Editing Delaunay triangulation (section)

== Visual Delaunay definition: Flipping ==
From the above properties an important feature arises: Looking at two triangles {{math|△''ABD'', △''BCD''}} with the common edge {{mvar|{{overline|BD}}}} (see figures), if the sum of the angles {{mvar|α + γ ≤ 180°}}, the triangles meet the Delaunay condition.

This is an important property because it allows the use of a ''flipping'' technique. If two triangles do not meet the Delaunay condition, switching the common edge {{mvar|{{overline|BD}}}} for the common edge {{mvar|{{overline|AC}}}} produces two triangles that do meet the Delaunay condition:

<gallery>
File:Delaunay geometry.png|This triangulation does not meet the Delaunay condition (the sum of {{mvar|α}} and {{mvar|γ}} is bigger than 180°).
File:Point inside circle - Delaunay condition broken.svg|This pair of triangles does not meet the Delaunay condition (there is a point within the interior of the circumcircle).
File:Edge Flip - Delaunay condition ok.svg|''Flipping'' the common edge produces a valid Delaunay triangulation for the four points.  
</gallery>

This operation is called a ''flip'', and can be generalised to three and higher dimensions.{{r|DRS}}