Channel surface: Difference between revisions
Content deleted Content added
Salix alba (talk | contribs) add a reference |
Salix alba (talk | contribs) add image of torus and focal curves |
||
| Line 1: | Line 1: | ||
[[Image:Torus and focal line.png|thumb|right|300px|A section of a [[torus]], a special case of a cyclide. The black lines are the two sheets of the focal surface, which here both degenerate to curves. The surface can be generated as envelopes of spheres centered on these lines.]] |
|||
A '''channel''' or '''canal surface''' is a [[surface]] formed as the [[envelope (mathematics)|envelope]] of a family of [[sphere]]s whose centers lie on a [[space curve]]. One sheet of the [[focal surface]] of a channel surface will be the generating curve. |
A '''channel''' or '''canal surface''' is a [[surface]] formed as the [[envelope (mathematics)|envelope]] of a family of [[sphere]]s whose centers lie on a [[space curve]]. One sheet of the [[focal surface]] of a channel surface will be the generating curve. |
||
Revision as of 08:44, 15 May 2007
A channel or canal surface is a surface formed as the envelope of a family of spheres whose centers lie on a space curve. One sheet of the focal surface of a channel surface will be the generating curve.
A surface of revolution is a channel surface whose centers lie on a straight line. Dupin cyclides form a special class of surfaces which are channel surfaces in two distinct ways: for cyclides both sheets of the focal surface are curves; in fact they are both conics sections.
References
- Hilbert, David; Cohn-Vossen, Stephan (1952). Geometry and the Imagination (2nd ed. ed.). Chelsea. p. 219. ISBN 0-8284-1087-9.
{{cite book}}:|edition=has extra text (help)CS1 maint: multiple names: authors list (link)
 | This geometry-related article is a stub. You can help Wikipedia by expanding it. |