Farthest-point optimized point sets with maximized minimum distance

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Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics - HPG '11. New York, New York, USA: ACM Press, 2011, pp. 135-142. ISBN 978-1-4503-0896-0. Available under: doi: 10.1145/2018323.2018345
Zusammenfassung

Efficient sampling often relies on irregular point sets that uniformly cover the sample space. We present a flexible and simple optimization strategy for such point sets. It is based on the idea of increasing the mutual distances by successively moving each point to the “farthest point,” i.e., the location that has the maximum distance from the rest of the point set. We present two iterative algorithms based on this strategy. The first is our main algorithm which distributes points in the plane. Our experimental results show that the resulting distributions have almost optimal blue noise properties and are highly suitable for image plane sampling. The second is a variant oft he main algorithm that partitions any point set into equally sized subsets, each with large mutual distances; the resulting partitionings yield improved results in more general integration problems such as those occurring in physically based rendering.

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ACM SIGGRAPH Symposium on High Performance Graphics - HPG '11, 5. Aug. 2011 - 7. Aug. 2011, Vancouver, British Columbia, Canada
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ISO 690SCHLÖMER, Thomas, Daniel HECK, Oliver DEUSSEN, 2011. Farthest-point optimized point sets with maximized minimum distance. ACM SIGGRAPH Symposium on High Performance Graphics - HPG '11. Vancouver, British Columbia, Canada, 5. Aug. 2011 - 7. Aug. 2011. In: Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics - HPG '11. New York, New York, USA: ACM Press, 2011, pp. 135-142. ISBN 978-1-4503-0896-0. Available under: doi: 10.1145/2018323.2018345
BibTex
@inproceedings{Schlomer2011Farth-17724,
  year={2011},
  doi={10.1145/2018323.2018345},
  title={Farthest-point optimized point sets with maximized minimum distance},
  isbn={978-1-4503-0896-0},
  publisher={ACM Press},
  address={New York, New York, USA},
  booktitle={Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics - HPG '11},
  pages={135--142},
  author={Schlömer, Thomas and Heck, Daniel and Deussen, Oliver}
}
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