Add Axes method for drawing infinite lines.

Clean up axline

Add axline image test

Fix test image

Add what's new

Add note about log axes

Error if trying to draw line on non-linear axes

Fix scale checking

Fix docstring interpolation

Chnage to using xy1, xy2

Fix docs and closeness checking

Raise error if points are the same

Swap axline test to image comparison

Author: QuLogic

doc/users/next_whats_new/2017-12-08-axline.rst

@@ -0,0 +1,5 @@
+New `axline` method
+-------------------
+
+A new `axline` method has been added to draw infinitely long lines that pass
+through two points.

lib/matplotlib/axes/_axes.py

@@ -919,6 +919,79 @@ def axvline(self, x=0, ymin=0, ymax=1, **kwargs):
         self._request_autoscale_view(scalex=scalex, scaley=False)
         return l
 
+    @docstring.dedent_interpd
+    def axline(self, xy1, xy2, **kwargs):
+        """
+        Add an infinitely long straight line that passes through two points.
+
+        Parameters
+        ----------
+        xy1, xy2 : (float, float)
+            Points for the line to pass through.
+
+        Returns
+        -------
+        :class:`~matplotlib.lines.Line2D`
+
+        Other Parameters
+        ----------------
+        Valid kwargs are :class:`~matplotlib.lines.Line2D` properties,
+        with the exception of 'transform':
+
+        %(_Line2D_docstr)s
+
+        Examples
+        --------
+        * Draw a thick red line passing through (0, 0) with a gradient of 1::
+
+            >>> axline((0, 0), (1, 1), linewidth=4, color='r')
+
+
+        See Also
+        --------
+        axhline : for horizontal lines
+        axvline : for vertical lines
+
+        Notes
+        -----
+        Currently this method does not work properly with non-linear axes.
+        """
+        if not self.get_xscale() == self.get_yscale() == 'linear':
+            raise NotImplementedError('axline() is only supported on '
+                                      'linearly scaled axes')
+
+        if "transform" in kwargs:
+            raise TypeError("'transform' is not allowed as a kwarg; "
+                            "axline generates its own transform.")
+
+        x1, y1 = xy1
+        x2, y2 = xy2
+        # If x values the same, we have a vertical line
+        if np.allclose(x1, x2):
+            if np.allclose(y1, y2):
+                raise ValueError(
+                    'Cannot draw a line through two identical points '
+                    f'(got x1={x1}, x2={x2}, y1={y1}, y2={y2}).')
+            line = self.axvline(x1, **kwargs)
+            return line
+
+        slope = (y2 - y1) / (x2 - x1)
+        intercept = y1 - (slope * x1)
+
+        xtrans = mtransforms.BboxTransformTo(self.viewLim)
+        viewLimT = mtransforms.TransformedBbox(
+            self.viewLim,
+            mtransforms.Affine2D().rotate_deg(90).scale(-1, 1))
+        ytrans = (mtransforms.BboxTransformTo(viewLimT) +
+                  mtransforms.Affine2D().scale(slope).translate(0, intercept))
+        trans = mtransforms.blended_transform_factory(xtrans, ytrans)
+
+        line = mlines.Line2D([0, 1], [0, 1],
+                             transform=trans + self.transData,
+                             **kwargs)
+        self.add_line(line)
+        return line
+
     @docstring.dedent_interpd
     def axhspan(self, ymin, ymax, xmin=0, xmax=1, **kwargs):
         """

lib/matplotlib/tests/test_axes.py

@@ -3641,6 +3641,21 @@ def test_eb_line_zorder():
     ax.set_title("errorbar zorder test")
 
 
+@check_figures_equal()
+def test_axline(fig_test, fig_ref):
+    ax = fig_test.subplots()
+    ax.set(xlim=(-1, 1), ylim=(-1, 1))
+    ax.axline((0, 0), (1, 1))
+    ax.axline((0, 0), (1, 0), color='C1')
+    ax.axline((0, 0.5), (1, 0.5), color='C2')
+
+    ax = fig_ref.subplots()
+    ax.set(xlim=(-1, 1), ylim=(-1, 1))
+    ax.plot([-1, 1], [-1, 1])
+    ax.axhline(0, color='C1')
+    ax.axhline(0.5, color='C2')
+
+
 @image_comparison(['vlines_basic', 'vlines_with_nan', 'vlines_masked'],
                   extensions=['png'])
 def test_vlines():