org.apache.commons.math3.geometry.euclidean.twod
Class Line

java.lang.Object
  org.apache.commons.math3.geometry.euclidean.twod.Line

All Implemented Interfaces:

Embedding<Euclidean2D,Euclidean1D>, Hyperplane<Euclidean2D>

public class Line
extends Object
implements Hyperplane<Euclidean2D>, Embedding<Euclidean2D,Euclidean1D>

This class represents an oriented line in the 2D plane.

An oriented line can be defined either by prolongating a line segment between two points past these points, or by one point and an angular direction (in trigonometric orientation).

Since it is oriented the two half planes at its two sides are unambiguously identified as a left half plane and a right half plane. This can be used to identify the interior and the exterior in a simple way by local properties only when part of a line is used to define part of a polygon boundary.

A line can also be used to completely define a reference frame in the plane. It is sufficient to select one specific point in the line (the orthogonal projection of the original reference frame on the line) and to use the unit vector in the line direction and the orthogonal vector oriented from left half plane to right half plane. We define two coordinates by the process, the abscissa along the line, and the offset across the line. All points of the plane are uniquely identified by these two coordinates. The line is the set of points at zero offset, the left half plane is the set of points with negative offsets and the right half plane is the set of points with positive offsets.

Since:

3.0

Version:

$Id: Line.java 7721 2013-02-14 14:07:13Z CardosoP $

Constructor Summary

Line(Line line)
Copy constructor.

Line(Vector2D p, double angle)
Build a line from a point and an angle.

Line(Vector2D p1, Vector2D p2)
Build a line from two points.

Method Summary

boolean	contains(Vector2D p) Check if the line contains a point.
Line	copySelf() Copy the instance.
double	distance(Vector2D p) Compute the distance between the instance and a point.
double	getAngle() Get the angle of the line.
double	getOffset(Line line) Get the offset (oriented distance) of a parallel line.
double	getOffset(Vector<Euclidean2D> point) Get the offset (oriented distance) of a point.
double	getOriginOffset() Get the offset of the origin.
Vector2D	getPointAt(Vector1D abscissa, double offset) Get one point from the plane.
Line	getReverse() Get the reverse of the instance.
static Transform<Euclidean2D,Euclidean1D>	getTransform(AffineTransform transform) Get a Transform embedding an affine transform.
Vector2D	intersection(Line other) Get the intersection point of the instance and another line.
boolean	isParallelTo(Line line) Check the instance is parallel to another line.
void	reset(Vector2D p, double alpha) Reset the instance as if built from a line and an angle.
void	reset(Vector2D p1, Vector2D p2) Reset the instance as if built from two points.
void	revertSelf() Revert the instance.
boolean	sameOrientationAs(Hyperplane<Euclidean2D> other) Check if the instance has the same orientation as another hyperplane.
void	setAngle(double angle) Set the angle of the line.
void	setOriginOffset(double offset) Set the offset of the origin.
Vector2D	toSpace(Vector<Euclidean1D> point) Transform a sub-space point into a space point.
Vector1D	toSubSpace(Vector<Euclidean2D> point) Transform a space point into a sub-space point.
void	translateToPoint(Vector2D p) Translate the line to force it passing by a point.
SubLine	wholeHyperplane() Build a sub-hyperplane covering the whole hyperplane.
PolygonsSet	wholeSpace() Build a region covering the whole space.

Methods inherited from class java.lang.Object

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

Constructor Detail

Line

public Line(Vector2D p1,
            Vector2D p2)

Build a line from two points.

The line is oriented from p1 to p2

Parameters:

p1 - first point

p2 - second point

Line

public Line(Vector2D p,
            double angle)

Build a line from a point and an angle.

Parameters:

p - point belonging to the line

angle - angle of the line with respect to abscissa axis

Line

public Line(Line line)

Copy constructor.

The created instance is completely independent from the original instance, it is a deep copy.

Parameters:

line - line to copy

Method Detail

copySelf

public Line copySelf()

Copy the instance.

The instance created is completely independant of the original one. A deep copy is used, none of the underlying objects are shared (except for immutable objects).

Specified by:

copySelf in interface Hyperplane<Euclidean2D>

Returns:

a new hyperplane, copy of the instance

reset

public void reset(Vector2D p1,
                  Vector2D p2)

Reset the instance as if built from two points.

The line is oriented from p1 to p2

Parameters:

p1 - first point

p2 - second point

reset

public void reset(Vector2D p,
                  double alpha)

Reset the instance as if built from a line and an angle.

Parameters:

p - point belonging to the line

alpha - angle of the line with respect to abscissa axis

revertSelf

public void revertSelf()

Revert the instance.

getReverse

public Line getReverse()

Get the reverse of the instance.

Get a line with reversed orientation with respect to the instance. A new object is built, the instance is untouched.

Returns:

a new line, with orientation opposite to the instance orientation

toSubSpace

public Vector1D toSubSpace(Vector<Euclidean2D> point)

Transform a space point into a sub-space point.

Specified by:

toSubSpace in interface Embedding<Euclidean2D,Euclidean1D>

Parameters:

point - n-dimension point of the space

Returns:

(n-1)-dimension point of the sub-space corresponding to the specified space point

See Also:

Embedding.toSpace(org.apache.commons.math3.geometry.Vector)

toSpace

public Vector2D toSpace(Vector<Euclidean1D> point)

Transform a sub-space point into a space point.

Specified by:

toSpace in interface Embedding<Euclidean2D,Euclidean1D>

Parameters:

point - (n-1)-dimension point of the sub-space

Returns:

n-dimension point of the space corresponding to the specified sub-space point

See Also:

Embedding.toSubSpace(org.apache.commons.math3.geometry.Vector)

intersection

public Vector2D intersection(Line other)

Get the intersection point of the instance and another line.

Parameters:

other - other line

Returns:

intersection point of the instance and the other line or null if there are no intersection points

wholeHyperplane

public SubLine wholeHyperplane()

Build a sub-hyperplane covering the whole hyperplane.

Specified by:

wholeHyperplane in interface Hyperplane<Euclidean2D>

Returns:

a sub-hyperplane covering the whole hyperplane

wholeSpace

public PolygonsSet wholeSpace()

Build a region covering the whole space.

Specified by:

wholeSpace in interface Hyperplane<Euclidean2D>

Returns:

a region containing the instance (really a PolygonsSet instance)

getOffset

public double getOffset(Line line)

Get the offset (oriented distance) of a parallel line.

This method should be called only for parallel lines otherwise the result is not meaningful.

The offset is 0 if both lines are the same, it is positive if the line is on the right side of the instance and negative if it is on the left side, according to its natural orientation.

Parameters:

line - line to check

Returns:

offset of the line

getOffset

public double getOffset(Vector<Euclidean2D> point)

Get the offset (oriented distance) of a point.

The offset is 0 if the point is on the underlying hyperplane, it is positive if the point is on one particular side of the hyperplane, and it is negative if the point is on the other side, according to the hyperplane natural orientation.

Specified by:

getOffset in interface Hyperplane<Euclidean2D>

Parameters:

point - point to check

Returns:

offset of the point

sameOrientationAs

public boolean sameOrientationAs(Hyperplane<Euclidean2D> other)

Check if the instance has the same orientation as another hyperplane.

This method is expected to be called on parallel hyperplanes. The method should not re-check for parallelism, only for orientation, typically by testing something like the sign of the dot-products of normals.

Specified by:

sameOrientationAs in interface Hyperplane<Euclidean2D>

Parameters:

other - other hyperplane to check against the instance

Returns:

true if the instance and the other hyperplane have the same orientation

getPointAt

public Vector2D getPointAt(Vector1D abscissa,
                           double offset)

Get one point from the plane.

Parameters:

abscissa - desired abscissa for the point

offset - desired offset for the point

Returns:

one point in the plane, with given abscissa and offset relative to the line

contains

public boolean contains(Vector2D p)

Check if the line contains a point.

Parameters:

p - point to check

Returns:

true if p belongs to the line

distance

public double distance(Vector2D p)

Compute the distance between the instance and a point.

This is a shortcut for invoking FastMath.abs(getOffset(p)), and provides consistency with what is in the org.apache.commons.math3.geometry.euclidean.threed.Line class.

Parameters:

p - to check

Returns:

distance between the instance and the point

Since:

3.1

isParallelTo

public boolean isParallelTo(Line line)

Check the instance is parallel to another line.

Parameters:

line - other line to check

Returns:

true if the instance is parallel to the other line (they can have either the same or opposite orientations)

translateToPoint

public void translateToPoint(Vector2D p)

Translate the line to force it passing by a point.

Parameters:

p - point by which the line should pass

getAngle

public double getAngle()

Get the angle of the line.

Returns:

the angle of the line with respect to the abscissa axis

setAngle

public void setAngle(double angle)

Set the angle of the line.

Parameters:

angle - new angle of the line with respect to the abscissa axis

getOriginOffset

public double getOriginOffset()

Get the offset of the origin.

Returns:

the offset of the origin

setOriginOffset

public void setOriginOffset(double offset)

Set the offset of the origin.

Parameters:

offset - offset of the origin

getTransform

public static Transform<Euclidean2D,Euclidean1D> getTransform(AffineTransform transform)
                                                       throws MathIllegalArgumentException

Get a Transform embedding an affine transform.

Parameters:

transform - affine transform to embed (must be inversible otherwise the apply(Hyperplane) method would work only for some lines, and fail for other ones)

Returns:

a new transform that can be applied to either Vector2D, Line or SubHyperplane instances

Throws:

MathIllegalArgumentException - if the transform is non invertible