Algorithms

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….

After several readings, I’ve understood the way of working the new and very interesting feature of Kangaroo 2: “Grab”. Now, we can actually grab the Grasshopper objects from Rhino viewport! Also, on one hand, the new Kangaroo has a very special way of working (not common to us, native Grasshopper users) and on the other hand, it is very very easy to use and understand now. I loved that. Here is the classical truss exercise I’ve made with my students…

It is a nice exercise to study various components of point-to-curve transformations and vice versa. Tower Crane was our second-week exercise at İstanbul Bilgi University Faculty of Architecture Parametric Modeling class, asking students to design and draw a parametric object that has joints and parts that are moving alongside straight lines. Below is the most “safe-side” solution for me, although there are also very complicated solutions such as Mertcan’s.

This is a classical method of generating tree-like forms utilizing a simple command “Arc SED”. The idea is simple, as the command draws arcs using an input direction vector, so this could easily be implemented creating a “smooth” composition of curves just by iteration. Actually, this has been a previous study, discussed before here, using Hoopsnake. Now, this time I’m implementing the same algorithm using Anemone and a couple of other changes. Here is the Grasshopper definition (Anemone Components should be…

Utilizing “Force Field” components of Grasshopper to show my students how it is easy to develop flexible surfaces in design. The classical parametric canopy design is introduced in this video: In vector calculus, a vector field is an assignment of a vector to each point in a subset of space. A vector field in the plane, for instance, can be visualized as a collection of arrows with a given magnitude and direction each attached to a point in the plane….

Based on this post, the problem of modeling tree-like fractal shapes is still a good question for the early years of computational design education. Last time, I used Rhino’s macro to study these fractal trees in an “impossibly” limited interface. But this time I used a VB.NET script. Here is the code inside of the VB.net component: Here are the inputs. x is the number of iterations. The Crv input is a line needed for the first iteration. t represents how…

Some facade studies as early sketches of an architectural project; all of them are utilizing a similar Grasshopper approach. My favorite “Graph Mapper” generates the overall gridal deformation, then some of them are drawing geometry for membranes, while others are generated to be realized from sheet metal. Hopefully, one or two of these could be further studied: “Below, I am sharing my favorite among these codes. I had to pull off some geometric acrobatics to affect all four facades of…