Lloyd's algorithm: Difference between revisions

Revision as of 06:39, 26 September 2019

Revision as of 23:50, 6 March 2020

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** Trivially, a set of [[Tetrahedron|tetrahedra]] is obtained by connecting triangles of the cell's hull with the cell's site.

Integration of a cell and computation of its [[Centroid|centroid]] (center of mass) is now given as a weighted combination of its simplices' [[Circumscribed circle|circumcenters]]centroids (in the following called <math display="inline">\mathbf{c}_i</math>).

* Two dimensions:

** For a triangle the circumcircle and its center are uniquecentroid and can be easily computed, e.g. using [[Circumscribed circleCentroid#CircumcenterBy geometric coordinatesdecomposition|cartesian coordinates]].

** Weighting computes as simplex-to-cell '''area''' ratios.

* Three dimensions: