ome.util.math.geom2D

Class PlanePoint

java.lang.Object

ome.util.math.geom2D.PlanePoint

public class PlanePoint
extends java.lang.Object

Represents a point in the Euclidean space R².

Because this space is built on the vector space R², any instance of this class also represents a vector in R². Moreover, unless otherwise stated, we assume the orthonormal frame {O, e₁, e₂} where O=(0,0), e₁=(1, 0), e₂=(0, 1).

Since:

OME2.2

Field Summary

Fields

Modifier and Type	Field and Description
double	x1 The first element.
double	x2 The second element.

Constructor Summary

Constructors

Constructor and Description
PlanePoint(double x1, double x2) Creates a new instance.

Method Summary

Modifier and Type	Method and Description
double	angle(PlanePoint vec) Calculates the angle between this vector and the specified argument, provided none of these vectors is the null vector.
PlanePoint	diff(PlanePoint vec) Calculates the sum of this vector with the reciprocal of the specified argument.
double	distance(PlanePoint p) Calculates the distance between this point and the specified argument.
double	dot(PlanePoint vec) Calulates the dot product of this vector by the specified argument.
boolean	equals(double x1, double x2) Check to see if the point values are equal.
boolean	equals(java.lang.Object o) Overridden to reflect equality of abstract values (data object) as opposite to object identity.
int	hashCode() Overridden to reflect equality of abstract values (data object) as opposite to object identity.
double	norm() Calculates the Euclidian norm of this vector.
PlanePoint	normalize() Calculates the unit vector of this vector, provided this is not the null vector.
PlanePoint	scalar(double k) Multiplies this vector by the specified scalar.
PlanePoint	sum(PlanePoint vec) Calculates the sum of this vector with the specified argument.
PlanePoint	vec(double x1, double x2) Calculates the vector associated to this point and the specified argument.
PlanePoint	vec(PlanePoint p) Calculates the vector associated to this point and the specified argument.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

Field Detail

x1

public final double x1

The first element.

x2

public final double x2

The second element.

Constructor Detail

PlanePoint

public PlanePoint(double x1,
                  double x2)

Creates a new instance.

Parameters:

x1 - The first element of the point

x2 - The second element of the point

Method Detail

distance

public double distance(PlanePoint p)

Calculates the distance between this point and the specified argument. We use the standard distance of two points in the Euclidean space R². That is, if A=(a₁, b₁) and B=(a₂, b₂) are two points of R², then the distance is defined by the square root of (a₁ - a₂)² + (b₁ - b₂)² .

Parameters:

p - The other point. Mustn't be null.

Returns:

The distance between this point and p.

sum

public PlanePoint sum(PlanePoint vec)

Calculates the sum of this vector with the specified argument. This is the standard sum of two vectors in the R² group and is given by the sum of their components.

Parameters:

vec - The other vector. Mustn't be a null reference.

Returns:

The sum of this vector with vec.

diff

public PlanePoint diff(PlanePoint vec)

Calculates the sum of this vector with the reciprocal of the specified argument. The sum is the standard sum of two vectors in the R² group — the sum of their components. Under this sum, the reciprocal of an element v=(x₁, x₂) of R² is given by -v=(-x₁, -x₂).

Parameters:

vec - The other vector. Mustn't be a null reference.

Returns:

The sum of this vector with -vec.

scalar

public PlanePoint scalar(double k)

Multiplies this vector by the specified scalar. This is the standard scalar multiplication in the vector space R², which is done by multiplying each component by the specified scalar.

Parameters:

k - The scalar.

Returns:

The vector obtained by multiplying this vector by k.

vec

public PlanePoint vec(PlanePoint p)

Calculates the vector associated to this point and the specified argument. This is the map that makes the set A = R² an affine space over the vector space V = R² and is defined by:

f: AxA ---> V
f(a, b) = b - a = (b₁ - a₁, b₂ - a₂)

This method returns f(t, p), where t is this point and p is the specified argument.

Parameters:

p - The other point. Mustn't be a null reference.

Returns:

The vector associated to this point and p.

vec

public PlanePoint vec(double x1,
                      double x2)

Calculates the vector associated to this point and the specified argument. This is the map that makes the set A = R² an affine space over the vector space V = R² and is defined by:

f: AxA ---> V
f(a, b) = b - a = (b₁ - a₁, b₂ - a₂)

This method returns f(t, p), where t is this point and p is the specified argument.

Parameters:

x1 - The first element of the point

x2 - The second element of the point

Returns:

The vector associated to this point and p.

dot

public double dot(PlanePoint vec)

Calulates the dot product of this vector by the specified argument. We use the standard dot product of two vectors in R². That is, if v=(v₁, v₂) and w=(w₁, w₂) are two vectors of R², then the dot product is defined by v₁*w₁ + v₂*w₂.

Parameters:

vec - The other vector in the product. Mustn't be a null reference.

Returns:

The dot product.

norm

public double norm()

Calculates the Euclidian norm of this vector. That is, the square root of the dot product of this vector by itself.

Returns:

The norm of this vector.

normalize

public PlanePoint normalize()

Calculates the unit vector of this vector, provided this is not the null vector. If this is not the null vector, then the returned vector is given by t / ||t||, where t is this vector and ||t|| is its norm. Otherwise we return the null vector.

Returns:

A unit vector if this is not the null vector, the null vector otherwise.

angle

public double angle(PlanePoint vec)

Calculates the angle between this vector and the specified argument, provided none of these vectors is the null vector. We use the standard definition of an angle between two non-null vectors. This is given by the arc cosine of the dot product of the two vectors divided by the product of their norms: acos(v.w / ||v||*||w||). If any of the two vectors is the null vector we throw an exception.

Parameters:

vec - The other vector. Mustn't be a null reference and mustn't be the null vector.

Returns:

The angle between this vector and vec, in the range of 0 through pi.

Throws:

java.lang.IllegalArgumentException - If this vector or vec or both are the null vector.

equals

public boolean equals(java.lang.Object o)

Overridden to reflect equality of abstract values (data object) as opposite to object identity.

Overrides:

equals in class java.lang.Object

See Also:

Object.equals(Object)

equals

public boolean equals(double x1,
                      double x2)

Check to see if the point values are equal.

Parameters:

x1 - The comparison point's first element.

x2 - The comparison point's second element.

Returns:

true if the points are equal, false otherwise.

hashCode

public int hashCode()

Overridden to reflect equality of abstract values (data object) as opposite to object identity.

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()