math.geom2d.conic
Class Parabola2D

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

All Implemented Interfaces:

Serializable, Cloneable, Conic2D, ContinuousCurve2D, Curve2D, SmoothCurve2D, Boundary2D, ContinuousBoundary2D, ContinuousOrientedCurve2D, OrientedCurve2D, Shape2D

public class Parabola2D
extends AbstractSmoothCurve2D
implements ContinuousBoundary2D, Conic2D, 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

See Also:

Serialized Form

Nested Class Summary

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

Conic2D.Type

Field Summary

protected double	a The parameter of the parabola.
protected double	theta orientation of the parabola
protected double	xv Coordinate of the vertex
protected double	yv Coordinate of the vertex

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

GeneralPath	appendPath(GeneralPath path) Throws an infiniteShapeException
CurveSet2D<ParabolaArc2D>	clip(Box2D box) Clip the parabola by a box.
Parabola2D	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 Parabola2D	create(Point2D vertex, Point2D focus) Creates a parabola by supplying the vertex and the focus.
boolean	equals(Object obj)
void	fill(Graphics2D g2) Throws an infiniteShapeException
double	getAngle() Returns orientation angle of parabola.
Collection<ContinuousBoundary2D>	getBoundaryCurves() Returns the different continuous curves composing the boundary
Box2D	getBoundingBox() Returns the bounding box of the shape.
double[]	getConicCoefficients() Returns the coefficient of the Cartesian representation of the conic.
Conic2D.Type	getConicType()
double	getCurvature(double t) Returns the curvature of the parabola at the given position.
double	getDistance(double x, double y) get 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	getDistance(Point2D p) get 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	getDomain() Returns the domain delimited by this boundary.
double	getEccentricity() Return 1, by definition for a parabola.
Point2D	getFocus() Returns the focus of the parabola.
double	getFocusDistance()
Collection<Point2D>	getIntersections(LinearShape2D line) Returns the intersection points of the curve with the specified line.
double	getParameter()
Point2D	getPoint(double t) Gets the point from a parametric representation of the curve.
double	getPosition(Point2D point) Returns position of point on the parabola.
Parabola2D	getReverseCurve() Returns the parabola with same vertex, direction vector in opposite direction and opposite parameter p.
double	getSignedDistance(double x, double y) The same as getSignedDistance(Point2D), but by passing 2 double as arguments.
double	getSignedDistance(Point2D p) Get the signed distance of the curve to the given point: this distance is positive if the point lies outside the shape, and is negative if the point lies inside the shape.
ParabolaArc2D	getSubCurve(double t0, double t1) Returns a new ParabolaArc2D, or null if t1
double	getT0() Returns the parameter of the first point of the line, which is always Double.NEGATIVE_INFINITY.
double	getT1() Returns the parameter of the last point of the line, which is always Double.POSITIVE_INFINITY.
Vector2D	getTangent(double t)
Vector2D	getVector1() Returns the first direction vector of the parabola
Vector2D	getVector2() Returns the second direction vector of the parabola.
Point2D	getVertex()
double	getWindingAngle(Point2D point) Return the angle portion that the curve turn around the given point.
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.
double	project(Point2D point) Returns position of point on the parabola.
String	toString()
Parabola2D	transform(AffineTransform2D trans) Transforms the parabola by an affine transform.

Methods inherited from class math.geom2d.curve.AbstractSmoothCurve2D

getLeftTangent, getRightTangent, getSingularPoints, getSmoothPieces, isSingular

Methods inherited from class math.geom2d.curve.AbstractContinuousCurve2D

draw, getAsAWTShape, getAsPolyline, getContinuousCurves, getFirstPoint, getLastPoint, wrapCurve

Methods inherited from class java.lang.Object

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

Methods inherited from interface math.geom2d.curve.ContinuousCurve2D

getAsPolyline, getLeftTangent, getRightTangent, getSmoothPieces

Methods inherited from interface math.geom2d.curve.Curve2D

draw, getAsAWTShape, getContinuousCurves, getFirstPoint, getLastPoint, getSingularPoints, isSingular

Field Detail

xv

protected double xv

Coordinate of the vertex

yv

protected double yv

Coordinate of the vertex

theta

protected double theta

orientation of the parabola

a

protected double a

The parameter of the parabola. If positive, the parabola is direct.

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.

getConicType

public Conic2D.Type getConicType()

Specified by:

getConicType in interface Conic2D

getConicCoefficients

public double[] getConicCoefficients()

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:

getConicCoefficients in interface Conic2D

getEccentricity

public double getEccentricity()

Return 1, by definition for a parabola.

Specified by:

getEccentricity in interface Conic2D

getBoundaryCurves

public Collection<ContinuousBoundary2D> getBoundaryCurves()

Description copied from interface: Boundary2D

Returns the different continuous curves composing the boundary

Specified by:

getBoundaryCurves in interface Boundary2D

getDomain

public Domain2D getDomain()

Description copied from interface: Boundary2D

Returns the domain delimited by this boundary.

Specified by:

getDomain in interface Boundary2D

Returns:

the domain delimited by this boundary

getWindingAngle

public double getWindingAngle(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:

getWindingAngle in interface OrientedCurve2D

Parameters:

point - a point of the plane

Returns:

a signed angle

getSignedDistance

public double getSignedDistance(Point2D p)

Description copied from interface: OrientedCurve2D

Get the signed distance of the curve to the given point: this distance is positive if the point lies outside the shape, and is negative if the point lies inside the shape. In this case, absolute value of distance is equals to the distance to the border of the shape.

Specified by:

getSignedDistance in interface OrientedCurve2D

Parameters:

p - a point of the plane

Returns:

the signed distance to the curve

getSignedDistance

public double getSignedDistance(double x,
                                double y)

Description copied from interface: OrientedCurve2D

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

Specified by:

getSignedDistance 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.

getTangent

public Vector2D getTangent(double t)

Specified by:

getTangent in interface SmoothCurve2D

getCurvature

public double getCurvature(double t)

Returns the curvature of the parabola at the given position.

Specified by:

getCurvature in interface SmoothCurve2D

isClosed

public boolean isClosed()

Returns false, as a parabola is an open curve.

Specified by:

isClosed in interface ContinuousCurve2D

getT0

public double getT0()

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

Specified by:

getT0 in interface Curve2D

getT1

public double getT1()

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

Specified by:

getT1 in interface Curve2D

getPoint

public Point2D getPoint(double t)

Description copied from interface: Curve2D

Gets the point from a parametric representation of 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:

getPoint in interface Curve2D

getPosition

public double getPosition(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:

getPosition in interface Curve2D

Parameters:

point - a point belonging to the curve

Returns:

the position of the point on the curve

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

getIntersections

public Collection<Point2D> getIntersections(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:

getIntersections in interface Curve2D

getReverseCurve

public Parabola2D getReverseCurve()

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

Specified by:

getReverseCurve in interface Conic2D

Specified by:

getReverseCurve in interface ContinuousCurve2D

Specified by:

getReverseCurve in interface Curve2D

Specified by:

getReverseCurve in interface SmoothCurve2D

Specified by:

getReverseCurve in interface Boundary2D

Specified by:

getReverseCurve in interface ContinuousBoundary2D

Specified by:

getReverseCurve in interface ContinuousOrientedCurve2D

Specified by:

getReverseCurve in interface OrientedCurve2D

getSubCurve

public ParabolaArc2D getSubCurve(double t0,
                                 double t1)

Returns a new ParabolaArc2D, or null if t1

Specified by:

getSubCurve in interface ContinuousCurve2D

Specified by:

getSubCurve in interface Curve2D

Specified by:

getSubCurve in interface SmoothCurve2D

Specified by:

getSubCurve 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.

getDistance

public double getDistance(Point2D p)

Description copied from interface: Shape2D

get 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:

getDistance in interface Shape2D

getDistance

public double getDistance(double x,
                          double y)

Description copied from interface: Shape2D

get 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:

getDistance in interface Shape2D

appendPath

public GeneralPath appendPath(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(Graphics2D g2)

Throws an infiniteShapeException

Specified by:

fill in interface Boundary2D

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

getBoundingBox

public Box2D getBoundingBox()

Description copied from interface: Shape2D

Returns the bounding box of the shape.

Specified by:

getBoundingBox 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 ContinuousBoundary2D

Specified by:

transform in interface ContinuousOrientedCurve2D

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

toString

public String toString()

Overrides:

toString in class Object

equals

public boolean equals(Object obj)

Overrides:

equals in class 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