This was a couple of weeks ago, together with my six-year old son Mete, we decided to make a “ball” out of old memory cards. I was curious about a subdivision method, using only planar quadrilaterals to construct a sphere (named as Sixty Square Sphere. There are a couple of models on www. Of course look much better than mine :=). However my son was expecting a “ball” to play. Then, both of our expectations have been partially met, I think. You see the component configuration of squares that create triangular […]

## square

For the last 10 days I’ve been searching for a proper algorithm in representing surfaces using planar shapes. It is obvious that triangulation is an answer but there is an interesting research topic of planar remeshing using shapes other than quads, hexagons or any other regular polygons. Especially in computer graphics, such things refer to optimization of models to decrease the load of GPUs. In Grasshopper community, this has also been discussed and there is a great implementation at Trada pavilion by Ramboll Computational Design Team (link here). There are […]

This was the first step to the generation of Cairo Pentagonal Tiling. It is the dual of a semi-regular tiling of snub square. The first step was easy. Just dispatch cells of a square grid, then evaluate them according to the ratio of 0.366 approx. which is derived from the bisector of an equilateral triangle. Here is the definition: [GHX: 0.9.0014] Now, we have a snub square tiling, composed of tilted squares, but in order to process it further and explore different potentials, I had to tell Grasshopper about the equal […]

Octahedron is a platonic solid with 8 faces of identical equilateral triangles. It has a close relationship with cube as it’s dual. In order to construct an octahedron, we first have to create a square. Main problem of drawing the square is determining the right angle (perpendicular axis) to any point in euclidean space. We’ll draw it here as a two dimensional projection. However it can also be established in three dimensions with the same method (except using spheres instead of circles). Start from any two point in the space; […]

This is a semi-regular tessellation of vertex arrangement 4.8.8. It’s octagonal and square forms are all generated from data lists provided by new version of subdivide component (Old one was processing points in a different fashion. I don’t know why they changed that). Anyway, a lexical operation is needed to convert this list into a more useful for this exercise. You can download the source definition here [2011_12_25_srtessela]. However you need to define a surface in order to start it. The component labeled with “pattern” is actually the data list […]