Add line plot and warning about too few/many points

_episodes/03-plotting.md

@@ -19,8 +19,8 @@ keypoints:
 # Plotting in Python
 
 The words *plotting* and *plot* have their origin in [plotters](https://en.wikipedia.org/wiki/Plotter),
-devices that use pens to replicate the human act of drawing and are able to produce
-high quality results.
+devices that use pens to replicate the human act of drawing.
+Plotters became popular thanks to their ability to produce high quality results.
 
 The Python community has developed several frameworks to generate plots,
 also known as charts or graphs.
@@ -415,7 +415,7 @@ fig.savefig("fig/subplot.png")
 And we got a great looking result.
 
 If instead of independent panels, you are plotting facets or dependent variables,
-you should additionally, specify that the subplots should have
+you should additionally specify that the subplots should have
 the same minimum and maximum limits for both X and Y axis.
 
 This can either be done manually by iterating over each `Axes`
@@ -445,23 +445,26 @@ Notice that sharing both axis automatically hid the axis on the inner subplots.
 {: .callout }
 
 
-
-
-
 ### Line plots
 
 Line plots are one of the most common kinds of plot you can create
 with `matplotlib`.
 
 As we saw above, you can create a line plot by providing a set of X and Y coordinates.
-Consecutive points will be The order of the points will dictate how lines 
-in a specific order.
+The order of the points will dictate how lines will be drawn.
+Consecutive points will be connected with a line.
+
+Picking on our example from before:
 
 ~~~
 import matplotlib.pyplot as plt
 import numpy as np
 
-x = np.linspace(0, 2, 100)            # Generate an array of 100 values between 0 and 2
+start = 0
+stop = 2
+samples = 100
+
+x = np.linspace(start, stop, samples) # Generate an array of 100 values between 0 and 2
 
 plt.plot(x, x, label='linear')        # A Figure and Axes are implicitly created here
 plt.plot(x, x**2, label='quadratic')  # subsequent calls are added to the same Axes
@@ -474,9 +477,59 @@ plt.savefig("my-simple-plot.png")     # This is the same as before
 ~~~
 {: .language-python }
 
-which produces the exact same output as before.
-
 ![my-simple-plot.png](../fig/my-simple-plot.png)
+
+The `numpy` function `linspace()` creates an array with values `[0, 0.02, 0.04, ...]`. Due to the small increment the plot looks like a smooth curve.
+The `plot()` function takes `X` values as its first attribute and `Y` values for the second.
+Given `plot(X, Y)` it then takes a pair of coordinates from both variables as with: `(X[0], Y[0]), (X[1], Y[1]), ...`.
+
+> ## Beware of too many or too few data points
+>
+> Keep in mind that `matplotlib` will try to plot all the data you pass as arguments.
+> If your provide thousands of data points, you may not see a significant visual change
+> but your plotting code will take considerably longer to produce a result.
+> Similarly, if you don't provide enough points, the linear interpolation produced by
+> `matplotlib` may introduce misleading visual effects.
+{: .callout }
+
+> ## Nice and smooth
+>
+> Modify the values in `start`, `stop` and `samples`,
+> to produce alternative versions of the above plot with different degrees of *smoothness*.
+> Play also with different mathematical expressions other than `x ** 2` or `x ** 3`.
+>
+> `numpy`'s [documentation][numpy-docs] has a [nice list of mathematical functions][numpy-math-functions].
+> For example, the `sin()` function is available as `np.sin()`.
+>
+> > ## Solution
+> >
+> > Using only `4` samples the curve doesn't look as smooth as before.
+x = np.linspace(0, 2, 4)
+> > ![simple-plot with few datapoints](../fig/my-simple-plot-jagged-curve.png)
+> >
+> > And a sine plot would look like:
+> >
+> > ~~~
+> > start = 0
+> > stop = 5
+> > samples = 100
+> >
+> > x = np.linspace(start, stop, samples)
+> >
+> > plt.plot(x, np.sin(x), label='sin')
+> > plt.plot(x, np.sin(x**3), label='sin-cubic')
+> > ~~~
+> > {: .language-python }
+> >
+> > ![simple-sine plot](../fig/my-sine-plot.png)
+> >
+> > Notice also that as the values of `X` become larger,
+> > the number of samples is not enough
+> > and visual artifacts start to appear in. the `sine-cubic` plot.
+> {: .solution }
+{: .challenge }
+
+
 ### Histograms
 
 ~~~

_includes/links.md

@@ -92,7 +92,8 @@
 [mypy]: http://mypy-lang.org/
 [np-home]: https://numpy.org/
 [numfocus]: https://numfocus.org/
-[numpy-docs]:  https://numpy.org/doc/stable/
+[numpy-docs]: https://numpy.org/doc/stable/
+[numpy-math-functions]: https://numpy.org/doc/stable/reference/routines.math.html
 [old-formatting]: https://docs.python.org/2/library/stdtypes.html#string-formatting
 [os-file-dir]: https://docs.python.org/3.8/library/os.html#os-file-dir
 [os-module]: https://docs.python.org/3/library/os.html