Algorithms

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 fifth point for each shape and divide subsurfaces into four…

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 of interesting research about him, and he shows us how…

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 of a chain of these constructions creates curves with continuous…

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 subdivision and a combination of vector / plane management to…

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 Grasshopper, I tried to simulate his process by adding real-time…

Here is a funny sketching system for the “SPEC” homework. 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 0 to 30 by 1. After that, polylines are constructed using…

This is the basic definition of one point attractor on a grid of points. 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 difficulty in such definition, because the operational complexity is still very…

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 this construction is the connection from the left side of…

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. However, there were other design parameters such as the sunlight and orientations of each functional cell. Combining a couple of graph components helped me create diverse solutions later used in the functional-formal interpretation phase. Unfortunately, later on, the competition was…

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 we’ve talked about earlier on this website. The same solution…