Sphere

java.lang.Object
- ProGAL.geom3d.volumes.Sphere

All Implemented Interfaces:

Shape, Volume
```
public class Sphere
extends java.lang.Object
implements Volume
```
A sphere represented by a center-point and a radius.

Field Summary

Fields
Modifier and Type Field and Description

protected Point center

protected double radius

Fields
Modifier and Type	Field and Description
`protected Point`	`center`
`protected double`	`radius`

Constructor Summary

Constructors
Constructor and Description
`Sphere(Circle c)` creates a sphere with the specified circle as equator
`Sphere(CTetrahedron tetr)`
`Sphere(double x, double y, double z, double radius)`
`Sphere(Point[] ps)`
`Sphere(Point center, double radius)` Constructs a sphere with the specified center and the specified radius.
`Sphere(Point p0, Point p1, Point p2, Point p3)`
`Sphere(PointWeighted p)` Constructs a sphere with the weighted point as center and a radius with the square root of the points weight.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`Sphere`	`clone()` Returns a deep clone of this sphere.
`static double`	`computeSphere_fast(Point p0, Point p1, Point p2, Point p3, Point center)` Calculates the radius and center of the sphere touching the four specified points.
`void`	`contains(java.util.List<Vertex> points, double eps)`
`boolean`	`contains(Point p)` Returns true if the given point is in the sphere.
`boolean`	`containsNone(java.util.List<Point> points)` Returns true if none of the given points is in the sphere.
`boolean`	`containsNoneButAtMostOne(Vertex v, java.util.List<Vertex> points)`
`int`	`containsNumber(java.util.List<Vertex> points)` Returns number of points inside the sphere
`PointList`	`generatePointsOnSphere(int n)` TODO: Comment, move up and test
`PointList`	`generateRandomPointsOnSphere(int n)` TODO: Comment, move up and test
`Point`	`getCenter()` Get the center
`LineSegment`	`getIntersection(Line line)` Gets the secant on the line.
`static Circle`	`getIntersection(Sphere s1, Sphere s2)`
`java.lang.Double`	`getIntersectionAngle(Circle c, Point p, Vector dir)`
`Point[]`	`getIntersections(Circle c)`
`static Point[]`	`getIntersections(Sphere s1, Sphere s2, Sphere s3)` Find the two, one or zero points that is at the intersection of the three sphere shells.
`static Sphere`	`getMinSphere(Circle c)` Get the sphere with the specified circle as equator
`static Sphere`	`getMinSphere(PointList points)` Gets the smallest sphere containing a set of points.
`static Sphere`	`getMinSphere(Point p1, Point p2)` Get the smallest sphere through two given points.
`static Sphere`	`getMinSphere(Point p0, Point p1, Point p2)` Get the smallest sphere through three points.
`static Sphere`	`getMinSphere(Point p0, Point p1, Point p2, Point p3)` Constructs the sphere through four points.
`double`	`getRadius()` Get the radius
`double`	`getRadiusSquared()` Get the squared radius
`double`	`getSurfaceArea()` Get the surface area
`double`	`getVolume()` Get the volume
`double[]`	`intersectionParameters(Line line)` Returns the two line-parameters that indicate where `line` intersects this sphere.
`boolean`	`isEmpty(java.util.List<Vertex> points, double eps)` returns TRUE if the interior of the sphere (for a given eps reduction of the radius) is empty
`boolean`	`isEmpty(Point[] points, double eps)`
`boolean`	`isInside(Point p)` Returns true if the point is inside this sphere
`boolean`	`isInside(Point p, double eps)` Returns true iff the squared distance from the point to the sphere center is less than the squared radius minus `eps`
`boolean`	`isIntersected(Sphere sphere)` Returns true if this sphere is intersected or touched by another sphere.
`boolean`	`overlaps(Volume vol)` Returns true if the sphere overlaps with `vol`.
`double`	`powerDistance(Point p)` Gets the squared distance of a point from a sphere surface (negative if the point is inside the sphere).
`void`	`setCenter(Point center)`
`void`	`setCenter(Point p0, Point p1, Point p2, Point p3)`
`void`	`setRadius(double radius)`
`void`	`toConsole()` Writes this sphere to `System.out`.
`void`	`toConsole(int dec)` Writes this sphere to `System.out` with `dec` decimals precision.
`java.lang.String`	`toString()` Return a string representation of this sphere.
`java.lang.String`	`toString(int dec)` Return a string representation of this sphere with `dec` decimals precision
`static double`	`unionVolume_Grid(java.util.Collection<Sphere> spheres)` Estimate the volume of the union of a set of spheres.

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

Field Detail

center
```
protected Point center
```

radius
```
protected double radius
```

Constructor Detail

Sphere
```
public Sphere(Point center,
              double radius)
```
Constructs a sphere with the specified center and the specified radius.

Sphere

public Sphere(double x,
              double y,
              double z,
              double radius)

Sphere
```
public Sphere(Point[] ps)
```

Sphere

public Sphere(Point p0,
              Point p1,
              Point p2,
              Point p3)

Sphere
```
public Sphere(CTetrahedron tetr)
```

Sphere
```
public Sphere(PointWeighted p)
```
Constructs a sphere with the weighted point as center and a radius with the square root of the points weight.

Sphere
```
public Sphere(Circle c)
```
creates a sphere with the specified circle as equator

Method Detail

computeSphere_fast

public static double computeSphere_fast(Point p0,
                                        Point p1,
                                        Point p2,
                                        Point p3,
                                        Point center)

Calculates the radius and center of the sphere touching the four specified points. The radius is returned and if center!=null the coordinates of center are overwritten with the coordinates of the circumsphere. Uses 46 "heavy" operations (multiplication/division).

getCenter
```
public Point getCenter()
```
Get the center

Specified by:

getCenter in interface Shape

getRadius
```
public double getRadius()
```
Get the radius

getRadiusSquared
```
public double getRadiusSquared()
```
Get the squared radius

getSurfaceArea
```
public double getSurfaceArea()
```
Get the surface area

getVolume
```
public double getVolume()
```
Get the volume

Specified by:

getVolume in interface Volume

isInside
```
public boolean isInside(Point p)
```
Returns true if the point is inside this sphere

isInside
```
public boolean isInside(Point p,
                        double eps)
```
Returns true iff the squared distance from the point to the sphere center is less than the squared radius minus eps

isEmpty

public boolean isEmpty(Point[] points,
                       double eps)

isEmpty
```
public boolean isEmpty(java.util.List<Vertex> points,
                       double eps)
```
returns TRUE if the interior of the sphere (for a given eps reduction of the radius) is empty

contains

public void contains(java.util.List<Vertex> points,
                     double eps)

setCenter
```
public void setCenter(Point center)
```

setCenter

public void setCenter(Point p0,
                      Point p1,
                      Point p2,
                      Point p3)

setRadius
```
public void setRadius(double radius)
```

isIntersected
```
public boolean isIntersected(Sphere sphere)
```
Returns true if this sphere is intersected or touched by another sphere.

getIntersection
```
public LineSegment getIntersection(Line line)
```
Gets the secant on the line. TODO: Rename.

intersectionParameters
```
public double[] intersectionParameters(Line line)
```
Returns the two line-parameters that indicate where line intersects this sphere. TODO: Coordinate line-intersection methods (see above).

getIntersections

public Point[] getIntersections(Circle c)

getIntersectionAngle

public java.lang.Double getIntersectionAngle(Circle c,
                                             Point p,
                                             Vector dir)

containsNone
```
public boolean containsNone(java.util.List<Point> points)
```
Returns true if none of the given points is in the sphere.

containsNumber

public int containsNumber(java.util.List<Vertex> points)

Returns number of points inside the sphere

containsNoneButAtMostOne

public boolean containsNoneButAtMostOne(Vertex v,
                                        java.util.List<Vertex> points)

contains
```
public boolean contains(Point p)
```
Returns true if the given point is in the sphere.

powerDistance
```
public double powerDistance(Point p)
```
Gets the squared distance of a point from a sphere surface (negative if the point is inside the sphere).

toString
```
public java.lang.String toString()
```
Return a string representation of this sphere.

Overrides:

toString in class java.lang.Object

toString
```
public java.lang.String toString(int dec)
```
Return a string representation of this sphere with dec decimals precision

toConsole
```
public void toConsole()
```
Writes this sphere to System.out.

toConsole
```
public void toConsole(int dec)
```
Writes this sphere to System.out with dec decimals precision.

overlaps
```
public boolean overlaps(Volume vol)
```
Returns true if the sphere overlaps with vol. TODO: Implement for all volumes.

Specified by:

overlaps in interface Volume

clone
```
public Sphere clone()
```
Returns a deep clone of this sphere.

Specified by:

clone in interface Volume

Overrides:

clone in class java.lang.Object

getMinSphere
```
public static Sphere getMinSphere(Circle c)
```
Get the sphere with the specified circle as equator

getMinSphere

public static Sphere getMinSphere(Point p1,
                                  Point p2)

Get the smallest sphere through two given points.

getMinSphere

public static Sphere getMinSphere(Point p0,
                                  Point p1,
                                  Point p2)

Get the smallest sphere through three points.

getMinSphere

public static Sphere getMinSphere(Point p0,
                                  Point p1,
                                  Point p2,
                                  Point p3)

Constructs the sphere through four points. An error is thrown if the points are coplanar.

getMinSphere
```
public static Sphere getMinSphere(PointList points)
```
Gets the smallest sphere containing a set of points. Uses a randomized, O(n) expected time algorithm.

getIntersection

public static Circle getIntersection(Sphere s1,
                                     Sphere s2)

getIntersections

public static Point[] getIntersections(Sphere s1,
                                       Sphere s2,
                                       Sphere s3)

Find the two, one or zero points that is at the intersection of the three sphere shells. If the three spheres intersect in more than two points or one sphere contains another, the result of this method not specified.

unionVolume_Grid
```
public static double unionVolume_Grid(java.util.Collection<Sphere> spheres)
```
Estimate the volume of the union of a set of spheres. A grid is placed around the spheres and the volume of the cells are used to compute an upper and a lower bound. The average value of the upper and lower bound is used. Typically the result is accurate to 1/100 (not to 1/1000) and takes around 150ms to compute.

generateRandomPointsOnSphere

public PointList generateRandomPointsOnSphere(int n)

TODO: Comment, move up and test

generatePointsOnSphere

public PointList generatePointsOnSphere(int n)

TODO: Comment, move up and test

Class Sphere

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

center

radius

Constructor Detail

Sphere

Sphere

Sphere

Sphere

Sphere

Sphere

Sphere

Method Detail

computeSphere_fast

getCenter

getRadius

getRadiusSquared

getSurfaceArea

getVolume

isInside

isInside

isEmpty

isEmpty

contains

setCenter

setCenter

setRadius

isIntersected

getIntersection

intersectionParameters

getIntersections

getIntersectionAngle

containsNone

containsNumber

containsNoneButAtMostOne

contains

powerDistance

toString

toString

toConsole

toConsole

overlaps

clone

getMinSphere

getMinSphere

getMinSphere

getMinSphere

getMinSphere

getIntersection

getIntersections

unionVolume_Grid

generateRandomPointsOnSphere

generatePointsOnSphere