A channel or canal surface is a surface formed as the envelope
of a family of spheres whose centers lie on a space curve, its ''directrix''. If the radii of the generating spheres are constant the canal surface is called pipe surface. Simple examples are:
* right circular cylinder
(pipe surface, directrix is a line, the axis of the cylinder)
(pipe surface, directrix is a circle),
* right circular cone
(canal surface, directrix is a line (the axis), radii of the spheres not constant),
* surface of revolution
(canal surface, directrix is a line),
Canal surfaces play an essential role in descriptive geometry, because in case of an orthographic projection its contour curve can be drawn as the envelope of circles.
*In technical area canal surfaces can be used for ''blending surfaces'' smoothly.
Envelope of a pencil of implicit surfaces
Given the pencil of implicit surface