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 […]

Below is the Python code you can run in Rhino, that draws a cubic Bézier curve (degree 3). As you can see, the Rhino Python code is very slow and inefficient because we calculate every point with lots of computations. Instead, we can use the spline formulae to make this quicker but I wanted to show that the mathematical construction is parallel to the geometric one. This is a nested […]

Yes, interesting topics started to reveal themselves, when I dig into the function curves, especially in the parametric representation. The first interesting application is the “derivative”. Nobody in high school told me that the derivative of a function at a given point gives the slope of the graph at that point. Moreover, it is possible to convert the slope value into an angle in degrees, showing the angle of the […]

This RhinoPython script handles the simple graphs of two-dimensional parametric functions. Therefore, it approximates these functions by drawing parametric curves. It generates many points by solving the functions. The graph of parametric functions is a major topic in most Design Mathematics courses. Because it looks like the building block of many concepts of CAD. However, there is much more to learn before saying that the third degree NURBS is a […]

Jumping into the world of mathematics as a designer seemed to be frightening at the beginning but I opened a new elective course at Bilgi, Design Mathematics. Starting today, I’ll try to log my experiences with the students while we are trying to understand mathematics. The ultimate objective is to find paths that may lead to answering the following question; “what is the relationship between design and math”? Next week, […]

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. # Drawing Cycloid-like Curves # 07.08.2017 www.designcoding.net – Tugrul Yazar import rhinoscriptsyntax as rs curv = rs.GetObject(“Select curve”) qual = rs.GetInteger(“Quality”,100) radi = rs.GetReal(“a radius”,4) radi2 = rs.GetReal(“Circle radius”,4) cua = rs.OffsetCurve(curv,[1,1,0],radi2) cevre = 2 * 3.1415 * radi mimi = [] for […]

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 […]

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 […]

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. # Drawing Simple Fractal Curves # 31.07.2017 www.designcoding.net – Tugrul Yazar import rhinoscriptsyntax as rs import copy initials = rs.GetObject(“Select Initial Shape”,4) referenceA = rs.GetPoint(“Place Reference […]

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. According to ChatGPT: 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 […]

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 […]

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 […]

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 […]