A surface of revolution is a surface generated by revolving a plane
curve C about a line L lying in the same plane as the
curve. The line L is called the axis of revolution
For the construction of this surface let L be the
z-axis. In order to construct a surface of revolution using a
parametric equation, it is important to first understand how a circle
is constructed in the plane since the surface is made up of a series
of circles at various heights. That is, if one slices the surface
with a plane that is parallel to the xy-plane, the intersection
is a circle. The parametric equation for a circle of radius 1 in the
xy-plane is
In a surface of revolution, the radius may be different at each height, so if the radius at height v is r(v), then the equation of the surface is
where
Optical Illusion & Projection in Domes: A Study of Guarino Guarini's |