### Abstract

Natural neighbor interpolation is a weighted average interpolation method that is based on Voronoi tessellation. In this paper, we present and implement an algorithm for performing natural neighbor interpolation using graphics hardware. Unlike traditional software-based approaches that process one query at a time, we develop a scheme that computes the entire scalar field induced by natural neighbor interpolation, at which point a query is a trivial array lookup, arid range queries over the field are easy to perform. Our approach is faster than the best known software implementations and makes use of general purpose stream programming capabilities of current graphics cards. We also present a simple scheme that requires no advanced graphics capabilities and can process natural neighbor queries faster than existing software-based approaches. Finally, recognizing the limitation incurred by the bounded size of graphics frame buffers, we propose a sub-division approach that allows performing queries locally in a subdivision of the input domain. This approach can reduce to a negligibly small degree (< 1%) the loss of precision caused by the naive scaling method while still processing queries faster than the software-based approaches when the number of sites is large.

Original language | English (US) |
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Title of host publication | Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics |

Editors | C. Demetrescu, R. Sedgewick, R. Tamassia |

Pages | 111-120 |

Number of pages | 10 |

State | Published - 2005 |

Event | Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics - Vancouver, BC, Canada Duration: Jan 22 2005 → Jan 22 2005 |

### Other

Other | Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics |
---|---|

Country | Canada |

City | Vancouver, BC |

Period | 1/22/05 → 1/22/05 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics*(pp. 111-120)

**Hardware-assisted natural neighbor interpolation.** / Fan, Quanfu; Efrat, Alon; Koltun, Vladlen; Krishnan, Shankar; Venkatasubramanian, Suresh.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics.*pp. 111-120, Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics, Vancouver, BC, Canada, 1/22/05.

}

TY - GEN

T1 - Hardware-assisted natural neighbor interpolation

AU - Fan, Quanfu

AU - Efrat, Alon

AU - Koltun, Vladlen

AU - Krishnan, Shankar

AU - Venkatasubramanian, Suresh

PY - 2005

Y1 - 2005

N2 - Natural neighbor interpolation is a weighted average interpolation method that is based on Voronoi tessellation. In this paper, we present and implement an algorithm for performing natural neighbor interpolation using graphics hardware. Unlike traditional software-based approaches that process one query at a time, we develop a scheme that computes the entire scalar field induced by natural neighbor interpolation, at which point a query is a trivial array lookup, arid range queries over the field are easy to perform. Our approach is faster than the best known software implementations and makes use of general purpose stream programming capabilities of current graphics cards. We also present a simple scheme that requires no advanced graphics capabilities and can process natural neighbor queries faster than existing software-based approaches. Finally, recognizing the limitation incurred by the bounded size of graphics frame buffers, we propose a sub-division approach that allows performing queries locally in a subdivision of the input domain. This approach can reduce to a negligibly small degree (< 1%) the loss of precision caused by the naive scaling method while still processing queries faster than the software-based approaches when the number of sites is large.

AB - Natural neighbor interpolation is a weighted average interpolation method that is based on Voronoi tessellation. In this paper, we present and implement an algorithm for performing natural neighbor interpolation using graphics hardware. Unlike traditional software-based approaches that process one query at a time, we develop a scheme that computes the entire scalar field induced by natural neighbor interpolation, at which point a query is a trivial array lookup, arid range queries over the field are easy to perform. Our approach is faster than the best known software implementations and makes use of general purpose stream programming capabilities of current graphics cards. We also present a simple scheme that requires no advanced graphics capabilities and can process natural neighbor queries faster than existing software-based approaches. Finally, recognizing the limitation incurred by the bounded size of graphics frame buffers, we propose a sub-division approach that allows performing queries locally in a subdivision of the input domain. This approach can reduce to a negligibly small degree (< 1%) the loss of precision caused by the naive scaling method while still processing queries faster than the software-based approaches when the number of sites is large.

UR - http://www.scopus.com/inward/record.url?scp=32144460834&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=32144460834&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0898715962

SN - 9780898715965

SP - 111

EP - 120

BT - Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics

A2 - Demetrescu, C.

A2 - Sedgewick, R.

A2 - Tamassia, R.

ER -