Class Vector3D

java.lang.Object

org.jlab.geom.prim.Vector3D

All Implemented Interfaces:

Transformable, Showable

public final class Vector3D
extends Object
implements Transformable, Showable

A 3D vector represented by three Cartesian coordinates (x, y, z).

Though internally represented in Cartesian coordinates, the position of a point can be set using spherical coordinates via setMagThetaPhi(double, double, double), and the spherical coordinates of any vector can be obtained via mag(), theta(), and phi().

In addition to containing functions for performing normal mathematical procedures involving vectors such as negate/inverse, addition, subtraction, scalar products, dot products, cross products, and normalization, Vector3D can be used to rotate a point or vector around an arbitrary axes that passes through the origin via rotate(Point3D, doubele) and rotate(Vector3D, double). The inverse of the rotation functions is provided via angle(Vector3D, Vector3D).

Author:

gavalian

Constructor Summary

Constructors

Constructor	Description
Vector3D()	Constructs a new empty Vector3D that is a null vector, ie (0,0,0).
Vector3D(double[] xyz)	Constructs a new Vector3D with the given xyz[0], xyz[1], xyz[2] components
Vector3D(double x, double y, double z)	Constructs a new Vector3D with the given x, y, and z components.
Vector3D(Vector3D vector)	Constructs a new Vector3D identical to the given vector.

Method Summary

Modifier and Type	Method	Description
Vector3D	add(double a)
Vector3D	add(Vector3D vector)	Adds the given vector to this vector.
double	angle(Vector3D v)	Angle between this and another vector
double	angle(Vector3D vector0, Vector3D vector1)	Calculates the clockwise angle of rotation from the image of the first given vector to the image of the second given vector projected onto a plane who's normal is this vector and using this vector as an axis.
Vector3D	asUnit()	Create unit vector from this
Vector3D	clone()	Returns a new instance of this vector.
double	compare(Vector3D vector)	Returns a value greater than or equal to zero proportional to the amount that the two vectors differ.
void	copy(Vector3D vector)	Sets the components of this vector to be equal the components of the given vector.
double	costheta()
Vector3D	cross(Vector3D vector)	Constructs a new Vector3D containing the cross product of this vector and the given vector.
Vector3D	divide(double a)
double	dot(Vector3D vector)	Returns the dot product of this vector and the given vector.
static Vector3D	fromSpherical(double r, double phi, double theta)	Creates a new Vector3D instance from spherical coordinates
boolean	isNull()	Returns true if this vector is a null vector.
double	mag()	Returns the magnitude of this vector.
double	mag2()	Returns the square of the magnitude of this vector.
static void	main(String[] args)
Vector3D	multiply(double a)
void	negative()	Negates this vector's components.
double	phi()	Returns the angle between the x axis and the orthogonal projection of this vector onto the x-y plane.
Vector3D	projection(Vector3D v)	Projection of this vector onto another vector
double	r()
double	r2()
double	rho()	Returns the length of the orthogonal projection of this vector onto the x-y plane.
double	rho2()
void	rotate(Point3D point, double angle)	Rotates the given point clockwise around the axis produced by this vector by the given angle
void	rotate(Vector3D vector, double angle)	Rotates the given vector clockwise around the axis produced by this vector by the given angle.
void	rotateX(double angle)	Rotates this object clockwise around the x axis.
void	rotateY(double angle)	Rotates this object clockwise around the y axis.
void	rotateZ(double angle)	Rotates this object clockwise around the z axis.
void	scale(double factor)	Scales each of this vectors components by the given scale factor.
boolean	setMag(double mag)	Sets the magnitude of this vector to equal the given magnitude unless vector is a null vector.
void	setMagThetaPhi(double mag, double theta, double phi)	Sets this vector based on the given spherical coordinates.
void	setX(double x)	Sets the x component.
void	setXYZ(double x, double y, double z)	Sets the x, y and z components of this vector.
void	setY(double y)	Sets the y component.
void	setZ(double z)	Sets the z component.
void	show()	Invokes System.out.println(this).
Vector3D	sub(Vector3D vector)	Subtracts the given vector from this vector
Vector3D	subtract(double a)
double	theta()	Returns the angle between this vector and the z axis.
Point3D	toPoint3D()	Constructs a new Point3D using this vector's x, y, and z components.
String	toString()
String	toStringBrief()
String	toStringBrief(int ndigits)
void	translateXYZ(double x, double y, double z)	Does nothing; vectors cannot be translated.
boolean	unit()	Sets the magnitude of this vector to equal one unless this vector is a null vector.
double	x()	Returns the x component.
double	y()	Returns the y component.
double	z()	Returns the z component.

Methods inherited from class java.lang.Object

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

Constructor Details

Vector3D

public Vector3D()

Constructs a new empty Vector3D that is a null vector, ie (0,0,0).

Vector3D

public Vector3D(double x,
 double y,
 double z)

Constructs a new Vector3D with the given x, y, and z components.

Parameters:

x - the x component

y - the y component

z - the z component

Vector3D

public Vector3D(double[] xyz)

Constructs a new Vector3D with the given xyz[0], xyz[1], xyz[2] components

Parameters:

xyz - where x/y/z-components are xyz[0]/[1]/[2]

Vector3D

public Vector3D(Vector3D vector)

Constructs a new Vector3D identical to the given vector.

Parameters:

vector - the vector to copy

Method Details

copy

public void copy(Vector3D vector)

Sets the components of this vector to be equal the components of the given vector.

Parameters:

vector - the vector to copy

clone

public Vector3D clone()

Returns a new instance of this vector.

Overrides:

clone in class Object

fromSpherical

public static Vector3D fromSpherical(double r,
 double phi,
 double theta)

Creates a new Vector3D instance from spherical coordinates

Parameters:

r - radial distance from the origin

phi - azimuthal angle from the positive x-axis (right-handed)

theta - polar angle from the positive z-axis

setXYZ

public void setXYZ(double x,
 double y,
 double z)

Sets the x, y and z components of this vector.

Parameters:

x - the x component

y - the y component

z - the z component

setX

public void setX(double x)

Sets the x component.

Parameters:

x - the x component

setY

public void setY(double y)

Sets the y component.

Parameters:

y - the y component

setZ

public void setZ(double z)

Sets the z component.

Parameters:

z - the z component

x

public double x()

Returns the x component.

Returns:

the x component

y

public double y()

Returns the y component.

Returns:

the y component

z

public double z()

Returns the z component.

Returns:

the z component

r2

public double r2()

r

public double r()

phi

public double phi()

Returns the angle between the x axis and the orthogonal projection of this vector onto the x-y plane.

Returns:

the phi component of this vector's spherical coordinates

costheta

public double costheta()

theta

public double theta()

Returns the angle between this vector and the z axis.

Returns:

the theta component of this vector's spherical coordinates

rho2

public double rho2()

rho

public double rho()

Returns the length of the orthogonal projection of this vector onto the x-y plane.

Returns:

sqrt(x*x + y*y)

isNull

public boolean isNull()

Returns true if this vector is a null vector.

Returns:

true if this vector is a null vector

mag2

public double mag2()

Returns the square of the magnitude of this vector.

Returns:

the square of the magnitude of this vector

mag

public double mag()

Returns the magnitude of this vector.

Returns:

the magnitude of this vector

setMagThetaPhi

public void setMagThetaPhi(double mag,
 double theta,
 double phi)

Sets this vector based on the given spherical coordinates.

Parameters:

mag - the magnitude

theta - the angle between the vector and the z axis

phi - the angle between the x axis and the orthogonal projection of the vector onto the x-y plane

negative

public void negative()

Negates this vector's components.

add

public Vector3D add(Vector3D vector)

Adds the given vector to this vector.

Parameters:

vector - the vector to add to this vector

sub

public Vector3D sub(Vector3D vector)

Subtracts the given vector from this vector

Parameters:

vector - the vector to subtract from this vector

scale

public void scale(double factor)

Scales each of this vectors components by the given scale factor.

Parameters:

factor - the amount to scale the components of this vector

unit

public boolean unit()

Sets the magnitude of this vector to equal one unless this vector is a null vector.

Returns:

returns false if this vector is a null vector

asUnit

public Vector3D asUnit()

Create unit vector from this

Returns:

unit vector

setMag

public boolean setMag(double mag)

Sets the magnitude of this vector to equal the given magnitude unless vector is a null vector.

Parameters:

mag - the desired magnitude

Returns:

returns false if this vector is a null vector

add

public Vector3D add(double a)

subtract

public Vector3D subtract(double a)

multiply

public Vector3D multiply(double a)

divide

public Vector3D divide(double a)

dot

public double dot(Vector3D vector)

Returns the dot product of this vector and the given vector.

Parameters:

vector - the vector to dot product with this vector

Returns:

the dot product

cross

public Vector3D cross(Vector3D vector)

Constructs a new Vector3D containing the cross product of this vector and the given vector.

Parameters:

vector - the vector to cross product with this vector

Returns:

the cross product

toPoint3D

public Point3D toPoint3D()

Constructs a new Point3D using this vector's x, y, and z components.

Returns:

a point representation of this vector

compare

public double compare(Vector3D vector)

Returns a value greater than or equal to zero proportional to the amount that the two vectors differ. If the two vectors are equal then the returned value is 0.

Parameters:

vector - the vector to compare to

Returns:

the comparison result

rotate

public void rotate(Point3D point,
 double angle)

Rotates the given point clockwise around the axis produced by this vector by the given angle

Parameters:

point - the point to rotate

angle - the angle of rotation

rotate

public void rotate(Vector3D vector,
 double angle)

Rotates the given vector clockwise around the axis produced by this vector by the given angle.

Parameters:

vector - the vector to rotate

angle - the angle of rotation

angle

public double angle(Vector3D vector0,
 Vector3D vector1)

Calculates the clockwise angle of rotation from the image of the first given vector to the image of the second given vector projected onto a plane who's normal is this vector and using this vector as an axis.

Parameters:

vector0 - the first vector

vector1 - the second vector

Returns:

the angle between the two vectors

projection

public Vector3D projection(Vector3D v)

Projection of this vector onto another vector

Parameters:

v - another vector

Returns:

projection of this vector onto v

angle

public double angle(Vector3D v)

Angle between this and another vector

Parameters:

v - another vector

Returns:

the angle between the two vectors

translateXYZ

public void translateXYZ(double x,
 double y,
 double z)

Does nothing; vectors cannot be translated.

Specified by:

translateXYZ in interface Transformable

Parameters:

x - ignored

y - ignored

z - ignored

rotateX

public void rotateX(double angle)

Description copied from interface: Transformable

Rotates this object clockwise around the x axis.

Specified by:

rotateX in interface Transformable

Parameters:

angle - rotation angle in radians

rotateY

public void rotateY(double angle)

Description copied from interface: Transformable

Rotates this object clockwise around the y axis.

Specified by:

rotateY in interface Transformable

Parameters:

angle - rotation angle in radians

rotateZ

public void rotateZ(double angle)

Description copied from interface: Transformable

Rotates this object clockwise around the z axis.

Specified by:

rotateZ in interface Transformable

Parameters:

angle - rotation angle in radians

show

public void show()

Invokes System.out.println(this).

Specified by:

show in interface Showable

toString

public String toString()

Overrides:

toString in class Object

toStringBrief

public String toStringBrief(int ndigits)

toStringBrief

public String toStringBrief()

main

public static void main(String[] args)