Gauss and UTM Conformal Projections and the Plane Rectangular Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 264

Fig. 6.1 A figure correctly represented by conformal projection
with true shape, i.e., that the ellipsoid can be unfolded or unrolled onto the plane
without distortions. Hence, within a large area, the scale factor m varies from point
to point, i.e., m is dependent on the position of points. To sum up, the conformality
of conformal projection is that, in conformal projection, the scale factor m is
independent of direction but dependent on the position of points.
Map projections are of many kinds. Taking into account the nature of distortions,
apart from the aforementioned conformal projection, there are also equidistant
projections (the distances between any arbitrary two points on the ellipsoid remain
unchanged after projection onto the plane) and equivalent projections (the area on
the ellipsoid is preserved after projection onto the plane).
Conformality is the unique property that differentiates the conformal projection
from other projections. The general conditions for a conformal projection are based
on this property.
6.2 General Condition for Conformal Projection
6.2.1 Overview
Conformal projection is one kind of map projection, and the Gauss projection and
UTM projection are two kinds of conformal projection. Therefore, the conformal
projection needs to be studied prior to study concerning the Gauss projection or
UTM projection. The task of this section is to derive the general condition for
conformal projection, in combination with the particular conditions for Gauss and
UTM projections; the formula for the Gauss projection or UTM projection will then
be derived.
To derive the general condition for the conformal projection, we have to grasp its
unique property that differs it other projections, i.e., in conformal projection the