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

java.lang.Object
  extended by 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:
IntervalsSet, PolygonsSet, PolyhedronsSet

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

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

Since:
3.0
Version:
$Id: AbstractRegion.java 1244107 2012-02-14 16:17:55Z erans $

Nested Class Summary
private static class AbstractRegion.Sides
          Utility class holding the already found sides.
 
Nested classes/interfaces inherited from interface org.apache.commons.math3.geometry.partitioning.Region
Region.Location
 
Field Summary
private  Vector<S> barycenter
          Barycenter.
private  double size
          Size of the instance.
private  BSPTree<S> tree
          Inside/Outside BSP tree.
 
Constructor Summary
protected AbstractRegion()
          Build a region representing the whole space.
protected AbstractRegion(BSPTree<S> tree)
          Build a region from an inside/outside BSP tree.
protected AbstractRegion(Collection<SubHyperplane<S>> boundary)
          Build a Region from a Boundary REPresentation (B-rep).
  AbstractRegion(Hyperplane<S>[] hyperplanes)
          Build a convex region from an array of bounding hyperplanes.
 
Method Summary
 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.
private  void characterize(BSPTree<S> node, SubHyperplane<S> sub, Characterization<S> characterization)
          Filter the parts of an hyperplane belonging to the boundary.
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(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.
 Vector<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.
private  void insertCuts(BSPTree<S> node, 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.
private  void recurseBuildBoundary(BSPTree<S> node)
          Recursively build the boundary shell tree.
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  void recurseSides(BSPTree<S> node, SubHyperplane<S> sub, AbstractRegion.Sides sides)
          Search recursively for inside leaf nodes on each side of the given hyperplane.
private  BSPTree<S> recurseTransform(BSPTree<S> node, Transform<S,T> transform)
          Recursively transform an inside/outside BSP-tree.
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.


size

private double size
Size of the instance.


barycenter

private Vector<S extends Space> barycenter
Barycenter.

Constructor Detail

AbstractRegion

protected AbstractRegion()
Build a region representing the whole space.


AbstractRegion

protected AbstractRegion(BSPTree<S> tree)
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

AbstractRegion

protected AbstractRegion(Collection<SubHyperplane<S>> boundary)
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

AbstractRegion

public AbstractRegion(Hyperplane<S>[] hyperplanes)
Build a convex region from an array of bounding hyperplanes.

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

insertCuts

private void insertCuts(BSPTree<S> node,
                        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

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

checkPoint

public Region.Location checkPoint(Vector<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

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 plusInside and plusOutside fields both 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

recurseBuildBoundary

private void recurseBuildBoundary(BSPTree<S> node)
Recursively build the boundary shell tree.

Parameters:
node - current node in the inout tree

characterize

private void characterize(BSPTree<S> node,
                          SubHyperplane<S> sub,
                          Characterization<S> characterization)
Filter the parts of an hyperplane belonging to the boundary.

The filtering consist in splitting the specified sub-hyperplane into several parts lying in inside and outside cells of the tree. The principle is to call this method twice for each cut sub-hyperplane in the tree, once one the plus node and once on the minus node. The parts that have the same flag (inside/inside or outside/outside) do not belong to the boundary while parts that have different flags (inside/outside or outside/inside) do belong to the boundary.

Parameters:
node - current BSP tree node
sub - sub-hyperplane to characterize
characterization - placeholder where to put the characterized parts

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 Vector<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

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)

recurseSides

private void recurseSides(BSPTree<S> node,
                          SubHyperplane<S> sub,
                          AbstractRegion.Sides sides)
Search recursively for inside leaf nodes on each side of the given hyperplane.

The algorithm used here is directly derived from the one described in section III (Binary Partitioning of a BSP Tree) of the Bruce Naylor, John Amanatides and William Thibault paper Merging BSP Trees Yields Polyhedral Set Operations Proc. Siggraph '90, Computer Graphics 24(4), August 1990, pp 115-124, published by the Association for Computing Machinery (ACM)..

Parameters:
node - current BSP tree node
sub - sub-hyperplane
sides - object holding the sides found

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)
Recursively transform an inside/outside BSP-tree.

Parameters:
node - current BSP tree node
transform - transform to apply
Returns:
a new tree


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