Spherical Harmonics

Spherical harmonics for radiance maps in Python (numpy).

Features:

• Obtain coefficients for a radiance map (in equirectangular format)
• Numpy vectorised for efficiency
• Windowing function for reducing ringing artefacts
• Reconstruct radiance map from coefficients
• Obtain diffuse BRDF coefficients
• Render a diffuse map (given radiance map coefficients)
• Supports an arbitrary number of bands
• Plot the spherical harmonics in a figure
• Render a ground truth diffuse map to compare with.

The ground truth diffuse map can be a little slow to compute, so I've added the ability to render the diffuse values at a low resolution while sampling the high resolution source image. After rendering at a low resolution, I increase the resolution (so it's easier to see) using Lanczos interpolation. I found doing it this way was the most efficient while also producing high quality ground truth images.

Usage

python main.py --ibl_filename <path_to_ibl_file> --l_max <number_of_bands> --output_dir <output_directory> --resize_width <width>

For example:

python main.py --ibl_filename ./images/grace-new.exr --l_max 2

See the main function to see examples of functions you can utilise in your own code.

Dependencies

You can use pip to install the modules I've used, or use the requirements file:

pip install -r requirements.txt

The only gotcha is with imageio. By default it does not provide OpenEXR support. To add OpenEXR support to imageio, see here: https://imageio.readthedocs.io/en/stable/_autosummary/imageio.plugins.freeimage.html#module-imageio.plugins.freeimage

e.g., run the following in python (after installing imageio):

imageio.plugins.freeimage.download()

References

• Ramamoorthi, Ravi, and Pat Hanrahan. "An efficient representation for irradiance environment maps", 2001.
• Sloan, Peter-Pike, Jan Kautz, and John Snyder. "Precomputed radiance transfer for real-time rendering in dynamic, low-frequency lighting environments", 2002.
• "Spherical Harmonic Lighting: The Gritty Details" by Robin Green
• "Stupid Spherical Harmonics (SH) Tricks" by Peter Pike Sloan
• PBRT source code: https://www.csie.ntu.edu.tw/~cyy/courses/rendering/pbrt-2.00/html/sh_8cpp_source.html
• Probulator source code (I based my windowing code on this): https://github.com/kayru/Probulator
• Some radiance maps can be downloaded here: http://gl.ict.usc.edu/Data/HighResProbes/

Future Development

Depending on demand, the following may be addedd in future:

• Support other formats (e.g. cubemap, angular map, etc.)
• Change, remove, or support other modules (e.g. I use imageio for reading HDR images, cv2 for resizing, etc.)
• More optimisations
• Other windowing methods
• Other visualisations
• Restructure code

License

MIT License

Copyright (c) 2018 Andrew Chalmers

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.