org.apache.commons.math3.geometry.euclidean.threed

Class PolyhedronsSet

java.lang.Object

org.apache.commons.math3.geometry.partitioning.AbstractRegion<Euclidean3D,Euclidean2D>

org.apache.commons.math3.geometry.euclidean.threed.PolyhedronsSet

All Implemented Interfaces:

Region<Euclidean3D>

public class PolyhedronsSet
extends AbstractRegion<Euclidean3D,Euclidean2D>

This class represents a 3D region: a set of polyhedrons.

Since:

3.0

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
private class	PolyhedronsSet.FacetsContributionVisitor Visitor computing geometrical properties.
private static class	PolyhedronsSet.RotationTransform 3D rotation as a Transform.
private static class	PolyhedronsSet.TranslationTransform 3D translation as a transform.

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 static double	DEFAULT_TOLERANCE Default value for tolerance.

Constructor Summary

Constructors

Constructor and Description
PolyhedronsSet() Deprecated. as of 3.3, replaced with PolyhedronsSet(double)
PolyhedronsSet(BSPTree<Euclidean3D> tree) Deprecated. as of 3.3, replaced with PolyhedronsSet(BSPTree, double)
PolyhedronsSet(BSPTree<Euclidean3D> tree, double tolerance) Build a polyhedrons set from a BSP tree.
PolyhedronsSet(java.util.Collection<SubHyperplane<Euclidean3D>> boundary) Deprecated. as of 3.3, replaced with PolyhedronsSet(Collection, double)
PolyhedronsSet(java.util.Collection<SubHyperplane<Euclidean3D>> boundary, double tolerance) Build a polyhedrons set from a Boundary REPresentation (B-rep) specified by sub-hyperplanes.
PolyhedronsSet(double tolerance) Build a polyhedrons set representing the whole real line.
PolyhedronsSet(double xMin, double xMax, double yMin, double yMax, double zMin, double zMax) Deprecated. as of 3.3, replaced with PolyhedronsSet(double, double, double, double, double, double, double)
PolyhedronsSet(double xMin, double xMax, double yMin, double yMax, double zMin, double zMax, double tolerance) Build a parallellepipedic box.
PolyhedronsSet(java.util.List<Vector3D> vertices, java.util.List<int[]> facets, double tolerance) Build a polyhedrons set from a Boundary REPresentation (B-rep) specified by connected vertices.

Method Summary

Methods

Modifier and Type	Method and Description
private SubHyperplane<Euclidean3D>	boundaryFacet(Vector3D point, BSPTree<Euclidean3D> node) Check if a point belongs to the boundary part of a node.
private static BSPTree<Euclidean3D>	buildBoundary(double xMin, double xMax, double yMin, double yMax, double zMin, double zMax, double tolerance) Build a parallellepipedic box boundary.
private static java.util.List<SubHyperplane<Euclidean3D>>	buildBoundary(java.util.List<Vector3D> vertices, java.util.List<int[]> facets, double tolerance) Build boundary from vertices and facets.
PolyhedronsSet	buildNew(BSPTree<Euclidean3D> tree) Build a region using the instance as a prototype.
protected void	computeGeometricalProperties() Compute some geometrical properties.
private static int[][]	findReferences(java.util.List<Vector3D> vertices, java.util.List<int[]> facets) Find the facets that reference each edges.
SubHyperplane<Euclidean3D>	firstIntersection(Vector3D point, Line line) Get the first sub-hyperplane crossed by a semi-infinite line.
private SubHyperplane<Euclidean3D>	recurseFirstIntersection(BSPTree<Euclidean3D> node, Vector3D point, Line line) Get the first sub-hyperplane crossed by a semi-infinite line.
PolyhedronsSet	rotate(Vector3D center, Rotation rotation) Rotate the region around the specified point.
private static int[][]	successors(java.util.List<Vector3D> vertices, java.util.List<int[]> facets, int[][] references) Find the successors of all vertices among all facets they belong to.
PolyhedronsSet	translate(Vector3D translation) Translate the region by the specified amount.

Methods inherited from class org.apache.commons.math3.geometry.partitioning.AbstractRegion

applyTransform, checkPoint, checkPoint, checkPoint, checkPoint, contains, copySelf, getBarycenter, getBoundarySize, getSize, getTolerance, getTree, intersection, isEmpty, isEmpty, isFull, isFull, projectToBoundary, setBarycenter, setBarycenter, setSize, side

Methods inherited from class java.lang.Object

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

Field Detail

DEFAULT_TOLERANCE

private static final double DEFAULT_TOLERANCE

Default value for tolerance.

See Also:

Constant Field Values

Constructor Detail

PolyhedronsSet

public PolyhedronsSet(double tolerance)

Build a polyhedrons set representing the whole real line.

Parameters:

tolerance - tolerance below which points are considered identical

Since:

3.3

PolyhedronsSet

public PolyhedronsSet(BSPTree<Euclidean3D> tree,
              double tolerance)

Build a polyhedrons set from a 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

This constructor is aimed at expert use, as building the tree may be a difficult task. It is not intended for general use and for performances reasons does not check thoroughly its input, as this would require walking the full tree each time. Failing to provide a tree with the proper attributes, will therefore generate problems like NullPointerException or ClassCastException only later on. This limitation is known and explains why this constructor is for expert use only. The caller does have the responsibility to provided correct arguments.

Parameters:

tree - inside/outside BSP tree representing the region

tolerance - tolerance below which points are considered identical

Since:

3.3

PolyhedronsSet

public PolyhedronsSet(java.util.Collection<SubHyperplane<Euclidean3D>> boundary,
              double tolerance)

Build a polyhedrons set from a Boundary REPresentation (B-rep) specified by sub-hyperplanes.

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 polyhedrons with holes or a set of disjoint 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

Since:

3.3

PolyhedronsSet

public PolyhedronsSet(java.util.List<Vector3D> vertices,
              java.util.List<int[]> facets,
              double tolerance)

Build a polyhedrons set from a Boundary REPresentation (B-rep) specified by connected vertices.

The boundary is provided as a list of vertices and a list of facets. Each facet is specified as an integer array containing the arrays vertices indices in the vertices list. Each facet normal is oriented by right hand rule to the facet vertices list.

Some basic sanity checks are performed but not everything is thoroughly assessed, so it remains under caller responsibility to ensure the vertices and facets are consistent and properly define a polyhedrons set.

Parameters:

vertices - list of polyhedrons set vertices

facets - list of facets, as vertices indices in the vertices list

tolerance - tolerance below which points are considered identical

Throws:

MathIllegalArgumentException - if some basic sanity checks fail

Since:

3.5

PolyhedronsSet

public PolyhedronsSet(double xMin,
              double xMax,
              double yMin,
              double yMax,
              double zMin,
              double zMax,
              double tolerance)

Build a parallellepipedic box.

Parameters:

xMin - low bound along the x direction

xMax - high bound along the x direction

yMin - low bound along the y direction

yMax - high bound along the y direction

zMin - low bound along the z direction

zMax - high bound along the z direction

tolerance - tolerance below which points are considered identical

Since:

3.3

PolyhedronsSet

@Deprecated
public PolyhedronsSet()

Deprecated. as of 3.3, replaced with PolyhedronsSet(double)

Build a polyhedrons set representing the whole real line.

PolyhedronsSet

@Deprecated
public PolyhedronsSet(BSPTree<Euclidean3D> tree)

Deprecated. as of 3.3, replaced with PolyhedronsSet(BSPTree, double)

Build a polyhedrons set from a 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

Parameters:

tree - inside/outside BSP tree representing the region

PolyhedronsSet

@Deprecated
public PolyhedronsSet(java.util.Collection<SubHyperplane<Euclidean3D>> boundary)

Deprecated. as of 3.3, replaced with PolyhedronsSet(Collection, double)

Build a polyhedrons set 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 polyhedrons with holes or a set of disjoint 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

PolyhedronsSet

@Deprecated
public PolyhedronsSet(double xMin,
                         double xMax,
                         double yMin,
                         double yMax,
                         double zMin,
                         double zMax)

Deprecated. as of 3.3, replaced with PolyhedronsSet(double, double, double, double, double, double, double)

Build a parallellepipedic box.

Parameters:

xMin - low bound along the x direction

xMax - high bound along the x direction

yMin - low bound along the y direction

yMax - high bound along the y direction

zMin - low bound along the z direction

zMax - high bound along the z direction

Method Detail

buildBoundary

private static BSPTree<Euclidean3D> buildBoundary(double xMin,
                                 double xMax,
                                 double yMin,
                                 double yMax,
                                 double zMin,
                                 double zMax,
                                 double tolerance)

Build a parallellepipedic box boundary.

Parameters:

xMin - low bound along the x direction

xMax - high bound along the x direction

yMin - low bound along the y direction

yMax - high bound along the y direction

zMin - low bound along the z direction

zMax - high bound along the z direction

tolerance - tolerance below which points are considered identical

Returns:

boundary tree

Since:

3.3

buildBoundary

private static java.util.List<SubHyperplane<Euclidean3D>> buildBoundary(java.util.List<Vector3D> vertices,
                                                       java.util.List<int[]> facets,
                                                       double tolerance)

Build boundary from vertices and facets.

Parameters:

vertices - list of polyhedrons set vertices

facets - list of facets, as vertices indices in the vertices list

tolerance - tolerance below which points are considered identical

Returns:

boundary as a list of sub-hyperplanes

Throws:

MathIllegalArgumentException - if some basic sanity checks fail

Since:

3.5

findReferences

private static int[][] findReferences(java.util.List<Vector3D> vertices,
                     java.util.List<int[]> facets)

Find the facets that reference each edges.

Parameters:

vertices - list of polyhedrons set vertices

facets - list of facets, as vertices indices in the vertices list

Returns:

references array such that r[v][k] = f for some k if facet f contains vertex v

Throws:

MathIllegalArgumentException - if some facets have fewer than 3 vertices

Since:

3.5

successors

private static int[][] successors(java.util.List<Vector3D> vertices,
                 java.util.List<int[]> facets,
                 int[][] references)

Find the successors of all vertices among all facets they belong to.

Parameters:

vertices - list of polyhedrons set vertices

facets - list of facets, as vertices indices in the vertices list

references - facets references array

Returns:

indices of vertices that follow vertex v in some facet (the array may contain extra entries at the end, set to negative indices)

Throws:

MathIllegalArgumentException - if the same vertex appears more than once in the successors list (which means one facet orientation is wrong)

Since:

3.5

buildNew

public PolyhedronsSet buildNew(BSPTree<Euclidean3D> tree)

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<Euclidean3D>

Specified by:

buildNew in class AbstractRegion<Euclidean3D,Euclidean2D>

Parameters:

tree - inside/outside BSP tree representing the new region

Returns:

the built region

computeGeometricalProperties

protected void computeGeometricalProperties()

Compute some geometrical properties.

The properties to compute are the barycenter and the size.

Specified by:

computeGeometricalProperties in class AbstractRegion<Euclidean3D,Euclidean2D>

firstIntersection

public SubHyperplane<Euclidean3D> firstIntersection(Vector3D point,
                                           Line line)

Get the first sub-hyperplane crossed by a semi-infinite line.

Parameters:

point - start point of the part of the line considered

line - line to consider (contains point)

Returns:

the first sub-hyperplane crossed by the line after the given point, or null if the line does not intersect any sub-hyperplane

recurseFirstIntersection

private SubHyperplane<Euclidean3D> recurseFirstIntersection(BSPTree<Euclidean3D> node,
                                                  Vector3D point,
                                                  Line line)

Get the first sub-hyperplane crossed by a semi-infinite line.

Parameters:

node - current node

point - start point of the part of the line considered

line - line to consider (contains point)

Returns:

the first sub-hyperplane crossed by the line after the given point, or null if the line does not intersect any sub-hyperplane

boundaryFacet

private SubHyperplane<Euclidean3D> boundaryFacet(Vector3D point,
                                       BSPTree<Euclidean3D> node)

Check if a point belongs to the boundary part of a node.

Parameters:

point - point to check

node - node containing the boundary facet to check

Returns:

the boundary facet this points belongs to (or null if it does not belong to any boundary facet)

rotate

public PolyhedronsSet rotate(Vector3D center,
                    Rotation rotation)

Rotate the region around the specified point.

The instance is not modified, a new instance is created.

Parameters:

center - rotation center

rotation - vectorial rotation operator

Returns:

a new instance representing the rotated region

translate

public PolyhedronsSet translate(Vector3D translation)

Translate the region by the specified amount.

The instance is not modified, a new instance is created.

Parameters:

translation - translation to apply

Returns:

a new instance representing the translated region