Bowyer-Watson algorithm is one of the possible approaches to implement the Delaunay triangulation, which takes a set of points and generates a triangulation such that no point is inside the circumcircle of any triangle of the triangulation.

https://en.wikipedia.org/wiki/Delaunay_triangulation

The algorithm consists in incrementally adding the points of the set to the triangulation, removing any triangle whose circumcircle contains the point leaving a star-shaped polygonal hole, which is then triangulated using the new point as a vertex of each new triangle.

This whole project is inspired by Sebastian Lague's intros (for example https://www.youtube.com/watch?v=X-iSQQgOd1A), check him out if you're interested in, quote, "creating stuff out of code".

This code attempts to render some interesting procedural graphic effects based on the properties of each triangle, such as vertical position, area, or distance from the center.

Two different methods for the BowyerWatson triangulation are implemented: a slower one that brute-forcely scans the whole triangulation to find the triangles to remove, and a fast one which works on the assumption that only contiguous triangles will contain the point in their respective circumcircle.

The quick implementation works by searching for the first triangle containing the point in its circumcircle, then checking each contiguous triangle recoursively until no match is found. This method allows for much quicker triangulation, but adds complexity in managing and mantaining the contiguity between triangles.

Copyright 2021 Marco Gardini

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