Definition
An instance S of the parameterized data type subdivision<I> is a subdivision of the two-dimensional plane, i.e., an embedded planar graph with straight line edges (see also sections Planar Maps and Parameterized Planar Maps). With each node v of S is associated a point, called the position of v and with each face of S is associated an information from data type I , called the information type of S .
#include < LEDA/geo/subdivision.h >
Creation
subdivision< I> | S(GRAPH< point,I> & G) | creates an instance S of type subdivision<I> and initializes it to
the subdivision represented by the parameterized directed graph G
.
The node entries of G
(of type point) define the positions of the
corresponding nodes of S. Every face f
of S is assigned the
information of one of its bounding edges in G
.
Precondition G represents a planar subdivision, i.e., a straight line embedded planar map. |
Operations
point | S.position(node v) | returns the position of node v . |
const I& | S.inf(face f) | returns the information of face f . |
face | S.locate_point(point p) | returns the face containing point p . |
face | S.outer_face() | returns the outer face of S. |
Implementation
Planar subdivisions are implemented by parameterized planar maps and an additional data structure for point location based on partially persistent search trees[25]. Operations position and inf take constant time, a locate_point operation takes (expected) time O(log n) . Here n is the number of nodes. The space requirement is O(n + m) and the initialization time is O(n + m log m) , where m is the number of edges in the map.