Neighborhood

Call f a binary predicate taking two geo-values as arguments. If u is a geo-value, a Neighborhood of u in $\mathbb {U}$ is the set of geo-values V($\bf u$) such that:

V($$\bf u$$) = {$$\bf v$$ $$\in$$ $$\mathbb {U}$$    /    f ($$\bf u$$,$$\bf v$$) = true}

u is called the center of the Neighborhood. A neighbor is, of course, an element of the Neighborhood. The neighborhood can be made to contain no more than a fixed number of neighbors, even if more geo-values actually satisfy criterion f. The retained geo-values could be selected according to their variogram distance from the center, or according to their ``nature'' (i.e. the geo-value's property is a ``hard datum'' or is a previously simulated value), etc.

In geostatistics two types of neighborhoods are often used: elliptical neighborhoods and window (or template) neighborhoods. An elliptical neighborhood is a neighborhood for which f ($\bf u$,$\bf v$) = true if v is inside a given ellipsoid centered on u. A window neighborhood, is defined by a set of vectors $\bf h_{1}^{}$,...,$\bf h_{n}^{}$ and:

f ($$\bf u$$,$$\bf v$$) = true    if    $$\exists$$ j $$\in$$ [1, n]    $$\bf v$$ = $$\bf u$$ + $$\bf h_{j}^{}$$

Refinement of

Container

Associated Types

• Geovalue type

  A::value_type

  value_type is the type of geovalue stored into the neighborhood.

• Neighborhood Iterator

  A::iterator

  A neighborhood iterator is a model of Forward Iterator (see previous description). It is an iterator that returns a geo-value when dereferenced, and supports operator = (assignment), operator ++ (increment), operator * (dereference) and operator != (comparison).

Notations

A		A type that is a model of Neighborhood
a		Object of type A
I		A type the is a model of Forward Iterator
u		An object of a type that models Location

Valid Expressions

• find neighbors

  a.find_neighbors(u)

  Return type:		void
  Semantics:		finds the neighbors of location u and stores them

• begin

  a.begin()

  Return type:		I
  Semantics:		returns an iterator to the first geo-value in the neighborhood

• end

  a.end()

  Return type:		I
  Semantics:		returns an iterator to one past the last geo-value in the neighborhood

• size

  a.size()

  Return type:		unsigned int
  Semantics:		returns the number of geo-values in the neighborhood

• Empty

  a.empty()

  Return type:		a type that is convertible to bool
  Semantics:		returns ``true'' if the size of the neighborhood is 0

Models

• elliptical_neighborhood