math.geom2d.conic
Class EllipseArc2D

java.lang.Object
  math.geom2d.curve.AbstractContinuousCurve2D
      math.geom2d.curve.AbstractSmoothCurve2D
          math.geom2d.conic.EllipseArc2D

All Implemented Interfaces:

java.lang.Cloneable, EllipseArcShape2D, ContinuousCurve2D, Curve2D, SmoothCurve2D, ContinuousOrientedCurve2D, OrientedCurve2D, SmoothOrientedCurve2D, GeometricObject2D, Shape2D

public class EllipseArc2D
extends AbstractSmoothCurve2D
implements SmoothOrientedCurve2D, EllipseArcShape2D, java.lang.Cloneable

An arc of ellipse. It is defined by a supporting ellipse, a starting angle, and a signed angle extent, both in radians. The ellipse arc is oriented counter-clockwise if angle extent is positive, and clockwise otherwise.

Author:

dlegland

Field Summary

Fields inherited from interface math.geom2d.Shape2D

ACCURACY

Constructor Summary

EllipseArc2D()
Construct a default Ellipse arc, centered on (0,0), with radii equal to 1 and 1, orientation equal to 0, start angle equal to 0, and angle extent equal to PI/2.

EllipseArc2D(double xc, double yc, double a, double b, double theta, double start, double extent)
Specify parameters of supporting ellipse, start angle, and angle extent.

EllipseArc2D(double xc, double yc, double a, double b, double theta, double start, double end, boolean direct)
Specify parameters of supporting ellipse, bounding angles and flag for direct ellipse.

EllipseArc2D(Ellipse2D ell, double start, double extent)
Specify supporting ellipse, start angle and angle extent.

EllipseArc2D(Ellipse2D ell, double start, double end, boolean direct)
Specify supporting ellipse, start angle and end angle, and a flag indicating whether the arc is directed or not.

Method Summary

boolean	almostEquals(GeometricObject2D obj, double eps) Checks if the two objects are similar up to a given threshold value.
java.awt.geom.GeneralPath	appendPath(java.awt.geom.GeneralPath path) Append the path of the curve to the given path.
Polyline2D	asPolyline(int n) Converts this continuous curve to an instance of LinearCurve2D with the given number of edges.
Box2D	boundingBox() Returns the bounding box of the shape.
CurveSet2D<? extends EllipseArc2D>	clip(Box2D box) Clips the ellipse arc by a box.
EllipseArc2D	clone() Overrides Object declaration to ensure Curve2D implementation are cloned as Curve2D.
boolean	contains(double x, double y) Checks if the shape contains the planar point defined by (x,y).
boolean	contains(Point2D point) Checks if the shape contains the given point.
boolean	containsAngle(double angle)
java.util.Collection<? extends EllipseArc2D>	continuousCurves() Returns the collection of continuous curves which constitute this curve.
static EllipseArc2D	create(Ellipse2D ell, double start, double extent) Deprecated. since 0.11.1
static EllipseArc2D	create(Ellipse2D ell, double start, double end, boolean direct) Deprecated. since 0.11.1
double	curvature(double t) Returns the curvature of the ellipse arc.
double	distance(double x, double y) Returns the distance of the shape to the given point, specified by x and y, or the distance of point to the frontier of the shape in the case of a plain (i.e. fillable) shape.
double	distance(Point2D point) Returns the distance of the shape to the given point, or the distance of point to the frontier of the shape in the case of a plain shape.
void	draw(java.awt.Graphics2D g2) Draws the curve on the given Graphics2D object.
boolean	equals(java.lang.Object obj)
double	getAngle(double position) Returns the angle associated with the given position
double	getAngleExtent()
java.awt.geom.GeneralPath	getGeneralPath()
double	getStartAngle()
Ellipse2D	getSupportingEllipse()
double	getT0() Deprecated. replaced by t0() (since 0.11.1).
double	getT1() Deprecated. replaced by t1() (since 0.11.1).
java.util.Collection<Point2D>	intersections(LinearShape2D line) Returns the intersection points of the curve with the specified line.
boolean	isBounded() Always return true: an ellipse arc is bounded by definition
boolean	isClosed() Returns false, as an ellipse arc is never closed.
boolean	isDirect() Returns true if the ellipse arc is direct, i.e. if the angle extent is positive (or zero).
boolean	isEmpty() Returns false.
boolean	isInside(Point2D p) Returns true if the point is 'inside' the domain bounded by the curve.
Point2D	point(double t) Returns the point located at the given position on the curve.
double	position(Point2D point) Computes the position of the point on the curve.
double	project(Point2D point) Returns the position of the closest orthogonal projection of the point on the curve, or of the closest singular point.
EllipseArc2D	reverse() Returns the ellipse arc which refers to the reversed parent ellipse, with same start angle, and with opposite angle extent.
double	signedDistance(double x, double y) The same as distanceSigned(Point2D), but by passing 2 double as arguments.
double	signedDistance(Point2D p) Returns the signed distance of the curve to the given point.
java.util.Collection<? extends EllipseArc2D>	smoothPieces() Returns a collection of curves containing only this circle arc.
EllipseArc2D	subCurve(double t0, double t1) Returns a new EllipseArc2D.
double	t0() Always returns 0
double	t1() Always returns the absolute value of the angle extent
Vector2D	tangent(double t) Returns the tangent of the curve at the given position.
java.lang.String	toString()
EllipseArc2D	transform(AffineTransform2D trans) Transforms the curve by an affine transform.
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, firstPoint, lastPoint

Methods inherited from class java.lang.Object

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

Methods inherited from interface math.geom2d.curve.SmoothCurve2D

normal

Methods inherited from interface math.geom2d.curve.ContinuousCurve2D

leftTangent, rightTangent

Methods inherited from interface math.geom2d.curve.Curve2D

asAwtShape, firstPoint, isSingular, lastPoint, singularPoints, vertices

Constructor Detail

EllipseArc2D

public EllipseArc2D()

Construct a default Ellipse arc, centered on (0,0), with radii equal to 1 and 1, orientation equal to 0, start angle equal to 0, and angle extent equal to PI/2.

EllipseArc2D

public EllipseArc2D(Ellipse2D ell,
                    double start,
                    double extent)

Specify supporting ellipse, start angle and angle extent.

Parameters:

ell - the supporting ellipse

start - the starting angle (angle between 0 and 2*PI)

extent - the angle extent (signed angle)

EllipseArc2D

public EllipseArc2D(Ellipse2D ell,
                    double start,
                    double end,
                    boolean direct)

Specify supporting ellipse, start angle and end angle, and a flag indicating whether the arc is directed or not.

Parameters:

ell - the supporting ellipse

start - the starting angle

end - the ending angle

direct - flag indicating if the arc is direct

EllipseArc2D

public EllipseArc2D(double xc,
                    double yc,
                    double a,
                    double b,
                    double theta,
                    double start,
                    double extent)

Specify parameters of supporting ellipse, start angle, and angle extent.

EllipseArc2D

public EllipseArc2D(double xc,
                    double yc,
                    double a,
                    double b,
                    double theta,
                    double start,
                    double end,
                    boolean direct)

Specify parameters of supporting ellipse, bounding angles and flag for direct ellipse.

Method Detail

create

@Deprecated
public static EllipseArc2D create(Ellipse2D ell,
                                             double start,
                                             double extent)

Deprecated. since 0.11.1

Specify supporting ellipse, start angle and end angle, and a flag indicating whether the arc is directed or not.

Parameters:

ell - the supporting ellipse

start - the starting angle

extent - the (signed) angle extent

create

@Deprecated
public static EllipseArc2D create(Ellipse2D ell,
                                             double start,
                                             double end,
                                             boolean direct)

Deprecated. since 0.11.1

Specify supporting ellipse, start angle and end angle, and a flag indicating whether the arc is directed or not.

Parameters:

ell - the supporting ellipse

start - the starting angle

end - the ending angle

direct - flag indicating if the arc is direct

getSupportingEllipse

public Ellipse2D getSupportingEllipse()

getStartAngle

public double getStartAngle()

getAngleExtent

public double getAngleExtent()

isDirect

public boolean isDirect()

Returns true if the ellipse arc is direct, i.e. if the angle extent is positive (or zero).

containsAngle

public boolean containsAngle(double angle)

getAngle

public double getAngle(double position)

Returns the angle associated with the given position

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

isInside

public boolean isInside(Point2D p)

Description copied from interface: OrientedCurve2D

Returns true if the point is 'inside' the domain bounded by the curve.

Specified by:

isInside in interface OrientedCurve2D

Parameters:

p - a point in the plane

Returns:

true if the point is on the left side of the curve.

signedDistance

public double signedDistance(Point2D p)

Description copied from interface: OrientedCurve2D

Returns the signed distance of the curve to the given point. The distance is positive if the point lies outside the shape, and negative if the point lies inside the shape. In both cases, absolute value of distance is equals to the distance to the border of the shape.

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)

Description copied from interface: OrientedCurve2D

The same as distanceSigned(Point2D), but by passing 2 double as arguments.

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

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 the curvature of the ellipse arc. Curvature is negative if the arc is indirect.

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()

Returns false, as an ellipse arc is never closed.

Specified by:

isClosed in interface ContinuousCurve2D

smoothPieces

public java.util.Collection<? extends EllipseArc2D> smoothPieces()

Returns a collection of curves containing only this circle arc.

Specified by:

smoothPieces in interface ContinuousCurve2D

Overrides:

smoothPieces in class AbstractSmoothCurve2D

asPolyline

public Polyline2D asPolyline(int n)

Description copied from class: AbstractContinuousCurve2D

Converts this continuous curve to an instance of LinearCurve2D with the given number of edges. Returns either an instance of Polyline2D or LinearRing2D, depending on the curve is closed or not. This method can be overridden to return the correct type.

Specified by:

asPolyline in interface ContinuousCurve2D

Overrides:

asPolyline in class AbstractContinuousCurve2D

Parameters:

n - the number of line segments

Returns:

a polyline with n line segments.

See Also:

ContinuousCurve2D.asPolyline(int)

t0

public double t0()

Always returns 0

Specified by:

t0 in interface Curve2D

getT0

@Deprecated
public double getT0()

Deprecated. replaced by t0() (since 0.11.1).

Specified by:

getT0 in interface Curve2D

t1

public double t1()

Always returns the absolute value of the angle extent

Specified by:

t1 in interface Curve2D

getT1

@Deprecated
public double getT1()

Deprecated. replaced by t1() (since 0.11.1).

Specified by:

getT1 in interface Curve2D

point

public Point2D point(double t)

Description copied from interface: Curve2D

Returns the point located at the given position on the curve. If the parameter lies outside the definition range, the parameter corresponding to the closest bound is used instead. This method can be used to draw an approximated outline of a curve, by selecting multiple values for t and drawing lines between them.

Specified by:

point in interface Curve2D

position

public double position(Point2D point)

Description copied from interface: Curve2D

Computes the position of the point on the curve. If the point does not belong to the curve, return Double.NaN. It is complementary to the point(double) method.

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)

Description copied from interface: Curve2D

Returns the position of the closest orthogonal projection of the point on the curve, or of the closest singular point. This function should always returns a valid value.

Specified by:

project in interface Curve2D

Parameters:

point - a point to project

Returns:

the position of the closest orthogonal projection

intersections

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

Description copied from interface: Curve2D

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

reverse

public EllipseArc2D reverse()

Returns the ellipse arc which refers to the reversed parent ellipse, with same start angle, and with opposite angle extent.

Specified by:

reverse in interface EllipseArcShape2D

Specified by:

reverse in interface ContinuousCurve2D

Specified by:

reverse in interface Curve2D

Specified by:

reverse in interface SmoothCurve2D

Specified by:

reverse in interface ContinuousOrientedCurve2D

Specified by:

reverse in interface OrientedCurve2D

Specified by:

reverse in interface SmoothOrientedCurve2D

continuousCurves

public java.util.Collection<? extends EllipseArc2D> continuousCurves()

Description copied from interface: Curve2D

Returns the collection of continuous curves which constitute this curve.

Specified by:

continuousCurves in interface Curve2D

Overrides:

continuousCurves in class AbstractContinuousCurve2D

Returns:

a collection of continuous curves.

subCurve

public EllipseArc2D subCurve(double t0,
                             double t1)

Returns a new EllipseArc2D.

Specified by:

subCurve in interface EllipseArcShape2D

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

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.

distance

public double distance(Point2D point)

Description copied from interface: Shape2D

Returns the distance of the shape to the given point, or the distance of point to the frontier of the shape in the case of a plain shape.

Specified by:

distance in interface Shape2D

distance

public double distance(double x,
                       double y)

Description copied from interface: Shape2D

Returns the distance of the shape to the given point, specified by x and y, or the distance of point to the frontier of the shape in the case of a plain (i.e. fillable) shape.

Specified by:

distance in interface Shape2D

isBounded

public boolean isBounded()

Always return true: an ellipse arc is bounded by definition

Specified by:

isBounded in interface Shape2D

isEmpty

public boolean isEmpty()

Returns false.

Specified by:

isEmpty in interface Shape2D

Returns:

true if the shape does not contain any point.

clip

public CurveSet2D<? extends EllipseArc2D> clip(Box2D box)

Clips the ellipse arc by a box. The result is an instance of CurveSet2D, which contains only instances of EllipseArc2D. If the ellipse arc is not clipped, the result is an instance of CurveSet2D which contains 0 curves.

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 Shape2D

Parameters:

box - the clipping box

Returns:

the clipped shape

boundingBox

public Box2D boundingBox()

Description copied from interface: Shape2D

Returns the bounding box of the shape.

Specified by:

boundingBox in interface Shape2D

Returns:

the bounding box of the shape.

transform

public EllipseArc2D transform(AffineTransform2D trans)

Description copied from interface: Curve2D

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

Specified by:

transform in interface EllipseArcShape2D

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 Shape2D

Parameters:

trans - an affine transform

Returns:

the transformed shape

contains

public boolean contains(double x,
                        double y)

Description copied from interface: Shape2D

Checks if the shape contains the planar point defined by (x,y).

Specified by:

contains in interface Shape2D

contains

public boolean contains(Point2D point)

Description copied from interface: Shape2D

Checks if the shape contains the given point.

Specified by:

contains in interface Shape2D

appendPath

public java.awt.geom.GeneralPath appendPath(java.awt.geom.GeneralPath path)

Description copied from interface: ContinuousCurve2D

Append the path of the curve to the given path.

Specified by:

appendPath in interface ContinuousCurve2D

Parameters:

path - a path to modify

Returns:

the modified path

getGeneralPath

public java.awt.geom.GeneralPath getGeneralPath()

draw

public void draw(java.awt.Graphics2D g2)

Description copied from interface: Curve2D

Draws the curve on the given Graphics2D object.

Specified by:

draw in interface Curve2D

Specified by:

draw in interface Shape2D

Overrides:

draw in class AbstractContinuousCurve2D

Parameters:

g2 - the graphics to draw the curve in

almostEquals

public boolean almostEquals(GeometricObject2D obj,
                            double eps)

Description copied from interface: GeometricObject2D

Checks if the two objects are similar up to a given threshold value. This method can be used to compare the results of geometric computations, that introduce errors due to numerical computations.

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

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

equals

public boolean equals(java.lang.Object obj)

Overrides:

equals in class java.lang.Object

clone

public EllipseArc2D clone()

Description copied from interface: Curve2D

Overrides Object declaration to ensure Curve2D implementation are cloned as Curve2D.

Specified by:

clone in interface Curve2D

Specified by:

clone in class AbstractSmoothCurve2D

Returns:

the cloned curve