# Talk:Alpha shape

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Field:  Geometry

So is it "alpha shape" or "alpha-shape"? Probably doesn't matter, but it would be nice to have some internal consistency. --Matt Westwood 13:46, 11 September 2011 (UTC)

## Edelsbrunner

Are there any references which do not include Edelsbrunner? What is it that is supposed to let me know that this is something of merit, and not just Edelsbrunner's latest mathematical toy? Sanpitch (talk) 03:01, 14 September 2011 (UTC)

Yes, about 1750 of them.David Eppstein (talk) 04:16, 14 September 2011 (UTC)

## Definition

According to Edelsbrunner et al:

Given a set S of points in the plane and an arbitrary real number α, the α-shape of S is the straight line graph whose vertices are the α-extreme points and whose edges connect the respective α-neighbors.

(emphasis mine). Thus the edges of the α-shape are straight line segments. (There is a related notion, that of the α-hull, whose edges are the arcs of circles.) Moreover, the images in that article show examples of the α-hull and α-shape, where it is clear that one is supposed to have curvilinear edges and the other linear ones. Sławomir Biały (talk) 15:49, 17 September 2011 (UTC)

## Examples

The examples should show results of varying alpha. —DIV (137.111.13.4 (talk) 23:08, 2 November 2015 (UTC))