S
 Type of the space.public interface Region<S extends Space>
Region are subsets of a space, they can be infinite (whole space, half space, infinite stripe ...) or finite (polygons in 2D, polyhedrons in 3D ...). Their main characteristic is to separate points that are considered to be inside the region from points considered to be outside of it. In between, there may be points on the boundary of the region.
This implementation is limited to regions for which the boundary
is composed of several subhyperplanes
,
including regions with no boundary at all: the whole space and the
empty region. They are not necessarily finite and not necessarily
pathconnected. They can contain holes.
Regions can be combined using the traditional sets operations : union, intersection, difference and symetric difference (exclusive or) for the binary operations, complement for the unary operation.
Note that this interface is not intended to be implemented by Apache Commons Math users, it is only intended to be implemented within the library itself. New methods may be added even for minor versions, which breaks compatibility for external implementations.
Modifier and Type  Interface and Description 

static class 
Region.Location
Enumerate for the location of a point with respect to the region.

Modifier and Type  Method and Description 

Region<S> 
buildNew(BSPTree<S> newTree)
Build a region using the instance as a prototype.

Region.Location 
checkPoint(Point<S> point)
Check a point with respect to the region.

boolean 
contains(Region<S> region)
Check if the instance entirely contains another region.

Region<S> 
copySelf()
Copy the instance.

Point<S> 
getBarycenter()
Get the barycenter of the instance.

double 
getBoundarySize()
Get the size of the boundary.

double 
getSize()
Get the size of the instance.

BSPTree<S> 
getTree(boolean includeBoundaryAttributes)
Get the underlying BSP tree.

SubHyperplane<S> 
intersection(SubHyperplane<S> sub)
Get the parts of a subhyperplane that are contained in the region.

boolean 
isEmpty()
Check if the instance is empty.

boolean 
isEmpty(BSPTree<S> node)
Check if the subtree starting at a given node is empty.

boolean 
isFull()
Check if the instance covers the full space.

boolean 
isFull(BSPTree<S> node)
Check if the subtree starting at a given node covers the full space.

BoundaryProjection<S> 
projectToBoundary(Point<S> point)
Project a point on the boundary of the region.

Side 
side(Hyperplane<S> hyperplane)
Compute the relative position of the instance with respect to an
hyperplane.

Region<S> buildNew(BSPTree<S> newTree)
This method allow to create new instances without knowing exactly the type of the region. It is an application of the prototype design pattern.
The leaf nodes of the BSP tree must have a
Boolean
attribute representing the inside status of
the corresponding cell (true for inside cells, false for outside
cells). In order to avoid building too many small objects, it is
recommended to use the predefined constants
Boolean.TRUE
and Boolean.FALSE
. The
tree also must have either null internal nodes or
internal nodes representing the boundary as specified in the
getTree
method).
newTree
 inside/outside BSP tree representing the new regionRegion<S> copySelf()
The instance created is completely independant of the original
one. A deep copy is used, none of the underlying objects are
shared (except for the underlying tree Boolean
attributes and immutable objects).
boolean isEmpty()
boolean isEmpty(BSPTree<S> node)
node
 root node of the subtree (must have Region
tree semantics, i.e. the leaf nodes must have
Boolean
attributes representing an inside/outside
property)boolean isFull()
boolean isFull(BSPTree<S> node)
node
 root node of the subtree (must have Region
tree semantics, i.e. the leaf nodes must have
Boolean
attributes representing an inside/outside
property)boolean contains(Region<S> region)
region
 region to check against the instanceRegion.Location checkPoint(Point<S> point)
point
 point to checkRegion.Location.INSIDE
, Region.Location.OUTSIDE
or Region.Location.BOUNDARY
BoundaryProjection<S> projectToBoundary(Point<S> point)
point
 point to checkBSPTree<S> getTree(boolean includeBoundaryAttributes)
Regions are represented by an underlying inside/outside BSP
tree whose leaf attributes are Boolean
instances
representing inside leaf cells if the attribute value is
true
and outside leaf cells if the attribute is
false
. These leaf attributes are always present and
guaranteed to be non null.
In addition to the leaf attributes, the internal nodes which
correspond to cells split by cut subhyperplanes may contain
BoundaryAttribute
objects representing
the parts of the corresponding cut subhyperplane that belong to
the boundary. When the boundary attributes have been computed,
all internal nodes are guaranteed to have nonnull
attributes, however some BoundaryAttribute
instances may have their getPlusInside
and getPlusOutside
methods both
returning null if the corresponding cut subhyperplane does not
have any parts belonging to the boundary.
Since computing the boundary is not always required and can be
timeconsuming for large trees, these internal nodes attributes
are computed using lazy evaluation only when required by setting
the includeBoundaryAttributes
argument to
true
. Once computed, these attributes remain in the
tree, which implies that in this case, further calls to the
method for the same region will always include these attributes
regardless of the value of the
includeBoundaryAttributes
argument.
includeBoundaryAttributes
 if true, the boundary attributes
at internal nodes are guaranteed to be included (they may be
included even if the argument is false, if they have already been
computed due to a previous call)BoundaryAttribute
double getBoundarySize()
double getSize()
Point<S> getBarycenter()
Side side(Hyperplane<S> hyperplane)
hyperplane
 reference hyperplaneSide.PLUS
, Side.MINUS
, Side.BOTH
or Side.HYPER
(the latter result can occur only if the tree
contains only one cut hyperplane)SubHyperplane<S> intersection(SubHyperplane<S> sub)
The parts of the subhyperplane that belong to the boundary are not included in the resulting parts.
sub
 subhyperplane traversing the regionCopyright © 2003–2014 The Apache Software Foundation. All rights reserved.