## equation

Previous studies on trigonometric surface equations showed me an interesting alternative. This is the modification of the breatstroke surface definition (here). This time, I’m trying to fix the equation and change input values in a fashion that the waves of the surface is not symmetrical. Here are a few experiments on it; (Size, 44.8, X=10, Y=5, animating X’s from 0 to 32) (Size: 42, X=7, Y=5, animating X’s from 0 to 32) (Size: 38.1, X=3, Y=5, animating X’s from 0 to 32) The equation is (cos(y²) – sin((x/5)-y²)) * 10. […]

This was before Spherical Fantasies, while I was tring to update my surface equation definition. In between designerly intentions and mathematical facts, it’s hard to maintain a process, while keeping the definition yet simple and open to exploration. Grasshopper definition is here: [GHX: 0.8.0066] A little tired of mathematical definitions, I started to give names to the animate surfaces I develop. Like the Spherical one, this is also a trigonometric equation of z = cos(x) + sin(x-y2) / 2. The most boring part of these are becoming the sliders. I wanted […]

This is about conforming distortions on surfaces and creating imperfect (say ugly) surfaces. I started with planar surfaces, however continued with spherical ones. There are interesting results when applying trigonometric functions to spherical surfaces. Example surface equations: W=(sin(x*y)) / 2 and W=(cos(x)+sin(x-y²)) / 2 Please be patient if animations are loading slowly. But they represent a way of creating free-form-looking surfaces, highly mathematical behind the scene. Here is the Grasshopper definition: [GHX: 0.8.0066] As you see, I used UVW coordinate system of the sphere, subdivided into 20 pieces. W represents […]

[GHX: 0.8.0066] This is another popular “math surface” being rediscovered by designers. Saddle surfaces, (on the right) as mentioned earlier (here) has another type named “Monkey Saddle” (on the left). This surface was a dramatic example of how Grasshopper is capable of controlling equations and showing graphical results instantly. 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 adding z values to them according to that equation. Monkey Saddle’s center point (0,0,0) […]