the superellipse explorer

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The Super-ellipse Explorer by Wim van de Velde

Better than fractals?

A surprisingly simple equation, that allows us to generate 'any' shape to infinite precision, very compact, and fast to compute, was invented by a Belgian biologist, researching on the resilience of bamboo... I (Wim) couldn't resist and fabricated (after Ingrid Farasyn reminded me how polar coordinates work) an Excel version. Fascinating, indeed. Anything from straight lines, circles, rectangles, spirals, lemons, petals, flowers, hearts, hairpins, nails, light bulbs, bottle-like shapes to a stylized Pampers logo, ...  with just a few parameters.

Download a Microsoft Excel implementation of the super-ellipse here.  If you find a nice super-ellipse, why not email me the  parameters and I will post the best on this webpage.

Web links on the super-ellipse

• The formula is implemented in a series of plug-ins for the main CAD and graphics illustration packages and soon Microsoft Office, made by Genicap.  See http://www.genicap.com/ or http://www.point1design.com/pages/clients/genicap/index.html.  
• More stunning examples can be found at http://www.genicap.com/gallery/engineering.html or http://www.genicap.com/gallery/3d_illustration.html.
• Genicap as have a white paper at http://www.point1design.com/pages/clients/genicap/tech_super.html.
• See http://mathworld.wolfram.com/Superellipse.html or http://www.geniaal.be/html/fs002science.htm for a mathematical background.