Version 5.0 The LEDA User Manual

double CLOSEST PAIR(list& L, point& r1 , point& r2 )
CLOSEST PAIR takes as input a list of points L. It computes a pair
of points r1, r2 ∈ L with minimal Euclidean distance and returns the
squared distance between r1 and r2. The algorithm ([76]) has running
time O(n log n) where n is the number of input points.
• Miscellaneous Functions
void
Bounding Box(const list& L, point& pl, point& pb, point& pr, point& pt)
computes four points pl, pb, pr, pt from L such that
(xleft, ybot, xright, ytop) with xleft = pl.xcoord( ), ybot = pb.ycoord( ),
xright = pr.xcoord( ) and ytop = pt.ycoord( ) is the smallest isooriented
rectangle containing all points of L. Precondition: L is not
empty.
bool Is Simple Polygon(const list& L)
takes as input a list of points L and returns true if L is the vertex sequence
of a simple polygon and false otherwise. The algorithms has running time
O(n log n), where n is the number of points in L.
• Properties of Geometric Graphs
We give procedures to check properties of geometric graph. We give procedures to verify
properties of geometric graph. A geometric graph is a straight-line embedded map. Every
node is mapped to a point in the plane and every dart is mapped to the line segment
connecting its endpoints.
We use geo graph as a template parameter for geometric graph.
geo graph must provide a function
Any instantiation of
VECTOR edge vector(const geo graph& G, const edge& e)
that returns a vector from the source to the target of e. In order to use any of these
template functions the file /LEDA/geo/generic/geo check.h must be included.
template
bool Is CCW Ordered(const geo graph& G)
returns true if for all nodes v the neighbors of v are in increasing
counter-clockwise order around v.
template
bool Is CCW Weakly Ordered(const geo graph& G)
returns true if for all nodes v the neighbors of v are in non-decreasing
counter-clockwise order around v.