Version 5.0 The LEDA User Manual

ool
Is Delaunay Diagram(const GRAPH & G, delaunay voronoi kind kind)
checks whether G is a nearest (kind = NEAREST ) or furthest (kind =
FURTHEST ) site Delaunay diagram of its vertex set. G is a Delaunay
diagram if it is a convex subdivision, if the vertices of any bounded face
are co-circular, and if every triangulation of G is a Delaunay triangulation.
• Voronoi Diagrams
void VORONOI(const list& L, GRAPH & VD)
VORONOI takes as input a list of points (sites) L. It computes a directed
graph V D representing the planar subdivision defined by the Voronoi
diagram of L. For each node v of VD G[v] is the corresponding Voronoi
vertex (point) and for each edge e G[e] is the site (point) whose Voronoi
region is bounded by e. The algorithm has running time O(n 2 ) in the
worst case and O(n log n) with high probability, where n is the number
of sites.
void F VORONOI(const list& L, GRAPH & FVD)
computes the farthest point Voronoi Diagram FVD of the points in L.
circle LARGEST EMPTY CIRCLE(const list& L)
computes a largest circle whose center lies inside the convex hull of L
that contains no point of L in its interior. Returns the trivial circle if L
is empty.
circle SMALLEST ENCLOSING CIRCLE(const list& L)
computes a smallest circle containing all points of L in its interior.
void ALL EMPTY CIRCLES(const list& L, list& CL)
computes the list CL of all empty circles passing through three or more
points of L.
void ALL ENCLOSING CIRCLES(const list& L, list& CL)
computes the list CL of all enclosing circles passing through three or more
points of L.
An annulus is either the region between two concentric circles or the region between two
parallel lines.
bool
MIN AREA ANNULUS(const list& L, point& center, point& ipoint,
point& opoint, line& l1 )
computes the minimum area annulus containing the points of L. The
function returns false if all points in L are collinear and returns true
otherwise. In the former case a line passing through the points in L is
returned in l1 , and in the latter case the annulus is returned by its center
and a point on the inner and the outer circle, respectively.