Capacity-Constrained Point Distributions : A Variant of Lloyd's Method

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2009
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978-1-60558-726-4
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ACM Transactions on Graphics ( Proceedings of SIGGRAPH ). 2009, 28(3), 86. Available under: doi: 10.1145/1531326.1531392
Zusammenfassung

We present a new general-purpose method for optimizing existing point sets. The resulting distributions possess high-quality blue noise characteristics and adapt precisely to given density functions. Our method is similar to the commonly used Lloyd's method while avoiding its drawbacks. We achieve our results by utilizing the concept of capacity, which for each point is determined by the area of its Voronoi region weighted with an underlying density function. We demand that each point has the same capacity. In combination with a dedicated optimization algorithm, this capacity constraint enforces that each point obtains equal importance in the distribution. Our method can be used as a drop-in replacement for Lloyd's method, and combines enhancement of blue noise characteristics and density function adaptation in one operation.

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Lloyd's method, point distributions, blue noise
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ISO 690BALZER, Michael, Thomas SCHLÖMER, Oliver DEUSSEN, 2009. Capacity-Constrained Point Distributions : A Variant of Lloyd's Method. ISBN 978-1-60558-726-4. In: ACM Transactions on Graphics ( Proceedings of SIGGRAPH ). 2009, 28(3), 86. Available under: doi: 10.1145/1531326.1531392
BibTex
@article{Balzer2009Capac-5934,
  year={2009},
  doi={10.1145/1531326.1531392},
  title={Capacity-Constrained Point Distributions : A Variant of Lloyd's Method},
  number={3},
  volume={28},
  journal={ACM Transactions on Graphics ( Proceedings of SIGGRAPH )},
  author={Balzer, Michael and Schlömer, Thomas and Deussen, Oliver},
  note={Article Number: 86}
}
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