Super Ellipse

Because Super Shape does not look like a great fit for Stained Glass design generation, I had to continue on researching the topic of formulas. This time I tried out the Super Ellipse.

The Super Ellipse has 3 parameters of which 2 are for regulating the size of the shape across x and y axis. The other one is a more important parameter which is used to achieve different curvatures of the shape.

However, it could be extended a bit more, introducing another exponent m. With this addition, the shape can have two control points for the curve.

I’ve made a Processing script to test it out and see how it would perform.  Here are some examples of what Super Ellipse is capable of:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Then, I made some adjustments to the formula so that only 1/4 of it is rendered due to the reason that I need to generate a line / curve. Moreover, it turns out that out of 4 parameters, two of them could be used to generate starting and ending coordinates of the curve which is exactly what I need.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This is a very versatile formula as it is capable of generating straight lines, smooth curves, and 90° angles. So far, it does look like a potential function for further development.

Here is a website where the Super Ellipse is plotted on the graph