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.

100

DESCRIPTIVE GEOMETRY

at d, or at e, according as 0 is assumed on the upper or on the
under surface of the cone.
Assuming the point on the upper surface of the cone, the element in question will be vertically projected at b'-d', and the
point 0 must be vertically projected at ot on the straight line
through o, perpendicular to G-L.
243. Shade Lines. Shade lines upon cylindrical and conical surfaces, since such lines are purely imaginary elements of the surface,
unless they occur at the intersection of base and surface, are best
not represented by heavy lines.
When the plane of the base of a cylinder or cone is perpendicular to the plane of projection, the projection of the base upon this
plane of projection is a straight line, and as a rule will represent
a line in space, which is partially a shade line and partially not.
For the sake of appearance the projection of the base under
these conditions will be drawn either wholly a heavy line or
wholly a light line according as the portion which should be
represented as a shade line exceeds or does not exceed in length
that portion which should be represented as a light line.
In Fig. 99, remembering the direction taken by the rays of
light, it is evident that the upper base of the cylinder and that
portion of the surface to the left and limited by the two elements
D-E and F-G will be in the light, and that the remainder of the
surface will be in the dark. Therefore the only shade lines to be
represented in this case are D-M-F and E-L-G.
When projecting on IT, D-il-Fis visible and its horizontal projection d,-m,-f, is drawn as a heavy line. When projecting on Vthe portion M-F of the shade line D-JI-F and the portion L-G of the shade
line E-L-G are visible. Since, then, only the small portion m'-f'
of the vertical projection of the upper base should be represented
as a heavy line, the whole line is made a light line. Since the larger
portion l'-g' of the vertical projection of the lower base should be
represented as a heavy line, the whole line is made a heavy line.
In Fig. 104 the shade line to be represented is approximately
D-F-E. Since the larger portion f'-e' of the vertical projection
of the base should be made a heavy line, the whole line f'-g is
made a heavy line.