PolarPlots Tutorial

Polar Plots Tutorial

This Notebook demonstrates how to create polar plots in VCS

Prepare modules and function to visualize

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In [1]:
import vcs
import vcsaddons
import numpy

# class to visualize canvas
import tempfile
import base64
class VCSAddonsNotebook(object):
    def __init__(self, x):
        self.x = x
    def _repr_png_(self):
        fnm = tempfile.mktemp()+".png"
        x.png(fnm)
        encoded = base64.b64encode(open(fnm, "rb").read())
        return encoded
    def __call__(self):
        return self
    
def show(canvas):
    return VCSAddonsNotebook(canvas)()

Prepare data and vcs objects

Here we define some dataset for later use in the notebook, feel free to set r to any of these to see the changes

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In [2]:
# Angles
nPoints = 75
theta0 = .001
e = numpy.exp(1.)
pi = numpy.pi
thetaN =  2.*pi
delta = (thetaN-theta0)/(nPoints-1)
theta = numpy.arange(theta0,thetaN,delta)

# Archimede's spiral
r_archimede = theta
# Rose Curves
nPetals = 6
r_rose = 4.*numpy.cos(nPetals*theta)
# simple
r_simple = 5. * numpy.sin(theta)
# Another simple one
r_simple_2 = 4. - 4.*numpy.cos(theta)
# Leaf
r_leaf = (1 + 0.9*numpy.cos(8*theta))*(1 + 0.1*numpy.cos(24*theta))*(0.9 + 0.05*numpy.cos(200*theta))*(1 +numpy.sin(theta))
# Love
r_love = 2*pi/numpy.sqrt(theta) + pi/4. -2.*numpy.sin(theta)+numpy.sin(theta)*numpy.sqrt(numpy.abs(numpy.cos(theta)))/(numpy.sin(theta)+1.4)

# set which curve to vizualize
r = r_archimede

# Initialize vcs canvas
x=vcs.init(bg=True, geometry=(600,600))

Basic (default) Plot

Let's plot this with a very basic plot. Back To Top

In [3]:
# Create polar graphic method
polar = vcsaddons.createpolar()
# Associate vcs canvas with it
polar.x = x
# Plot
show(polar.plot(r,theta))
Out[3]:

Controlling the markers

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In [4]:
polar.markersizes = [2.]
polar.markercolors = ["red"]
polar.markertypes = ["square"]
x.clear()
show(polar.plot(r,theta))
Out[4]:

Plotting Multiple Sets (groups) At Once

We can plot 3 different sets/groups at once, each with their own set of color/markers Back To Top

In [5]:
r2 = numpy.array([r,r_simple,r_simple_2])
polar.markercolors = ["red","green","blue"]
polar.markertypes = ["square","dot","diamond"]
polar.markersizes = [2.,5.,2.]
x.clear()
show(polar.plot(r2,theta))
Out[5]:

Clockwise Plots

Sometimes it can be useful to have $\theta$ rotating clockwise.

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In [6]:
polar.markercolors = ["red"]
polar.markersizes= [1]
polar.markertypes = ["square"]
import EzTemplate
M = EzTemplate.Multi(columns=2,rows=1)
x.clear()
polar.plot(r,theta,template=M.get(row=0,column=0))
polar.clockwise = True
show(polar.plot(r,theta,template=M.get(row=0,column=1)))
Out[6]:

Connecting The Markers

We can also connect markers.

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In [7]:
polar.clockwise = False
polar.linepriority=1
polar.linetypes=["dot"]
polar.linecolors = ["blue"]
polar.linewidths = [3.]
x.clear()
show(polar.plot(r,theta))
Out[7]:
In [8]:
polar.theta_tick_count = 3
x.clear()
show(polar.plot(r,theta))
Out[8]:

Controlling Magnitude (Radial) Labels/Ticks

We can control the value of the magnitude labels. Using vcs templates and text orientation objects we can control these labels angle.

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In [9]:
ticks = {}
for a in range(45,361,45):
    ticks[float(a)/180.*numpy.pi] = r"$%i^o$" % a
polar.xticlabels1 = ticks
#polar.yticlabels1 = {1.:"one",3.:"three"}
polar.datawc_y1 = 0
polar.datawc_y2= 7
polar.yticlabels1 = {1.:"one",3.:"three",5:"five"}
polar.magnitude_tick_angle = pi/4.
#polar.yticlabels1 = None
x.clear()
to = vcs.createtextorientation()
to.angle = -45
tmpl = vcs.createtemplate()
tmpl.ylabel1.textorientation = to
show(polar.plot(r,theta, template=tmpl))
Out[9]:

Angular ($\theta$) Offset

Sometimes we need $\theta$ to start at some other values than 0 radians.

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In [10]:
polar.theta_offset = pi/4.
to.angle = -90
x.clear()
show(polar.plot(r,theta, template=tmpl))
Out[10]:

Magnitude Sub ticks

We can add sub ticks on the magnitude (radial) circles Using vcs template and line objects we can control the appearance of these subticks

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In [11]:
# reset a few things
polar.theta_offset = 0.
polar.magnitude_tick_angle = 0
to.angle = 0

dot = vcs.createline()
dot.type="dot"
dot.color = ["grey"]
tmpl.ymintic1.line = dot
tmpl.ymintic1.priority = 1
polar.magnitude_mintics = [.5,1.5,2.5,3.5,4.5,5.5,6.5,7.5]
x.clear()
show(polar.plot(r,theta, template=tmpl))
Out[11]:

Non Linear Magnitude (Radial) Scales

Sometimes it can be useful to have a non linear scale for the radius

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In [12]:
polar.magnitude_ticks = [1,1.1,2,7]
polar.datawc_y1 = 1.e20
polar.datawc_y2 = 1.e20
x.clear()
show(polar.plot(r,theta, template=tmpl))
Out[12]:

Using Amplitude To Control Markers Colors

It can be useful to link the markers color to the magnitude

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In [13]:
x.clear()
polar = vcsaddons.createpolar()
polar.x=x
polar.markercolors = [16, 66, 116, 143, 162, 181, 200, 219]
polar.markercolorsource = "magnitude"
tmpl = vcs.createtemplate()
tmpl.legend.x1=.9
tmpl.legend.x2=.99
tmpl.legend.y1 = .2
tmpl.legend.y2=.8
x.clear()
show(polar.plot(r,theta,template=tmpl))
Out[13]:

Using $\theta$ To Control Markers Colors

It can be useful to link the markers color to $\theta$

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In [14]:
x.clear()
polar = vcsaddons.createpolar()
polar.x=x
polar.markercolors = [16, 66, 116, 143, 162, 181, 200, 219]
polar.markercolorsource = "theta"
tmpl = vcs.createtemplate()
tmpl.legend.priority=0
x.clear()
show(polar.plot(r,theta,template=tmpl))
Out[14]: