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 […]

Since the mid-20th century, the hyperbolic paraboloid surface has been one of the most popular mathematical forms for architects. Named Hypar in short, this is the Quadric Surface equation of the Hyperbolic Paraboloid. Erik Demaine summarizes several examples from architecture such as the roof of the Girls’ Grammar School in London (designed by Chamberlin, Powell, and Bonn), the Philips pavilion at the 1958 Brussels exhibition designed by Le Corbusier, and […]

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 […]

An octahedron is a polyhedron and platonic solid with 8 faces of identical equilateral triangles. In this post, I will try to explain the drawing and unrolling process of the octahedron. It has a close relationship with the cube as it’s dual. In order to construct an octahedron, we first have to create a square. The main problem of drawing the square is determining the right angle (perpendicular axis) to […]

[2011_12_25_divide] here is the fundamental of surface subdivision in Grasshopper. In order to design a parametric truss exercise, this is the 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 potential regarding attraction with other entities, such as point or […]

I am learning Grasshopper. In this Circle Crossing definition, I tried to create the above pattern (also described in Sunflower Spiral) as simply as possible, this definition creates not only spirals but is also capable of more tessellations I guess. Maybe a three-dimensional equivalent might be studied in the future. As you can see from the definition, I started with a large circle. Then, I divided it into segments and […]

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 […]

Recording History in Rhinoceros3D has interesting potential. You might utilize it in the process of design exploration. We’ll try to show its concept and limitations; First, build two surfaces; one is planar at the world XY plane, and the other represents 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 the “Record History” button […]

The dodecahedron is a Platonic Solid with 12 equilateral pentagonal faces. It has a close relationship with its 20-sided dual, Icosahedron. Mete Tüneri showed the following method of Dodecahedron construction, using only distances, corners of the pentagon, and a visionary 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 […]

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 […]

This experiment is based on a traditional surface-component definition. However, the variation of components 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 its 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 […]

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 the singularity of design artifacts 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 […]

Icosidodecahedron is an Archimedian Solid, a thing in between the Platonic Solids of Icosahedron (d20) and Dodecahedron (d12). It is a rectified version of an Icosahedron, constructed by dividing every edge into two equal segments and joining these segments to create a composition of equilateral pentagons and triangles. Archimedian Solids consist of at least two equilateral polygons, whereas Platonic Solids are constructed by only one. We’ll deduce an Icosidodecahedron from […]

Sunflower Spiral (or Phyllotaxis) can be constructed in Grasshopper according to Vogel’s model of parametric relationships. This model uses polar coordinates. You can download the Grasshopper definition file here: (The Grasshopper file is still working after more than 11 years -15.12.2022. This is such a powerful quality of Grasshopper, I think.) It’s a good example of utilizing polar coordinates. It’s also fun to play with the parameters and constraints of […]

We’ll use the “Animate” function in Grasshopper3D to create a stop-motion animation. First, you need to determine the parameters you’ll animate, which means defining 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 which is the value of “t” between 0.0 to 1.0. This single change affects various […]

Today’s polyhedra is the beautiful icosahedron. It is one of the five Platonic Solids with twenty equilateral triangular faces. Its dual is the dodecahedron, which has pentagonal faces. Here, I explained the process of modeling an icosahedron. After creating 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 the pentagon’s edges. You […]

A truncated Tetrahedron is an Archimedian Solid, created by slicing a Tetrahedron. Its faces are regular hexagons and triangles. Assuming you’ve created a Tetrahedron, first join its 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 create the […]

This is a semi-regular tessellation of vertex arrangement 4.8.8. Its octagonal and square forms are all generated from data lists provided by the new version of subdivide component (The 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 one for this exercise. You can download the source definition here […]

The tetrahedron is a platonic solid with 4 equal triangular faces (which are also equilateral), 6 equal edges, and 4 vertices. While creating this shape, we will take a closer look at length transfers using compass-like tools both in two and three-dimensional space. In order to define the edge length of the first triangle (which is a straight line), start with any two points in cartesian space. Using a compass […]

The smooth and continuous nature of the “Sine Surface” has garnered significant popularity among designers and architects alike. This captivating curved surface offers a visually pleasing aesthetic that adds an elegant touch to various design projects. Its flowing contours and gentle undulations create a sense of harmony and organic beauty. Recently, I delved into this with the help of Grasshopper’s Graph Mapping functionality, I began my artistic journey. Although I […]