A computational framework for tracking grain boundaries in 3D image data: Quantifying boundary curvatures and velocities in polycrystalline materials

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Publication date: 28 February 2026

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Most of the algorithms described here are quite straightforward to implement. Some of them can be written in just a few lines of code, and those that require a bit more effort can be better understood by reading through the relevant papers and links I have provided. The exception to this are those that rely on the Delaunay triangulation to work. Robust Delaunay triangulations in 3D are fairly complex and there isn’t any publicly available software that I’m aware of that leverages them for dithering in the way I’ve described.

His industry accolades include five Grammy awards, induction into both the UK Music Hall of Fame and the Rock and Roll Hall of Fame - both with Black Sabbath and as a solo artist, in separate years - and the Ivor Novello Award for Lifetime Achievement, with Black Sabbath.

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