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

447. Problem 311. To make an isometric drawing of any curve of
double curvature when referred to three rectangular coordinate planes.
Let it be required to make an isometric drawing of the helix,
when the helix is referred to the three orthographic planes of projection P, V, and H.
Fig. 187 represents the orthographic projection of the helix,
from which the three coordinate lines of any point of the curve
may be determined.
The isometric projection of the curve is shown in Fig. 186, where
x'-o'-y' represents the isometric projection of the plane V, where

FIG. 186 FIG. 187

x'-o'-z' represents the isometric projection of the plane H, and
where z'-o'-y' represents the isometric projection of the plane P.
The isometric axis o'-x' represents the isometric projection of
G-L, o'-z' represents the isometric projection of P-p,, and o'-y'
represents the isometric projection of P-p'.
The isometric projection of any point of the curve, for example
the point M, may be found thus: