The Superformula equation, coined by John Gielis in 2000, is a generalisation of the ‘Superellipse’ or ‘Lamé Curve’ named after Gabriel Lame.
The Superformula is said to describe complex shapes and curves found throughout nature. After some previous work in 2D I decided to explore ‘Supershapes’ in 3D to allow me to hopefully create some more visually interesting experiments. I found Dan Shiffman’s (youtube link) online lessons and coding challenges to be useful during this project – it helped me understand the transformation between 2D and 3D worlds by learning how to create spherical geometry in Processing 3.0 without just using the standard functions e.g. box, sphere etc. This allows you to create a sphere that can be manipulated with mathematical equations such as the Superformula. This mini project was also a great way to learn how to transform the given equation into the Processing language (as can be seen in my notes below) along with how to convert between Cartesian and Polar coordinates.
Formula Conversion into Processing language
Basic Superformula Examples
Taking the knowledge from previous experiments in animating between simple Supershapes, I did some further experimenting. I switched from using the TRIANGLE_STRIP spherical geometry to a points based system and used a moveable camera to create some abstract visualisations.