# Compute the Power Diagram of Weighted Sites in 2-Dimensional Space

### Description

Compute the power diagram of weighted sites in 2-dimensional space.

### Usage

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### Arguments

`xi,eta,w` |
vectors of equal length, where |

`rect` |
vetor of length |

`x` |
a power diagram as returned from |

`weights` |
logical. If |

`add` |
logical. Should the power diagram be plotted on top of current graphics? |

`col,lwd,...` |
further arguments graphic parameters used by |

### Details

The function `power_diagram`

implements an algorithm by Edelsbrunner and Shah (1996) which computes
regular triangulations and thus its dual representation, the power diagram. For point location, an algorithm
devised by Devillers (2002) is used.

### Author(s)

Björn Bähre bjobae@gmail.com

(slightly modified by Dominic Schuhmacher dschuhm1@uni-goettingen.de)

### References

H. Edelsbrunner, N. R. Shah (1996), Incremental Topological Flipping Works for Regular Triangulations, Algorithmica 15, 223–241.

O. Devillers (2002), The Delaunay Hierarchy, International Journal of Foundations of Computer Science 13, 163–180.

### Examples

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