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:
“The chess pieces are the block alphabet which shapes thoughts; and these thoughts, although making a visual design on the chess-board, express their beauty abstractly, like a poem.... I have come to the personal conclusion that while all artists are not chess players, all chess players are artists.”
—Marcel Duchamp (1887–1968)