org.apache.commons.math3.geometry.partitioning

Class AbstractRegion<S extends Space,T extends Space>

java.lang.Object

org.apache.commons.math3.geometry.partitioning.AbstractRegion<S,T>

Type Parameters:

S - Type of the space.

T - Type of the sub-space.

All Implemented Interfaces:

Region<S>

Direct Known Subclasses:

ArcsSet, IntervalsSet, PolygonsSet, PolyhedronsSet, SphericalPolygonsSet

public abstract class AbstractRegion<S extends Space,T extends Space>
extends java.lang.Object
implements Region<S>

Abstract class for all regions, independently of geometry type or dimension.

Since:

3.0

Nested Class Summary

Nested classes/interfaces inherited from interface org.apache.commons.math3.geometry.partitioning.Region

Region.Location

Field Summary

Fields

Modifier and Type	Field and Description
private Point<S>	barycenter Barycenter.
private double	size Size of the instance.
private double	tolerance Tolerance below which points are considered to belong to hyperplanes.
private BSPTree<S>	tree Inside/Outside BSP tree.

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	AbstractRegion(BSPTree<S> tree, double tolerance) Build a region from an inside/outside BSP tree.
protected	AbstractRegion(java.util.Collection<SubHyperplane<S>> boundary, double tolerance) Build a Region from a Boundary REPresentation (B-rep).
protected	AbstractRegion(double tolerance) Build a region representing the whole space.
	AbstractRegion(Hyperplane<S>[] hyperplanes, double tolerance) Build a convex region from an array of bounding hyperplanes.

Method Summary

Methods

Modifier and Type	Method and Description
AbstractRegion<S,T>	applyTransform(Transform<S,T> transform) Transform a region.
abstract AbstractRegion<S,T>	buildNew(BSPTree<S> newTree) Build a region using the instance as a prototype.
protected Region.Location	checkPoint(BSPTree<S> node, Point<S> point) Check a point with respect to the region starting at a given node.
protected Region.Location	checkPoint(BSPTree<S> node, Vector<S> point) Check a point with respect to the region starting at a given node.
Region.Location	checkPoint(Point<S> point) Check a point with respect to the region.
Region.Location	checkPoint(Vector<S> point) Check a point with respect to the region.
protected abstract void	computeGeometricalProperties() Compute some geometrical properties.
boolean	contains(Region<S> region) Check if the instance entirely contains another region.
AbstractRegion<S,T>	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.
double	getTolerance() Get the tolerance below which points are considered to belong to hyperplanes.
BSPTree<S>	getTree(boolean includeBoundaryAttributes) Get the underlying BSP tree.
private void	insertCuts(BSPTree<S> node, java.util.Collection<SubHyperplane<S>> boundary) Recursively build a tree by inserting cut sub-hyperplanes.
SubHyperplane<S>	intersection(SubHyperplane<S> sub) Get the parts of a sub-hyperplane that are contained in the region.
boolean	isEmpty() Check if the instance is empty.
boolean	isEmpty(BSPTree<S> node) Check if the sub-tree 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 sub-tree starting at a given node covers the full space.
BoundaryProjection<S>	projectToBoundary(Point<S> point) Project a point on the boundary of the region.
private SubHyperplane<S>	recurseIntersection(BSPTree<S> node, SubHyperplane<S> sub) Recursively compute the parts of a sub-hyperplane that are contained in the region.
private BSPTree<S>	recurseTransform(BSPTree<S> node, Transform<S,T> transform, java.util.Map<BSPTree<S>,BSPTree<S>> map) Recursively transform an inside/outside BSP-tree.
protected void	setBarycenter(Point<S> barycenter) Set the barycenter of the instance.
protected void	setBarycenter(Vector<S> barycenter) Set the barycenter of the instance.
protected void	setSize(double size) Set the size of the instance.
Side	side(Hyperplane<S> hyperplane) Compute the relative position of the instance with respect to an hyperplane.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

tree

private BSPTree<S extends Space> tree

Inside/Outside BSP tree.

tolerance

private final double tolerance

Tolerance below which points are considered to belong to hyperplanes.

size

private double size

Size of the instance.

barycenter

private Point<S extends Space> barycenter

Barycenter.

Constructor Detail

AbstractRegion

protected AbstractRegion(double tolerance)

Build a region representing the whole space.

Parameters:

tolerance - tolerance below which points are considered identical.

AbstractRegion

protected AbstractRegion(BSPTree<S> tree,
              double tolerance)

Build a region from an inside/outside BSP tree.

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).

Parameters:

tree - inside/outside BSP tree representing the region

tolerance - tolerance below which points are considered identical.

AbstractRegion

protected AbstractRegion(java.util.Collection<SubHyperplane<S>> boundary,
              double tolerance)

Build a Region from a Boundary REPresentation (B-rep).

The boundary is provided as a collection of sub-hyperplanes. Each sub-hyperplane has the interior part of the region on its minus side and the exterior on its plus side.

The boundary elements can be in any order, and can form several non-connected sets (like for example polygons with holes or a set of disjoints polyhedrons considered as a whole). In fact, the elements do not even need to be connected together (their topological connections are not used here). However, if the boundary does not really separate an inside open from an outside open (open having here its topological meaning), then subsequent calls to the checkPoint method will not be meaningful anymore.

If the boundary is empty, the region will represent the whole space.

Parameters:

boundary - collection of boundary elements, as a collection of SubHyperplane objects

tolerance - tolerance below which points are considered identical.

AbstractRegion

public AbstractRegion(Hyperplane<S>[] hyperplanes,
              double tolerance)

Build a convex region from an array of bounding hyperplanes.

Parameters:

hyperplanes - array of bounding hyperplanes (if null, an empty region will be built)

tolerance - tolerance below which points are considered identical.

Method Detail

buildNew

public abstract AbstractRegion<S,T> buildNew(BSPTree<S> newTree)

Build a region using the instance as a prototype.

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).

Specified by:

buildNew in interface Region<S extends Space>

Parameters:

newTree - inside/outside BSP tree representing the new region

Returns:

the built region

getTolerance

public double getTolerance()

Get the tolerance below which points are considered to belong to hyperplanes.

Returns:

tolerance below which points are considered to belong to hyperplanes

insertCuts

private void insertCuts(BSPTree<S> node,
              java.util.Collection<SubHyperplane<S>> boundary)

Recursively build a tree by inserting cut sub-hyperplanes.

Parameters:

node - current tree node (it is a leaf node at the beginning of the call)

boundary - collection of edges belonging to the cell defined by the node

copySelf

public AbstractRegion<S,T> copySelf()

Copy the instance.

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).

Specified by:

copySelf in interface Region<S extends Space>

Returns:

a new region, copy of the instance

isEmpty

public boolean isEmpty()

Check if the instance is empty.

Specified by:

isEmpty in interface Region<S extends Space>

Returns:

true if the instance is empty

isEmpty

public boolean isEmpty(BSPTree<S> node)

Check if the sub-tree starting at a given node is empty.

Specified by:

isEmpty in interface Region<S extends Space>

Parameters:

node - root node of the sub-tree (must have Region tree semantics, i.e. the leaf nodes must have Boolean attributes representing an inside/outside property)

Returns:

true if the sub-tree starting at the given node is empty

isFull

public boolean isFull()

Check if the instance covers the full space.

Specified by:

isFull in interface Region<S extends Space>

Returns:

true if the instance covers the full space

isFull

public boolean isFull(BSPTree<S> node)

Check if the sub-tree starting at a given node covers the full space.

Specified by:

isFull in interface Region<S extends Space>

Parameters:

node - root node of the sub-tree (must have Region tree semantics, i.e. the leaf nodes must have Boolean attributes representing an inside/outside property)

Returns:

true if the sub-tree starting at the given node covers the full space

contains

public boolean contains(Region<S> region)

Check if the instance entirely contains another region.

Specified by:

contains in interface Region<S extends Space>

Parameters:

region - region to check against the instance

Returns:

true if the instance contains the specified tree

projectToBoundary

public BoundaryProjection<S> projectToBoundary(Point<S> point)

Project a point on the boundary of the region.

Specified by:

projectToBoundary in interface Region<S extends Space>

Parameters:

point - point to check

Returns:

projection of the point on the boundary

Since:

3.3

checkPoint

public Region.Location checkPoint(Vector<S> point)

Check a point with respect to the region.

Parameters:

point - point to check

Returns:

a code representing the point status: either Region.Location.INSIDE, Region.Location.OUTSIDE or Region.Location.BOUNDARY

checkPoint

public Region.Location checkPoint(Point<S> point)

Check a point with respect to the region.

Specified by:

checkPoint in interface Region<S extends Space>

Parameters:

point - point to check

Returns:

a code representing the point status: either Region.Location.INSIDE, Region.Location.OUTSIDE or Region.Location.BOUNDARY

checkPoint

protected Region.Location checkPoint(BSPTree<S> node,
                         Vector<S> point)

Check a point with respect to the region starting at a given node.

Parameters:

node - root node of the region

point - point to check

Returns:

a code representing the point status: either INSIDE, OUTSIDE or BOUNDARY

checkPoint

protected Region.Location checkPoint(BSPTree<S> node,
                         Point<S> point)

Check a point with respect to the region starting at a given node.

Parameters:

node - root node of the region

point - point to check

Returns:

a code representing the point status: either INSIDE, OUTSIDE or BOUNDARY

getTree

public BSPTree<S> getTree(boolean includeBoundaryAttributes)

Get the underlying BSP tree.

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 sub-hyperplanes may contain BoundaryAttribute objects representing the parts of the corresponding cut sub-hyperplane that belong to the boundary. When the boundary attributes have been computed, all internal nodes are guaranteed to have non-null attributes, however some BoundaryAttribute instances may have their getPlusInside and getPlusOutside methods both returning null if the corresponding cut sub-hyperplane does not have any parts belonging to the boundary.

Since computing the boundary is not always required and can be time-consuming 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.

Specified by:

getTree in interface Region<S extends Space>

Parameters:

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)

Returns:

underlying BSP tree

See Also:

BoundaryAttribute

getBoundarySize

public double getBoundarySize()

Get the size of the boundary.

Specified by:

getBoundarySize in interface Region<S extends Space>

Returns:

the size of the boundary (this is 0 in 1D, a length in 2D, an area in 3D ...)

getSize

public double getSize()

Get the size of the instance.

Specified by:

getSize in interface Region<S extends Space>

Returns:

the size of the instance (this is a length in 1D, an area in 2D, a volume in 3D ...)

setSize

protected void setSize(double size)

Set the size of the instance.

Parameters:

size - size of the instance

getBarycenter

public Point<S> getBarycenter()

Get the barycenter of the instance.

Specified by:

getBarycenter in interface Region<S extends Space>

Returns:

an object representing the barycenter

setBarycenter

protected void setBarycenter(Vector<S> barycenter)

Set the barycenter of the instance.

Parameters:

barycenter - barycenter of the instance

setBarycenter

protected void setBarycenter(Point<S> barycenter)

Set the barycenter of the instance.

Parameters:

barycenter - barycenter of the instance

computeGeometricalProperties

protected abstract void computeGeometricalProperties()

Compute some geometrical properties.

The properties to compute are the barycenter and the size.

side

public Side side(Hyperplane<S> hyperplane)

Compute the relative position of the instance with respect to an hyperplane.

Specified by:

side in interface Region<S extends Space>

Parameters:

hyperplane - reference hyperplane

Returns:

one of Side.PLUS, Side.MINUS, Side.BOTH or Side.HYPER (the latter result can occur only if the tree contains only one cut hyperplane)

intersection

public SubHyperplane<S> intersection(SubHyperplane<S> sub)

Get the parts of a sub-hyperplane that are contained in the region.

The parts of the sub-hyperplane that belong to the boundary are not included in the resulting parts.

Specified by:

intersection in interface Region<S extends Space>

Parameters:

sub - sub-hyperplane traversing the region

Returns:

filtered sub-hyperplane

recurseIntersection

private SubHyperplane<S> recurseIntersection(BSPTree<S> node,
                                   SubHyperplane<S> sub)

Recursively compute the parts of a sub-hyperplane that are contained in the region.

Parameters:

node - current BSP tree node

sub - sub-hyperplane traversing the region

Returns:

filtered sub-hyperplane

applyTransform

public AbstractRegion<S,T> applyTransform(Transform<S,T> transform)

Transform a region.

Applying a transform to a region consist in applying the transform to all the hyperplanes of the underlying BSP tree and of the boundary (and also to the sub-hyperplanes embedded in these hyperplanes) and to the barycenter. The instance is not modified, a new instance is built.

Parameters:

transform - transform to apply

Returns:

a new region, resulting from the application of the transform to the instance

recurseTransform

private BSPTree<S> recurseTransform(BSPTree<S> node,
                          Transform<S,T> transform,
                          java.util.Map<BSPTree<S>,BSPTree<S>> map)

Recursively transform an inside/outside BSP-tree.

Parameters:

node - current BSP tree node

transform - transform to apply

map - transformed nodes map

Returns:

a new tree