org.apache.commons.geometry.euclidean.twod

Class Line

java.lang.Object

org.apache.commons.geometry.core.partitioning.AbstractHyperplane<Vector2D>

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

All Implemented Interfaces:

Embedding<Vector2D,Vector1D>, EmbeddingHyperplane<Vector2D,Vector1D>, Hyperplane<Vector2D>

public final class Line
extends AbstractHyperplane<Vector2D>
implements EmbeddingHyperplane<Vector2D,Vector1D>

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

An oriented line can be defined either by extending a line segment between two points past these points, by specifying a point and a direction, or by specifying a point and an angle relative to the x-axis.

Since the line oriented, the two half planes on its sides are unambiguously identified as the left half plane and the right half plane. This can be used to identify the interior and the exterior in a simple way when a line is used to define a portion 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 (see getDirection() and the orthogonal vector oriented from the left half plane to the right half plane (see getOffsetDirection(). 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.

See Also:

Lines

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	Line.SubspaceTransform Class containing a transformed line instance along with a subspace (1D) transform.

Method Summary

Modifier and Type	Method and Description
double	abscissa(Vector2D point) Get the abscissa of the given point on the line.
double	angle(Line other) Compute the angle in radians between this instance's direction and the direction of the given line.
boolean	contains(Line line) Check if this instance completely contains the other line.
boolean	contains(Vector2D p) Check if the line contains a point.
double	distance(Line line) Compute the shortest distance between this instance and the given line.
double	distance(Vector2D p) Compute the distance between the instance and a point.
boolean	eq(Line other, Precision.DoubleEquivalence precision) Return true if this instance should be considered equivalent to the argument, using the given precision context for comparison.
boolean	equals(Object obj)
double	getAngle() Get the angle of the line in radians with respect to the abscissa (+x) axis.
Vector2D.Unit	getDirection() Get the direction of the line.
Vector2D	getOffsetDirection() Get the offset direction of the line.
Vector2D	getOrigin() Get the line origin point.
double	getOriginOffset() Get the signed distance from the origin of the 2D space to the closest point on the line.
int	hashCode()
Vector2D	intersection(Line other) Get the intersection point of the instance and another line.
boolean	isParallel(Line line) Check if the instance is parallel to another line.
double	offset(Line line) Get the offset (oriented distance) of the given line relative to this instance.
double	offset(Vector2D point)
Vector2D	pointAt(double abscissa, double offset) Get one point from the plane, relative to the coordinate system of the line.
Vector2D	project(Vector2D point)
Ray	rayFrom(double startLocation) Create a new ray instance that starts at the given 1D location and continues in the direction of the line to infinity.
Ray	rayFrom(Vector2D startPoint) Create a new ray instance that starts at the projection of the given point and continues in the direction of the line to infinity.
Line	reverse()
ReverseRay	reverseRayTo(double endLocation) Create a new convex line subset that starts at infinity and continues along the line up to the given 1D location.
ReverseRay	reverseRayTo(Vector2D endPoint) Create a new convex line subset that starts at infinity and continues along the line up to the projection of the given end point.
Segment	segment(double a, double b) Create a new line segment from the given 1D interval.
Segment	segment(Vector2D a, Vector2D b) Create a new line segment from two points.
boolean	similarOrientation(Hyperplane<Vector2D> other)
LineConvexSubset	span()
Line.SubspaceTransform	subspaceTransform(Transform<Vector2D> transform) Get an object containing the current line transformed by the argument along with a 1D transform that can be applied to subspace points.
Vector2D	toSpace(double abscissa) Convert the given abscissa value (1D location on the line) into a 2D point.
Vector2D	toSpace(Vector1D point)
String	toString()
Vector1D	toSubspace(Vector2D point)
Line	transform(Transform<Vector2D> transform)

Methods inherited from class org.apache.commons.geometry.core.partitioning.AbstractHyperplane

classify, getPrecision

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.apache.commons.geometry.core.partitioning.Hyperplane

classify

Methods inherited from interface org.apache.commons.geometry.core.Embedding

toSpace, toSubspace

Method Detail

getAngle

public double getAngle()

Get the angle of the line in radians with respect to the abscissa (+x) axis. The returned angle is in the range [0, 2pi).

Returns:

the angle of the line with respect to the abscissa (+x) axis in the range [0, 2pi)

getDirection

public Vector2D.Unit getDirection()

Get the direction of the line.

Returns:

the direction of the line

getOffsetDirection

public Vector2D getOffsetDirection()

Get the offset direction of the line. This vector is perpendicular to the line and points in the direction of positive offset values, meaning that it points from the left side of the line to the right when one is looking along the line direction.

Returns:

the offset direction of the line.

getOrigin

public Vector2D getOrigin()

Get the line origin point. This is the projection of the 2D origin onto the line and also serves as the origin for the 1D embedded subspace.

Returns:

the origin point of the line

getOriginOffset

public double getOriginOffset()

Get the signed distance from the origin of the 2D space to the closest point on the line.

Returns:

the signed distance from the origin to the line

reverse

public Line reverse()

Specified by:

reverse in interface Hyperplane<Vector2D>

transform

public Line transform(Transform<Vector2D> transform)

Specified by:

transform in interface Hyperplane<Vector2D>

subspaceTransform

public Line.SubspaceTransform subspaceTransform(Transform<Vector2D> transform)

Get an object containing the current line transformed by the argument along with a 1D transform that can be applied to subspace points. The subspace transform transforms subspace points such that their 2D location in the transformed line is the same as their 2D location in the original line after the 2D transform is applied. For example, consider the code below:

      SubspaceTransform st = line.subspaceTransform(transform);

      Vector1D subPt = Vector1D.of(1);

      Vector2D a = transform.apply(line.toSpace(subPt)); // transform in 2D space
      Vector2D b = st.getLine().toSpace(st.getTransform().apply(subPt)); // transform in 1D space
 

At the end of execution, the points a (which was transformed using the original 2D transform) and b (which was transformed in 1D using the subspace transform) are equivalent.

Parameters:

transform - the transform to apply to this instance

Returns:

an object containing the transformed line along with a transform that can be applied to subspace points

See Also:

transform(Transform)

span

public LineConvexSubset span()

Specified by:

span in interface Hyperplane<Vector2D>

segment

public Segment segment(double a,
                       double b)

Create a new line segment from the given 1D interval. The returned line segment consists of all points between the two locations, regardless of the order the arguments are given.

Parameters:

a - first 1D location for the interval

b - second 1D location for the interval

Returns:

a new line segment on this line

Throws:

IllegalArgumentException - if either of the locations is NaN or infinite

See Also:

Lines.segmentFromLocations(Line, double, double)

segment

public Segment segment(Vector2D a,
                       Vector2D b)

Create a new line segment from two points. The returned segment represents all points on this line between the projected locations of a and b. The points may be given in any order.

Parameters:

a - first point

b - second point

Returns:

a new line segment on this line

Throws:

IllegalArgumentException - if either point contains NaN or infinite coordinate values

See Also:

Lines.segmentFromPoints(Line, Vector2D, Vector2D)

reverseRayTo

public ReverseRay reverseRayTo(Vector2D endPoint)

Create a new convex line subset that starts at infinity and continues along the line up to the projection of the given end point.

Parameters:

endPoint - point defining the end point of the line subset; the end point is equal to the projection of this point onto the line

Returns:

a new, half-open line subset that ends at the given point

Throws:

IllegalArgumentException - if any coordinate in endPoint is NaN or infinite

See Also:

Lines.reverseRayFromPoint(Line, Vector2D)

reverseRayTo

public ReverseRay reverseRayTo(double endLocation)

Create a new convex line subset that starts at infinity and continues along the line up to the given 1D location.

Parameters:

endLocation - the 1D location of the end of the half-line

Returns:

a new, half-open line subset that ends at the given 1D location

Throws:

IllegalArgumentException - if endLocation is NaN or infinite

See Also:

Lines.reverseRayFromLocation(Line, double)

rayFrom

public Ray rayFrom(Vector2D startPoint)

Create a new ray instance that starts at the projection of the given point and continues in the direction of the line to infinity.

Parameters:

startPoint - point defining the start point of the ray; the start point is equal to the projection of this point onto the line

Returns:

a ray starting at the projected point and extending along this line to infinity

Throws:

IllegalArgumentException - if any coordinate in startPoint is NaN or infinite

See Also:

Lines.rayFromPoint(Line, Vector2D)

rayFrom

public Ray rayFrom(double startLocation)

Create a new ray instance that starts at the given 1D location and continues in the direction of the line to infinity.

Parameters:

startLocation - 1D location defining the start point of the ray

Returns:

a ray starting at the given 1D location and extending along this line to infinity

Throws:

IllegalArgumentException - if startLocation is NaN or infinite

See Also:

Lines.rayFromLocation(Line, double)

abscissa

public double abscissa(Vector2D point)

Get the abscissa of the given point on the line. The abscissa represents the distance the projection of the point on the line is from the line's origin point (the point on the line closest to the origin of the 2D space). Abscissa values increase in the direction of the line. This method is exactly equivalent to toSubspace(Vector2D) except that this method returns a double instead of a Vector1D.

Parameters:

point - point to compute the abscissa for

Returns:

abscissa value of the point

See Also:

toSubspace(Vector2D)

toSubspace

public Vector1D toSubspace(Vector2D point)

Specified by:

toSubspace in interface Embedding<Vector2D,Vector1D>

toSpace

public Vector2D toSpace(Vector1D point)

Specified by:

toSpace in interface Embedding<Vector2D,Vector1D>

toSpace

public Vector2D toSpace(double abscissa)

Convert the given abscissa value (1D location on the line) into a 2D point.

Parameters:

abscissa - value to convert

Returns:

2D point corresponding to the line abscissa value

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 is no unique intersection point (ie, the lines are parallel or coincident)

angle

public double angle(Line other)

Compute the angle in radians between this instance's direction and the direction of the given line. The return value is in the range [-pi, +pi). This method always returns a value, even for parallel or coincident lines.

Parameters:

other - other line

Returns:

the angle required to rotate this line to point in the direction of the given line

project

public Vector2D project(Vector2D point)

Specified by:

project in interface Hyperplane<Vector2D>

offset

public double offset(Vector2D point)

Specified by:

offset in interface Hyperplane<Vector2D>

offset

public double offset(Line line)

Get the offset (oriented distance) of the given line relative to this instance. Since an infinite number of distances can be calculated between points on two different lines, this method returns the value closest to zero. For intersecting lines, this will simply be zero. For parallel lines, this will be the perpendicular distance between the two lines, as a signed value.

The sign of the returned offset indicates the side of the line that the argument lies on. The offset is positive if the line lies on the right side of the instance and negative if the line lies on the left side of the instance.

Parameters:

line - line to check

Returns:

offset of the line

See Also:

distance(Line)

similarOrientation

public boolean similarOrientation(Hyperplane<Vector2D> other)

Specified by:

similarOrientation in interface Hyperplane<Vector2D>

pointAt

public Vector2D pointAt(double abscissa,
                        double offset)

Get one point from the plane, relative to the coordinate system of the line. Note that the direction of increasing offsets points to the right of the line. This means that if one pictures the line (abscissa) direction as equivalent to the +x-axis, the offset direction will point along the -y axis.

Parameters:

abscissa - desired abscissa (distance along the line) for the point

offset - desired offset (distance perpendicular to the line) 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.

Specified by:

contains in interface Hyperplane<Vector2D>

Overrides:

contains in class AbstractHyperplane<Vector2D>

Parameters:

p - point to check

Returns:

true if p belongs to the line

contains

public boolean contains(Line line)

Check if this instance completely contains the other line. This will be true if the two instances represent the same line, with perhaps different directions.

Parameters:

line - line to check

Returns:

true if this instance contains all points in the given line

distance

public double distance(Vector2D p)

Compute the distance between the instance and a point.

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

Parameters:

p - to check

Returns:

distance between the instance and the point

distance

public double distance(Line line)

Compute the shortest distance between this instance and the given line. This value will simply be zero for intersecting lines.

Parameters:

line - line to compute the closest distance to

Returns:

the shortest distance between this instance and the given line

See Also:

offset(Line)

isParallel

public boolean isParallel(Line line)

Check if 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)

eq

public boolean eq(Line other,
                  Precision.DoubleEquivalence precision)

Return true if this instance should be considered equivalent to the argument, using the given precision context for comparison. Instances are considered equivalent if they have equivalent origin points and make similar angles with the x-axis.

Parameters:

other - the point to compare with

precision - precision context to use for the comparison

Returns:

true if this instance should be considered equivalent to the argument

See Also:

Vector2D.eq(Vector2D, Precision.DoubleEquivalence)

hashCode

public int hashCode()

Overrides:

hashCode in class Object

equals

public boolean equals(Object obj)

Overrides:

equals in class Object

toString

public String toString()

Overrides:

toString in class Object