Update how CPT hinges are handled

doc/examples/ex19/ex19.sh

@@ -7,7 +7,7 @@
 gmt begin ex19
 	gmt grdmath -Rd -I1 -r Y COSD 2 POW = lat.nc
 	gmt grdmath X = lon.nc
-	gmt makecpt -Cwhite,blue -T0,1 -Z -N -H > lat.cpt
+	gmt makecpt -Cwhite,blue -T0/1 -N -H > lat.cpt
 	gmt makecpt -Crainbow -T-180/180 -H > lon.cpt
 	gmt subplot begin 3x1 -Fs6.5i/0 -M0 -Bbltr -Rd -JI0/6.5i
 		#   First make a worldmap with graded blue oceans and rainbow continents

doc/rst/source/colorbar_common.rst_

@@ -48,8 +48,7 @@ Optional Arguments
     is given then we read stdin.  By default all
     color changes are annotated. To use a subset, add an extra column to
     the CPT with a L, U, or B to annotate Lower, Upper, or Both
-    color segment boundaries (but see **-B**). If not given, the module
-    will read stdin. Like :doc:`grdview`, we can understand
+    color segment boundaries (but see **-B**). Like :doc:`grdview`, we can understand
     pattern specifications in the CPT. For CPTs where the
     *z* range is in meters, it may be useful to change to another unit
     when plotting.  To do so, append **+U**\ *unit* to the file name.

doc/rst/source/common_SYN_OPTs.rst_

@@ -40,7 +40,7 @@
 
 .. |SYN_OPT-i| replace:: **-i**\ :ref:`flags <-icols_full>`
 
-.. |SYN_OPT-j| replace:: **-j**\ :ref:`flags <distcalc_full>`
+.. |SYN_OPT-j| replace:: **-j**\ :ref:`flags <-distcalc_full>`
 
 .. |SYN_OPT-l| replace:: **-l**\ :ref:`flags <-l_full>`
 

doc/rst/source/cookbook/cpts.rst

@@ -17,6 +17,8 @@ original color scale, which can be either discrete or continuous, though
 some (like **globe**) are a mix of the two. The bottom half the color
 bar are built by using :doc:`/makecpt`
 **-T**-1/1/0.25, thus splitting the color scale into 8 discrete colors.
+Black and white triangles indicate which tables have hard or soft hinges,
+respectively.
 
 .. _CPT_files_a:
 

doc/rst/source/cookbook/features.rst

@@ -1128,45 +1128,91 @@ Master (dynamic) CPTs
 
 The CPTs distributed with GMT are *dynamic*.  This means they have several
 special properties that modify the behavior of programs that use them.
-All dynamic CPTs are normalized in one of two ways: If a CPT was designed
+Dynamic CPTs comes in a few different flavors: Some CPTs were designed
 to behave differently across a *hinge* value (e.g., a CPT designed specifically
 for topographic relief may include a discontinuity in color across the
-coastline at *z = 0*), then the CPT's *z*-values will range from -1, via 0
-at the hinge, to +1 at the other end.  The hinge value is specified via the special
-comment
-
-| ``# HINGE = <hinge-value>``
-
-CPTs without a hinge are instead normalized with *z*-values from 0 to 1.
-Dynamic CPTs will need to be stretched to the user's preferred range, and there
+coastline at *z = 0*), and when users select these CPTs they will be stretched
+to fit the user's desired data range separately for each side of this *hard* hinge.
+Basically, a *hard* hinge CPT is the juxtaposition of two different CPTs joined
+at the hinge and these sections are stretched independently. Such CPT files
+are identified as such via the special comment
+
+| ``# HARD_HINGE``
+
+and all hard hinges occur at data value *z = 0* (but you can change this value by
+adding **+h**\ *value* to the name of the CPT).
+Other CPTs may instead have a *soft* hinge which indicates a natural hinge or transition
+point in the CPT itself, unrelated to any natural data set *per se*. These CPTs
+are flagged by the special comment
+
+| ``# SOFT_HINGE``
+
+CPTs with soft hinges behave as regular (non-hinge) CPTs *unless* the user activates then by
+appending **+h**\ [*hinge*] to the CPT name.  This modifier will convert the soft
+hinge into a hard hinge at the user-specified data value *hinge* [which defaults to 0].
+Note that if your specified data range *excludes* an activated soft or hard hinge then we
+only perform color sampling from the *half* of the CPT that pertains to the data range.
+All dynamic CPTs will need to be stretched to the user's preferred range, and there
 are two modes of such scaling: Some CPTs designed for a specific application
 (again, the topographic relief is a good example) have a *default range*
 specified in the master table via the special comment
 
 
 | ``# RANGE = <zmin/zmax>``
 
-and when used by applications the normalized *z*-values will be stretched to reflect
-this natural range.  In contrast, CPTs without a natural range are instead
+and when used by applications the CPT may be automatically stretched to reflect
+this natural range.  In contrast, dynamic CPTs *without* a natural range are instead
 stretched to fit the range of the data in question (e.g., a grid's range).
-Exceptions to these rules are implemented in the two CPT-producing modules
+Exceptions to these rules are implemented in the two *CPT-producing* modules
 :doc:`/makecpt` and :doc:`/grd2cpt`, both of which can read dynamic CPTs
 and produce *static* CPTs satisfying a user's specific range needs.  These
-tools can also read static CPTs where the new range must be specified (or computed
+tools can also read static CPTs for which a new range must be specified (or computed
 from data), reversing the order of colors, and even isolating a section
-of an incoming CPT.  Here, :doc:`/makecpt` can be told the range of compute it from data tables
-while :doc:`/grd2cpt` can derive the range from one or more grids.
+of an incoming CPT.  Here, :doc:`/makecpt` can be told the data range or compute
+it from data tables while :doc:`/grd2cpt` can derive the range from one or more grids.
 
 .. figure:: /_images/GMT_hinge.*
    :width: 500 px
    :align: center
 
-   The top color bar is a dynamic master CPT (here, globe) with a hinge at sea level and
+   The top color bar is a dynamic master CPT (here, globe) with a hard hinge at sea level and
    a natural range from -10,000 to +10,000 meters. However, our data range
    is asymmetrical, going from -8,000 meter depths up to +3,000 meter elevations.
    Because of the hinge, the two sides of the CPT will be stretched separately
    to honor the desired range while utilizing the full color range.
 
+All CPT master tables can be found in Chapter :ref:`Of Colors and Color Legends`
+where those with hard or soft hinges are identified by triangles at their hinges.
+
+CPTs from color lists
+~~~~~~~~~~~~~~~~~~~~~
+
+GMT can build color tables "on the fly" from a comma-separated list of colors
+and a range of *z*-values to go with them.  As illustrated below, there are
+four different ways to create such CPTs. In this example, we will operate with
+a list of three colors: red,yellow and purple, given to modules with the option **-C**\ red,yellow,purple,
+and utilize a fixed data range of *z = 0-6*.
+Four different CPTs result because we either select a *continuous* or *discrete table*, and because the *z*-intervals are
+either *equidistant* or *arbitrary*.  The top continuous color table with equidistant spacing (a) is selected
+with the range **-T**\ 0/6, meaning the colors will continuously change from red (at *z = 0*) via
+yellow (at *z = 3*) to purple (at *z = 6*). Next, a discrete table with the same range (b)
+is obtained with **-T**\ 0/6/2, yielding colors that are either constant red (*z = 0-2*), yellow (*z = 2-4*)
+or purple (*z = 4-6*). The next discrete table (c) illustrates how to specify arbitrary
+node points in the CPT by providing a comma-separated list of values (**-T**\ 0,4,5.5,6). Now, the constant
+color intervals have unequal ranges, illustrated by red (*z = 0-4*), yellow (*z = 4-5.5*) and purple (*z = 5.5-6*).  Finally, we
+create a continuous color table (d) with arbitrary nodes by giving **-T**\ 0,2,6 and adding **-Z**;
+the latter option forces a continuous CPT pinned to a given list of node values.  Now, the colors
+continuously change from red (at *z = 0*) via yellow (at *z = 2*) to purple (at *z = 6*).
+Modules that obtain the *z*-range indirectly (e.g., :doc:`/grdimage`) may use the exact data range
+to set the quivalent of a **-T**\ *min/max* option.  You may append **+i**\ *dz* to the
+color list to have the *min* and *max* values rounded down and up to nearest multiple of *dz*, respectively.
+
+.. figure:: /_images/GMT_colorlist.*
+   :width: 500 px
+   :align: center
+
+   Lists of colors (here red,yellow,purple) can be turned into discrete or continuous CPT tables on the fly.
+
 Cyclic (wrapped) CPTs
 ~~~~~~~~~~~~~~~~~~~~~
 
@@ -1227,7 +1273,10 @@ A few modules (:doc:`/grdimage`, :doc:`/grdview`) that expects a CPT option will
 provide a default CPT if none is provided.  By default, the default CPT is the
 "turbo" color table, but this is overridden if the user uses the @eart_relief
 (we select "geo") or @srtm_relief (we select "srtm") data sets.  After selection,
-these CPTs are read and scaled to match the range of the grid values.
+these CPTs are read and scaled to match the range of the grid values. You may append
+**+i**\ *dz* to the CPT to have the exact range rounded to nearest multiple of *dz*.
+THis is helpful if you plan to place a colorbar and prefer start and stop *z*-values
+that are multiples of *dz*.
 
 The Drawing of Vectors
 ----------------------
@@ -2544,4 +2593,3 @@ any of these directories.
 
 .. [19]
    Requires building GMT with GDAL.
-

doc/rst/source/create_cpt.rst_

@@ -0,0 +1,11 @@
+**-C**\ [*cpt*\ \|\ *master*\ [**+h**\ [*hinge*]][**+i**\ *zinc*][**+u**\ \|\ **U**\ *unit*] \|\ *color1,color2*\ [,\ *color3*\ ,...]]
+    Name of the CPT. If given a GMT Master soft-hinge CPT (see :ref:`Of Colors and Color Legends`) then
+    you can enable the hinge at data value *hinge* [0] via **+h**, whereas for hard-hinge CPTs you
+    can adjust the location of the hinge [0].  For other CPTs, you may convert their *z*-values
+    from meter to another distance unit (append **+U**\ *unit*) or from another unit to meter (append **+u**\ *unit*),
+    with *unit* taken from **e**\ \|\ **f**\ \|\ **k**\ \|\ **M**\ \|\ **n**\ \|\ **u**.
+    Alternatively, give *color1,color2*\ [*,color3*\ ,...]
+    to build a linear continuous CPT from those colors automatically,
+    where *z* starts at 0 and is incremented by one for each color.
+    In this case *color*\ **n** can be a r/g/b triplet, a color name,
+    or an HTML hexadecimal color (e.g. #aabbcc).

doc/rst/source/explain_distcalc.rst_

@@ -1,2 +1,2 @@
-**-je**\ \|\ **f**\ \|\ **g** :ref:`(more ...) <distcalc_full>`
+**-je**\ \|\ **f**\ \|\ **g** :ref:`(more ...) <-distcalc_full>`
     Determine how spherical distances are calculated.

doc/rst/source/explain_distcalc_full.rst_

@@ -1,4 +1,4 @@
-.. _distcalc_full:
+.. _-distcalc_full:
 
 **-je**\ \|\ **f**\ \|\ **g**
     Determine how spherical distances are calculated in modules that support this.

doc/rst/source/grd2cpt.rst

@@ -90,15 +90,7 @@ Optional Arguments
 
 .. _-C:
 
-
-**-C**\ *cpt*
-    Selects the master color table to use in the interpolation. Choose
-    among the built-in tables (type **grd2cpt** to see the list) or give
-    the name of an existing CPT [Default gives the turbo CPT].
-    Yet another option is to specify -Ccolor1,color2[,color3,...]
-    to build a linear continuous CPT from those colors automatically. 
-    In this case *color*\ **n** can be a r/g/b triplet, a color name,
-    or an HTML hexadecimal color (e.g. #aabbcc ).
+.. include:: create_cpt.rst_
 
 .. _-D:
 
@@ -213,30 +205,42 @@ Optional Arguments
 **-W**\ [**w**]
     Do not interpolate the input color table but pick the output colors
     starting at the beginning of the map. This is particularly useful in
-    combination with a categorical color table. Cannot be used in
-    combination with **-Z**.  Alternatively, use **-Ww** to produce
-    a wrapped (cyclic) color table that endlessly repeats its range.
+    combination with a categorical color table. Alternatively, use **-Ww**
+    to produce a wrapped (cyclic) color table that endlessly repeats its range.
 
 .. _-Z:
 
 **-Z**
-    Will create a continuous color palette. [Default is discontinuous,
-    i.e., constant color intervals]
+    Force a continuous CPT [Default is discontinuous].
 
 .. include:: explain_help.rst_
 
 .. include:: explain_grd_inout_short.rst_
 
 .. include:: explain_transparency.rst_
 
-Color Aliasing
---------------
-
-For best result when **-E** is used we recommend you do no append
-a specific *nlevels*.  This way the original CPT is used exactly
-as is but the *z* boundaries are adjusted to match the grid limits.
-Otherwise you may, depending on the nature of the input CPT, miss
-aspects of the color changes by aliasing the signal.
+Color Hinges
+------------
+
+Some of the GMT master dynamic CPTs are actually two separate CPTs
+meeting at a *hinge*.  Usually, colors may change dramatically across
+the hinge, which is used to separate two different domains (e.g., land
+and ocean across the shoreline, for instance).  CPTs with a hinge will
+have their two parts stretched to the required range separately, i.e.,
+the bottom part up to the hinge will be stretched independently of the
+part from the hinge to the top, according to the prescribed new range.
+Hinges are either *hard* or *soft*.  Soft hinges must be *activated* by
+appending **+h**\ [*hinge*] to the CPT name.
+If the selected range does not include an activated soft or hard hinge then
+we only resample colors from the half of the CPT that pertains to the range.
+See :ref:`Of Colors and Color Legends` for more information.
+
+Discrete versus Continuous CPT
+------------------------------
+
+All CPTs can be stretched, but only continuous CPTs can be sampled
+at new nodes (i.e., by given an increment in **-T**).  We impose this
+limitation to avoid aliasing the original CPT.
 
 Examples
 --------
@@ -265,7 +269,7 @@ file relief, run
 
     gmt grd2cpt mydata.nc -Crelief -L0/10000 -T0/200/20 > mydata.cpt
 
-.. include:: explain_cpt.rst_
+.. include:: cpt_notes.rst_
 
 See Also
 --------

doc/rst/source/grd2kml.rst

@@ -54,17 +54,7 @@ Optional Arguments
 
 .. _-C:
 
-**-C**\ [*cpt* \|\ *master*\ [**+i**\ *zinc*] \|\ *color1,color2*\ [,\ *color3*\ ,...]]
-    Name of the CPT (for *grd_z* only). Alternatively,
-    supply the name of a GMT color master dynamic CPT [turbo, but geo
-    for @earth_relief and srtm for @srtm_relief data] to
-    automatically determine a continuous CPT from
-    the grid's z-range; you may round up/down the z-range by adding **+i**\ *zinc*.
-    Yet another option is to specify **-C**\ *color1*\ ,\ *color2*\ [,\ *color3*\ ,...]
-    to build a linear continuous CPT from those colors automatically.
-    In this case *color1* etc can be a r/g/b triplet, a color name,
-    or an HTML hexadecimal color (e.g. #aabbcc ).  If no argument is given to **-C**
-    then under modern mode we select the current CPT.
+.. include:: use_cpt_grd.rst_
 
 .. _-E:
 

doc/rst/source/grdimage.rst

@@ -75,7 +75,7 @@ remotely located Jessica Rabbit::
 
     gmt grdimage -JI15c -Rd https://larryfire.files.wordpress.com/2009/07/untooned_jessicarabbit.jpg -pdf jess
 
-.. include:: explain_cpt.rst_
+.. include:: cpt_notes.rst_
 
 See Also
 --------

doc/rst/source/grdimage_common.rst_

@@ -66,17 +66,7 @@ Optional Arguments
 
 .. _-C:
 
-**-C**\ [*cpt* \|\ *master*\ [**+i**\ *zinc*] \|\ *color1,color2*\ [,\ *color3*\ ,...]]
-    Name of the CPT (for *grd_z* only). Alternatively,
-    supply the name of a GMT color master dynamic CPT [turbo, but geo
-    for @earth_relief and srtm for @srtm_relief data] to
-    automatically determine a continuous CPT from
-    the grid's z-range; you may round up/down the z-range by adding **+i**\ *zinc*.
-    Yet another option is to specify **-C**\ *color1*\ ,\ *color2*\ [,\ *color3*\ ,...]
-    to build a linear continuous CPT from those colors automatically.
-    In this case *color1* etc can be a r/g/b triplet, a color name,
-    or an HTML hexadecimal color (e.g. #aabbcc ).  If no argument is given to **-C**
-    then under modern mode we select the current CPT.
+.. include:: use_cpt_grd.rst_
 
 .. _-D:
 

doc/rst/source/grdvector_common.rst_

@@ -37,16 +37,7 @@ Optional Arguments
 
 .. _-C:
 
-**-C**\ [*cpt* \|\ *master*\ [**+i**\ *zinc*] \|\ *color1,color2*\ [,\ *color3*,...]]
-    Use *cpt* to assign colors based on vector length. Alternatively,
-    supply the name of a GMT color master dynamic CPT [turbo] to
-    automatically determine a continuous CPT from
-    the grid's z-range; you may round up/down the z-range by adding **+i**\ *zinc*..
-    Yet another option is to specify **-C**\ *color1,color2*\ [,\ *color3*,...]
-    to build a linear continuous cpt from those colors automatically.  
-    In this case *color*\ **n** can be a r/g/b triplet, a color name,
-    or an HTML hexadecimal color (e.g. #aabbcc ).  If no argument is given to **-C**
-    then under modern mode we select the current CPT.
+.. include:: use_cpt_grd.rst_
 
 .. _-G:
 

doc/rst/source/grdview_common.rst_

@@ -33,18 +33,7 @@ Optional Arguments
 
 .. _-C:
 
-**-C**\ [*cpt* \|\ *master*\ [**+i**\ *zinc*] \|\ *color1,color2*\ [,\ *color3*\ ,...]]
-    The name of the CPT. Must be present if you want
-    (1) mesh plot with contours (**-Qm**), or
-    (2) shaded/colored perspective image (**-Qs** or
-    **-Qi**). For **-Qs**: You can specify that you want to skip a
-    z-slice by setting the red r/g/b component to -; to use a pattern give red =
-    **P\|p**\ *pattern*\ [**+b**\ *color*\ ][**+f**\ *color*\ ][**+r**\ *dpi*\ ].
-    Alternatively, supply the name of a GMT color master dynamic CPT [turbo, but
-    geo for @earth_relief and srtm for @srtm_relief data] to
-    automatically determine a continuous CPT from
-    the grid's z-range; you may round up/down the z-range by adding **+i**\ *zinc*.
-    If no argument is given to **-C** then under modern mode we select the current CPT.
+.. include:: use_cpt_grd.rst_
 
 .. _-G: