Delaunay (VisAD 2.0 API)

java.lang.Object
- visad.Delaunay

All Implemented Interfaces:

Serializable

Direct Known Subclasses:

DelaunayClarkson, DelaunayCustom, DelaunayFast, DelaunayOverlap, DelaunayWatson
```
public abstract class Delaunay
extends Object
implements Serializable
```
Delaunay represents an abstract class for calculating an N-dimensional Delaunay triangulation, that can be extended to allow for various triangulation algorithms.

See Also:
Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`int[][]`	`Edges` tri/tetra edges --> global edge number.
`int`	`NumEdges` number of unique global edge numbers
`int[][]`	`Tri` triangles/tetrahedra --> vertices.
`int[][]`	`Vertices` vertices --> triangles/tetrahedra.
`int[][]`	`Walk` triangles/tetrahedra --> triangles/tetrahedra.

Constructor Summary

Constructors
Constructor and Description

Delaunay()
The abstract constructor initializes the class's data arrays.

Constructors
Constructor and Description
`Delaunay()` The abstract constructor initializes the class's data arrays.

Method Summary

Methods
Modifier and Type	Method and Description
`Object`	`clone()`
`static Delaunay`	`factory(float[][] samples, boolean exact)` The factory class method heuristically decides which extension to the Delaunay abstract class to use in order to construct the fastest triangulation, and calls that extension, returning the finished triangulation.
`void`	`finish_triang(float[][] samples)` calculate a triangulation's helper arrays, Walk and Edges, if the triangulation algorithm hasn't calculated them already.
`boolean`	`getNonConvex()`
`void`	`improve(float[][] samples, int pass)` use edge-flipping to bring the current triangulation closer to the true Delaunay triangulation.
`static float[][]`	`perturb(float[][] samples, float epsilon, boolean copy)` increments samples coordinates by random numbers between -epsilon and epsilon, in order to eliminate triangulation problems such as co-linear and co-located points
`String`	`sampleString(float[][] samples)`
`static float[][]`	`scale(float[][] samples, float mult, boolean copy)` alters the values of the samples by multiplying them by the mult factor
`void`	`setNonConvex()` set flag indicating this Delaunay topology is non-convex
`boolean`	`test(float[][] samples)` check this triangulation in various ways to make sure it is constructed correctly.
`boolean`	`test(float[][] samples, boolean printErrors)`
`String`	`toString()`

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

- Field Detail
  - Tri
```
public int[][] Tri
```
    triangles/tetrahedra --> vertices.
    Tri = new int[ntris][dim + 1]
    This is the key output, a list of triangles (in two dimensions, tetrahedra in three dimensions, etc). ntris is the number of triangles.
    In 2-D, Tri[i] is an array of 3 integers, which are three indices into the samples[0] and samples[1] arrays to get the x and y values of the three vertices of the triangle.
    In 3-D, Tri[i] is an array of 4 integers, which are four indices into the samples[0], samples[1] and samples[2] arrays to get the x, y and z values of the four vertices of the tetrahedron.
    This pattern continues for higher dimensionalities.
  - Vertices
```
public int[][] Vertices
```
    vertices --> triangles/tetrahedra.
    Vertices = new int[nrs][nverts[i]]
    nrs is the number of samples (the length of the samples[0] and samples[1] arrays. For sample i, Vertices[i] is a (variable length) list of indices into the Tri array above, giving the indices of the triangles that include vertex i.
    nverts is an array as the second index of the Vertices array since different vertices may be part of different numbers of triangles.
    You can use Tri and Vertices together to traverse the triangulation. If you don't need to traverse, then you can probably ignore all arrays except Tri.
  - Walk
```
public int[][] Walk
```
    triangles/tetrahedra --> triangles/tetrahedra.
    Walk = new int[ntris][dim + 1]
    Also useful for traversing the triangulation, in this case giving the indices of triangles that share edges with the current triangle.
  - Edges
```
public int[][] Edges
```
    tri/tetra edges --> global edge number.
    Edges = new int[ntris][3 * (dim - 1)];
    'global edge number' is the number of an edge that is unique among the whole triangulation. This number is not an index into any array, but will match for a shared edge between two triangles.
  - NumEdges
```
public int NumEdges
```
    number of unique global edge numbers
- Constructor Detail
  - Delaunay
```
public Delaunay()
         throws VisADException
```
    The abstract constructor initializes the class's data arrays.
    
    Throws:
    
    VisADException - a VisAD error occurred
- Method Detail
  - setNonConvex
```
public void setNonConvex()
```
    set flag indicating this Delaunay topology is non-convex
  - getNonConvex
```
public boolean getNonConvex()
```
    Returns:
    flag indicating whether this Delaunay topology is non-convex
  - clone
```
public Object clone()
```
    Overrides:
    
    clone in class Object
    
    Returns:
    clone of this Delaunay as a DelaunayCustom
  - factory
```
public static Delaunay factory(float[][] samples,
               boolean exact)
                        throws VisADException
```
    The factory class method heuristically decides which extension to the Delaunay abstract class to use in order to construct the fastest triangulation, and calls that extension, returning the finished triangulation. The method chooses from among the Fast, Clarkson, and Watson methods.
    
    Parameters:
    samples - locations of points for topology - dimensioned float[dimension][number_of_points]
    exact - flag indicating need for exact Delaunay triangulation
    
    Returns:
    a topology using an appropriate sub-class of Delaunay
    
    Throws:
    
    VisADException - a VisAD error occurred
  - scale
```
public static float[][] scale(float[][] samples,
              float mult,
              boolean copy)
```
    alters the values of the samples by multiplying them by the mult factor
    
    Parameters:
    samples - locations of points for topology - dimensioned float[dimension][number_of_points]
    mult - multiplication factor
    copy - specifies whether scale should modify and return the argument samples array or a copy
    
    Returns:
    array of scaled values
  - perturb
```
public static float[][] perturb(float[][] samples,
                float epsilon,
                boolean copy)
```
    increments samples coordinates by random numbers between -epsilon and epsilon, in order to eliminate triangulation problems such as co-linear and co-located points
    
    Parameters:
    samples - locations of points for topology - dimensioned float[dimension][number_of_points]
    epsilon - size limit on random perturbations
    copy - specifies whether perturb should modify and return the argument samples array or a copy
    
    Returns:
    array of perturbed values
  - test
```
public boolean test(float[][] samples)
```
    check this triangulation in various ways to make sure it is constructed correctly. This method is expensive, provided mainly for debugging purposes.
    
    Parameters:
    samples - locations of points for topology - dimensioned float[dimension][number_of_points]
    
    Returns:
    flag that is false to indicate there are problems with the triangulation
  - test
```
public boolean test(float[][] samples,
           boolean printErrors)
```
  - improve
```
public void improve(float[][] samples,
           int pass)
             throws VisADException
```
    use edge-flipping to bring the current triangulation closer to the true Delaunay triangulation.
    
    Parameters:
    samples - locations of points for topology - dimensioned float[dimension][number_of_points]
    pass - the number of passes the algorithm should take over all edges (however, the algorithm terminates if no edges are flipped for an entire pass).
    
    Throws:
    
    VisADException - a VisAD error occurred
  - finish_triang
```
public void finish_triang(float[][] samples)
                   throws VisADException
```
    calculate a triangulation's helper arrays, Walk and Edges, if the triangulation algorithm hasn't calculated them already. Any extension to the Delaunay class should call finish_triang() at the end of its triangulation constructor.
    
    Parameters:
    samples - locations of points for topology - dimensioned float[dimension][number_of_points]
    
    Throws:
    
    VisADException - a VisAD error occurred
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object
    
    Returns:
    a String representation of this
  - sampleString
```
public String sampleString(float[][] samples)
```
    Parameters:
    samples - locations of points for topology - dimensioned float[dimension][number_of_points] - may be null
    
    Returns:
    a String representation of this, including samples if it is non-null

Class Delaunay

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

Tri

Vertices

Walk

Edges

NumEdges

Constructor Detail

Delaunay

Method Detail

setNonConvex

getNonConvex

clone

factory

scale

perturb

test

test

improve

finish_triang

toString

sampleString