From d6430190cb08451a42302d385ba42a622e2e59ae Mon Sep 17 00:00:00 2001 From: Will Schlitzer Date: Tue, 22 Dec 2020 15:05:45 +0000 Subject: [PATCH] Add descriptions for cylindric projections (#761) * Add description on cyl_cassini.py * Add description on cyl_equal_area.py * Add description on cyl_equidistant.py * Add description on cyl_mercator.py * Add description on cyl_miller.py * Add description on cyl_stereographic.py * Add description on cyl_transverse_mercator.py * Add description on cyl_universal_transverse_mercator.py --- examples/projections/cyl/cyl_cassini.py | 9 +++++++++ examples/projections/cyl/cyl_equal_area.py | 7 ++++++- examples/projections/cyl/cyl_equidistant.py | 4 ++++ examples/projections/cyl/cyl_mercator.py | 10 ++++++++++ examples/projections/cyl/cyl_miller.py | 7 +++++++ examples/projections/cyl/cyl_stereographic.py | 8 ++++++++ examples/projections/cyl/cyl_transverse_mercator.py | 6 ++++++ .../cyl/cyl_universal_transverse_mercator.py | 12 ++++++++++++ 8 files changed, 62 insertions(+), 1 deletion(-) diff --git a/examples/projections/cyl/cyl_cassini.py b/examples/projections/cyl/cyl_cassini.py index 0231cec17a4..7ac6907e162 100644 --- a/examples/projections/cyl/cyl_cassini.py +++ b/examples/projections/cyl/cyl_cassini.py @@ -2,6 +2,15 @@ Cassini Cylindrical ============================ +This cylindrical projection was developed in 1745 by César-François Cassini de Thury +for the survey of France. It is occasionally called Cassini-Soldner since the latter +provided the more accurate mathematical analysis that led to the development of the +ellipsoidal formulae. The projection is neither conformal nor equal-area, and behaves +as a compromise between the two end-members. The distortion is zero along the central +meridian. It is best suited for mapping regions of north-south extent. The central +meridian, each meridian 90° away, and equator are straight lines; all other meridians +and parallels are complex curves. + ``Clon0/lat0/width``: ``lon0`` and ``lat0`` specifies the projection center. """ import pygmt diff --git a/examples/projections/cyl/cyl_equal_area.py b/examples/projections/cyl/cyl_equal_area.py index 33a729a2884..74fc8eb4312 100644 --- a/examples/projections/cyl/cyl_equal_area.py +++ b/examples/projections/cyl/cyl_equal_area.py @@ -2,7 +2,12 @@ Cylindrical equal-area ====================== -``Ylon0/lat0/width``: Give central meridian ``lon0``, the standard parallel ``lat0``, and the figure ``width``. +This cylindrical projection is actually several projections, depending on what +latitude is selected as the standard parallel. However, they are all equal area and +hence non-conformal. All meridians and parallels are straight lines. + +``Ylon0/lat0/width``: Give central meridian ``lon0``, the standard parallel ``lat0``, +and the figure ``width``. """ import pygmt diff --git a/examples/projections/cyl/cyl_equidistant.py b/examples/projections/cyl/cyl_equidistant.py index 3b548987503..7a236466ad6 100644 --- a/examples/projections/cyl/cyl_equidistant.py +++ b/examples/projections/cyl/cyl_equidistant.py @@ -2,6 +2,10 @@ Cylindrical equidistant ======================= +This simple cylindrical projection is really a linear scaling of longitudes and +latitudes. The most common form is the Plate Carrée projection, where the scaling of +longitudes and latitudes is the same. All meridians and parallels are straight lines. + ``Qwidth``: Give the figure ``width``. """ import pygmt diff --git a/examples/projections/cyl/cyl_mercator.py b/examples/projections/cyl/cyl_mercator.py index bfe22ba87a9..2cfdce4329c 100644 --- a/examples/projections/cyl/cyl_mercator.py +++ b/examples/projections/cyl/cyl_mercator.py @@ -2,6 +2,16 @@ Mercator ======== +The Mercator projection takes its name from the Flemish cartographer Gheert Cremer, +better known as Gerardus Mercator, who presented it in 1569. The projection is a +cylindrical and conformal, with no distortion along the equator. A major navigational +feature of the projection is that a line of constant azimuth is straight. Such a line +is called a rhumb line or loxodrome. Thus, to sail from one point to another one only +had to connect the points with a straight line, determine the azimuth of the line, and +keep this constant course for the entire voyage. The Mercator projection has been used +extensively for world maps in which the distortion towards the polar regions grows +rather large. + ``M[lon0/][lat0/]width``: Give central meridian ``lon0`` (optional) and standard parallel ``lat0`` (optional). """ diff --git a/examples/projections/cyl/cyl_miller.py b/examples/projections/cyl/cyl_miller.py index b25249a98d5..4d2503793a2 100644 --- a/examples/projections/cyl/cyl_miller.py +++ b/examples/projections/cyl/cyl_miller.py @@ -2,6 +2,13 @@ Miller cylindrical ================== +This cylindrical projection, presented by Osborn Maitland Miller of the American +Geographic Society in 1942, is neither equal nor conformal. All meridians and +parallels are straight lines. The projection was designed to be a compromise between +Mercator and other cylindrical projections. Specifically, Miller spaced the parallels +by using Mercator’s formula with 0.8 times the actual latitude, thus avoiding the +singular poles; the result was then divided by 0.8. + ``J[lon0/]width``: Give the optional central meridian ``lon0`` and the figure ``width``. """ import pygmt diff --git a/examples/projections/cyl/cyl_stereographic.py b/examples/projections/cyl/cyl_stereographic.py index befe28e28dd..7e5c1c13ed4 100644 --- a/examples/projections/cyl/cyl_stereographic.py +++ b/examples/projections/cyl/cyl_stereographic.py @@ -2,6 +2,14 @@ Cylindrical Stereographic ========================= +The cylindrical stereographic projections are certainly not as notable as other +cylindrical projections, but are still used because of their relative simplicity and +their ability to overcome some of the downsides of other cylindrical projections, like +extreme distortions of the higher latitudes. The stereographic projections are +perspective projections, projecting the sphere onto a cylinder in the direction of the +antipodal point on the equator. The cylinder crosses the sphere at two standard +parallels, equidistant from the equator. + ``Cyl_stere/[lon0/][lat0/]width``: Give central meridian ``lon0`` (optional) and standard parallel ``lat0`` (optional). The standard parallel is typically one of these (but can be any value): diff --git a/examples/projections/cyl/cyl_transverse_mercator.py b/examples/projections/cyl/cyl_transverse_mercator.py index fc8bb2198b9..854d780b309 100644 --- a/examples/projections/cyl/cyl_transverse_mercator.py +++ b/examples/projections/cyl/cyl_transverse_mercator.py @@ -2,6 +2,12 @@ Transverse Mercator =================== +The transverse Mercator was invented by Johann Heinrich Lambert in 1772. In this +projection the cylinder touches a meridian along which there is no distortion. The +distortion increases away from the central meridian and goes to infinity at 90° from +center. The central meridian, each meridian 90° away from the center, and equator are +straight lines; other parallels and meridians are complex curves. + ``T[lon0/][lat0/]width``: Give central meridian ``lon0``, the latitude of the origin ``lat0`` (optional), and the figure width. """ diff --git a/examples/projections/cyl/cyl_universal_transverse_mercator.py b/examples/projections/cyl/cyl_universal_transverse_mercator.py index 47259c5bd6c..aaea1844c66 100644 --- a/examples/projections/cyl/cyl_universal_transverse_mercator.py +++ b/examples/projections/cyl/cyl_universal_transverse_mercator.py @@ -2,6 +2,18 @@ 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 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. + +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. + ``U[UTM Zone/][lat0/]width``: Give UTM Zone ``UTM Zone``, and the figure width. """ import pygmt