Points by Curvature

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 positive ones maybe).

The development of geometry began by measuring the world as discrete objects. Moving beyond measuring nature, it evolved into reasoning, calculation, and mathematics. Platonic solids were one of the most elegant and beautiful ideas reached by geometry. Pondering why there are only five of them was a tribute to collective human intelligence. Earlier in this blog, we modeled polyhedra, like the Platonic solids, using geometric construction methods. This process was like solving a puzzle. To construct a point whose distances…

This is another popular “math surface” being rediscovered by designers nowadays, in 2012. Saddle surfaces, seen above as mentioned earlier (here) have a special type named “Monkey Saddle Surface”. This surface was a dramatic example of how Grasshopper can control equations and instantly show graphical results. The mathematical equations start with Z=… this makes it very easy for us to transform any x-y grid centers (a 2d data tree of 3d points) and add z values to them according to…

This is a basic formation of component-based design in a dataflow environment. A double-curved surface is subdivided and re-constructed using straight sections. Parametric model of a surface construction by variable components. The main data list of subsurfaces are distributed into four distinct lists, that will be used to construct lines out of double-curved quadrilateral faces. Such definitions could be further advanced by adding a precise fabrication detail.

As the design of free-form architectural surfaces becomes easier, questioning and foreseeing the feasibility of the construction of these surfaces becomes important. Such an inquiry requires sufficient knowledge of architectural geometry besides the knowledge of materials and structural systems. In this article, we present a preliminary example of a guide. It supports the design and production process of building surfaces with different geometric properties is presented. This guide aims to reveal the relationship between Gaussian curvature and surface paneling. It…