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.

OBLIQUE PROJECTION

207

Fig. 187 shows that the distance of 1 from the plane Pis m-u,,
that its distance from V is n,-w, and that its distance from H is
w —Mn.
In Fig. 186 make o'-w' equal to the distance of 1 from the plane
P, and through w' draw w'-r' parallel to o'-z'. Make w'-r' equal
to the distance of M from V, and through r' draw r'-m' parallel to
o'-y. Make r-m' equal to the distance of M from -. The point
m' is the isometric projection of M, and other points may be found
in the same way.
448. Oblique Projection. In orthographic and in isometric projection the observer is assumed at an infinite distance from the plane
of projection, and the resultant parallel projecting lines are taken
perpendicular to the plane of projection.
If the projecting lines are taken oblique to the plane of projection, the system of projection is called oblique projection.
449. Cavalier Perspective or Cabinet Projection. When the projecting lines are assumed parallel to each other and at an inclination of
45 degrees to the plane of projection, the system of projection is
called cavalier perspective or cabinet projection.
In Fig. 188 let a'-B represent a straight
line perpendicular to V and piercing it at a'. a
Through B draw a projecting line B-b' at an in- B 'clination of 45 degrees to V and piercing Vat b'.
The line a'-b' is the cabinet projection of a'-B.
No restriction whatever is made upon the
direction which the projecting lines shall take FIG. 188
so long as they are inclined at an angle of 45 degrees with the plane
of projection. In any given problem, however, the projecting lines
must be parallel.
450. Observations. Since the projecting lines are inclined 45
degrees to the plane of projection, the cabinet projection of a
straight line perpendicular to the plane of projection will be equal
to the line itself.
The cabinet projection of a straight line in the plane of projection will be the line itself.
The cabinet projection of a straight line parallel to the plane of
projection will be equal to the line itself.