Another famous shape of architectural geometry is a set of definitions creating minimal surfaces. I’ve found the trigonometric equation of the Gyroid and created a simple logic for approximating it as points in Grasshopper. However, when I searched the net for similar solutions, I found lots of them including the same approach as mine (Wynstan Wu’s definition). I was planning to develop a script in Grasshopper to take these estimated […]

When I was a student, 3D modeling and rendering on the computer was an advanced skill. I only managed to create my first rendering in the 4th-year project.  Then, it became a special talent for designers, even opening a freelance business. However, that came to an end when that technology expanded, reaching everybody. Ten years ago, different ecological analysis methods on geometric designs were also another specialized field that everybody […]

As far as I understood, it is impossible to physically construct double-curved surfaces from quadrilateral and planar faces. This definition tries to find an optimized alternative to this problem. Any surface, single or double curved, is divided into standard sub surfaces. But this time, those surfaces are treated as planar surfaces, therefore one corner is moved to meet this requirement. The output consists of only planar surfaces ready for fabrication. […]

This is another popular “math surface” being rediscovered by designers nowadays, in 2012. Saddle surfaces, seen above as mentioned earlier (here) have a special type named “Monkey Saddle Surface”. This surface was a dramatic example of how Grasshopper can control equations and instantly show graphical results. The mathematical equations start with Z=… this makes it very easy for us to transform any x-y grid centers (a 2d data tree of […]

QuickShaper (QS) an experimental computer utility for Shape Grammars. It aims to assist designers and students in creating and exploring rule-based designs. QS is first presented and published with Birgül Çolakoğlu at the 25th eCAADe Conference held at Frankfurt / Germany in September 29th, 2007. QS is a scripted utility, written in MaxScript, developed within Autodesk’s 3D Studio MAX version 9. It is not tested on earlier versions. QS works […]

I tried different approaches to drawing platonic solids using Grasshopper’s native components. However, it seems impossible now. In geometric definition, a platonic solid is a set of points, distributed on a sphere with equal distances. If the set contains 12 points, then it’s an icosahedron. I found lots of information about these objects and mathematicians seem to love analyzing them. They created different approaches to building an icosahedron. One of […]

[RFA: Revit 2012] It seems simple at first sight, but creating a window definition in Revit requires a lot more time than I expected. A freelance job led me to create this parametric object, when I saw the architect’s sketch of all window types of the building side by side. There was a clear connection between all of them, leading me to define a single window object. Of course I’m […]

This is another old-school approach to parametric modeling, today known better as part of Building Information Modeling. I tried to create parametric objects in order to understand and learn the capabilities of Revit.  That was very useful for me in learning this interface. I specially chose Le Corbusier’s chair set as my first experiment on family creation in Revit. On his 100th anniversary of Eastern Voyage, Le Corbusier’s soul returned […]

After Puzzling, I tried to establish more of Escher’s basic grid transformations using Grasshopper’s native components. This definition simulates Escher’s transformation of four-cornered grids. The postulate is based on the fact that every quadrilateral (or triangular) planar shape can create regular tessellations without gaps or overlaps. In the traditional method, this tessellation is achieved by rotating the shape 180 degrees and copying afterward. However, in Grasshopper we simply define the […]

Nowadays, I found myself back into traditional hand sketching. Several failed attempts on Grasshopper led me back there. NURBS (and Grasshopper) somehow limits our conception of surfaces to four-cornered (or two-directional) manifolds. Although it sounds like limiting our designs, having four-cornered component spaces has still lots of experimental fields for designers. Escher is a cult person, who transforms the euclidean coordinate system to meet his design intentions. There are lots […]

This topic of trees and recursive computing is inspired by the method shown here at the Rhino Python 101 Primer. This is a beautiful method of recursion that creates tree-like shapes, composed of arcs. I constructed these arcs by using the Arc SED (start, end, direction) method. This requires start and end points and a vector that is tangent to the arc (at the start point). Therefore, the overall look […]

Today, we’ve discussed ways of subdividing entities to create parametric definitions. Curves can be divided into segments, creating snake-like object definitions. This exercise is important regarding the management of data. Vectors and planes are used as reference entities here. Nowadays, it became clear to me that, reference planes are very important because they both include reference points and related vectors as well. The definition studied in this post includes a curve […]

This was an interesting topic in design computing class. Geometric constructions based on strict relationships are becoming exciting in parametric modeling environments. I think muqarnas includes such a relationship. There is a primary method of modeling this shape, introduced by Mete Tüneri. His solution to a simple parametric muqarnas object includes a surface with six reference points, with two boolean differences (one cylinder and one box) creating the component. In […]

Here is a funny sketching system for the “SPEC” homework. [GHX: 0.8.0066] Four (or more) points are created using 2d sliders (MD slider) and decomposed these points into x,y and z numbers. Then, they are re-populated in 3d points by changing their plane. X coordinates are connected into Y, and Y coordinates are connected to Z’s. Tricky part comes then, the X number is defined by a serie of numbers started from […]

This is the basic definition of one point attractor on a grid of points. [GHX: 0.8.0066] Here, the fundamentals of data tree matching can be studied. A hexagonal grid is exploded into points and new polygons are created there. Instead of a standard point distance relation to polygon size, this time the distance factor affects the rotational angle of these polygons. Although the structure of data trees is getting complicated, this has no […]

Maybe a huge kitsch for contemporary architecture, I know, but a good example of a fundamental problem of constructing geometric relationships. In ARCH362 today, we’ve examined the geometric modeling process that opens us to parametric relationships just by converting it into a diagram of design history. You may follow the construction of such a diagram step by step and see the possible parameters emerge from it. The only rule of […]

Here are three technical tips, that might help you model in Rhinoceros faster. Please note that, in most cases, you’ll find CTRL+F1,F2,F3 and F4 very helpful in modeling and transforming objects in digital space. These key combinations will focus you on Top, Front, Left and Perspective views (maximized) respectively. Also, when you try to express your design process (especially supporting geometries) using different linetypes, it’s possible that you’ll never like those preset linetypes. By […]

That was about six months ago, our study for a design competition required a spatial allocation algorithm. An office building with a rectangular plot and a strict functional requirement forced me to the good old Voronoi diagrams, subdividing a surface. Here is the definition file: [GHX: 0.8.0066]. However, there were other design parameters such as the sunlight and orientations of each functional cell. Combining a couple of graph components helped me […]

This is the old-method Parametric Truss definition. Interestingly this quickly became a solid solution, used and taught for years. I couldn’t find a better answer yet. As Grasshopper updates, some of the components in this definition change but the overall structure remains. Subdivision of a free-form surface and addition of geometric components has, of course, a wide range of alternatives. Maybe we should combine this with different problems and solutions […]

[GHX:0.8.0066] This is a rather traditional geometry exercise we used to make in MaxScript. Grasshopper is also quite capable of associative geometry and real-time parametric designs of objects. The exercise of designing a furniture family should be based on design research, followed by shape alternatives and sketches (both digital and hand), then might be finalized using this parametric design environment. However, the example presented here is one of the most simplistic […]