Parallel Projections - Transformations and Projections in Computer Graphics - page 53

I will sette as I doe often in woorke use, a paire of paralleles, or [twin] lines of one
lengthe, thus =, bicause noe 2. thynges, can be moare equalle.
—Robert Recorde, 1557

2.1 Orthographic Projections

The term orthographic (or orthography) is derived from the Greek oρθo (correct) and
γραϕoζ (that writes). This term is used in several areas, such as orthographic projection
of a sphere (page 206) and the orthography of a language. The latter is the set of rules
that specify correct writing in a language. An example of an orthographic rule in English
is i comes before e (as in “view”) except after a c (as in “ceiling”).
The family of orthographic projections is the simplest of the three types of parallel
projections. The principle is to imagine a box around the object to be projected and to
project the object “flat” on each of the six sides of the box (Figure 2.2a). If the object
is simple and familiar, three projections, on three orthogonal sides, may be enough
(Figure 2.2b). If the object is complex or is unfamiliar, a perspective projection may
be needed in addition to the three or six parallel projections. For even more complex
objects, sectional views may be necessary. Such a view is obtained by passing an
imaginary plane through the object and drawing a projection of the plane.

(a) (b)

Figure 2.2: Six and Three Orthographic Projections.

Ifonesideoftheboxisthe xy plane, then a point P =( x, y, z ) is projected on this
side by removing its z coordinate to become P ∗ =( x, y ). This operation can be carried
out formally by multiplying P by matrix T z of Equation (2.1). Similarly, matrices T x