Project 2: Spherical Harmonics¶

Quick Scrolling¶

Description
Methodology
Results
Jupyter Notebook
Methods and Classes

Description¶

A few functions are made for plotting/visualizing spherical harmonics.

Methodology¶

We use sph_harmonics.BibicallyAccurateSphericalHarmonics to plot 3D spherical harmonics.

The convenience function sph_harmonics.imageCropper is included to crop off excess fat from the images generated by matplotlib.

An example is below for l=26, m=13

# Lets make a nice plot of our favorite spherical harmonic function.
l=26
m=13
elev = 25
azimRot = 45
nangles = 600
dpi=250

# Plot and save
BibicallyAccurateSphericalHarmonics(l=l, m=m, sphType='real', nangles=nangles, elev=elev, azimRot=azimRot, dpi=dpi, filename='L26_m13.png', doPlot=True)

# Crop image for convenience.
imageCropper(filename='L26_m13.png', outname='L26_m13.png', left_inches=0.5, right_inches=0.4, top_inches=1.2, bottom_inches=1.15, dpi=dpi)

We can also make a number of images and turn them into a gif using sph_harmonics.gifMaker. Simply gather an ordererd list of filenames you want to turn into a gif and then run gifMaker()

An example is provided below. In this case we take many snapshots of different angular rotations to envision the function rotating in space!

# Lets make a gif (do not run high dpi or high nangles unless you value your time)
from IPython.display import Image

l=1
m=0
nangles = 25
dpi=50
nFrames = 200

# vary the angles
elev_angles = np.linspace(0, 2*np.pi, nFrames) * 360 / 2.0 / np.pi # 1 full 360 degree rotation
azim_angles = np.linspace(0, 2*np.pi, nFrames) * 360 / 2.0 / np.pi # 1 full 360 degree rotation


filename_list = []
for i, _ in enumerate(elev_angles):
        # Make filename
        # !!! make sure the folder L1_M0_GIF exists before running !!!
        filename = './L1_M0_GIF/'+str(i)+'.png'

        # Generate a snapshot and save it
        BibicallyAccurateSphericalHarmonics(l=l, m=m, sphType='real',
                        nangles=nangles, elev=elev_angles[i], azimRot=azim_angles[i],
                        dpi=dpi, filename=filename,
                        doPlot=False)
        # Crop some fat off the image
        imageCropper(filename=filename, outname=filename, left_inches=0.5, right_inches=0.4, top_inches=1.2, bottom_inches=1.15, dpi=dpi)

        # Append filename
        filename_list.append(filename)

# Make a cute little gif of our function rotating :)
gifMaker(output_filename='./L1_M0_GIF/L1_M0.gif', duration=5, filenames=filename_list)

# Display gif:
Image(url='./L1_M0_GIF/L1_M0.gif')