The Extended Oloid and Its Contacting Quadrics. Basel, U. & Dirnbock, H.
abstract   bibtex   
The oloid is the convex hull of two circles with equal radius in perpendicular planes so that the center of each circle lies on the other circle. It is part of a developable surface which we call extended oloid. We determine the tangential system of all contacting quadrics Qλ of the extended oloid O where λ is the system parameter. From this result we conclude parameter equations of the touching curve Cλ between O and Qλ, and of the edge of regression of O. Properties of the curves Cλ are investigated, including the case that λ → ∞. The self-polar tetrahedron of the tangential system Qλ is obtained. The common generating lines of O and any ruled surface Qλ are determined. Furthermore, we derive the curves which are the images of Cλ when O is developed onto the plane.
@article{basel_extended_nodate,
	title = {The {Extended} {Oloid} and {Its} {Contacting} {Quadrics}},
	abstract = {The oloid is the convex hull of two circles with equal radius in perpendicular planes so that the center of each circle lies on the other circle. It is part of a developable surface which we call extended oloid. We determine the tangential system of all contacting quadrics Qλ of the extended oloid O where λ is the system parameter. From this result we conclude parameter equations of the touching curve Cλ between O and Qλ, and of the edge of regression of O. Properties of the curves Cλ are investigated, including the case that λ → ∞. The self-polar tetrahedron of the tangential system Qλ is obtained. The common generating lines of O and any ruled surface Qλ are determined. Furthermore, we derive the curves which are the images of Cλ when O is developed onto the plane.},
	language = {en},
	author = {Basel, Uwe and Dirnbock, Hans},
	keywords = {⛔ No DOI found},
	pages = {17},
}

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