math.geom2d.line
Class AbstractLine2D

java.lang.Object
  math.geom2d.curve.AbstractContinuousCurve2D
      math.geom2d.curve.AbstractSmoothCurve2D
          math.geom2d.line.AbstractLine2D

All Implemented Interfaces:

java.lang.Cloneable, CirculinearContinuousCurve2D, CirculinearCurve2D, CirculinearElement2D, CirculinearShape2D, ContinuousCurve2D, Curve2D, SmoothCurve2D, ContinuousOrientedCurve2D, OrientedCurve2D, SmoothOrientedCurve2D, GeometricObject2D, LinearElement2D, LinearShape2D, Shape2D

Direct Known Subclasses:

InvertedRay2D, LineArc2D, LineSegment2D, Ray2D, StraightLine2D

public abstract class AbstractLine2D
extends AbstractSmoothCurve2D
implements SmoothOrientedCurve2D, LinearElement2D

Base class for straight curves, such as straight lines, rays, or edges.

Internal representation of straight objects is parametric: (x0, y0) is a point in the object, and (dx, dy) is a direction vector of the line.

If the line is defined by two point, we can set (x0,y0) to the first point, and (dx,dy) to the vector (p1, p2).

Then, coordinates for a point (x,y) such as x=x0+t*dx and y=y0+t=dy, t between 0 and 1 give a point inside p1 and p2, t<0 give a point 'before' p1, and t>1 give a point 'after' p2, so it is convenient to easily manage edges, rays and straight lines.

Field Summary

Fields inherited from interface math.geom2d.Shape2D

ACCURACY

Method Summary

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.
double[]	cartesianEquation() Returns the coefficient of the Cartesian representation of the line.
CurveSet2D<? extends AbstractLine2D>	clip(Box2D box) When a curve is clipped, the result is a set of curves.
abstract AbstractLine2D	clone() Ensures public declaration of clone(), and ensures valid return type.
boolean	contains(Point2D p) Checks if the shape contains the given point.
java.util.Collection<? extends AbstractLine2D>	continuousCurves() Returns a collection of lines containing only this line.
double	curvature(double t) Returns 0 as for every straight object.
Vector2D	direction() Returns the direction vector of this linear shape.
double	distance(double x, double y) Returns the distance of the StraightObject2d to the given point.
double	distance(Point2D p) Returns the distance of the StraightObject2d to the given point.
static Point2D	getIntersection(AbstractLine2D line1, AbstractLine2D line2) Returns the unique intersection of two straight objects.
Point2D	getSymmetric(double x, double y) Return the symmetric of point with coordinate (x, y) relative to this straight line.
Point2D	getSymmetric(Point2D p) Return the symmetric of point p relative to this straight line.
double	horizontalAngle() Gets Angle with axis (O,i), counted counter-clockwise.
Point2D	intersection(LinearShape2D line) Returns the unique intersection with a linear shape.
java.util.Collection<Point2D>	intersections(LinearShape2D line) Returns the intersection points of the curve with the specified line.
boolean	isClosed() Always returns false, because we can not come back to starting point if we always go straight...
static boolean	isColinear(AbstractLine2D line1, AbstractLine2D line2) Tests if the two linear objects are located on the same straight line.
boolean	isColinear(LinearShape2D linear) Tests if the given linear shape is parallel to this shape.
boolean	isEmpty() Returns false, unless both dx and dy equal 0.
boolean	isInside(Point2D p) Returns true if the given point lies to the left of the line when traveling along the line in the direction given by its direction vector.
static boolean	isParallel(AbstractLine2D line1, AbstractLine2D line2) Tests if the two linear objects are parallel.
boolean	isParallel(LinearShape2D line) Tests if the this object is parallel to the given one.
double	length()
double	length(double pos)
Point2D	origin() Returns the origin point of this linear shape.
StraightLine2D	parallel(Point2D point) Creates a straight line parallel to this object, and going through the given point.
double[][]	parametric() Returns the matrix of parametric representation of the line.
StraightLine2D	perpendicular(Point2D point) Creates a straight line perpendicular to this object, and going through the given point.
double[]	polarCoefficients() Returns polar coefficients of this linear shape.
double[]	polarCoefficientsSigned() Returns the signed polar coefficients.
double	position(double distance)
double	position(Point2D point) Returns the position of the point on the line arc.
double	positionOnLine(double x, double y) Computes position on the line of the point given by (x,y).
double	positionOnLine(Point2D point)
double	project(Point2D point) Returns the position of the closest point on the line arc.
Point2D	projectedPoint(double x, double y) Returns the projection of point p on the line.
Point2D	projectedPoint(Point2D p) Returns the projection of point p on the line.
double	signedDistance(double x, double y) Returns the signed distance of the StraightObject2d to the given point.
double	signedDistance(Point2D p) Returns the signed distance of the StraightObject2d to the given point.
java.util.Collection<? extends AbstractLine2D>	smoothPieces() Returns a collection of lines containing only this line.
AbstractLine2D	subCurve(double t0, double t1) Returns a new AbstractLine2D, which is the portion of this AbstractLine2D delimited by parameters t0 and t1.
StraightLine2D	supportingLine() Returns the straight line that contains this linear shape.
Vector2D	tangent(double t) Returns the tangent of the curve at the given position.
abstract AbstractLine2D	transform(AffineTransform2D transform) Transforms the curve by an affine transform.
CirculinearElement2D	transform(CircleInversion2D inv) Transforms the shape by a circle inversion.
double	windingAngle(Point2D point) Return the angle portion that the curve turn around the given point.

Methods inherited from class math.geom2d.curve.AbstractSmoothCurve2D

isSingular, leftTangent, normal, rightTangent, singularPoints, vertices

Methods inherited from class math.geom2d.curve.AbstractContinuousCurve2D

asAwtShape, asPolyline, draw, firstPoint, lastPoint

Methods inherited from class java.lang.Object

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

Methods inherited from interface math.geom2d.circulinear.CirculinearElement2D

parallel

Methods inherited from interface math.geom2d.curve.SmoothCurve2D

normal

Methods inherited from interface math.geom2d.curve.ContinuousCurve2D

appendPath, asPolyline, leftTangent, rightTangent

Methods inherited from interface math.geom2d.curve.Curve2D

asAwtShape, draw, firstPoint, getT0, getT1, isSingular, lastPoint, point, singularPoints, t0, t1, vertices

Methods inherited from interface math.geom2d.Shape2D

boundingBox, contains, isBounded

Methods inherited from interface math.geom2d.GeometricObject2D

almostEquals

Method Detail

getIntersection

public static Point2D getIntersection(AbstractLine2D line1,
                                      AbstractLine2D line2)

Returns the unique intersection of two straight objects. If the intersection doesn't exist (parallel lines, short edge), return null.

isColinear

public static boolean isColinear(AbstractLine2D line1,
                                 AbstractLine2D line2)

Tests if the two linear objects are located on the same straight line.

isParallel

public static boolean isParallel(AbstractLine2D line1,
                                 AbstractLine2D line2)

Tests if the two linear objects are parallel.

isColinear

public boolean isColinear(LinearShape2D linear)

Tests if the given linear shape is parallel to this shape.

isParallel

public boolean isParallel(LinearShape2D line)

Tests if the this object is parallel to the given one.

parametric

public double[][] parametric()

Returns the matrix of parametric representation of the line. Result has the form:

[ x0 dx ]

[ y0 dy ]

It can be easily extended to higher dimensions and/or higher polynomial forms.

cartesianEquation

public double[] cartesianEquation()

Returns the coefficient of the Cartesian representation of the line. Cartesian equation has the form: ax+by+c=0

Returns:

the array {a, b, c}.

polarCoefficients

public double[] polarCoefficients()

Returns polar coefficients of this linear shape.

Returns:

an array of 2 elements, the first one is the distance to the origin, the second one is the angle with horizontal, between 0 and 2*PI.

polarCoefficientsSigned

public double[] polarCoefficientsSigned()

Returns the signed polar coefficients. Distance to origin can be negative: this allows representation of directed lines.

Returns:

an array of 2 elements, the first one is the signed distance to the origin, the second one is the angle with horizontal, between 0 and 2*PI.

positionOnLine

public double positionOnLine(Point2D point)

positionOnLine

public double positionOnLine(double x,
                             double y)

Computes position on the line of the point given by (x,y). The position is the number t such that if the point belong to the line, it location is given by x=x0+t*dx and y=y0+t*dy.

If the point does not belong to the line, the method returns the position of its projection on the line.

projectedPoint

public Point2D projectedPoint(Point2D p)

Returns the projection of point p on the line. The returned point can be used to compute distance from point to line.

Parameters:

p - a point outside the line (if point p lies on the line, it is returned)

Returns:

the projection of the point p on the line

projectedPoint

public Point2D projectedPoint(double x,
                              double y)

Returns the projection of point p on the line. The returned point can be used to compute distance from point to line.

Parameters:

x - coordinate x of point to be projected

y - coordinate y of point to be projected

Returns:

the projection of the point p on the line

getSymmetric

public Point2D getSymmetric(Point2D p)

Return the symmetric of point p relative to this straight line.

Parameters:

p - a point outside the line (if point p lies on the line, it is returned)

Returns:

the projection of the point p on the line

getSymmetric

public Point2D getSymmetric(double x,
                            double y)

Return the symmetric of point with coordinate (x, y) relative to this straight line.

Parameters:

x - x-coordinate of point to be projected

y - y-coordinate of point to be projected

Returns:

the projection of the point (x,y) on the line

parallel

public StraightLine2D parallel(Point2D point)

Creates a straight line parallel to this object, and going through the given point.

Parameters:

point - the point to go through

Returns:

the parallel through the point

perpendicular

public StraightLine2D perpendicular(Point2D point)

Creates a straight line perpendicular to this object, and going through the given point.

Parameters:

point - the point to go through

Returns:

the perpendicular through the point

origin

public Point2D origin()

Returns the origin point of this linear shape.

Specified by:

origin in interface LinearShape2D

Returns:

a point in the linear shape.

direction

public Vector2D direction()

Returns the direction vector of this linear shape.

Specified by:

direction in interface LinearShape2D

Returns:

a direction vector

horizontalAngle

public double horizontalAngle()

Gets Angle with axis (O,i), counted counter-clockwise. Result is given between 0 and 2*pi.

Specified by:

horizontalAngle in interface LinearShape2D

intersection

public Point2D intersection(LinearShape2D line)

Returns the unique intersection with a linear shape. If the intersection doesn't exist (parallel lines, short edges), return null.

Specified by:

intersection in interface LinearShape2D

supportingLine

public StraightLine2D supportingLine()

Description copied from interface: LinearShape2D

Returns the straight line that contains this linear shape. The direction is the same, and if possible the direction vector should be the same.

Specified by:

supportingLine in interface LinearShape2D

Returns:

the straight line that contains this linear shape

length

public double length()

Specified by:

length in interface CirculinearCurve2D

Returns:

the length of the curve

length

public double length(double pos)

Specified by:

length in interface CirculinearCurve2D

Returns:

the length from the beginning to the position given by pos

position

public double position(double distance)

Specified by:

position in interface CirculinearCurve2D

Returns:

the position located at a given geodesic distance from the origin

transform

public CirculinearElement2D 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 CirculinearContinuousCurve2D

Specified by:

transform in interface CirculinearCurve2D

Specified by:

transform in interface CirculinearElement2D

Specified by:

transform in interface CirculinearShape2D

Parameters:

inv - the circle inversion

Returns:

the transformed shape

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

windingAngle

public double windingAngle(Point2D point)

Description copied from interface: OrientedCurve2D

Return the angle portion that the curve turn around the given point. Result is a signed angle.

Specified by:

windingAngle in interface OrientedCurve2D

Parameters:

point - a point of the plane

Returns:

a signed angle

signedDistance

public double signedDistance(Point2D p)

Returns the signed distance of the StraightObject2d to the given point. The signed distance is positive if point lies 'to the right' of the line, when moving in the direction given by direction vector. This method is not designed to be used directly, because AbstractLine2D is an abstract class, but it can be used by subclasses to help computations.

Specified by:

signedDistance in interface OrientedCurve2D

Parameters:

p - a point of the plane

Returns:

the signed distance to the curve

signedDistance

public double signedDistance(double x,
                             double y)

Returns the signed distance of the StraightObject2d to the given point. The signed distance is positive if point lies 'to the right' of the line, when moving in the direction given by direction vector. This method is not designed to be used directly, because AbstractLine2D is an abstract class, but it can be used by subclasses to help computations.

Specified by:

signedDistance in interface OrientedCurve2D

Parameters:

x - x-coord of a point

y - y-coord of a point

Returns:

the signed distance of the point (x,y) to the curve

isInside

public boolean isInside(Point2D p)

Returns true if the given point lies to the left of the line when traveling along the line in the direction given by its direction vector.

Specified by:

isInside in interface OrientedCurve2D

Parameters:

p - the point to test

Returns:

true if point p lies on the 'left' of the line.

tangent

public Vector2D tangent(double t)

Description copied from interface: SmoothCurve2D

Returns the tangent of the curve at the given position.

Specified by:

tangent in interface SmoothCurve2D

Parameters:

t - a position on the curve

Returns:

the tangent vector computed for position t

See Also:

SmoothCurve2D.normal(double)

curvature

public double curvature(double t)

Returns 0 as for every straight object.

Specified by:

curvature in interface ContinuousCurve2D

Parameters:

t - the position on the curve

Returns:

the curvature of the curve for position t

isClosed

public boolean isClosed()

Always returns false, because we can not come back to starting point if we always go straight...

Specified by:

isClosed in interface ContinuousCurve2D

smoothPieces

public java.util.Collection<? extends AbstractLine2D> smoothPieces()

Returns a collection of lines containing only this line.

Specified by:

smoothPieces in interface CirculinearContinuousCurve2D

Specified by:

smoothPieces in interface ContinuousCurve2D

Overrides:

smoothPieces in class AbstractSmoothCurve2D

intersections

public java.util.Collection<Point2D> intersections(LinearShape2D line)

Returns the intersection points of the curve with the specified line. The length of the result array is the number of intersection points.

Specified by:

intersections in interface Curve2D

position

public double position(Point2D point)

Returns the position of the point on the line arc. If the point belongs to the line, this position is defined by the ratio:

t = (xp - x0)/dx <\code>, or equivalently:

t = (yp - y0)/dy <\code>.

If point does not belong to line, returns Double.NaN.

Specified by:

position in interface Curve2D

Parameters:

point - a point belonging to the curve

Returns:

the position of the point on the curve

See Also:

Curve2D.point(double)

project

public double project(Point2D point)

Returns the position of the closest point on the line arc. If the point belongs to the line, this position is defined by the ratio:

t = (xp - x0)/dx <\code>, or equivalently:

t = (yp - y0)/dy <\code>.

If point does not belong to line, returns t0, or t1, depending on which one is the closest.

Specified by:

project in interface Curve2D

Parameters:

point - a point to project

Returns:

the position of the closest orthogonal projection

subCurve

public AbstractLine2D subCurve(double t0,
                               double t1)

Returns a new AbstractLine2D, which is the portion of this AbstractLine2D delimited by parameters t0 and t1. Casts the result to StraightLine2D, Ray2D or LineSegment2D when appropriate.

Specified by:

subCurve in interface CirculinearContinuousCurve2D

Specified by:

subCurve in interface CirculinearCurve2D

Specified by:

subCurve in interface CirculinearElement2D

Specified by:

subCurve in interface ContinuousCurve2D

Specified by:

subCurve in interface Curve2D

Specified by:

subCurve in interface SmoothCurve2D

Specified by:

subCurve in interface ContinuousOrientedCurve2D

Specified by:

subCurve in interface SmoothOrientedCurve2D

Specified by:

subCurve in interface LinearElement2D

Parameters:

t0 - position of the start of the sub-curve

t1 - position of the end of the sub-curve

Returns:

the portion of original curve comprised between t0 and t1.

continuousCurves

public java.util.Collection<? extends AbstractLine2D> continuousCurves()

Returns a collection of lines containing only this line.

Specified by:

continuousCurves in interface CirculinearCurve2D

Specified by:

continuousCurves in interface Curve2D

Overrides:

continuousCurves in class AbstractContinuousCurve2D

Returns:

a collection of continuous curves.

distance

public double distance(Point2D p)

Returns the distance of the StraightObject2d to the given point. This method is not designed to be used directly, because AbstractLine2D is an abstract class, but it can be called by subclasses to help computations.

Specified by:

distance in interface Shape2D

distance

public double distance(double x,
                       double y)

Returns the distance of the StraightObject2d to the given point. This method is not designed to be used directly, because AbstractLine2D is an abstract class, but it can be called by subclasses to help computations.

Specified by:

distance in interface Shape2D

Parameters:

x - the x-coordinate of the point

y - the y-coordinate of the point

Returns:

distance between this object and the point (x,y)

contains

public boolean contains(Point2D p)

Description copied from interface: Shape2D

Checks if the shape contains the given point.

Specified by:

contains in interface Shape2D

isEmpty

public boolean isEmpty()

Returns false, unless both dx and dy equal 0.

Specified by:

isEmpty in interface Shape2D

Returns:

true if the shape does not contain any point.

transform

public abstract AbstractLine2D transform(AffineTransform2D transform)

Description copied from interface: Curve2D

Transforms the curve by an affine transform. The result is an instance of Curve2D.

Specified by:

transform in interface ContinuousCurve2D

Specified by:

transform in interface Curve2D

Specified by:

transform in interface SmoothCurve2D

Specified by:

transform in interface ContinuousOrientedCurve2D

Specified by:

transform in interface OrientedCurve2D

Specified by:

transform in interface SmoothOrientedCurve2D

Specified by:

transform in interface LinearElement2D

Specified by:

transform in interface LinearShape2D

Specified by:

transform in interface Shape2D

Parameters:

transform - an affine transform

Returns:

the transformed shape

clip

public CurveSet2D<? extends AbstractLine2D> clip(Box2D box)

Description copied from interface: Curve2D

When a curve is clipped, the result is a set of curves.

Specified by:

clip in interface CirculinearContinuousCurve2D

Specified by:

clip in interface CirculinearCurve2D

Specified by:

clip in interface CirculinearElement2D

Specified by:

clip in interface ContinuousCurve2D

Specified by:

clip in interface Curve2D

Specified by:

clip in interface SmoothCurve2D

Specified by:

clip in interface ContinuousOrientedCurve2D

Specified by:

clip in interface OrientedCurve2D

Specified by:

clip in interface SmoothOrientedCurve2D

Specified by:

clip in interface LinearElement2D

Specified by:

clip in interface Shape2D

Parameters:

box - the clipping box

Returns:

the clipped shape

clone

public abstract AbstractLine2D clone()

Ensures public declaration of clone(), and ensures valid return type.

Specified by:

clone in interface Curve2D

Specified by:

clone in class AbstractSmoothCurve2D

Returns:

the cloned curve