Channel surface

In geometry and topology, 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 a pipe surface. Simple examples are:

• right circular cylinder (pipe surface, directrix is a line, the axis of the cylinder)
• torus (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.