Definitions (of several geometric terms)
A Delaunay triangulation
of a vertex set is a triangulation of the vertex
set with the property that no vertex in the vertex set falls in the
interior of the circumcircle (circle that passes through all three
vertices) of any triangle in the triangulation.
A Voronoi diagram
of a vertex set is a subdivision of the plane into
polygonal regions (some of which may be infinite), where each region is
the set of points in the plane that are closer to some input vertex than to
any other input vertex. (The Voronoi diagram is the geometric dual of the
A Planar Straight Line Graph (PSLG)
is a collection of vertices and segments.
Segments are edges
whose endpoints are vertices in the PSLG, and whose presence in any
mesh generated from the PSLG is enforced.
A constrained Delaunay triangulation
of a PSLG is similar to a Delaunay
triangulation, but each PSLG segment is present as a single edge in the
triangulation. A constrained Delaunay triangulation is not truly a
Delaunay triangulation. Some of its triangles might not be Delaunay,
but they are all constrained Delaunay.
A conforming Delaunay triangulation (CDT)
of a PSLG is a true Delaunay
triangulation in which each PSLG segment may have been subdivided into
several edges by the insertion of additional vertices, called
Steiner points. Steiner
points are necessary to allow the segments to exist in the mesh while
maintaining the Delaunay property. Steiner points are also inserted
to meet constraints on the minimum angle and maximum triangle area.
A constrained conforming Delaunay triangulation
(CCDT) of a PSLG is a constrained Delaunay triangulation that includes
Steiner points. It usually takes fewer vertices to make a good-quality CCDT
than a good-quality CDT, because the triangles do not need to be Delaunay
(although they still must be constrained Delaunay).
Return to Triangle home page.