#grasshopper

Here is a method for coding the dodecahedron and all its irregular variants in Grasshopper as quickly as possible. I utilized the golden ratio rectangles, usually used to construct the sister polyhedron, the icosahedron. However, the magic component of the Grasshopper, the Faceted Dome rescued me again to generate the dual of it, the dodecahedron. This is a special platonic solid, which has 12 regular pentagonal faces. There are several techniques that I generally prefer to use in Grasshopper. You…

This is the continuation of my previous study on the Fibonacci lattice on a spherical surface, creating a Fibonacci Dome structure. The panelization of curved forms with flat surfaces has been a favorite topic in architectural geometry. The trigonometric layout of the Fibonacci sequence generates a spherical formation, while the Faceted Dome component handles planarity. Here, I further enhanced the previous code into a pavilion design. The essential part of the code is about the placement of points on the half…

This work emerged out of necessity. In the design and application process of wooden frame structures, where we put thousands of pieces together like a puzzle, the issue of preparing and updating quantity and measurement lists requires the most effort. Hours spent on this and the possibility of making mistakes are very high. However, with the Quantity Surveyor I developed in Grasshopper, you can generate measurement lists almost in real-time. All that needs to be done is to model each…

The regular dodecahedron is one of the five Platonic solids, characterized by having 12 regular pentagonal faces, 20 vertices, and 30 edges. When you elongate it, you extend its structure in one or more directions, resulting in a shape that retains the basic properties of the dodecahedron but is stretched out. The elongated dodecahedron might not catch your eye at first—it’s just a long version of a shape you’ve probably seen before, and it seems pretty basic. But don’t be…

Today’s computational curve is the beautiful Sierpinski Triangle. It is a fractal named after the Polish mathematician Waclaw Sierpinski, who described it in 1915, though it had been previously described by other mathematicians. It is a self-replicating pattern that arises from a simple recursive process. To construct the fractal, you start with an equilateral triangle and then repeatedly remove smaller equilateral triangles from its interior, leaving holes. Each iteration involves dividing each triangle into four smaller triangles and removing the…

The rhombic dodecahedron is a polyhedron with twelve rhombus-shaped faces, where each face has four sides of equal length. It is possible to construct the space-filling variant of the rhombic dodecahedron by arranging multiple such rhombic dodecahedra in a regular pattern so that they fill space without leaving any gaps. In his 1611 work on snowflakes titled “Strena seu de Nive Sexangula,” Johannes Kepler observed that honey bees utilize the geometric structure of rhombic dodecahedra to construct honeycombs. These honeycombs…

Lissajous curves, named after the French physicist Jules Antoine Lissajous are a family of curves that emerge from the interaction between two harmonic oscillations. They have applications in various fields including physics, engineering, and signal processing. They are commonly used in electronic devices such as oscilloscopes to visualize the phase relationship between two oscillating signals. Similarly, they are also useful in mechanical engineering for analyzing and designing mechanisms that involve harmonic motion. Lissajous curve functions can help in understanding the…

Geodesic refers to the shortest path between two points on a curved surface. It is based on the principles of geodesy, which is the science of measuring the Earth’s shape. On the other hand, in architecture and design, a geodesic dome is a spherical or hemispherical structure consisting of a network of geodesic lines (great-circle arcs) forming triangles. Therefore, the dome’s framework provides strength and stability, distributing stress throughout its structure. Buckminster Fuller popularized and developed the concept of the…

Stellated polyhedra are three-dimensional geometric shapes formed by extending the faces of a regular polyhedron (a solid with flat faces) beyond their original boundaries until they intersect with each other. The term “stellate” comes from the Latin word “stella,” meaning star and these polyhedra often have a star-like appearance due to their extended faces. They are popular because of their aesthetic qualities. I studied these forms many times before. This time, I implemented the stellations and negative stellations (the excavated…

I have been studying the Bezier-De Casteljau algorithm for several years. Last week, I finally managed to understand and implement B-Spline Construction in Rhino and Grasshopper Python code, using the Cox-De Boor algorithm. This algorithm calculates the effect of control points on a B-Spline with many control points. After this, I am not limited to the degree+1 control points. This animation shows both algorithms working together. This Rhino Python code in a Grasshopper definition can handle three tasks. The first…