Elements of descriptive geometry, with applications to isometric projection and othe forms of one-plane projection; a text-book for colleges and ingineering schools by O. E. Randall.

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DESCRIPTIVE GEOMETRY

228. The Development of Surfaces. By the development of a
surface we mean its rectification, or its measure or appearance
when laid out on a plane.
Just as a curved line is rectified by rolling the curve out on
a rectilinear tangent to the curve, so a surface is developed by
rolling the surface out on a plane tangent to the surface.
In cases of prisms and pyramids, or of any surfaces made up
of plane faces, the plane of one of the faces is taken as the plane
of development, and the successive faces are brought into coincidence with the plane of development by revolving them one
after another about the edges as axes.
In cases of cylinders and cones, or other surfaces of single
curvature, a plane tangent to the surface along some element is
taken as the plane of development, and the surface is then rolled
out element after element, peeling off, as it were, the outer
coating of the surface and spreading it out on the plane.
The development of a surface may be used as a templet, or
pattern, for cutting out a plane surface form, which by a process
converse to that employed in development may be made to take
the shape of the original surface.