#tutorial

The snub square tiling is one of the semi-regular tessellations, where regular triangles and squares match perfectly to fill the plane without gaps or overlaps. The Euclidean construction of Snub Square tiling is possible by utilizing the basic compass and straightedge operations. I made this construction in Rhinoceros to show that there is no need for any numerical input to locate the points and draw the tiling. There are two major techniques explained there. One of them is the basic…

This is a 3d modeling tutorial for the platonic solid of dodecahedron. Modeling a dodecahedron is a good exercise for the basic transformation commands such as Rotate3D in Rhinoceros. You will see that it is possible to calculate the rotation angle by using sphere intersections. I learned this elegant method while teaching Architectural Geometry classes 12 years ago. It is based on the fact that, given a rotation axis and the rotation point, you can draw the path traced by…

This is a short video tutorial on the B-Spline decomposition I studied earlier here. This tutorial demonstrates how to decompose a B-Spline curve into Bezier curves using Rhino. Despite the original Bezier-de Casteljau algorithm requiring degree+1 control points, Rhino allows drawing a degree-3 curve with any number of control points. By examining knot points and dividing segments appropriately, the B-Spline curve can be manually subdivided into Bezier curves. This involves placing control points, dividing segments, and connecting points in a…

In this short tutorial, I am going to show you how to locate a parametric point on a Bezier curve. This will be a third-degree cubic Bezier curve. So, I start by placing four control points. I name these points from P0 to P3. Then, I connect them by a polyline in order. I explode the polyline into the segments. The parameter of my point must be a number between 0 and 1. I will divide the segments, so I…

De Boor’s algorithm, a maestro of basis spline refinement, meticulously navigates through knots, unraveling the intricacies of B-splines with mathematical precision. Meanwhile, De Casteljau, the geometric orchestrator, takes center stage in the Bezier ballet, elegantly guiding control points through a recursive dance. Together, these algorithms fuse art and mathematics, seamlessly sculpting curves and splines with technical finesse, creating a harmonious symphony of numerical intricacies in computational geometry. ChatGPT is so emotional today. I have been studying the Bezier-De Casteljau algorithm…

Here is the method I used for approximately modeling the Gyroid, a triply-periodic minimal surface. It is very popular in architecture because the symmetrical solids and voids it generates are interesting. I modeled this for the Common-action Wall project we exhibited together with Fulya Akipek in 2017. After several attempts to generate it in Grasshopper, I decided to model it in Rhino. There are some sources on the internet, explaining the geometric modeling process. However, none of them was giving…

While digging through the lecture archive, I found this video I made in 2017. We introduce Platonic solids and Archimedean solids in the Design Geometry course at Istanbul Bilgi University. This video shows how we can create an Archimedean solid, the Truncated Tetrahedron, by folding it from a flat sheet. While doing this, I intersected the spheres by using the relations between the side lengths of the solid, and I calculated the rotation angles accordingly. First of all, I drew…

We continue with the Grasshopper for Beginners series by explaining Rhino+Gh workflow principles. What does GH add to Rhino‘s standard drawing and modeling functions? To put the question differently, what does GH do that conventional modeling programs, such as Rhino, can’t? What is the difference and relationship between Rhino+Gh? Let’s take an example to answer these questions. Our example is about parametrically describing a surface model and deriving its alternatives. First, we will try to create a surface using only…

Let’s continue the Grasshopper for Beginners series. We start with the traditional “Hello World!” displayed on the Rhino screen: Placing the Components In most CAD programs, the text creation function, which is the equivalent of the Text command, is performed by a component called Text Tag (Tag) in GH. The Text Tag (Tag) component is in the Dimension panel under the Display tab. If you’re not comfortable with tabs and panels yet, you can revisit this section from the beginning….

In this 5th episode of Grasshopper for Beginners, the interface continued by exploring the interface of Grasshopper. With the help of these two methods (tabs and search box), we can find the components. We can select them with the left click and place them on the canvas with the left click again. Now take random components and try to place them on the canvas with both methods. Therefore, components with different functions are the building blocks of GH definitions. The…