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

## Class 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:
$Id: Line.java 1560115 2014-01-21 17:49:13Z luc$
• ### Constructor Summary

Constructors
Constructor and Description
Line(Line line)
Copy constructor.
Line(Vector2D p, double angle)
Deprecated.
Line(Vector2D p, double angle, double tolerance)
Build a line from a point and an angle.
Line(Vector2D p1, Vector2D p2)
Deprecated.
Line(Vector2D p1, Vector2D p2, double tolerance)
Build a line from two points.
• ### Method Summary

Methods
Modifier and Type Method and Description
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(Point<Euclidean2D> point)
Get the offset (oriented distance) of a point.
double getOffset(Vector<Euclidean2D> vector)
Get the offset (oriented distance) of a vector.
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.
double getTolerance()
Get the tolerance below which points are considered to belong to the hyperplane.
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.
Point<Euclidean2D> project(Point<Euclidean2D> point)
Project a point to the hyperplane.
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(Point<Euclidean1D> point)
Transform a sub-space point into a space point.
Vector2D toSpace(Vector<Euclidean1D> vector)
Transform a sub-space point into a space point.
Vector1D toSubSpace(Point<Euclidean2D> point)
Transform a space point into a sub-space point.
Vector1D toSubSpace(Vector<Euclidean2D> vector)
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,
double tolerance)
Build a line from two points.

The line is oriented from p1 to p2

Parameters:
p1 - first point
p2 - second point
tolerance - tolerance below which points are considered identical
Since:
3.3
• #### Line

public Line(Vector2D p,
double angle,
double tolerance)
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
tolerance - tolerance below which points are considered identical
Since:
3.3
• #### Line

@Deprecated
public Line(Vector2D p1,
Vector2D p2)
Deprecated. as of 3.3, replaced with Line(Vector2D, Vector2D, double)
Build a line from two points.

The line is oriented from p1 to p2

Parameters:
p1 - first point
p2 - second point
• #### Line

@Deprecated
public Line(Vector2D p,
double angle)
Deprecated. as of 3.3, replaced with Line(Vector2D, double, double)
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> vector)
Transform a space point into a sub-space point.
Parameters:
vector - n-dimension point of the space
Returns:
(n-1)-dimension point of the sub-space corresponding to the specified space point
• #### toSpace

public Vector2D toSpace(Vector<Euclidean1D> vector)
Transform a sub-space point into a space point.
Parameters:
vector - (n-1)-dimension point of the sub-space
Returns:
n-dimension point of the space corresponding to the specified sub-space point
• #### toSubSpace

public Vector1D toSubSpace(Point<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
Embedding.toSpace(org.apache.commons.math3.geometry.Point<T>)
• #### toSpace

public Vector2D toSpace(Point<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
Embedding.toSubSpace(org.apache.commons.math3.geometry.Point<S>)
• #### 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
• #### project

public Point<Euclidean2D> project(Point<Euclidean2D> point)
Project a point to the hyperplane.
Specified by:
project in interface Hyperplane<Euclidean2D>
Parameters:
point - point to project
Returns:
projected point
Since:
3.3
• #### getTolerance

public double getTolerance()
Get the tolerance below which points are considered to belong to the hyperplane.
Specified by:
getTolerance in interface Hyperplane<Euclidean2D>
Returns:
tolerance below which points are considered to belong to the hyperplane
Since:
3.3
• #### 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> vector)
Get the offset (oriented distance) of a vector.
Parameters:
vector - vector to check
Returns:
offset of the vector
• #### getOffset

public double getOffset(Point<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