Delaunay Triangulation - Visual Delaunay Definition: Flipping

Visual Delaunay Definition: Flipping

From the above properties an important feature arises: Looking at two triangles ABD and BCD with the common edge BD (see figures), if the sum of the angles α and γ is less than or equal to 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 BD for the common edge AC produces two triangles that do meet the Delaunay condition:

  • This triangulation does not meet the Delaunay condition (the sum of α and γ is bigger than 180°).

  • This triangulation does not meet the Delaunay condition (the circumcircles contain more than three points).

  • Flipping the common edge produces a Delaunay triangulation for the four points.

Read more about this topic:  Delaunay Triangulation

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