We can create tessellations of outer points in a Poincare Disk, using the manual method explained in the last post (here). But repeating that compass and straightedge process is becoming a little useless after a couple of repeats. If you say “ok. I understood the concept, let’s get faster!” then we can model just the same process in Grasshopper3D to examine varying results in seconds; If we connect any grid of points into this definition, we can clearly see the similar result we obtained by actually projecting the hyperbolic surface on […]

## July 2012

Poincare disk is still an interesting representation of hyperbolic space for me, full of mysteries. I’ve had several attempts to understand it previously (here and here). Finally I found a resource* explaining basic concepts about it. I tried to repeat some of the constructions in Rhinoceros, (without any logical purpose). The most important part is the conversion of an Euclidean point into a hyperbolic space. There is no clear formula, directly projecting a point into Hyperbolic space, but the method seems very interesting to me because we can do this […]

Previous studies on the timer component were based on understanding it’s use. This time, I tried to implement it in a geometric design task. Moreover, manipulating timer component to change the regular animation of parameters. Time does not have to be equally divided sequences. Rather, new possibilities may be emerged with different time flows. A simple triangulation system is developed with a potential manipulation, based on a timer. This definition is exciting and new for me because I’m not designing geometry here, rather I’m trying to manipulate the flow of […]

Joseph Bergin‘s pedagogical patterns for computer science education returned my attention to teaching methods I’ve searching for almost five years. Here is a phrase from a paper submitted to pedagogical pattern language project: Most educators and trainers are not taught how to teach. Rather, they often find themselves teaching by accident. Typically, a person with a skill that is in demand, such as a particular programming language, will be asked to teach it. People assume that if the person is good in this programming language, she will be good at teaching it. But knowing […]

We can model a musical composition using native Grasshopper components. After the experiments with timer component (here and here) I managed to build a definition that allows us to produce outputs in various time intervals. I converted a small part of Bach’s Bouree in E-Minor into Grasshopper as a guitar tablature. I used Guitar Pro 5’s MusicXML export function to convert classical guitar tablature into XML data, then organized that file in Excel to suit my datatree design in Grasshopper. The Vb.net script is freaking small here just sending number […]

[GHX:0.8.0066] Here is today’s improvement on my metronome with timer component, which started here. It’s very easy to tell Grasshopper about seconds and organize it according to it. Using an interval smaller than 1 seconds, this small script catches every second and returns a different value. However, it’s much harder to implement smaller values than seconds. It seemed easy at first sight but getting accurate results smaller than seconds require working with milliseconds. You can output current milliseconds value but there is another mechanism needed if I want to tell Grasshopper […]

Logical structure of computer-aided architectural design tools is based on object orientation. New design methodologies named Building Information Modeling or Virtual Building aim to improve this structure by synchronizing the digital object classes with real architectural products. Therefore, CAD becomes smart and parametric. But from the design educator’s point of view, most of the commercial CAD tools are not useful and too complicated to implement basic spatial concepts. This is the introduction to above conceptions using a short-term design exercise. Students at their first year of architectural education are introduced […]

This was before Spherical Fantasies, while I was tring to update my surface equation definition. In between designerly intentions and mathematical facts, it’s hard to maintain a process, while keeping the definition yet simple and open to exploration. Grasshopper definition is here: [GHX: 0.8.0066] A little tired of mathematical definitions, I started to give names to the animate surfaces I develop. Like the Spherical one, this is also a trigonometric equation of z = cos(x) + sin(x-y2) / 2. The most boring part of these are becoming the sliders. I wanted […]

This is about conforming distortions on surfaces and creating imperfect (say ugly) surfaces. I started with planar surfaces, however continued with spherical ones. There are interesting results when applying trigonometric functions to spherical surfaces. Example surface equations: W=(sin(x*y)) / 2 and W=(cos(x)+sin(x-y²)) / 2 Please be patient if animations are loading slowly. But they represent a way of creating free-form-looking surfaces, highly mathematical behind the scene. Here is the Grasshopper definition: [GHX: 0.8.0066] As you see, I used UVW coordinate system of the sphere, subdivided into 20 pieces. W represents […]

This is probably the most simple definition on this site but I think it’s very useful. Timer is a special component of Grasshopper that is significant in terms of real-time sketching paradigm. This basic use of timer includes a 1 second update to a Vb script. Inside of the script, system date’s seconds are returned, so we see a real-time increasing number at the output A. Beyond this point, It’s up to your imagination, how you can use that number. When I was a kid, we used to write programs […]

Truncated Icosahedron (5,6,6) is an Archimedian Solid, probably the most popular one because of it’s apperance as the soccer ball. It’s constructed by trimming one third of each edge of an Icosahedron, (a Platonic Solid described here). In order to find 1/3’s of each edge, I used duplicate border, explode and divide commands to get the points that construct the pentagons and hexagons, while paneling is done by using planar surface commands on closed polyline edges. (If you are interested in how we reached the initial solid, refer to the […]

Here is an interesting six-year-old quote from Rivka Oxman, telling us about a potential class of designers. The particular character, type, class or whatever we call could be more sophisticated people than we imagine today. It tells me that, advances in design computing does make high-end techniques available for large communities, and re-define basics of architectural geometry for everyone in digital age, but always there seem to remain a small group of avant-garde. If Ms. Oxman is right, then the question is, where will the balance be between “design” and […]

Truncated hexagonal tessellation (or named as 3-12-12) is represented in a hyperbolic space (as far as I understood it). The idea is simple if you don’t mix with complex equations. Below is the 2-dimensional representation of hyperbolic projection. Paper space is defined by the thick line there. Projection is based on a two-sheet hyperboloid surface. Euclidean version of this tessellation is described here. Here is the Grasshopper3D file containing above idea of hyperbolic representation of a semi-regular tessellation. [GHX: 0.8.0066] (Don’t left click it, right-click and save it to your computer)

[GHX: 0.8.0066] This is my second attempt on getting into non-euclidean representations of space. Althouth it seems easy at first sight, this represents a close point of theory between mathematics and contemporary computational design geometry. As always, architects tend to use mathematical terms such as “non-euclidean geometries” but as far as I saw, most of them have no idea about what it is. So, I’m trying to learn and understand this connection by experiencing small parts of it, sailing at the edges of architectural geometry, but trying not to get into […]