Understanding the behavior of the Delaunay triangulation algorithm with collinear points is crucial for assessing its robustness and precision in computational geometry applications.
During Delaunay triangulation, if a triangle is created from three (almost) collinear points, its big circumcircle will probably cover another point in the point set, which will in turn violate the Delaunay property. If such a case happens, the algorithm will perform a diagonal edge flip with an adjacent triangle, forming two new triangles, after which the Delaunay property should be satisfied. The resulting triangulation is the one that has very few "sliver triangles", which is desirable in graphic rendering, localization, etc.
Voronoi diagrams for collinear points will be parallel lines...
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