math.geom2d.conic
Class Parabola2D

java.lang.Object
  math.geom2d.curve.AbstractContinuousCurve2D
      math.geom2d.curve.AbstractSmoothCurve2D
          math.geom2d.conic.Parabola2D

All Implemented Interfaces:

java.lang.Cloneable, Conic2D, ContinuousCurve2D, Curve2D, SmoothCurve2D, Boundary2D, ContinuousOrientedCurve2D, Contour2D, OrientedCurve2D, GeometricObject2D, Shape2D

public class Parabola2D
extends AbstractSmoothCurve2D
implements Contour2D, Conic2D, java.lang.Cloneable

A parabola, defined by its vertex, its orientation, and its pedal. Orientation is defined as the orientation of derivative at vertex point, with the second derivative pointing to the top.

Following parametric representation is used:

x(t)=t

y(t)=a*t^2

This is a signed parameter (negative a makes the parabola point to opposite side).

Author:

dlegland

Nested Class Summary

Nested classes/interfaces inherited from interface math.geom2d.conic.Conic2D

Conic2D.Type

Field Summary

Fields inherited from interface math.geom2d.Shape2D

ACCURACY

Constructor Summary

Parabola2D()

Parabola2D(double xv, double yv, double a, double theta)

Parabola2D(Point2D vertex, double a, double theta)

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) Throws an infiniteShapeException
Box2D	boundingBox() Returns the bounding box of the shape.
CurveSet2D<ParabolaArc2D>	clip(Box2D box) Clip the parabola by a box.
Parabola2D	clone() Overrides Object declaration to ensure Curve2D implementation are cloned as Curve2D.
double[]	conicCoefficients() Returns the coefficient of the Cartesian representation of the conic.
Conic2D.Type	conicType()
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.
java.util.Collection<? extends Parabola2D>	continuousCurves() Returns the collection of continuous curves which constitute this curve.
static Parabola2D	create(Point2D vertex, Point2D focus) Creates a parabola by supplying the vertex and the focus.
double	curvature(double t) Returns the curvature of the parabola at the given position.
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.
Domain2D	domain() Returns the domain delimited by this boundary.
double	eccentricity() Return 1, by definition for a parabola.
boolean	equals(java.lang.Object obj)
void	fill(java.awt.Graphics2D g2) Throws an infiniteShapeException
double	getAngle() Returns orientation angle of parabola.
Point2D	getFocus() Returns the focus of the parabola.
double	getFocusDistance()
double	getParameter()
double	getT0() Deprecated. replaced by t0() (since 0.11.1).
double	getT1() Deprecated. replaced by t1() (since 0.11.1).
Vector2D	getVector1() Returns the first direction vector of the parabola
Vector2D	getVector2() Returns the second direction vector of the parabola.
Point2D	getVertex()
java.util.Collection<Point2D>	intersections(LinearShape2D line) Returns the intersection points of the curve with the specified line.
boolean	isBounded() Always returns false, because a parabola is not bounded.
boolean	isClosed() Returns false, as a parabola is an open curve.
boolean	isDirect() Returns true if the parameter a is positive.
boolean	isEmpty() Returns false, as a parabola is never empty.
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) Returns position of point on the parabola.
double	project(Point2D point) Returns position of point on the parabola.
Parabola2D	reverse() Returns the parabola with same vertex, direction vector in opposite direction and opposite parameter p.
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 new ParabolaArc2D, or null if t1
double	t0() Returns the parameter of the first point of the line, which is always Double.NEGATIVE_INFINITY.
double	t1() Returns the parameter of the last point of the line, which is always Double.POSITIVE_INFINITY.
Vector2D	tangent(double t) Returns the tangent of the curve at the given position.
java.lang.String	toString()
Parabola2D	transform(AffineTransform2D trans) Transforms the parabola 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, asPolyline, draw, firstPoint, lastPoint

Methods inherited from class java.lang.Object

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

Methods inherited from interface math.geom2d.curve.ContinuousCurve2D

asPolyline, leftTangent, rightTangent, smoothPieces

Methods inherited from interface math.geom2d.curve.Curve2D

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

Constructor Detail

Parabola2D

public Parabola2D()

Parabola2D

public Parabola2D(Point2D vertex,
                  double a,
                  double theta)

Parabola2D

public Parabola2D(double xv,
                  double yv,
                  double a,
                  double theta)

Method Detail

create

public static final Parabola2D create(Point2D vertex,
                                      Point2D focus)

Creates a parabola by supplying the vertex and the focus.

Parameters:

vertex - the vertex point of the parabola

focus - the focal point of the parabola

Returns:

the parabola with given vertex and focus

getFocus

public Point2D getFocus()

Returns the focus of the parabola.

getParameter

public double getParameter()

getFocusDistance

public double getFocusDistance()

getVertex

public Point2D getVertex()

getVector1

public Vector2D getVector1()

Returns the first direction vector of the parabola

getVector2

public Vector2D getVector2()

Returns the second direction vector of the parabola.

getAngle

public double getAngle()

Returns orientation angle of parabola. It is defined as the angle of the derivative at the vertex.

isDirect

public boolean isDirect()

Returns true if the parameter a is positive.

conicType

public Conic2D.Type conicType()

Specified by:

conicType in interface Conic2D

conicCoefficients

public double[] conicCoefficients()

Description copied from interface: Conic2D

Returns the coefficient of the Cartesian representation of the conic. Cartesian equation has the form :

a*x^2 + b*x*y + c*y^2 + d*x + e*y + f

The length of the array is then of size 6.

Specified by:

conicCoefficients in interface Conic2D

eccentricity

public double eccentricity()

Return 1, by definition for a parabola.

Specified by:

eccentricity in interface Conic2D

domain

public Domain2D domain()

Description copied from interface: Boundary2D

Returns the domain delimited by this boundary.

Specified by:

domain in interface Boundary2D

Returns:

the domain delimited by this boundary

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: Boundary2D

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

Specified by:

isInside in interface Boundary2D

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 at the given position.

Specified by:

curvature in interface ContinuousCurve2D

Parameters:

t - the position on the curve

Returns:

the curvature of the curve for position t

continuousCurves

public java.util.Collection<? extends Parabola2D> continuousCurves()

Description copied from interface: Curve2D

Returns the collection of continuous curves which constitute this curve.

Specified by:

continuousCurves in interface Curve2D

Specified by:

continuousCurves in interface Boundary2D

Overrides:

continuousCurves in class AbstractContinuousCurve2D

Returns:

a collection of continuous curves.

isClosed

public boolean isClosed()

Returns false, as a parabola is an open curve.

Specified by:

isClosed in interface ContinuousCurve2D

t0

public double t0()

Returns the parameter of the first point of the line, which is always Double.NEGATIVE_INFINITY.

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 parameter of the last point of the line, which is always Double.POSITIVE_INFINITY.

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)

Returns position of point on the parabola. If point is not on the parabola returns the positions on its "vertical" projection (i.e. its projection parallel to the symetry axis of the parabola).

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 position of point on the parabola. If point is not on the parabola returns the positions on its "vertical" projection (i.e. its projection parallel to the symetry axis of the parabola).

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 Parabola2D reverse()

Returns the parabola with same vertex, direction vector in opposite direction and opposite parameter p.

Specified by:

reverse in interface Conic2D

Specified by:

reverse in interface ContinuousCurve2D

Specified by:

reverse in interface Curve2D

Specified by:

reverse in interface SmoothCurve2D

Specified by:

reverse in interface Boundary2D

Specified by:

reverse in interface ContinuousOrientedCurve2D

Specified by:

reverse in interface Contour2D

Specified by:

reverse in interface OrientedCurve2D

subCurve

public ParabolaArc2D subCurve(double t0,
                              double t1)

Returns a new ParabolaArc2D, or null if t1

Specified by:

subCurve in interface ContinuousCurve2D

Specified by:

subCurve in interface Curve2D

Specified by:

subCurve in interface SmoothCurve2D

Specified by:

subCurve in interface ContinuousOrientedCurve2D

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

appendPath

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

Throws an infiniteShapeException

Specified by:

appendPath in interface ContinuousCurve2D

Parameters:

path - a path to modify

Returns:

the modified path

fill

public void fill(java.awt.Graphics2D g2)

Throws an infiniteShapeException

Specified by:

fill in interface Boundary2D

Parameters:

g2 - the Graphics to fill on

isBounded

public boolean isBounded()

Always returns false, because a parabola is not bounded.

Specified by:

isBounded in interface Shape2D

isEmpty

public boolean isEmpty()

Returns false, as a parabola is never empty.

Specified by:

isEmpty in interface Shape2D

Returns:

true if the shape does not contain any point.

clip

public CurveSet2D<ParabolaArc2D> clip(Box2D box)

Clip the parabola by a box. The result is an instance of CurveSet2D, which contains only instances of ParabolaArc2D. If the parabola is not clipped, the result is an instance of CurveSet2D which contains 0 curves.

Specified by:

clip in interface Conic2D

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 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 Parabola2D transform(AffineTransform2D trans)

Transforms the parabola by an affine transform. The transformed parabola is direct if this parabola and the affine transform are both either direct or indirect.

Specified by:

transform in interface Conic2D

Specified by:

transform in interface ContinuousCurve2D

Specified by:

transform in interface Curve2D

Specified by:

transform in interface SmoothCurve2D

Specified by:

transform in interface Boundary2D

Specified by:

transform in interface ContinuousOrientedCurve2D

Specified by:

transform in interface Contour2D

Specified by:

transform in interface OrientedCurve2D

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

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 Parabola2D 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