nbconvert1/tests/ipynbref/XKCD_plots.orig.py

## XKCD plots in Matplotlib

# This notebook originally appeared as a blog post at [Pythonic Perambulations](http://jakevdp.github.com/blog/2012/10/07/xkcd-style-plots-in-matplotlib/) by Jake Vanderplas.

# One of the problems I've had with typical matplotlib figures is that everything in them is so precise, so perfect.  For an example of what I mean, take a look at this figure:

# In[1]:
from IPython.display import Image
Image('http://jakevdp.github.com/figures/xkcd_version.png')

# Out[1]:
#     <IPython.core.display.Image at 0x2fef710>


# Sometimes when showing schematic plots, this is the type of figure I want to display.  But drawing it by hand is a pain: I'd rather just use matplotlib.  The problem is, matplotlib is a bit too precise.  Attempting to duplicate this figure in matplotlib leads to something like this:

# In[2]:
Image('http://jakevdp.github.com/figures/mpl_version.png')

# Out[2]:
#     <IPython.core.display.Image at 0x2fef0d0>


# It just doesn't have the same effect.  Matplotlib is great for scientific plots, but sometimes you don't want to be so precise.
# 
# This subject has recently come up on the matplotlib mailing list, and started some interesting discussions.
# As near as I can tell, this started with a thread on a
# [mathematica list](http://mathematica.stackexchange.com/questions/11350/xkcd-style-graphs)
# which prompted a thread on the [matplotlib list](http://matplotlib.1069221.n5.nabble.com/XKCD-style-graphs-td39226.html)
# wondering if the same could be done in matplotlib.
# 
# Damon McDougall offered a quick
# [solution](http://www.mail-archive.com/[e-mail]/msg25499.html)
# which was improved by Fernando Perez in [this notebook](http://nbviewer.ipython.org/3835181/), and
# within a few days there was a [matplotlib pull request](https://github.com/matplotlib/matplotlib/pull/1329) offering a very general
# way to create sketch-style plots in matplotlib.  Only a few days from a cool idea to a
# working implementation: this is one of the most incredible aspects of package development on github.
# 
# The pull request looks really nice, but will likely not be included in a released version of
# matplotlib until at least version 1.3.  In the mean-time, I wanted a way to play around with
# these types of plots in a way that is compatible with the current release of matplotlib.  To do that,
# I created the following code:

### The Code: XKCDify

# XKCDify will take a matplotlib ``Axes`` instance, and modify the plot elements in-place to make
# them look hand-drawn.
# First off, we'll need to make sure we have the Humor Sans font.
# It can be downloaded using the command below.
# 
# Next we'll create a function ``xkcd_line`` to add jitter to lines.  We want this to be very general, so
# we'll normalize the size of the lines, and use a low-pass filter to add correlated noise, perpendicular
# to the direction of the line.  There are a few parameters for this filter that can be tweaked to
# customize the appearance of the jitter.
# 
# Finally, we'll create a function which accepts a matplotlib axis, and calls ``xkcd_line`` on
# all lines in the axis.  Additionally, we'll switch the font of all text in the axes, and add
# some background lines for a nice effect where lines cross.  We'll also draw axes, and move the
# axes labels and titles to the appropriate location.

# In[3]:
"""
XKCD plot generator
-------------------
Author: Jake Vanderplas

This is a script that will take any matplotlib line diagram, and convert it
to an XKCD-style plot.  It will work for plots with line & text elements,
including axes labels and titles (but not axes tick labels).

The idea for this comes from work by Damon McDougall
  http://www.mail-archive.com/[e-mail]/msg25499.html
"""
import numpy as np
import pylab as pl
from scipy import interpolate, signal
import matplotlib.font_manager as fm


# We need a special font for the code below.  It can be downloaded this way:
import os
import urllib2
if not os.path.exists('Humor-Sans.ttf'):
    fhandle = urllib2.urlopen('http://antiyawn.com/uploads/Humor-Sans.ttf')
    open('Humor-Sans.ttf', 'wb').write(fhandle.read())

    
def xkcd_line(x, y, xlim=None, ylim=None,
              mag=1.0, f1=30, f2=0.05, f3=15):
    """
    Mimic a hand-drawn line from (x, y) data

    Parameters
    ----------
    x, y : array_like
        arrays to be modified
    xlim, ylim : data range
        the assumed plot range for the modification.  If not specified,
        they will be guessed from the  data
    mag : float
        magnitude of distortions
    f1, f2, f3 : int, float, int
        filtering parameters.  f1 gives the size of the window, f2 gives
        the high-frequency cutoff, f3 gives the size of the filter
    
    Returns
    -------
    x, y : ndarrays
        The modified lines
    """
    x = np.asarray(x)
    y = np.asarray(y)
    
    # get limits for rescaling
    if xlim is None:
        xlim = (x.min(), x.max())
    if ylim is None:
        ylim = (y.min(), y.max())

    if xlim[1] == xlim[0]:
        xlim = ylim
        
    if ylim[1] == ylim[0]:
        ylim = xlim

    # scale the data
    x_scaled = (x - xlim[0]) * 1. / (xlim[1] - xlim[0])
    y_scaled = (y - ylim[0]) * 1. / (ylim[1] - ylim[0])

    # compute the total distance along the path
    dx = x_scaled[1:] - x_scaled[:-1]
    dy = y_scaled[1:] - y_scaled[:-1]
    dist_tot = np.sum(np.sqrt(dx * dx + dy * dy))

    # number of interpolated points is proportional to the distance
    Nu = int(200 * dist_tot)
    u = np.arange(-1, Nu + 1) * 1. / (Nu - 1)

    # interpolate curve at sampled points
    k = min(3, len(x) - 1)
    res = interpolate.splprep([x_scaled, y_scaled], s=0, k=k)
    x_int, y_int = interpolate.splev(u, res[0]) 

    # we'll perturb perpendicular to the drawn line
    dx = x_int[2:] - x_int[:-2]
    dy = y_int[2:] - y_int[:-2]
    dist = np.sqrt(dx * dx + dy * dy)

    # create a filtered perturbation
    coeffs = mag * np.random.normal(0, 0.01, len(x_int) - 2)
    b = signal.firwin(f1, f2 * dist_tot, window=('kaiser', f3))
    response = signal.lfilter(b, 1, coeffs)

    x_int[1:-1] += response * dy / dist
    y_int[1:-1] += response * dx / dist

    # un-scale data
    x_int = x_int[1:-1] * (xlim[1] - xlim[0]) + xlim[0]
    y_int = y_int[1:-1] * (ylim[1] - ylim[0]) + ylim[0]
    
    return x_int, y_int


def XKCDify(ax, mag=1.0,
            f1=50, f2=0.01, f3=15,
            bgcolor='w',
            xaxis_loc=None,
            yaxis_loc=None,
            xaxis_arrow='+',
            yaxis_arrow='+',
            ax_extend=0.1,
            expand_axes=False):
    """Make axis look hand-drawn

    This adjusts all lines, text, legends, and axes in the figure to look
    like xkcd plots.  Other plot elements are not modified.
    
    Parameters
    ----------
    ax : Axes instance
        the axes to be modified.
    mag : float
        the magnitude of the distortion
    f1, f2, f3 : int, float, int
        filtering parameters.  f1 gives the size of the window, f2 gives
        the high-frequency cutoff, f3 gives the size of the filter
    xaxis_loc, yaxis_log : float
        The locations to draw the x and y axes.  If not specified, they
        will be drawn from the bottom left of the plot
    xaxis_arrow, yaxis_arrow : str
        where to draw arrows on the x/y axes.  Options are '+', '-', '+-', or ''
    ax_extend : float
        How far (fractionally) to extend the drawn axes beyond the original
        axes limits
    expand_axes : bool
        if True, then expand axes to fill the figure (useful if there is only
        a single axes in the figure)
    """
    # Get axes aspect
    ext = ax.get_window_extent().extents
    aspect = (ext[3] - ext[1]) / (ext[2] - ext[0])

    xlim = ax.get_xlim()
    ylim = ax.get_ylim()

    xspan = xlim[1] - xlim[0]
    yspan = ylim[1] - xlim[0]

    xax_lim = (xlim[0] - ax_extend * xspan,
               xlim[1] + ax_extend * xspan)
    yax_lim = (ylim[0] - ax_extend * yspan,
               ylim[1] + ax_extend * yspan)

    if xaxis_loc is None:
        xaxis_loc = ylim[0]

    if yaxis_loc is None:
        yaxis_loc = xlim[0]

    # Draw axes
    xaxis = pl.Line2D([xax_lim[0], xax_lim[1]], [xaxis_loc, xaxis_loc],
                      linestyle='-', color='k')
    yaxis = pl.Line2D([yaxis_loc, yaxis_loc], [yax_lim[0], yax_lim[1]],
                      linestyle='-', color='k')

    # Label axes3, 0.5, 'hello', fontsize=14)
    ax.text(xax_lim[1], xaxis_loc - 0.02 * yspan, ax.get_xlabel(),
            fontsize=14, ha='right', va='top', rotation=12)
    ax.text(yaxis_loc - 0.02 * xspan, yax_lim[1], ax.get_ylabel(),
            fontsize=14, ha='right', va='top', rotation=78)
    ax.set_xlabel('')
    ax.set_ylabel('')

    # Add title
    ax.text(0.5 * (xax_lim[1] + xax_lim[0]), yax_lim[1],
            ax.get_title(),
            ha='center', va='bottom', fontsize=16)
    ax.set_title('')

    Nlines = len(ax.lines)
    lines = [xaxis, yaxis] + [ax.lines.pop(0) for i in range(Nlines)]

    for line in lines:
        x, y = line.get_data()

        x_int, y_int = xkcd_line(x, y, xlim, ylim,
                                 mag, f1, f2, f3)

        # create foreground and background line
        lw = line.get_linewidth()
        line.set_linewidth(2 * lw)
        line.set_data(x_int, y_int)

        # don't add background line for axes
        if (line is not xaxis) and (line is not yaxis):
            line_bg = pl.Line2D(x_int, y_int, color=bgcolor,
                                linewidth=8 * lw)

            ax.add_line(line_bg)
        ax.add_line(line)

    # Draw arrow-heads at the end of axes lines
    arr1 = 0.03 * np.array([-1, 0, -1])
    arr2 = 0.02 * np.array([-1, 0, 1])

    arr1[::2] += np.random.normal(0, 0.005, 2)
    arr2[::2] += np.random.normal(0, 0.005, 2)

    x, y = xaxis.get_data()
    if '+' in str(xaxis_arrow):
        ax.plot(x[-1] + arr1 * xspan * aspect,
                y[-1] + arr2 * yspan,
                color='k', lw=2)
    if '-' in str(xaxis_arrow):
        ax.plot(x[0] - arr1 * xspan * aspect,
                y[0] - arr2 * yspan,
                color='k', lw=2)

    x, y = yaxis.get_data()
    if '+' in str(yaxis_arrow):
        ax.plot(x[-1] + arr2 * xspan * aspect,
                y[-1] + arr1 * yspan,
                color='k', lw=2)
    if '-' in str(yaxis_arrow):
        ax.plot(x[0] - arr2 * xspan * aspect,
                y[0] - arr1 * yspan,
                color='k', lw=2)

    # Change all the fonts to humor-sans.
    prop = fm.FontProperties(fname='Humor-Sans.ttf', size=16)
    for text in ax.texts:
        text.set_fontproperties(prop)
    
    # modify legend
    leg = ax.get_legend()
    if leg is not None:
        leg.set_frame_on(False)
        
        for child in leg.get_children():
            if isinstance(child, pl.Line2D):
                x, y = child.get_data()
                child.set_data(xkcd_line(x, y, mag=10, f1=100, f2=0.001))
                child.set_linewidth(2 * child.get_linewidth())
            if isinstance(child, pl.Text):
                child.set_fontproperties(prop)
    
    # Set the axis limits
    ax.set_xlim(xax_lim[0] - 0.1 * xspan,
                xax_lim[1] + 0.1 * xspan)
    ax.set_ylim(yax_lim[0] - 0.1 * yspan,
                yax_lim[1] + 0.1 * yspan)

    # adjust the axes
    ax.set_xticks([])
    ax.set_yticks([])      

    if expand_axes:
        ax.figure.set_facecolor(bgcolor)
        ax.set_axis_off()
        ax.set_position([0, 0, 1, 1])
    
    return ax

### Testing it Out

# Let's test this out with a simple plot.  We'll plot two curves, add some labels,
# and then call ``XKCDify`` on the axis.  I think the results are pretty nice!

# In[4]:
%pylab inline

# Out[4]:
#     
#     Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].
#     For more information, type 'help(pylab)'.
# 
# In[5]:
np.random.seed(0)

ax = pylab.axes()

x = np.linspace(0, 10, 100)
ax.plot(x, np.sin(x) * np.exp(-0.1 * (x - 5) ** 2), 'b', lw=1, label='damped sine')
ax.plot(x, -np.cos(x) * np.exp(-0.1 * (x - 5) ** 2), 'r', lw=1, label='damped cosine')

ax.set_title('check it out!')
ax.set_xlabel('x label')
ax.set_ylabel('y label')

ax.legend(loc='lower right')

ax.set_xlim(0, 10)
ax.set_ylim(-1.0, 1.0)

#XKCDify the axes -- this operates in-place
XKCDify(ax, xaxis_loc=0.0, yaxis_loc=1.0,
        xaxis_arrow='+-', yaxis_arrow='+-',
        expand_axes=True)


# Out[5]:
#     <matplotlib.axes.AxesSubplot at 0x2fecbd0>


# image file: tests/ipynbref/XKCD_plots_orig_files/XKCD_plots_orig_fig_00.png

### Duplicating an XKCD Comic

# Now let's see if we can use this to replicated an XKCD comic in matplotlib.
# This is a good one:

# In[6]:
Image('http://imgs.xkcd.com/comics/front_door.png')

# Out[6]:
#     <IPython.core.display.Image at 0x2ff4a10>


# With the new ``XKCDify`` function, this is relatively easy to replicate.  The results
# are not exactly identical, but I think it definitely gets the point across!

# In[7]:
# Some helper functions
def norm(x, x0, sigma):
    return np.exp(-0.5 * (x - x0) ** 2 / sigma ** 2)

def sigmoid(x, x0, alpha):
    return 1. / (1. + np.exp(- (x - x0) / alpha))
    
# define the curves
x = np.linspace(0, 1, 100)
y1 = np.sqrt(norm(x, 0.7, 0.05)) + 0.2 * (1.5 - sigmoid(x, 0.8, 0.05))

y2 = 0.2 * norm(x, 0.5, 0.2) + np.sqrt(norm(x, 0.6, 0.05)) + 0.1 * (1 - sigmoid(x, 0.75, 0.05))

y3 = 0.05 + 1.4 * norm(x, 0.85, 0.08)
y3[x > 0.85] = 0.05 + 1.4 * norm(x[x > 0.85], 0.85, 0.3)

# draw the curves
ax = pl.axes()
ax.plot(x, y1, c='gray')
ax.plot(x, y2, c='blue')
ax.plot(x, y3, c='red')

ax.text(0.3, -0.1, "Yard")
ax.text(0.5, -0.1, "Steps")
ax.text(0.7, -0.1, "Door")
ax.text(0.9, -0.1, "Inside")

ax.text(0.05, 1.1, "fear that\nthere's\nsomething\nbehind me")
ax.plot([0.15, 0.2], [1.0, 0.2], '-k', lw=0.5)

ax.text(0.25, 0.8, "forward\nspeed")
ax.plot([0.32, 0.35], [0.75, 0.35], '-k', lw=0.5)

ax.text(0.9, 0.4, "embarrassment")
ax.plot([1.0, 0.8], [0.55, 1.05], '-k', lw=0.5)

ax.set_title("Walking back to my\nfront door at night:")

ax.set_xlim(0, 1)
ax.set_ylim(0, 1.5)

# modify all the axes elements in-place
XKCDify(ax, expand_axes=True)


# Out[7]:
#     <matplotlib.axes.AxesSubplot at 0x2fef210>


# image file: tests/ipynbref/XKCD_plots_orig_files/XKCD_plots_orig_fig_01.png

# Pretty good for a couple hours's work!
# 
# I think the possibilities here are pretty limitless: this is going to be a hugely
# useful and popular feature in matplotlib, especially when the sketch artist PR is mature
# and part of the main package.  I imagine using this style of plot for schematic figures
# in presentations where the normal crisp matplotlib lines look a bit too "scientific".
# I'm giving a few talks at the end of the month... maybe I'll even use some of
# this code there.
# 
# This post was written entirely in an IPython Notebook: the notebook file is available for
# download [here](http://jakevdp.github.com/downloads/notebooks/XKCD_plots.ipynb).
# For more information on blogging with notebooks in octopress, see my
# [previous post](http://jakevdp.github.com/blog/2012/10/04/blogging-with-ipython/)
# on the subject.