I learnt this method from the open math resources website. I couldn’t help myself repeat it in Rhinoceros. It was quite fun to solve circle tangency problems in 2D, this is one of them: drawing the circle that passes three given points, not using ready-made commands but only geometric tools of circle (compass) and ruler (line). Here is the sequence of it: First of all, we need to know that the circle we are looking for is centered at somewhere on the perpendicular paths between the points. This means, we […]
First year Architectural Geometry course includes euclidean constructions as a study of associative geometry. We have exercised below questions to study this topic. These are three mutually tangent circles, that can be drawn using only compass and ruler, without built-in tangency functions in Rhino. Such exercises are expected to improve students’ reasoning. We believe architectural geometry education should encourage a conception that allows students to think about what they are doing and control their process, rather than just using commands to produce forms randomly.
Since last week, I’m very curious about circle packing. There are a couple of complete solutions on the internet. I’m still at early steps of such a solution yet. A full circle packing means that it does not include any gaps and each circle is tangent to all possible neighbors. Sounds easy in Grasshopper but I couldn’t see any solution yet. There a some circle packing attempts but they have gaps. Also I don’t want to use an evolutionary solver (Galapagos) or physical engine (Kangaroo) because I believe there is […]
After a couple of days with studying the mysterious Doyle spiral, I’ve decided to test an approach of circle packing from conformal geometry. Poincare disk (studied earlier at here, here and here and here) is used as the hyperbolic representation of space. First, I linked a regular hexagonal grid data structure and rebuilt it after the hyperbolic distortion finding this result: Pretty much like a voronoi subdivision, but a very different thing in fact. My second attempt was to create a circle packing out of this: However I couldn’t manage to […]
This was an interesting challenge for me to find out if an architect can use Visual Programming Languages (VPL’s) also for graphical purposes? Now, I would say “not exactly” because this definition took much time than I expected. The aim was to create an algorithm for a business card design that has variable outputs. Each card should be different, but without using any randomization. This is achieved with a definition you can check here: [2012_01_10-cards] and Rhino file here [3DM:2012_01_10-cards] to take inputs such as your name and e-mail address. This project […]
Trying to create above pattern (as described in Sunflower Spiral) as simple as possible, this definition (can be downloaded here: [2011_12_24_circles] creates not only spirals, but also capable of more fundamental tessellations. Maybe a three-dimensional equivalent should be studied.