The cylinder is a surface of revolution. The
slice through a cylinder parallel to the base at any height is a circle of
the same radius as the cylinder. Let *r* denote the radius of the
cylinder and *v* be any height. Then, the parametric equation for the
cylinder is *r*cos*u*, *r*sin*u*,
*v*)*v* for the cylinder,
it is important to note where the origin is and where the cylinder is in
relation to the origin.

The construction of this cylinder is based on measurements from a side-elevation. The radius is 6.40 cm, the height
is 5.30 cm, and the origin is located at the center of the base of the
base cone. Above the cylinder is the trapezoidal layer which has a
measured height of 2.55 cm. Consequently, the top of the cylinder has
*v* equal to -2.55 and the bottom has *v* equal to

where the range of *v* is [-7.85, -2.55] and that of *u* is [0,
2pi]. Notice that in the computer model image, the cylinder contains
alternate segments that are left out in order to represent windows as seen
in the side-elevation.

Optical Illusion & Projection in Domes: A Study of Guarino
Guarini's Santissima Sindone |