math.geom2d.conic
Class ParabolaArc2D

java.lang.Object
  math.geom2d.curve.AbstractContinuousCurve2D
      math.geom2d.curve.AbstractSmoothCurve2D
          math.geom2d.conic.ParabolaArc2D

All Implemented Interfaces:

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

public class ParabolaArc2D
extends AbstractSmoothCurve2D
implements SmoothOrientedCurve2D, java.lang.Cloneable

An arc of parabola, defined by a parent parabola, and two limits for the parametrization.

Author:

dlegland

Field Summary

Fields inherited from interface math.geom2d.Shape2D

ACCURACY

Constructor Summary

ParabolaArc2D(Parabola2D parabola, double t0, double t1)

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 ParabolaArc2D>	clip(Box2D box) Clip the parabola arc by a box.
ParabolaArc2D	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.
static ParabolaArc2D	create(Parabola2D parabola, double t0, double t1)
double	curvature(double t) Returns the curvature of the parabola 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 p) 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.
boolean	equals(java.lang.Object obj)
java.awt.geom.GeneralPath	getGeneralPath()
Parabola2D	getParabola()
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() Returns true if the arc is bounded, i.e. if both limits are finite.
boolean	isClosed() Returns false, by definition of a parabola arc
boolean	isEmpty() Return true if t1
boolean	isInside(Point2D point) 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.
ParabolaArc2D	reverse() Returns the parabola arc which refers to the reversed parent parabola, and with inverted parameterization bounds.
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.
ParabolaArc2D	subCurve(double t0, double t1) Returns a portion of the original curve, delimited by two positions on the curve.
double	t0() Returns the position of the first point of the parabola arc.
double	t1() Returns the position of the last point of the parabola arc.
Vector2D	tangent(double t) Returns the tangent of the curve at the given position.
java.lang.String	toString()
ParabolaArc2D	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, smoothPieces, vertices

Methods inherited from class math.geom2d.curve.AbstractContinuousCurve2D

asAwtShape, continuousCurves, draw, 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, smoothPieces

Methods inherited from interface math.geom2d.curve.Curve2D

asAwtShape, continuousCurves, draw, firstPoint, isSingular, lastPoint, singularPoints, vertices

Constructor Detail

ParabolaArc2D

public ParabolaArc2D(Parabola2D parabola,
                     double t0,
                     double t1)

Method Detail

create

public static ParabolaArc2D create(Parabola2D parabola,
                                   double t0,
                                   double t1)

getParabola

public Parabola2D getParabola()

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)

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

isInside

public boolean isInside(Point2D point)

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:

point - a point in the plane

Returns:

true if the point is on the left side of 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 parabola arc.

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, by definition of a parabola arc

Specified by:

isClosed in interface ContinuousCurve2D

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()

Returns the position of the first point of the parabola arc.

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()

Returns the position of the last point of the parabola arc.

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 ParabolaArc2D reverse()

Returns the parabola arc which refers to the reversed parent parabola, and with inverted parameterization bounds.

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

subCurve

public ParabolaArc2D subCurve(double t0,
                              double t1)

Description copied from interface: Curve2D

Returns a portion of the original curve, delimited by two positions on the curve.

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 p)

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()

Returns true if the arc is bounded, i.e. if both limits are finite.

Specified by:

isBounded in interface Shape2D

isEmpty

public boolean isEmpty()

Return true if t1

Specified by:

isEmpty in interface Shape2D

Returns:

true if the shape does not contain any point.

clip

public CurveSet2D<? extends ParabolaArc2D> clip(Box2D box)

Clip the parabola arc by a box. The result is an instance of CurveSet2D, which contains only instances of ParabolaArc2D. If the parabola 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 ParabolaArc2D 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 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()

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 ParabolaArc2D 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