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

Check. Same as in Case 1.
CASE 3. When the cylinder is one of revolution with its axis parallel to G-L.
Construction. Let the cylinder be represented as in Fig. 121.
In assuming the point upon the surface, take the horizontal
projection o, at random. Through this point draw a profile plane
cutting the surface of the cylinder in the circumference of a circle
whose center is C. The
point in which this circum$S — e, t - -- -s, ference is intersected by
_a,_'L-::,-~Nb, the horizontal projecting
- -- - ^ -o line of O must be the point
cG ---- _ | -,': ~ L upon the surface. Revolve.:,, _, I the profile plane about its
-at ' t.,w' d'Ft horizontal trace as an axis
)a' ' ' _ b
$ -. s' into H. The circle C will: --- - - take the position of the
circle whose center is c1,
and the horizontal projectFIG. 121
ing line will take the position o,-oH'. Therefore either oH or kH may be taken as the revolved
position of the point upon the surface. Let us take the point 0,
which in this revolved position is vertically projected at ol but in
true position is vertically projected at o'.
The element 0-D through 0 is a line of the required plane, and
since this line is parallel to G-L, we know that the traces of the
required plane will both be parallel to G-L.
Through o, draw e,-oH-fH tangent at oR to the circle whose
center is cH.
This line is the revolved position of a line tangent to a curve
of the surface at a point on 0-D, and therefore is the revolved
position of a line of the required plane. The line E-F in true
position pierces H at e,, a point in the required horizontal trace,
and pierces V in ft, a point in the required vertical trace. The
two traces S-s, and S-s' are now located.
Check. Pass another profile plane cutting from the surface of
the cylinder the circumference of a circle, and from O-D a point