math.geom2d
Class Point2D

java.lang.Object
  math.geom2d.Point2D

All Implemented Interfaces:

java.lang.Cloneable, java.lang.Iterable<Point2D>, CirculinearShape2D, GeometricObject2D, PointShape2D, Shape2D

public class Point2D
extends java.lang.Object
implements GeometricObject2D, PointShape2D, java.lang.Cloneable, CirculinearShape2D

A point in the plane defined by its 2 Cartesian coordinates x and y. The class provides static methods to compute distance between two points.

Field Summary

Fields inherited from interface math.geom2d.Shape2D

ACCURACY

Constructor Summary

Point2D()
Constructs a new Point2D at position (0,0).

Point2D(double x, double y)
Constructs a new Point2D at the given given position.

Point2D(java.awt.geom.Point2D point)
Constructs a new Point2D by copying coordinates of given java point.

Point2D(Point2D point)
Constructs a new Point2D by copying coordinates of given point.

Method Summary

boolean	almostEquals(GeometricObject2D obj, double eps) Test whether this object is the same as another point, with respect to a given threshold along each coordinate.
Box2D	boundingBox() Returns a bounding box with zero width and zero height, whose coordinates limits are point coordinates.
CirculinearDomain2D	buffer(double dist) Computes the buffer of the shape, formed by the set of points located at a distance from the shape that is lower or equal to d.
static int	ccw(Point2D p0, Point2D p1, Point2D p2) Computes the orientation of the 3 points: returns +1 is the path P0->P1->P2 turns Counter-Clockwise, -1 if the path turns Clockwise, and 0 if the point P2 is located on the line segment [P0 P1].
static Point2D	centroid(java.util.Collection<? extends Point2D> points) Computes the centroid, or center of mass, of a collection of points.
static Point2D	centroid(Point2D[] points) Computes the centroid, or center of mass, of an array of points.
static Point2D	centroid(Point2D[] points, double[] weights) Computes the weighted centroid, or center of mass, of an array of points.
static Point2D	centroid(Point2D pt1, Point2D pt2, Point2D pt3) Computes the centroid of three points.
PointSet2D	clip(Box2D box) Returns a PointSet2D, containing 0 or 1 point, depending on whether the point lies inside the specified box.
Point2D	clone() Creates a new Point2D object with same coordinates.
boolean	contains(double x, double y) Returns true if the two points are equal.
boolean	contains(Point2D p) Returns true if the two points are equal.
static Point2D	create(double x, double y) Deprecated. since 0.11.1
static Point2D	create(java.awt.geom.Point2D point) Deprecated. since 0.11.1
static Point2D	create(Point2D point) Static factory for creating a new point from an existing instance of javageom point.
static Point2D	createPolar(double rho, double theta) Creates a new point from polar coordinates rho and theta.
static Point2D	createPolar(double x0, double y0, double rho, double theta) Creates a new point from polar coordinates rho and theta, from the position (x0,y0).
static Point2D	createPolar(Point2D point, double rho, double theta) Creates a new point from polar coordinates rho and theta, from the given point.
double	distance(double x, double y) Computes the distance between current point and point with coordinate (x,y).
static double	distance(double x1, double y1, double x2, double y2) Computes the Euclidean distance between two points, given by their coordinates.
double	distance(Point2D point) Computes the distance between this and the point point.
static double	distance(Point2D p1, Point2D p2) Computes the Euclidean distance between two points.
void	draw(java.awt.Graphics2D g2) Draws the point on the specified Graphics2D, using default radius equal to 1.
void	draw(java.awt.Graphics2D g2, double r) Draws the point on the specified Graphics2D, by filling a disc with a given radius.
boolean	equals(java.lang.Object obj) Two points are considered equal if their Euclidean distance is less than Shape2D.ACCURACY.
java.awt.geom.Point2D.Double	getAsDouble() Converts point to a double version.
java.awt.geom.Point2D.Float	getAsFloat() Converts point to a float version.
java.awt.Point	getAsInt() Converts point to an integer version.
double	getX() Deprecated. replaces by x() (since 0.11.1)
double	getY() Deprecated. replaces by y() (since 0.11.1)
boolean	isBounded() Returns true if the point is bounded.
static boolean	isColinear(Point2D p1, Point2D p2, Point2D p3) Tests if the three points are colinear.
boolean	isEmpty() Returns false, as a point can not be empty.
java.util.Iterator<Point2D>	iterator()
static Point2D	midPoint(Point2D p1, Point2D p2)
Point2D	minus(Point2D p) Removes the coordinates of the given point from the coordinates of this point.
Point2D	minus(Vector2D v) Removes the coordinates of the given vector from the coordinates of this point.
Point2D	plus(Point2D p) Adds the coordinates of the given point to the coordinates of this point.
Point2D	plus(Vector2D v) Adds the coordinates of the given vector to the coordinates of this point.
java.util.Collection<Point2D>	points() Returns the points in the shape as a collection.
Point2D	rotate(double theta) Rotates the point by a given angle around the origin.
Point2D	rotate(Point2D center, double theta) Rotates the point by a given angle around an arbitrary center.
Point2D	scale(double k) Returns the new point scaled by the same amount in each direction.
Point2D	scale(double kx, double ky) Returns the new point scaled by amount given in each direction.
int	size() Returns the number of points in the set.
java.lang.String	toString()
Point2D	transform(AffineTransform2D trans) Returns the transformed point.
Point2D	transform(CircleInversion2D inv) Transforms the shape by a circle inversion.
Point2D	translate(double tx, double ty) Returns the new point translated by amount given in each direction.
double	x() Returns the x-coordinate of this point.
double	y() Returns the y-coordinate of this point.

Methods inherited from class java.lang.Object

getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

Point2D

public Point2D()

Constructs a new Point2D at position (0,0).

Point2D

public Point2D(double x,
               double y)

Constructs a new Point2D at the given given position. Please consider using the static factory method instead (0.8.1).

Point2D

public Point2D(java.awt.geom.Point2D point)

Constructs a new Point2D by copying coordinates of given java point. Please consider using the static factory method instead (0.8.1)

Point2D

public Point2D(Point2D point)

Constructs a new Point2D by copying coordinates of given point.

Method Detail

create

@Deprecated
public static Point2D create(double x,
                                        double y)

Deprecated. since 0.11.1

Static factory for creating a new point in cartesian coordinates.

create

@Deprecated
public static Point2D create(java.awt.geom.Point2D point)

Deprecated. since 0.11.1

Static factory for creating a new point from an existing instance of java point.

create

public static Point2D create(Point2D point)

Static factory for creating a new point from an existing instance of javageom point.

Since:

0.10.0

createPolar

public static Point2D createPolar(double rho,
                                  double theta)

Creates a new point from polar coordinates rho and theta.

createPolar

public static Point2D createPolar(Point2D point,
                                  double rho,
                                  double theta)

Creates a new point from polar coordinates rho and theta, from the given point.

createPolar

public static Point2D createPolar(double x0,
                                  double y0,
                                  double rho,
                                  double theta)

Creates a new point from polar coordinates rho and theta, from the position (x0,y0).

distance

public static double distance(double x1,
                              double y1,
                              double x2,
                              double y2)

Computes the Euclidean distance between two points, given by their coordinates. Uses robust computation (via Math.hypot() method).

Returns:

the Euclidean distance between p1 and p2.

distance

public static double distance(Point2D p1,
                              Point2D p2)

Computes the Euclidean distance between two points. Uses robust computation (via Math.hypot() method).

Parameters:

p1 - the first point

p2 - the second point

Returns:

the Euclidean distance between p1 and p2.

isColinear

public static boolean isColinear(Point2D p1,
                                 Point2D p2,
                                 Point2D p3)

Tests if the three points are colinear.

Returns:

true if three points lie on the same line.

ccw

public static int ccw(Point2D p0,
                      Point2D p1,
                      Point2D p2)

Computes the orientation of the 3 points: returns +1 is the path P0->P1->P2 turns Counter-Clockwise, -1 if the path turns Clockwise, and 0 if the point P2 is located on the line segment [P0 P1]. Algorithm taken from Sedgewick.

Parameters:

p0 - the initial point

p1 - the middle point

p2 - the last point

Returns:

+1, 0 or -1, depending on the relative position of the points

midPoint

public static Point2D midPoint(Point2D p1,
                               Point2D p2)

centroid

public static Point2D centroid(Point2D[] points)

Computes the centroid, or center of mass, of an array of points.

Parameters:

points - an array of points

Returns:

the centroid of the points

centroid

public static Point2D centroid(Point2D[] points,
                               double[] weights)

Computes the weighted centroid, or center of mass, of an array of points.

Parameters:

points - an array of points

weights - an array of weights the same size as points

Returns:

the centroid of the points

centroid

public static Point2D centroid(java.util.Collection<? extends Point2D> points)

Computes the centroid, or center of mass, of a collection of points.

Parameters:

points - a collection of points

Returns:

the centroid of the points

centroid

public static Point2D centroid(Point2D pt1,
                               Point2D pt2,
                               Point2D pt3)

Computes the centroid of three points.

Parameters:

pt1 - the first point

pt2 - the second point

pt3 - the third point

Returns:

the centroid of the 3 points

plus

public Point2D plus(Point2D p)

Adds the coordinates of the given point to the coordinates of this point.

plus

public Point2D plus(Vector2D v)

Adds the coordinates of the given vector to the coordinates of this point.

minus

public Point2D minus(Point2D p)

Removes the coordinates of the given point from the coordinates of this point.

minus

public Point2D minus(Vector2D v)

Removes the coordinates of the given vector from the coordinates of this point.

translate

public Point2D translate(double tx,
                         double ty)

Returns the new point translated by amount given in each direction.

Parameters:

tx - the translation in x direction

ty - the translation in y direction

Returns:

the translated point

scale

public Point2D scale(double kx,
                     double ky)

Returns the new point scaled by amount given in each direction.

Parameters:

kx - the scale factor in x direction

ky - the scale factor in y direction

Returns:

the scaled point

scale

public Point2D scale(double k)

Returns the new point scaled by the same amount in each direction.

Parameters:

k - the scale factor

Returns:

the scaled point

rotate

public Point2D rotate(double theta)

Rotates the point by a given angle around the origin.

Parameters:

theta - the angle of rotation, in radians

Returns:

the rotated point.

rotate

public Point2D rotate(Point2D center,
                      double theta)

Rotates the point by a given angle around an arbitrary center.

Parameters:

center - the center of the rotation

theta - the angle of rotation, in radians

Returns:

the rotated point.

getAsInt

public java.awt.Point getAsInt()

Converts point to an integer version. Coordinates are rounded to the nearest integer.

Returns:

an instance of java.awt.Point

getAsDouble

public java.awt.geom.Point2D.Double getAsDouble()

Converts point to a double version.

getAsFloat

public java.awt.geom.Point2D.Float getAsFloat()

Converts point to a float version. Coordinates are rounded to the nearest float.

x

public double x()

Returns the x-coordinate of this point.

getX

@Deprecated
public double getX()

Deprecated. replaces by x() (since 0.11.1)

y

public double y()

Returns the y-coordinate of this point.

getY

@Deprecated
public double getY()

Deprecated. replaces by y() (since 0.11.1)

buffer

public CirculinearDomain2D buffer(double dist)

Description copied from interface: CirculinearShape2D

Computes the buffer of the shape, formed by the set of points located at a distance from the shape that is lower or equal to d.

Specified by:

buffer in interface CirculinearShape2D

Parameters:

dist - the maximal distance between a point of the buffer and the shape

Returns:

the buffer of the shape

transform

public Point2D transform(CircleInversion2D inv)

Description copied from interface: CirculinearShape2D

Transforms the shape by a circle inversion. The result is still an instance a CirculinearShape2D.

Specified by:

transform in interface CirculinearShape2D

Parameters:

inv - the circle inversion

Returns:

the transformed shape

size

public int size()

Description copied from interface: PointShape2D

Returns the number of points in the set.

Specified by:

size in interface PointShape2D

Returns:

the number of points

points

public java.util.Collection<Point2D> points()

Description copied from interface: PointShape2D

Returns the points in the shape as a collection.

Specified by:

points in interface PointShape2D

Returns:

the collection of points

distance

public double distance(Point2D point)

Computes the distance between this and the point point.

Specified by:

distance in interface Shape2D

distance

public double distance(double x,
                       double y)

Computes the distance between current point and point with coordinate (x,y). Uses the Math.hypot() function for better robustness than simple square root.

Specified by:

distance in interface Shape2D

isBounded

public boolean isBounded()

Returns true if the point is bounded. A point is unbounded if at least one of its coordinates is infinite or NaN.

Specified by:

isBounded in interface Shape2D

Returns:

true if both coordinates of the point are finite

isEmpty

public boolean isEmpty()

Returns false, as a point can not be empty.

Specified by:

isEmpty in interface Shape2D

Returns:

true if the shape does not contain any point.

contains

public boolean contains(double x,
                        double y)

Returns true if the two points are equal.

Specified by:

contains in interface Shape2D

contains

public boolean contains(Point2D p)

Returns true if the two points are equal.

Specified by:

contains in interface Shape2D

clip

public PointSet2D clip(Box2D box)

Returns a PointSet2D, containing 0 or 1 point, depending on whether the point lies inside the specified box.

Specified by:

clip in interface PointShape2D

Specified by:

clip in interface Shape2D

Parameters:

box - the clipping box

Returns:

the clipped shape

boundingBox

public Box2D boundingBox()

Returns a bounding box with zero width and zero height, whose coordinates limits are point coordinates.

Specified by:

boundingBox in interface Shape2D

Returns:

the bounding box of the shape.

transform

public Point2D transform(AffineTransform2D trans)

Returns the transformed point.

Specified by:

transform in interface PointShape2D

Specified by:

transform in interface Shape2D

Parameters:

trans - an affine transform

Returns:

the transformed shape

draw

public void draw(java.awt.Graphics2D g2)

Draws the point on the specified Graphics2D, using default radius equal to 1.

Specified by:

draw in interface Shape2D

Parameters:

g2 - the graphics to draw the point

draw

public void draw(java.awt.Graphics2D g2,
                 double r)

Draws the point on the specified Graphics2D, by filling a disc with a given radius.

Parameters:

g2 - the graphics to draw the point

almostEquals

public boolean almostEquals(GeometricObject2D obj,
                            double eps)

Test whether this object is the same as another point, with respect to a given threshold along each coordinate.

Specified by:

almostEquals in interface GeometricObject2D

Parameters:

obj - the object to compare

eps - a threshold value, for example the minimal coordinate difference

Returns:

true if both object have the same value up to the threshold

iterator

public java.util.Iterator<Point2D> iterator()

Specified by:

iterator in interface java.lang.Iterable<Point2D>

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

equals

public boolean equals(java.lang.Object obj)

Two points are considered equal if their Euclidean distance is less than Shape2D.ACCURACY.

Overrides:

equals in class java.lang.Object

clone

public Point2D clone()

Creates a new Point2D object with same coordinates.

Overrides:

clone in class java.lang.Object