Ellipsoid (BoneJ Javadocs 0-SNAPSHOT API)

java.lang.Object
- org.bonej.geometry.Ellipsoid

```
public class Ellipsoid
extends Object
```
Represents an ellipsoid defined by its centroid, eigenvalues and 3x3 eigenvector matrix. Semiaxis lengths (radii) are calculated as the inverse square root of the eigenvalues.

Author:

Michael Doube

Field Summary

Fields
Modifier and Type Field and Description

int id
ID field for tracking this particular ellipsoid

Fields
Modifier and Type	Field and Description
`int`	`id` ID field for tracking this particular ellipsoid

Constructor Summary

Constructors
Constructor and Description
`Ellipsoid(double a, double b, double c, double cx, double cy, double cz, double[][] eigenVectors)` Construct an Ellipsoid from the radii (a,b,c), centroid (cx, cy, cz) and Eigenvectors.
`Ellipsoid(Object[] ellipsoid)` Instantiate an ellipsoid from the result of FitEllipsoid

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`boolean`	`contains(double x, double y, double z)` Method based on the inequality (X-X0)^T H (X-X0) ≤ 1 Where X is the test point, X0 is the centroid, H is the ellipsoid's 3x3 matrix
`void`	`contract(double increment)` Constrict all three axes by a fractional increment
`Ellipsoid`	`copy()` Perform a deep copy of this Ellipsoid
`void`	`dilate(double da, double db, double dc)` Dilate the ellipsoid semiaxes by independent absolute amounts
`double[]`	`getAxisAlignedBoundingBox()` Calculate the minimal axis-aligned bounding box of this ellipsoid Thanks to Tavian Barnes for the simplification of the maths https://tavianator.com/2014/06/exact-bounding-boxes-for-spheres-ellipsoids
`double[]`	`getCentre()`
`double[]`	`getRadii()` Gets a copy of the radii.
`double[][]`	`getRotation()` Return a copy of the ellipsoid's eigenvector matrix
`double[]`	`getSortedRadii()` Get the radii sorted in ascending order.
`double[][]`	`getSurfacePoints(double[][] vectors)`
`double[][]`	`getSurfacePoints(int nPoints)`
`double`	`getVolume()` Gets the volume of this ellipsoid, calculated as PI * a * b * c * 4 / 3
`double[]`	`getYMinAndMax()` Calculate the minimal and maximal y values bounding this ellipsoid
`double[]`	`getZMinAndMax()` Calculate the minimal and maximal z values bounding this ellipsoid
`void`	`rotate(double[][] rotation)` Rotate the ellipsoid by the given 3x3 Matrix
`void`	`setCentroid(double x, double y, double z)` Translate the ellipsoid to a given new centroid
`void`	`setRotation(double[][] rotation)` Set rotation to the supplied rotation matrix.
`static double[][]`	`transpose(double[][] a)` Transpose a 3x3 matrix in double[][] format.

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

- Field Detail
  - id
```
public int id
```
    ID field for tracking this particular ellipsoid
- Constructor Detail
  - Ellipsoid
```
public Ellipsoid(Object[] ellipsoid)
```
    Instantiate an ellipsoid from the result of FitEllipsoid
    
    Parameters:
    
    ellipsoid - the properties of an ellipsoid.
  - Ellipsoid
```
public Ellipsoid(double a,
                 double b,
                 double c,
                 double cx,
                 double cy,
                 double cz,
                 double[][] eigenVectors)
```
    Construct an Ellipsoid from the radii (a,b,c), centroid (cx, cy, cz) and Eigenvectors.
    
    Parameters:
    
    a - 1st radius.
    
    b - 2nd radius.
    
    c - 3rd radius.
    
    cx - centroid x-coordinate.
    
    cy - centroid y-coordinate.
    
    cz - centroid z-coordinate.
    
    eigenVectors - the orientation of the ellipsoid.
- Method Detail
  - contains
```
public boolean contains(double x,
                        double y,
                        double z)
```
    Method based on the inequality (X-X0)^T H (X-X0) ≤ 1 Where X is the test point, X0 is the centroid, H is the ellipsoid's 3x3 matrix
    
    Parameters:
    
    x - x-coordinate of the point.
    
    y - y-coordinate of the point.
    
    z - z-coordinate of the point.
    
    Returns:
    
    true if the point (x,y,z) lies inside or on the ellipsoid, false otherwise
  - contract
```
public void contract(double increment)
```
    Constrict all three axes by a fractional increment
    
    Parameters:
    
    increment - scaling factor.
  - copy
```
public Ellipsoid copy()
```
    Perform a deep copy of this Ellipsoid
    
    Returns:
    
    a copy of the instance.
  - dilate
```
public void dilate(double da,
                   double db,
                   double dc)
            throws IllegalArgumentException
```
    Dilate the ellipsoid semiaxes by independent absolute amounts
    
    Parameters:
    
    da - value added to the 1st radius.
    
    db - value added to the 2nd radius.
    
    dc - value added to the 3rd radius.
    
    Throws:
    
    IllegalArgumentException - if new semi-axes are non-positive.
  - getAxisAlignedBoundingBox
```
public double[] getAxisAlignedBoundingBox()
```
    Calculate the minimal axis-aligned bounding box of this ellipsoid Thanks to Tavian Barnes for the simplification of the maths https://tavianator.com/2014/06/exact-bounding-boxes-for-spheres-ellipsoids
    
    Returns:
    
    6-element array containing x min, x max, y min, y max, z min, z max
  - getCentre
```
public double[] getCentre()
```
  - getRadii
```
public double[] getRadii()
```
    Gets a copy of the radii.
    
    Returns:
    
    the semiaxis lengths a, b and c. Note these are not ordered by size, but the order does relate to the 0th, 1st and 2nd columns of the rotation matrix respectively.
  - getRotation
```
public double[][] getRotation()
```
    Return a copy of the ellipsoid's eigenvector matrix
    
    Returns:
    
    a 3x3 rotation matrix
  - setRotation
```
public void setRotation(double[][] rotation)
```
    Set rotation to the supplied rotation matrix. Does no error checking.
    
    Parameters:
    
    rotation - a 3x3 rotation matrix
  - getSortedRadii
```
public double[] getSortedRadii()
```
    Get the radii sorted in ascending order. Note that there is no guarantee that this ordering relates at all to the eigenvectors or eigenvalues.
    
    Returns:
    
    radii in ascending order
  - getSurfacePoints
```
public double[][] getSurfacePoints(int nPoints)
```
  - getSurfacePoints
```
public double[][] getSurfacePoints(double[][] vectors)
```
  - getVolume
```
public double getVolume()
```
    Gets the volume of this ellipsoid, calculated as PI * a * b * c * 4 / 3
    
    Returns:
    
    copy of the stored volume value.
  - getYMinAndMax
```
public double[] getYMinAndMax()
```
    Calculate the minimal and maximal y values bounding this ellipsoid
    
    Returns:
    
    array containing minimal and maximal y values
  - getZMinAndMax
```
public double[] getZMinAndMax()
```
    Calculate the minimal and maximal z values bounding this ellipsoid
    
    Returns:
    
    array containing minimal and maximal z values
  - rotate
```
public void rotate(double[][] rotation)
```
    Rotate the ellipsoid by the given 3x3 Matrix
    
    Parameters:
    
    rotation - a 3x3 rotation matrix
  - setCentroid
```
public void setCentroid(double x,
                        double y,
                        double z)
```
    Translate the ellipsoid to a given new centroid
    
    Parameters:
    
    x - new centroid x-coordinate
    
    y - new centroid y-coordinate
    
    z - new centroid z-coordinate
  - transpose
```
public static double[][] transpose(double[][] a)
```
    Transpose a 3x3 matrix in double[][] format. Does no error checking.
    
    Parameters:
    
    a - a matrix.
    
    Returns:
    
    new transposed matrix.

Class Ellipsoid

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

id

Constructor Detail

Ellipsoid

Ellipsoid

Method Detail

contains

contract

copy

dilate

getAxisAlignedBoundingBox

getCentre

getRadii

getRotation

setRotation

getSortedRadii

getSurfacePoints

getSurfacePoints

getVolume

getYMinAndMax

getZMinAndMax

rotate

setCentroid

transpose