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
Famous quotes containing the word visual:
“To write well, to have style ... is to paint. The master faculty of style is therefore the visual memory. If a writer does not see what he describes—countrysides and figures, movements and gestures—how could he have a style, that is originality?”
—Rémy De Gourmont (1858–1915)