Grasshopper: Superformula Tower

This workshop will utilize grasshopper to create a volumetric surface based on a series of the superformual equations: http://en.wikipedia.org/wiki/Superformula

In the workshop the tower is composed of five curves, though only three are used here for cleaner definition screenshots.

Fig 1. A collection of example curves using the superformula from wikipedia.

Our first step will be to create a curve using Grasshopper's function, xyz vector, and cv curve node.

To create a tower of these curves we copy that set of nodes 3x times. We then link a slider which will determine curve height to the z values of the xyz vector, with an expression multiplying that height by 0,1,2 based on which set of curves we are working with. To expand our ability to tweak the curve set we link a graph to one of the variables in our equations using the "list item" node to select the appropriate value. In this case I link the output of the graph to the "a" variable, however you can explore varying any of the variables in the function.

In order to create more control of the geometry we will attach a graph similar to the one we used for the variables to a scale node. In order insure that our curves will scale relative to their centers, we link the curve outputs to a brepArea node which will give us the curve centroid.

For the final step we will input the outputs of the scale node to a loft node holding "shift" to allow us to input multiple streams into the loft node. It is important to input the nodes in the order that they are being lofted. For this example I turned on closed surface under loft options.