Lloyd's algorithm: Difference between revisions

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Lloyd's algorithm for 2D Voronoi diagrams uses weighted average of all simplex centroids not circumcenter.
Grammar after previous change (extraneous "can" in the sentence)
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Integration of a cell and computation of its [[Centroid|centroid]] (center of mass) is now given as a weighted combination of its simplices' centroids (in the following called <math display="inline">\mathbf{c}_i</math>).
* Two dimensions:
** For a triangle the centroid and can be easily computed, e.g. using [[Centroid#By geometric decomposition|cartesian coordinates]].
** Weighting computes as simplex-to-cell '''area''' ratios.
* Three dimensions: