## December 2011

In the post of “animated parameters” we created a video file using Grasshopper’s “animate” functionality. A sequence of images are then joined together to form a video file. This time, we’ll create an animated gif image that can be played on web without even using a video player. It is a much simplier solution but however it does not have the potentials of a “real” video file such as mp4 or flv. If you own photoshop cs5, just open the first frame you’ve generated from “animate” function in Grasshopper and activate […]

One of the most interesting mathematical forms for architects, since mid-20th century is the Quadric Surface equation of Hyperbolic Paraboloid. Erik Demaine has put a short biography together in his website. According to him; Hypars and joining hypars in a few special ways have been used extensively in architecture. For example, Curt Siegel’s 1962 book Structure and Form in Modern Architecture (page 256) illustrates the roof of the Girls’ Grammar School in London (designed by Chamberlin, Powell, and Bonn) which is what we call a “5-hat” with five hypars spread apart slightly. […]

When an educational system does not meet the requirements of a paradigm, new teaching approaches start to emerge. Today, design computing pushes forward a similar transformation on architectural education. Design studio, as the dominant setting for architectural learning, is the center of this transformation. There are numerous researches, experiencing and defining this transformation from various perspectives as “cases”. However as Oxman (2008) highlights, we still need to define a general pedagogical formation for digital design instructors, taking one more step after the popular cognitive explanation of Schön and Wiggins (1992). […]

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; […]

[2011_12_25_divide] here is the fundamental of surface subdivision in Grasshopper. In order to design a parametric truss exercise, this is generally accepted starting point. Get a surface from the file, subdivide it into U and V directions to create point lists and then manipulate these points to create something interesting. Having a list of points would also present good potentials regarding attraction with other entities, such as point or curve attractors. As you probably notice, this is the new version of Grasshopper, which also includes NURBS objects. As a parametric […]

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.

This time, in order to develop a potential “dummy” surface for Grasshopper experiences, I built a better definition. The Graph Surface definition uses a polygon as a basis, divides the edges and moves them according to various parameters. It’s fun to play with mapping different graph types and various polygons and subdivision values. Surprisingly, this definition led me to a wide range of possibilities I haven’t planned. Especially, shifting the graph along the edge of polygon (as seen above) creates interesting moves. You can download and test the definition here: [2011 12 […]

Record History functionality in Rhinoceros3D has interesting potentials which might be utilized in a process of design exploration. We’ll try to show it’s concept and limitations; First, build two surfaces, one is planar at world xy plane, and the other represents … say the “initial” form of your design. Put another surface on the planar one, as if it’s an ideal “component” of the finished geometric composition. Activate “Record History” button at the bottom of Rhinoceros window, then array your component on the planar surface. You’ll see the Record History […]

Dodecahedron is a Platonic Solid with 12 equilateral pentagonal faces. It has a close relationship with it’s 20-sided dual, Icosahedron. Mete Tüneri showed the following method of Dodecahedron construction, using only distances, corners of pentagon and a visionay equilateral triangle underneath. We’ll construct Dodecahedron, assuming that we’ve drawn an initial equilateral pentagon. We need to find out the pentagon’s angle of 3d rotation. First, put spheres at points a and c, with the radius of a to c. Intersection of these spheres result a circle. We know that, every point on […]

NURBS surfaces by nature, like four-corner topologies with U and V directions. Şebnem Yalınay Çinici has formulated a tectonic exercise of “Primitive Hut”, which in my point of view is a tough geometric challenge; a subdivision on a real three-corner manifold. That seems very easy at the beginning as both Rhinoceros and Grasshopper are able to create surfaces with three corners, by either lofting, meshing or edge curve methods. However, those surfaces, then cannot be used to develop sub-surfaces because the need to define U and V directions. Then, Rhino seems […]

This experiment is based on a traditional surface-component definition. However, the variation of component is associated with Gaussian curvature. We just control the subdivision and a multiplier value. Results are interesting in as an educational tool to explain NURBS surface curvature and it’s utilization for Design Geometry. Different surface shapes generate exciting results. Of course this could be much improved by recognizing positive and negative curvature values, (probably only accepting positive ones maybe). Grasshopper definition can be downloaded here [2011_12_22_gauss].

ARCH 362: PARAMETRIC MODELING : Undergraduate Elective Course at İstanbul Bilgi University Faculty of Architecture student exercise: Deniz Yazıcı (YTU/CADU 2008)   COURSE BRIEF (2011) Digital paradigm transferred parametric modeling as an alternative conception in architecture, emphasizing a focal shift from singularity of design artifact to the explicit and generative process of designing. While architects start to experience the construction of algorithms, computers played an increasingly important role in the adaptation of this new conception utilizing design geometry. Architectural education also started to evolve itself to meet the requirements of this […]

Icosidodecahedron is an Archimedian Solid, a thing in between the Platonic Solids of Icosahedron (d20) and Dodecahedron (d12). It is a rectified version of Icosahedron, constructed with dividing every edge of it into two equal segments, and joining these segments to create a composition of equilateral pentagons and triangles. Archimedian Solids consists of at least two equilateral polygons, whereas Platonic Solids are constructed by only one. We’ll deduce an Icosidodecahedron from Icosahedron below; First, you should create an Icosahedron, the Platonic father of Icosidodecaheron. After that, all faces should be […]

Last update of Grasshopper3D brought powerful new components. As you can see, “the famous self-styled indicator” of a computational design process, has now became “public”, as the connectivity diagram can now be constructed as volumetric (3d). Another new component distributes desired number of points into a volume. Coupling them, we may at last say R.I.P. to Mr. Georgy Voronoi, and get going further on.

Sunflower (or Fermat’s, or Phyllotaxis) spiral can be constructed in Grasshopper3D according to the Vogel’s model of parametric relationships using polar coordinates. Definition file can be downloaded here [GHX: 0.8.0066] It’s a good example of utilizing polar coordinates. It’s also fun to play with parameters and constraints, also there are very interesting results if you also connect the polar angle value to the “z” of point component

First, you need to install Grasshopper3D plug-in to Rhinoceros3D. If you did so, you may run the plug-in by typing “grasshopper” on the command bar. In this post, we will show you how to put an icon to the Rhinoceros3D interface that calls “grasshopper” command.                               Go to “Tools / Toolbar Layout” from the application menu. In Toolbars window, select “Standard” and hit “Toolbar / Add Button” menu item. Now, a new empty button is added to […]

We’ll use “Animate” function in Grasshopper3D to create a stop-motion animation. First, you need to determine the parameters you’ll animate, that means to define maximum-minimum values of it. In our example, we’ll be using a simple bezier curve generation algorithm. You can download it here [2011_12_21_bezier curve.ghx]. In this definition, we plan to animate one parameter that is the value of “t” between 0.0 to 1.0. This single change effects various things in the model. You may find them by studying the definition. There is a list of points moving along […]

Icosahedron is one of the five Platonic Solids with twenty equilateral triangular faces. It’s dual is Dodecahedron, which has pentagonal faces. Here, Icosahedron is constructed by using pentagons. Interesting thing is it’s close relationship with Dodecahedron, although they seem to be very different. This time we won’t lose time with two dimensional pentagon drawing. Maybe we’ll discuss that later. Assuming you’ve created a regular pentagon, you should find the “tip” point of the Icosahedron by intersecting spheres from at least three of the corner points with a radius of pentagon’s […]

Truncated Tetrahedron is an Archimedian Solid, created by slicing a Tetrahedron. It’s faces are regular hexagons and triangles. Assuming you’ve created a Tetrahedron, first join it’s faces to create a polysurface. Now, you may re-create the lines of Tetrahedron’s edges, either by drawing them or generating them (Curve/Curve from Objects/Duplicate Edge). While the edge lines are selected, hit (Curve/Point Object/Divide Curve By/Number of Segments) and type 3 to the number of segments to be created. Now all edges should be divided equally into three parts. Draw the equilateral triangles, connecting the […]

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 […]