Oloïde

In the universe of the directed surfaces, the oloïde is by definition the convex envelope of two orthogonal circles passing each one by the center of the other. The oloïdes are also called orthobicycle.

This surface is part of developable surface being pressed on the two circles.

The oloïde is a algebraic Surface of degree 8:

$4x^2+4y^2+$

4x^3+4xy^2+4xz^2+

$-7x^4-18x^2y^2-11y^4-6x^2z^2-10y^2z^2+z^4+$

$-8x^5-8xy^4-6x^3y^2-48x^3z^2-52xy^2z^2-8xz^4+$

$2x^6+22x^2y^4+14x^4y^2+10y^6-46x^4z^2-46x^2y^2z^2-50x^2z^4-12y^2z^4-2z^6+$

$4x^7+12x^3y^4+12x^5y^2-4xy^6-12x^5z^2+12x^3y^2z^2+24xy^4z^2-36x^3z^4+$

$x^8-6x^4y^4-8x^2y^6-3y^8+6x^4y^2z^2+12x^2y^4z^2+6y^6z^2-6x^4z^4+12x^2y^2z^4-9x^4z^4-20x^2z^6+6y^2z^6-3z^8=0$

A site on the subject

http://www.heldermann-verlag.de/jgg/jgg01_05/jgg0113.pdf

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