Region (patrius 4.3 API)

Type Parameters:

S - Type of the space.

All Known Implementing Classes:

AbstractRegion, IntervalsSet, PolygonsSet, PolyhedronsSet
```
public interface Region<S extends Space>
```
This interface represents a region of a space as a partition.
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 sub-hyperplanes, including regions with no boundary at all: the whole space and the empty region. They are not necessarily finite and not necessarily path-connected. 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.

Since:

3.0

Version:

$Id: Region.java 18108 2017-10-04 06:45:27Z bignon $

Nested Class Summary

Nested Classes
Modifier and Type Interface and Description

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

Nested Classes
Modifier and Type	Interface and Description
`static class`	`Region.Location` Enumerate for the location of a point with respect to the region.

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method and Description
`Region<S>`	`buildNew(BSPTree<S> newTree)` Build a region using the instance as a prototype.
`Region.Location`	`checkPoint(Vector<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.
`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.
`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.
`Side`	`side(Hyperplane<S> hyperplane)` Compute the relative position of the instance with respect to an hyperplane.

- Method Detail
  - buildNew
```
Region<S> 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).
    
    Parameters:
    
    newTree - inside/outside BSP tree representing the new region
    
    Returns:
    
    the built region
  - copySelf
```
Region<S> 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).
    
    Returns:
    
    a new region, copy of the instance
  - isEmpty
```
boolean isEmpty()
```
    Check if the instance is empty.
    
    Returns:
    
    true if the instance is empty
  - isEmpty
```
boolean isEmpty(BSPTree<S> node)
```
    Check if the sub-tree starting at a given node is empty.
    
    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
```
boolean contains(Region<S> region)
```
    Check if the instance entirely contains another region.
    
    Parameters:
    
    region - region to check against the instance
    
    Returns:
    
    true if the instance contains the specified tree
  - checkPoint
```
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
  - getTree
```
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.
    
    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
```
double getBoundarySize()
```
    Get the size of the boundary.
    
    Returns:
    
    the size of the boundary (this is 0 in 1D, a length in 2D, an area in 3D ...)
  - getSize
```
double getSize()
```
    Get the size of the instance.
    
    Returns:
    
    the size of the instance (this is a length in 1D, an area in 2D, a volume in 3D ...)
  - getBarycenter
```
Vector<S> getBarycenter()
```
    Get the barycenter of the instance.
    
    Returns:
    
    an object representing the barycenter
  - side
```
Side side(Hyperplane<S> hyperplane)
```
    Compute the relative position of the instance with respect to an hyperplane.
    
    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
```
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.
    
    Parameters:
    
    sub - sub-hyperplane traversing the region
    
    Returns:
    
    filtered sub-hyperplane

Interface Region<S extends Space>

Nested Class Summary

Method Summary

Method Detail

buildNew

copySelf

isEmpty

isEmpty

contains

checkPoint

getTree

getBoundarySize

getSize

getBarycenter

side

intersection