Marker size/alpha scaling with window size/zoom in plot/scatter

Question

When exploring data sets with many points on an xy chart, I can adjust the alpha and/or marker size to give a good quick visual impression of where the points are most densely clustered. However when I zoom in or make the window bigger, the a different alpha and/or marker size is needed to give the same visual impression.

How can I have the alpha value and/or the marker size increase when I make the window bigger or zoom in on the data? I am thinking that if I double the window area I could double the marker size, and/or take the square root of the alpha; and the opposite for zooming.

Note that all points have the same size and alpha. Ideally the solution would work with plot(), but if it can only be done with scatter() that would be helpful also.

Answer 1

You can achieve what you want with matplotlib event handling. You have to catch zoom and resize events separately. It's a bit tricky to account for both at the same time, but not impossible. Below is an example with two subplots, a line plot on the left and a scatter plot on the right. Both zooming (factor) and resizing of the figure (fig_factor) re-scale the points according to the scaling factors in figure size and x- and y- limits. As there are two limits defined -- one for the x and one for the y direction, I used here the respective minima for the two factors. If you'd rather want to scale with the larger factors, change the min to max in both event functions.

from matplotlib import pyplot as plt
import numpy as np

fig, axes = plt.subplots(nrows=1, ncols = 2)
ax1,ax2 = axes
fig_width = fig.get_figwidth()
fig_height = fig.get_figheight()
fig_factor = 1.0

##saving some values
xlim = dict()
ylim = dict()
lines = dict()
line_sizes = dict()
paths = dict()
point_sizes = dict()

## a line plot
x1 = np.linspace(0,np.pi,30)
y1 = np.sin(x1)

lines[ax1] = ax1.plot(x1, y1, 'ro', markersize = 3, alpha = 0.8)
xlim[ax1] = ax1.get_xlim()
ylim[ax1] = ax1.get_ylim()
line_sizes[ax1] = [line.get_markersize() for line in lines[ax1]]


## a scatter plot
x2 = np.random.normal(1,1,30)
y2 = np.random.normal(1,1,30)

paths[ax2] = ax2.scatter(x2,y2, c = 'b', s = 20, alpha = 0.6)
point_sizes[ax2] = paths[ax2].get_sizes()

xlim[ax2] = ax2.get_xlim()
ylim[ax2] = ax2.get_ylim()


def on_resize(event):
    global fig_factor

    w = fig.get_figwidth()
    h = fig.get_figheight()

    fig_factor = min(w/fig_width,h/fig_height)

    for ax in axes:
        lim_change(ax)


def lim_change(ax):
    lx = ax.get_xlim()
    ly = ax.get_ylim()

    factor = min(
        (xlim[ax][1]-xlim[ax][0])/(lx[1]-lx[0]),
        (ylim[ax][1]-ylim[ax][0])/(ly[1]-ly[0])
    )

    try:
        for line,size in zip(lines[ax],line_sizes[ax]):
            line.set_markersize(size*factor*fig_factor)
    except KeyError:
        pass


    try:
        paths[ax].set_sizes([s*factor*fig_factor for s in point_sizes[ax]])
    except KeyError:
        pass

fig.canvas.mpl_connect('resize_event', on_resize)
for ax in axes:
    ax.callbacks.connect('xlim_changed', lim_change)
    ax.callbacks.connect('ylim_changed', lim_change)
plt.show()

The code has been tested in Pyton 2.7 and 3.6 with matplotlib 2.1.1.

EDIT

Motivated by the comments below and this answer, I created another solution. The main idea here is to only use one type of event, namely draw_event. At first the plots did not update correctly upon zooming. Also ax.draw_artist() followed by a fig.canvas.draw_idle() like in the linked answer did not really solve the problem (however, this might be platform/backend specific). Instead I added an extra call to fig.canvas.draw() whenever the scaling changes (the if statement prevents infinite loops).

In addition, do avoid all the global variables, I wrapped everything into a class called MarkerUpdater. Each Axes instance can be registered separately to the MarkerUpdater instance, so you could also have several subplots in one figure, of which some are updated and some not. I also fixed another bug, where the points in the scatter plot scaled wrongly -- they should scale quadratic, not linear (see here).

Finally, as it was missing from the previous solution, I also added updating for the alpha value of the markers. This is not quite as straight forward as the marker size, because alpha values must not be larger than 1.0. For this reason, in my implementation the alpha value can only be decreased from the original value. Here I implemented it such that the alpha decreases when the figure size is decreased. Note that if no alpha value is provided to the plot command, the artist stores None as alpha value. In this case the automatic alpha tuning is off.

What should be updated in which Axes can be defined with the features keyword -- see below if __name__ == '__main__': for an example how to use MarkerUpdater.

EDIT 2

As pointed out by @ImportanceOfBeingErnest, there was a problem with infinite recursion with my answer when using the TkAgg backend, and apparently problems with the figure not refreshing properly upon zooming (which I couldn't verify, so probably that was implementation dependent). Removing the fig.canvas.draw() and adding ax.draw_artist(ax) within the loop over the Axes instances instead fixed this issue.

EDIT 3

I updated the code to fix an ongoing issue where figure is not updated properly upon a draw_event. The fix was taken from this answer, but modified to also work for several figures.

In terms of an explanation of how the factors are obtained, the MarkerUpdater instance contains a dict that stores for each Axes instance the figure dimensions and the limits of the axes at the time it is added with add_ax. Upon a draw_event, which is for instance triggered when the figure is resized or the user zooms in on the data, the new (current) values for figure size and axes limits are retrieved and a scaling factor is calculated (and stored) such that zooming in and increasing the figure size makes the markers bigger. Because x- and y-dimensions may change at different rates, I use min to pick one of the two calculated factors and always scale against the original size of the figure.

If you want your alpha to scale with a different function, you can easily change the lines that adjust the alpha value. For instance, if you want a power law instead of a linear decrease, you can write path.set_alpha(alpha*facA**n), where n is the power.

from matplotlib import pyplot as plt
import numpy as np

##plt.switch_backend('TkAgg')
class MarkerUpdater:
    def __init__(self):
        ##for storing information about Figures and Axes
        self.figs = {}

        ##for storing timers
        self.timer_dict = {}

    def add_ax(self, ax, features=[]):
        ax_dict = self.figs.setdefault(ax.figure,dict())
        ax_dict[ax] = {
            'xlim' : ax.get_xlim(),
            'ylim' : ax.get_ylim(),
            'figw' : ax.figure.get_figwidth(),
            'figh' : ax.figure.get_figheight(),
            'scale_s' : 1.0,
            'scale_a' : 1.0,
            'features' : [features] if isinstance(features,str) else features,
        }
        ax.figure.canvas.mpl_connect('draw_event', self.update_axes)

    def update_axes(self, event):

        for fig,axes in self.figs.items():
            if fig is event.canvas.figure:

                for ax, args in axes.items():
                    ##make sure the figure is re-drawn
                    update = True

                    fw = fig.get_figwidth()
                    fh = fig.get_figheight()
                    fac1 = min(fw/args['figw'], fh/args['figh'])


                    xl = ax.get_xlim()
                    yl = ax.get_ylim()
                    fac2 = min(
                        abs(args['xlim'][1]-args['xlim'][0])/abs(xl[1]-xl[0]),
                        abs(args['ylim'][1]-args['ylim'][0])/abs(yl[1]-yl[0])
                    )

                    ##factor for marker size
                    facS = (fac1*fac2)/args['scale_s']

                    ##factor for alpha -- limited to values smaller 1.0
                    facA = min(1.0,fac1*fac2)/args['scale_a']

                    ##updating the artists
                    if facS != 1.0:
                        for line in ax.lines:
                            if 'size' in args['features']:
                                line.set_markersize(line.get_markersize()*facS)

                            if 'alpha' in args['features']:
                                alpha = line.get_alpha()
                                if alpha is not None:
                                    line.set_alpha(alpha*facA)


                        for path in ax.collections:
                            if 'size' in args['features']:
                                path.set_sizes([s*facS**2 for s in path.get_sizes()])

                            if 'alpha' in args['features']:
                                alpha = path.get_alpha()
                                if alpha is not None:
                                    path.set_alpha(alpha*facA)

                        args['scale_s'] *= facS
                        args['scale_a'] *= facA

                self._redraw_later(fig)



    def _redraw_later(self, fig):
        timer = fig.canvas.new_timer(interval=10)
        timer.single_shot = True
        timer.add_callback(lambda : fig.canvas.draw_idle())
        timer.start()

        ##stopping previous timer
        if fig in self.timer_dict:
            self.timer_dict[fig].stop()

        ##storing a reference to prevent garbage collection
        self.timer_dict[fig] = timer

if __name__ == '__main__':
    my_updater = MarkerUpdater()

    ##setting up the figure
    fig, axes = plt.subplots(nrows = 2, ncols =2)#, figsize=(1,1))
    ax1,ax2,ax3,ax4 = axes.flatten()

    ## a line plot
    x1 = np.linspace(0,np.pi,30)
    y1 = np.sin(x1)
    ax1.plot(x1, y1, 'ro', markersize = 10, alpha = 0.8)
    ax3.plot(x1, y1, 'ro', markersize = 10, alpha = 1)

    ## a scatter plot
    x2 = np.random.normal(1,1,30)
    y2 = np.random.normal(1,1,30)
    ax2.scatter(x2,y2, c = 'b', s = 100, alpha = 0.6)

    ## scatter and line plot
    ax4.scatter(x2,y2, c = 'b', s = 100, alpha = 0.6)
    ax4.plot([0,0.5,1],[0,0.5,1],'ro', markersize = 10) ##note: no alpha value!

    ##setting up the updater
    my_updater.add_ax(ax1, ['size'])  ##line plot, only marker size
    my_updater.add_ax(ax2, ['size'])  ##scatter plot, only marker size
    my_updater.add_ax(ax3, ['alpha']) ##line plot, only alpha
    my_updater.add_ax(ax4, ['size', 'alpha']) ##scatter plot, marker size and alpha

    plt.show()