonal grid. I followed this tutorial to turn this Python script into a Rhino command. This is…

This is done because I needed to represent relationships between different factors and layers of a design process. Although this method of “Chord Diagrams” is a very common technique in information design, it became very hard to find an effective tool for generating those diagrams quickly. There seem to be a solution called “Circos” but however, even installing it on the computer became very boring for me. So I decided to make a Grasshopper definition that generates simple circular relationship diagrams….