Improve documentation of UTM projection (#2061)

Co-authored-by: Dongdong Tian <[email protected]>

Author: yvonnefroehlich

examples/projections/cyl/cyl_universal_transverse_mercator.py

@@ -2,19 +2,33 @@
 Universal Transverse Mercator
 =============================
 
-A particular subset of the transverse Mercator is the Universal Transverse
-Mercator (UTM) which was adopted by the US Army for large-scale military maps.
-Here, the globe is divided into 60 zones between 84°S and 84°N, most of which
-are 6° (in longitude) wide. Each of these UTM zones have their unique central
-meridian. Furthermore, each zone is divided into latitude bands but these are
-not needed to specify the projection for most cases.
+A particular subset of the
+:doc:`transverse Merctor </projections/cyl/cyl_transverse_mercator>`
+is the Universal Transverse Mercator (UTM) which was adopted by the US Army
+for large-scale military maps. Here, the globe is divided into 60 zones
+between 84°S and 84°N, most of which are 6° (in longitude) wide.
+Each of these UTM zones have their unique central meridian.
+Furthermore, each zone is divided into latitude bands but these are
+not needed to specify the projection for most cases. See Figure
+:ref:`Universal Transverse Mercator <GMT_utm_zones>` for all zone designations.
+
+.. _GMT_utm_zones:
+
+.. figure:: https://docs.generic-mapping-tools.org/latest/_images/GMT_utm_zones.png # noqa: W505
+   :width: 700 px
+   :align: center
+
+   Universal Transverse Mercator zone layout.
 
 In order to minimize the distortion in any given zone, a scale factor of 0.9996
-has been factored into the formulae. This makes the UTM projection a secant
-projection and not a tangent projection like the transverse Mercator above. The
-scale only varies by 1 part in 1,000 from true scale at equator. The
-ellipsoidal projection expressions are accurate for map areas that extend less
-than 10° away from the central meridian.
+has been factored into the formulae (although a standard, you can change this
+with :gmt-term:`PROJ_SCALE_FACTOR`). This makes the UTM projection a *secant*
+projection and not a *tangent* projection like the
+:doc:`transverse Merctor </projections/cyl/cyl_transverse_mercator>`.
+The scale only varies by 1 part in 1,000 from true scale at equator. The
+ellipsoidal projection expressions are accurate for map areas that extend
+less than 10° away from the central meridian. For larger regions we use the
+conformal latitude in the general spherical formulae instead.
 
 **u**\ *zone/scale* or **U**\ *zone/width*