Version 5.0 The LEDA User Manual

ool
MIN WIDTH ANNULUS(const list& L, point& center, point& ipoint,
point& opoint, line& l1 , line& l2 )
computes the minimum width annulus containing the points of L. The
function returns false if the minimum width annulus is a stripe and returns
true otherwise. In the former case the boundaries of the stripes are
returned in l1 and l2 and in the latter case the annulus is returned by its
center and a point on the inner and the outer circle, respectively.
void CRUST(const list& L0 , GRAPH & G)
takes a list L0 of points and traces to guess the curve(s) from which L0
are sampled. The algorithm is due to Amenta, Bern, and Eppstein. The
algorithm is guaranteed to succeed if L0 is a sufficiently dense sample
from a smooth closed curve.
bool
Is Voronoi Diagram(const GRAPH & G, delaunay voronoi kind kind)
checks whether G represents a nearest (kind = NEAREST ) or furthest
(kind = FURTHEST ) site Voronoi diagram.
Voronoi diagrams of point sites are represented as planar maps as follows:
There is a vertex for each vertex of the Voronoi diagram and, in addition,
a vertex “at infinity” for each ray of the Voronoi diagram. Vertices at
infinity have degree one. The edges of the graph correspond to the edges
of the Voronoi diagram. The chapter on Voronoi diagrams of the LEDAbook
[64] contains more details. Each edge is labeled with the site (class
POINT ) owning the region to its left and each vertex is labeled with
a triple of points (= the three defining points of a CIRCLE). For a
“finite” vertex the three points are any three sites associated with regions
incident to the vertex (and hence the center of the circle is the position
of the vertex in the plane) and for a vertex at infinity the three points
are collinear and the first point and the third point of the triple are the
sites whose regions are incident to the vertex at infinity. Let a and c be
the first and third point of the triple respectively; a and c encode the
geometric position of the vertex at infinity as follows: the vertex lies on
the perpendicular bisector of a and c and to the left of the segment ac.
• Line Segment Intersection
void SEGMENT INTERSECTION(const list& S,
GRAPH & G, bool embed = false)
takes a list of segments S as input and computes the planar graph G
induced by the set of straight line segments in S. The nodes of G are
all endpoints and all proper intersection points of segments in S. The
edges of G are the maximal relatively open subsegments of segments in S
that contain no node of G. The edges are directed as the corresponding
segments. If the flag embed is true, the corresponding planar map is
computed. Note that for each edge e G[e] is the input segment that
contains e (see the LEDA book for details).