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.

CHAPTER XI

REPRESENTATION OF WARPED SURFACES
251. The warped surface may be generated by a straight line moving in such a way that its consecutive positions do not remain in the
same plane. Evidently there can be as many warped surfaces as there
are distinct laws restricting the motion of straight lines in this way.
252. The Warped Surface with Two Linear Directrices and a Plane
Directer. The warped surface with two linear directrices and a
plane directer is generated by the movement of a straight line
which constantly touches
two linear directrices and
remains parallel to a plane /
directer.
253. The Hyperbolic /
Paraboloid. The hyper- //
bolic paraboloid is a warped
surface with two rectilin-
ear directrices and a plane
directer. ' i
This surface is repre- / s
sented by locating the two
rectilinear directrices, the / m
plane directer, and a suf- FIG. 109
ficient number of the rectilinear elements, or positions occupied by
the generatrix, to reveal the character of that portion of the surface
under consideration.
254. To assume a Rectilinear Element of the Hyperbolic Paraboloid. See Fig. 109. Let iM-N and O-P represent the rectilinear
directrices, and let S represent the plane directer.
Assume any point, as A, upon the directrix M-N, and through A,
by Section 172, draw the plane T parallel to S. By Section 151
find the point B in which the directrix O-P intersects S, and
103