Discovered by Rob Kusner, Director of the Center for Geometry, Analysis, Numerics and Graphics (GANG). The Kusner surface is an inversion of the Boy surface. The three discs are planes "reaching infinity".
Le Topologicon is a great comic book about topology. The author is Jean-Pierre Petit who discovered the first parameterization of the boy surface in 1981. He is also the co-founder of the non-profit organization Savoir-sans-frontiers. The book deals with moebius strips, klein bottles, boy surfaces, magnetic fields, surface stiching and a lot more interesting topics. In my opinion, the Topologicon is a must-read for everyone dealing with surface modelling, mesh modelling, subdivision surfaces, surface tesselation, vector fields, deformations, or topological space. Some example pages:
In topology, a smooth deformation from one surface in an other is called homotopy.The parameterization of this homotopy can be found on wolfram's page.
The Boy Surface has been found 1901 by Werner Boy. One obtains a topologicaly equivalent surface by attaching a Möbius strip to a disk along its boundary. Like the Möbius strip this surface is nonorientable.
This beautiful parameterization, based on complex numbers, was discovered in the late 1980s by Rob Kusner and Robert Bryant. In this post the boy surface has already been mentioned on eat-a-bug.
On this blog I documented some of my findings, ideas, and projects from the years 2009-2013. Its a private and non-commercial website, and the content isn´t updated any more, so please forgive broken links and outdated information. I keep it as a personal archive.
Discovered by Rob Kusner, Director of the Center for Geometry, Analysis, Numerics and Graphics (GANG). The Kusner surface is an inversion of the Boy surface. The three discs are planes "reaching infinity".
In topology, a smooth deformation from one surface in an other is called homotopy. The parameterization of this homotopy can be found on wolfram's page.
A proposal for a pavillion by Christophe Delsart and Yvan Ngnodjom based on the boy surface for the ARPAM project.
Download the definition here
NURBS surface generated with grasshopper 
KleinBottle.zip
Created with gifery.com
