A 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 canal surface will be the generating curve. An open surface with X-, Y-, and Z-contours shown. ... The form of envelope treated here is a manifold that manages to be tangent to some point of each member of a family of manifolds. ... A sphere is a perfectly symmetrical geometrical object. ... In mathematics, the concept of a curve tries to capture our intuitive idea of a geometrical one-dimensional and continuous object. ...

A Surface of revolution is a canal surface whose centers lie on a straight line. A Dupin cyclides are special class of canal surfaces, where the generating curve is conic section. For cyclides both sheets of the focal surface form conics sections. The parabola y=x2 rotated about the z-axis A surface of revolution is a surface created by rotating a curve lying on some plane (the generatrix) around a straight line (the axis of rotation) that lies on the same plane. ... In mathematics, a cyclide is the geometric inversion of a torus. ... It has been suggested that Latus rectum be merged into this article or section. ...