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SF.net SVN: matplotlib: [4767] branches/transforms
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From: <md...@us...> - 2007-12-18 17:46:03
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Revision: 4767
http://matplotlib.svn.sourceforge.net/matplotlib/?rev=4767&view=rev
Author: mdboom
Date: 2007-12-18 09:46:01 -0800 (Tue, 18 Dec 2007)
Log Message:
-----------
Preliminary version of "adding new scales and projections" document.
(In reST, since that appears to be where mpl documentation is
heading.)
Added Paths:
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branches/transforms/doc/
branches/transforms/doc/devel/
branches/transforms/doc/devel/add_new_projection.rst
Added: branches/transforms/doc/devel/add_new_projection.rst
===================================================================
--- branches/transforms/doc/devel/add_new_projection.rst (rev 0)
+++ branches/transforms/doc/devel/add_new_projection.rst 2007-12-18 17:46:01 UTC (rev 4767)
@@ -0,0 +1,192 @@
+===============================================
+Adding new scales and projections to matplotlib
+===============================================
+
+.. ::author Michael Droettboom
+
+Matplotlib supports the addition of new transformations that transform
+the data before it is displayed. Separable transformations, that work
+on a single dimension are called "scales", and non-separable
+transformations, that take data in two or more dimensions as input are
+called "projections".
+
+This document is intended for developers and advanced users who need
+to add more scales and projections to matplotlib.
+
+From the user's perspective, the scale of a plot can be set with
+``set_xscale`` and ``set_yscale``. Choosing the projection
+currently has no *standardized* method. [MGDTODO]
+
+Creating a new scale
+====================
+
+Adding a new scale consists of defining a subclass of ``ScaleBase``,
+that brings together the following elements:
+
+ - A transformation from data space into plot space.
+
+ - An inverse of that transformation. For example, this is used to
+ convert mouse positions back into data space.
+
+ - A function to limit the range of the axis to acceptable values. A
+ log scale, for instance, would prevent the range from including
+ values less than or equal to zero.
+
+ - Locators (major and minor) that determine where to place ticks in
+ the plot, and optionally, how to adjust the limits of the plot to
+ some "good" values.
+
+ - Formatters (major and minor) that specify how the tick labels
+ should be drawn.
+
+There are a number of ``Scale`` classes in ``scale.py`` that may be
+used as starting points for new scales. As an example, this document
+presents adding a new scale ``MercatorLatitudeScale`` which can be
+used to plot latitudes in a Mercator_ projection. For simplicity,
+this scale assumes that it has a fixed center at the equator. The
+code presented here is a simplification of actual code in
+``matplotlib``, with complications added only for the sake of
+optimization removed.
+
+First define a new subclass of ``ScaleBase``::
+
+ class MercatorLatitudeScale(ScaleBase):
+ """
+ Scales data in range -pi/2 to pi/2 (-90 to 90 degrees) using
+ the system used to scale latitudes in a Mercator projection.
+
+ The scale function:
+ ln(tan(y) + sec(y))
+
+ The inverse scale function:
+ atan(sinh(y))
+
+ Since the Mercator scale tends to infinity at +/- 90 degrees,
+ there is user-defined threshold, above and below which nothing
+ will be plotted. This defaults to +/- 85 degrees.
+
+ source:
+ http://en.wikipedia.org/wiki/Mercator_projection
+ """
+ name = 'mercator_latitude'
+
+This class must have a member ``name`` that defines the string used to
+select the scale. For example,
+``gca().set_yscale("mercator_latitude")`` would be used to select the
+Mercator latitude scale.
+
+Next define two nested classes: one for the data transformation and
+one for its inverse. Both of these classes must be subclasses of
+``Transform`` (defined in ``transforms.py``).::
+
+ class MercatorLatitudeTransform(Transform):
+ input_dims = 1
+ output_dims = 1
+
+There are two class-members that must be defined. ``input_dims`` and
+``output_dims`` specify number of input dimensions and output
+dimensions to the transformation. These are used by the
+transformation framework to do some error checking and prevent
+incompatible transformations from being connected together. When
+defining transforms for a scale, which are by definition separable and
+only have one dimension, these members should always be 1.
+
+``MercatorLatitudeTransform`` has a simple constructor that takes and
+stores the *threshold* for the Mercator projection (to limit its range
+to prevent plotting to infinity).::
+
+ def __init__(self, thresh):
+ Transform.__init__(self)
+ self.thresh = thresh
+
+The ``transform`` method is where the real work happens: It takes an N
+x 1 ``numpy`` array and returns a transformed copy. Since the range
+of the Mercator scale is limited by the user-specified threshold, the
+input array must be masked to contain only valid values.
+``matplotlib`` will handle masked arrays and remove the out-of-range
+data from the plot. Importantly, the transformation should return an
+array that is the same shape as the input array, since these values
+need to remain synchronized with values in the other dimension.::
+
+ def transform(self, a):
+ masked = ma.masked_where((a < -self.thresh) | (a > self.thresh), a)
+ return ma.log(ma.abs(ma.tan(masked) + 1.0 / ma.cos(masked)))
+
+Lastly for the transformation class, define a method to get the
+inverse transformation::
+
+ def inverted(self):
+ return MercatorLatitudeScale.InvertedMercatorLatitudeTransform(self.thresh)
+
+The inverse transformation class follows the same pattern, but
+obviously the mathematical operation performed is different::
+
+ class InvertedMercatorLatitudeTransform(Transform):
+ input_dims = 1
+ output_dims = 1
+
+ def __init__(self, thresh):
+ Transform.__init__(self)
+ self.thresh = thresh
+
+ def transform(self, a):
+ return npy.arctan(npy.sinh(a))
+
+ def inverted(self):
+ return MercatorLatitudeScale.MercatorLatitudeTransform(self.thresh)
+
+Now we're back to methods for the ``MercatorLatitudeScale`` class.
+Any keyword arguments passed to ``set_xscale`` and ``set_yscale`` will
+be passed along to the scale's constructor. In the case of
+``MercatorLatitudeScale``, the ``thresh`` keyword argument specifies
+the degree at which to crop the plot data. The constructor also
+creates a local instance of the ``Transform`` class defined above,
+which is made available through its ``get_transform`` method::
+
+ def __init__(self, axis, **kwargs):
+ thresh = kwargs.pop("thresh", (85 / 180.0) * npy.pi)
+ if thresh >= npy.pi / 2.0:
+ raise ValueError("thresh must be less than pi/2")
+ self.thresh = thresh
+ self._transform = self.MercatorLatitudeTransform(thresh)
+
+ def get_transform(self):
+ return self._transform
+
+The ``limit_range_for_scale`` method must be provided to limit the
+bounds of the axis to the domain of the function. In the case of
+Mercator, the bounds should be limited to the threshold that was
+passed in. Unlike the autoscaling provided by the tick locators, this
+range limiting will always be adhered to, whether the axis range is set
+manually, determined automatically or changed through panning and
+zooming::
+
+ def limit_range_for_scale(self, vmin, vmax, minpos):
+ return max(vmin, -self.thresh), min(vmax, self.thresh)
+
+Lastly, the ``set_default_locators_and_formatters`` method sets up the
+locators and formatters to use with the scale. It may be that the new
+scale requires new locators and formatters. Doing so is outside the
+scope of this document, but there are many examples in ``ticker.py``.
+The Mercator example uses a fixed locator from -90 to 90 degrees and a
+custom formatter class to put convert the radians to degrees and put a
+degree symbol after the value::
+
+ def set_default_locators_and_formatters(self, axis):
+ class DegreeFormatter(Formatter):
+ def __call__(self, x, pos=None):
+ # \u00b0 : degree symbol
+ return u"%d\u00b0" % ((x / npy.pi) * 180.0)
+
+ deg2rad = npy.pi / 180.0
+ axis.set_major_locator(FixedLocator(
+ npy.arange(-90, 90, 10) * deg2rad))
+ axis.set_major_formatter(DegreeFormatter())
+ axis.set_minor_formatter(DegreeFormatter())
+
+Now that the Scale class has been defined, it must be registered so
+that ``matplotlib`` can find it::
+
+ register_scale(MercatorLatitudeScale)
+
+.. _Mercator: http://en.wikipedia.org/wiki/Mercator_projection
\ No newline at end of file
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