We approximate the uniform measure on an equilateral triangle by a measure sup-ported on points. We find the optimal sets of points (-means) and corresponding approximation (quantization) error for ≤4, give numerical optimization results for ≤21, and a bound on the quantization error for →∞. The equilateral triangle has particularly efficient quantizations due to its connection with the triangular lattice. Our methods can be applied to uniform distributions on general sets with piecewise smooth boundaries.
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