Tetrahedralization

java.lang.Object
- de.grogra.imp3d.math.delaunay.Tetrahedralization

All Implemented Interfaces:

java.io.Serializable
```
public class Tetrahedralization
extends java.lang.Object
implements java.io.Serializable
```
A Delaunay tetrahedralization.

Author:

Hal Hildebrand

See Also:
Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`java.util.Set<Point3d>`	`fourCornersSet`
`boolean`	`showAuxiliaryCells`
`boolean`	`showAuxiliaryFaces`
`boolean`	`showDelaunayFaces`
`boolean`	`showVoronoiCells`
`static V[]`	`VERTICES` Cannonical enumeration of the vertex ordinals

Constructor Summary

Constructors
Constructor and Description

Tetrahedralization()
Construct a tetrahedralizaion using the supplied random number generator

Constructors
Constructor and Description
`Tetrahedralization()` Construct a tetrahedralizaion using the supplied random number generator

Method Summary

Methods
Modifier and Type	Method and Description
`void`	`compute()` Computes the Delaunay triangulation and Voronoi diagram for the current set of VoronoiCell s
`void`	`delete(VoronoiCell v)` Delete the vertex from the tetrahedralization.
`protected Tetrahedron`	`flip4to1(VoronoiCell n)` Perform the 4->1 bistellar flip.
`java.util.List<Point3d[]>`	`getDelaunayFaces()`
`java.util.List<Point3d[]>`	`getDelaunayRegion(VoronoiCell v)`
`java.util.LinkedList<OrientedFace>`	`getEars(VoronoiCell v)`
`static VoronoiCell[]`	`getFourCorners()`
`java.util.Collection<VoronoiCell>`	`getNeighbours(VoronoiCell v)` Answer the cleaned collection of neighbouring VoronoiCells around the indicated VoronoiCell.
`java.util.Collection<VoronoiCell>`	`getNeighboursAll(VoronoiCell v)` Answer the collection of neighbouring VoronoiCells around the indicated VoronoiCell.
`java.util.Deque<OrientedFace>`	`getStar(VoronoiCell v)`
`java.util.Set<Tetrahedron>`	`getTetrahedrons()` Answer the set of all tetrahedrons in this tetrahedralization
`java.util.Set<VoronoiCell>`	`getVertices()` Answer the set of all vertices in this tetrahedralization
`java.util.Collection<VoronoiCell>`	`getVirtualNeighbours(VoronoiCell v)` Answer the collection of neighbouring VoronoiCells (VoronoiCell.getId()==-1) around the indicated VoronoiCell.
`java.util.List<Point3d[]>`	`getVoronoiFaces()`
`java.util.Set<Point3d>`	`getVoronoiPointsSet()` returns a set of points that build the voronoi faces for this VoronoiCell
`java.util.List<Point3d[]>`	`getVoronoiRegion(VoronoiCell v)` Answer the faces of the voronoi region around the vertex
`void`	`insert(VoronoiCell v)` Insert the vertex into the tetrahedralization.
`void`	`insert(VoronoiCell[] array)`
`protected boolean`	`isAuxiliary(Point3d[] face)`
`boolean`	`isShowAuxiliaryCells()`
`boolean`	`isShowAuxiliaryFaces()`
`boolean`	`isShowDelaunayFaces()`
`boolean`	`isShowVoronoiCells()`
`Tetrahedron`	`locate(VoronoiCell query)` Locate the tetrahedron which contains the query point via a stochastic walk through the delaunay triangulation.
`Tetrahedron`	`myOwnPrivateIdaho()` Construct a Tetrahedron which is set up to encompass the numerical span
`void`	`setShowAuxiliaryCells(boolean value)`
`void`	`setShowAuxiliaryFaces(boolean value)`
`void`	`setShowDelaunayFaces(boolean value)`
`void`	`setShowVoronoiCells(boolean value)`
`void`	`traverse(java.util.Set<Tetrahedron> tetrahedrons, java.util.Set<VoronoiCell> vertices)` Traverse all the tetrahedrons in the tetrahedralization.
`void`	`update()`

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - fourCornersSet
```
public java.util.Set<Point3d> fourCornersSet
```
  - showAuxiliaryCells
```
public boolean showAuxiliaryCells
```
  - showAuxiliaryFaces
```
public boolean showAuxiliaryFaces
```
  - showDelaunayFaces
```
public boolean showDelaunayFaces
```
  - showVoronoiCells
```
public boolean showVoronoiCells
```
  - VERTICES
```
public static final V[] VERTICES
```
    Cannonical enumeration of the vertex ordinals
- Constructor Detail
  - Tetrahedralization
```
public Tetrahedralization()
```
    Construct a tetrahedralizaion using the supplied random number generator
    
    Parameters:
    random -
- Method Detail
  - compute
```
public void compute()
```
    Computes the Delaunay triangulation and Voronoi diagram for the current set of VoronoiCell s
  - delete
```
public void delete(VoronoiCell v)
```
    Delete the vertex from the tetrahedralization. This algorithm is the deleteInSphere algorithm from Ledoux. See "Flipping to Robustly Delete a Vertex in a Delaunay Tetrahedralization", H. Ledoux, C.M. Gold and G. Baciu, 2005
    
    Parameters:
    v - - the vertex to be deleted
  - flip4to1
```
protected Tetrahedron flip4to1(VoronoiCell n)
```
    Perform the 4->1 bistellar flip. This flip is the inverse of the 4->1 flip.
    
    Parameters:
    n - - the vertex who's star defines the 4 tetrahedron
    
    Returns:
    the tetrahedron created from the flip
  - getDelaunayFaces
```
public java.util.List<Point3d[]> getDelaunayFaces()
```
  - getDelaunayRegion
```
public java.util.List<Point3d[]> getDelaunayRegion(VoronoiCell v)
```
  - getEars
```
public java.util.LinkedList<OrientedFace> getEars(VoronoiCell v)
```
  - getFourCorners
```
public static VoronoiCell[] getFourCorners()
```
  - getNeighbours
```
public java.util.Collection<VoronoiCell> getNeighbours(VoronoiCell v)
```
    Answer the cleaned collection of neighbouring VoronoiCells around the indicated VoronoiCell. (cleaned --> without VoronoiCell.getId()==-1)
    
    Parameters:
    v - - the VoronoiCell determining the neighbourhood
    
    Returns:
    cleaned collection of neighbouring VoronoiCell
  - getNeighboursAll
```
public java.util.Collection<VoronoiCell> getNeighboursAll(VoronoiCell v)
```
    Answer the collection of neighbouring VoronoiCells around the indicated VoronoiCell.
    
    Parameters:
    v - - the VoronoiCell determining the neighbourhood
    
    Returns:
    the collection of neighbouring VoronoiCell
  - getStar
```
public java.util.Deque<OrientedFace> getStar(VoronoiCell v)
```
  - getTetrahedrons
```
public java.util.Set<Tetrahedron> getTetrahedrons()
```
    Answer the set of all tetrahedrons in this tetrahedralization
    
    Returns:
  - getVertices
```
public java.util.Set<VoronoiCell> getVertices()
```
    Answer the set of all vertices in this tetrahedralization
    
    Returns:
  - getVirtualNeighbours
```
public java.util.Collection<VoronoiCell> getVirtualNeighbours(VoronoiCell v)
```
    Answer the collection of neighbouring VoronoiCells (VoronoiCell.getId()==-1) around the indicated VoronoiCell.
    
    Parameters:
    v - - the VoronoiCell determining the neighbourhood
    
    Returns:
    collection of neighbouring VoronoiCell (VoronoiCell.getId()==-1)
  - getVoronoiFaces
```
public java.util.List<Point3d[]> getVoronoiFaces()
```
  - getVoronoiPointsSet
```
public java.util.Set<Point3d> getVoronoiPointsSet()
```
    returns a set of points that build the voronoi faces for this VoronoiCell
    
    Returns:
    set of voronoi points
  - getVoronoiRegion
```
public java.util.List<Point3d[]> getVoronoiRegion(VoronoiCell v)
```
    Answer the faces of the voronoi region around the vertex
    
    Parameters:
    v - - the vertex of interest
    
    Returns:
    the list of faces defining the voronoi region defined by v
  - insert
```
public void insert(VoronoiCell v)
```
    Insert the vertex into the tetrahedralization. See "Computing the 3D Voronoi Diagram Robustly: An Easy Explanation", by Hugo Ledoux
    
    Parameters:
    v - - the vertex to be inserted
  - insert
```
public void insert(VoronoiCell[] array)
```
  - isAuxiliary
```
protected boolean isAuxiliary(Point3d[] face)
```
  - isShowAuxiliaryCells
```
public boolean isShowAuxiliaryCells()
```
  - isShowAuxiliaryFaces
```
public boolean isShowAuxiliaryFaces()
```
  - isShowDelaunayFaces
```
public boolean isShowDelaunayFaces()
```
  - isShowVoronoiCells
```
public boolean isShowVoronoiCells()
```
  - locate
```
public Tetrahedron locate(VoronoiCell query)
```
    Locate the tetrahedron which contains the query point via a stochastic walk through the delaunay triangulation. This location algorithm is a slight variation of the 3D jump and walk algorithm found in: "Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations", Computational Geometry 12 (1999) 63-83.
    In this variant, the intial "random" triangle used is simply the one of the triangles in the last tetrahedron created by a flip, or the previously located tetrahedron.
    This location algorithm provides fast location results with no memory overhead. Further, because there is no search structure to maintain, this algorithm is ideally suited for incremental deletions and kinetic maintenance of the delaunay tetrahedralization.
    
    Parameters:
    query - - the query point
    
    Returns:
  - myOwnPrivateIdaho
```
public Tetrahedron myOwnPrivateIdaho()
```
    Construct a Tetrahedron which is set up to encompass the numerical span
    
    Returns:
  - setShowAuxiliaryCells
```
public void setShowAuxiliaryCells(boolean value)
```
  - setShowAuxiliaryFaces
```
public void setShowAuxiliaryFaces(boolean value)
```
  - setShowDelaunayFaces
```
public void setShowDelaunayFaces(boolean value)
```
  - setShowVoronoiCells
```
public void setShowVoronoiCells(boolean value)
```
  - traverse
```
public void traverse(java.util.Set<Tetrahedron> tetrahedrons,
            java.util.Set<VoronoiCell> vertices)
```
    Traverse all the tetrahedrons in the tetrahedralization. The set of tetrahedons will be filled with all the tetrahedrons and the set of vertices will be filled with all the vertices defining the tetrahedralization.
    
    Parameters:
    tetrahedrons -
    vertices -
  - update
```
public void update()
```

Class Tetrahedralization

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

fourCornersSet

showAuxiliaryCells

showAuxiliaryFaces

showDelaunayFaces

showVoronoiCells

VERTICES

Constructor Detail

Tetrahedralization

Method Detail

compute

delete

flip4to1

getDelaunayFaces

getDelaunayRegion

getEars

getFourCorners

getNeighbours

getNeighboursAll

getStar

getTetrahedrons

getVertices

getVirtualNeighbours

getVoronoiFaces

getVoronoiPointsSet

getVoronoiRegion

insert

insert

isAuxiliary

isShowAuxiliaryCells

isShowAuxiliaryFaces

isShowDelaunayFaces

isShowVoronoiCells

locate

myOwnPrivateIdaho

setShowAuxiliaryCells

setShowAuxiliaryFaces

setShowDelaunayFaces

setShowVoronoiCells

traverse

update