math.geom2d.conic
Class Parabola2D

java.lang.Object
  math.geom2d.conic.Parabola2D

All Implemented Interfaces:

java.awt.Shape, Conic2D, Boundary2D, ContinuousBoundary2D, ContinuousCurve2D, ContinuousOrientedCurve2D, Curve2D, OrientedCurve2D, SmoothCurve2D, SmoothOrientedCurve2D, Shape2D

public class Parabola2D
extends java.lang.Object
implements SmoothOrientedCurve2D, Conic2D, ContinuousBoundary2D

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

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.conic.Conic2D

CIRCLE, ELLIPSE, HYPERBOLA, NOT_A_CONIC, PARABOLA, POINT, STRAIGHT_LINE, TWO_LINES

Fields inherited from interface math.geom2d.curve.ContinuousCurve2D

CLOSED_EDGE, LOOP, OPEN_EDGE

Fields inherited from interface math.geom2d.Shape2D

ACCURACY, defaultClipWindow, EMPTY_SET

Constructor Summary

Parabola2D()

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

Parabola2D(Point2D vertex, double a, double theta)

Method Summary

java.awt.geom.GeneralPath	appendPath(java.awt.geom.GeneralPath path) returns the appended path of a ParabolaArc2D, with -100
CurveSet2D<ParabolaArc2D>	clip(Box2D box) Clip the parabola by a box.
boolean	contains(double x, double y)
boolean	contains(double arg0, double arg1, double arg2, double arg3) return false, as every curve.
boolean	contains(java.awt.geom.Point2D point)
boolean	contains(java.awt.geom.Rectangle2D arg0) return false, as every curve.
boolean	equals(java.lang.Object obj)
double	getAngle() Return orientation angle of parabola.
Polyline2D	getAsPolyline(int n) return the polyline of the parabola arc from t=-100 to t=100.
java.util.Collection<ContinuousBoundary2D>	getBoundaryCurves() Return the different continuous curves composing the boundary
Box2D	getBoundingBox() Returns the bounding box of the shape.
java.awt.Rectangle	getBounds() Return bounding box of the shape.
java.awt.geom.Rectangle2D	getBounds2D() Return more precise bounds for the shape.
double[]	getCartesianEquation() Return the coefficient of the cartesian representation of the conic.
Point2D	getCenter()
int	getConicType()
java.util.Collection<ContinuousCurve2D>	getContinuousCurves() Returns the collection of continuous curves which constitute this curve.
double	getCurvature(double t) returns the curvature of the ellipse.
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(java.awt.geom.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.
double	getEccentricity() Return 1, by definition for a parabola.
Point2D	getFirstPoint() return the constant Point2D.INFINITY_POINT.
Point2D	getFocus()
Point2D	getFocus1()
Point2D	getFocus2() Always return Point2D.INFINITY_POINT.
java.awt.geom.GeneralPath	getGeneralPath() compute path of a ParabolaArc2D with -100
java.util.Collection<Point2D>	getIntersections(StraightObject2D line) Returns the intersection points of the curve with the specified line.
Point2D	getLastPoint() return the constant Point2D.INFINITY_POINT.
double	getLength1() return 0.
double	getLength2() return 0.
java.awt.geom.PathIterator	getPathIterator(java.awt.geom.AffineTransform trans) return path iterator of a ParabolaArc2D with -100
java.awt.geom.PathIterator	getPathIterator(java.awt.geom.AffineTransform trans, double flatness) return path iterator of a ParabolaArc2D with -100
Point2D	getPoint(double t) Gets the point from a parametric representation of the curve.
Point2D	getPoint(double t, Point2D point) Same as getPoint(t), but gives the point as a parameter.
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(java.awt.geom.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.
java.util.Collection<? extends SmoothCurve2D>	getSmoothPieces() Returns a set of smooth curves.
ParabolaArc2D	getSubCurve(double t0, double t1) return 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() return the first vector of the parabola
Vector2D	getVector2() return second director vector of the parabola.
double	getWindingAngle(java.awt.geom.Point2D point) Return the angle portion that the curve turn around the given point.
boolean	intersects(double xr, double yr, double wr, double hr) Returns true if one of the edges of the rectangle intersects the parabola.
boolean	intersects(java.awt.geom.Rectangle2D rect) Returns true if one of the edges of the rectangle intersects the parabola.
boolean	isBounded() Always returns false, because a parabola is not bounded.
boolean	isCircle()
boolean	isClosed() Return true if the curve makes a loop, that is come back to starting point after covering the path.
boolean	isDegenerated()
boolean	isDirect() at the moment, return true.
boolean	isEllipse()
boolean	isHyperbola()
boolean	isInside(java.awt.geom.Point2D point) return true if the point is 'inside' the domain bounded by the curve.
boolean	isParabola()
boolean	isPoint()
boolean	isStraightLine()
boolean	isTwoLines()
double	project(Point2D point) Returns position of point on the parabola.
Parabola2D	transform(AffineTransform2D trans) Transforms the curve by an affine transform.

Methods inherited from class java.lang.Object

clone, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

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

getFocus

public Point2D getFocus()

getConicType

public int getConicType()

Specified by:

getConicType in interface Conic2D

isEllipse

public boolean isEllipse()

isParabola

public boolean isParabola()

isHyperbola

public boolean isHyperbola()

isCircle

public boolean isCircle()

isStraightLine

public boolean isStraightLine()

isTwoLines

public boolean isTwoLines()

isPoint

public boolean isPoint()

isDegenerated

public boolean isDegenerated()

getCartesianEquation

public double[] getCartesianEquation()

Description copied from interface: Conic2D

Return 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:

getCartesianEquation in interface Conic2D

getCenter

public Point2D getCenter()

getFocus1

public Point2D getFocus1()

getFocus2

public Point2D getFocus2()

Always return Point2D.INFINITY_POINT.

getVector1

public Vector2D getVector1()

return the first vector of the parabola

getVector2

public Vector2D getVector2()

return second director vector of the parabola.

getLength1

public double getLength1()

return 0.

getLength2

public double getLength2()

return 0.

getEccentricity

public double getEccentricity()

Return 1, by definition for a parabola.

Specified by:

getEccentricity in interface Conic2D

getAngle

public double getAngle()

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

isDirect

public boolean isDirect()

at the moment, return true.

getBoundaryCurves

public java.util.Collection<ContinuousBoundary2D> getBoundaryCurves()

Description copied from interface: Boundary2D

Return the different continuous curves composing the boundary

Specified by:

getBoundaryCurves in interface Boundary2D

getWindingAngle

public double getWindingAngle(java.awt.geom.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(java.awt.geom.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(java.awt.geom.Point2D point)

Description copied from interface: OrientedCurve2D

return 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.

getTangent

public Vector2D getTangent(double t)

Specified by:

getTangent in interface SmoothCurve2D

getCurvature

public double getCurvature(double t)

returns the curvature of the ellipse.

Specified by:

getCurvature in interface SmoothCurve2D

getAsPolyline

public Polyline2D getAsPolyline(int n)

return the polyline of the parabola arc from t=-100 to t=100.

Specified by:

getAsPolyline in interface ContinuousCurve2D

Parameters:

n - the number of line segments

Returns:

a closed polyline with n line segments.

getSmoothPieces

public java.util.Collection<? extends SmoothCurve2D> getSmoothPieces()

Description copied from interface: ContinuousCurve2D

Returns a set of smooth curves.

Specified by:

getSmoothPieces in interface ContinuousCurve2D

isClosed

public boolean isClosed()

Description copied from interface: ContinuousCurve2D

Return true if the curve makes a loop, that is come back to starting point after covering the path.

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

getPoint

public Point2D getPoint(double t,
                        Point2D point)

Description copied from interface: Curve2D

Same as getPoint(t), but gives the point as a parameter. This avoids repetitive memory allocations.

Specified by:

getPoint in interface Curve2D

getFirstPoint

public Point2D getFirstPoint()

return the constant Point2D.INFINITY_POINT.

Specified by:

getFirstPoint in interface Curve2D

Returns:

the first point of the curve

getLastPoint

public Point2D getLastPoint()

return the constant Point2D.INFINITY_POINT.

Specified by:

getLastPoint in interface Curve2D

Returns:

the last point of the curve.

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 java.util.Collection<Point2D> getIntersections(StraightObject2D 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 Boundary2D

Specified by:

getReverseCurve in interface ContinuousBoundary2D

Specified by:

getReverseCurve in interface ContinuousCurve2D

Specified by:

getReverseCurve in interface ContinuousOrientedCurve2D

Specified by:

getReverseCurve in interface Curve2D

Specified by:

getReverseCurve in interface OrientedCurve2D

Specified by:

getReverseCurve in interface SmoothCurve2D

Specified by:

getReverseCurve in interface SmoothOrientedCurve2D

getContinuousCurves

public java.util.Collection<ContinuousCurve2D> getContinuousCurves()

Description copied from interface: Curve2D

Returns the collection of continuous curves which constitute this curve.

Specified by:

getContinuousCurves in interface Curve2D

Returns:

a collection of continuous curves.

getSubCurve

public ParabolaArc2D getSubCurve(double t0,
                                 double t1)

return a new ParabolaArc2D, or null if t1

Specified by:

getSubCurve in interface ContinuousCurve2D

Specified by:

getSubCurve in interface ContinuousOrientedCurve2D

Specified by:

getSubCurve in interface Curve2D

Specified by:

getSubCurve in interface SmoothCurve2D

Specified by:

getSubCurve 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.

getDistance

public double getDistance(java.awt.geom.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

isBounded

public boolean isBounded()

Always returns false, because a parabola is not bounded.

Specified by:

isBounded in interface Shape2D

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 ContinuousOrientedCurve2D

Specified by:

clip in interface Curve2D

Specified by:

clip in interface OrientedCurve2D

Specified by:

clip in interface SmoothCurve2D

Specified by:

clip in interface SmoothOrientedCurve2D

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)

Description copied from interface: Curve2D

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

Specified by:

transform in interface Conic2D

Specified by:

transform in interface Boundary2D

Specified by:

transform in interface ContinuousBoundary2D

Specified by:

transform in interface ContinuousCurve2D

Specified by:

transform in interface ContinuousOrientedCurve2D

Specified by:

transform in interface Curve2D

Specified by:

transform in interface OrientedCurve2D

Specified by:

transform in interface SmoothCurve2D

Specified by:

transform in interface SmoothOrientedCurve2D

Specified by:

transform in interface Shape2D

Parameters:

trans - an affine transform

Returns:

the transformed shape

getBounds

public java.awt.Rectangle getBounds()

Return bounding box of the shape.

Specified by:

getBounds in interface java.awt.Shape

getBounds2D

public java.awt.geom.Rectangle2D getBounds2D()

Return more precise bounds for the shape.

Specified by:

getBounds2D in interface java.awt.Shape

contains

public boolean contains(double x,
                        double y)

Specified by:

contains in interface java.awt.Shape

contains

public boolean contains(java.awt.geom.Point2D point)

Specified by:

contains in interface java.awt.Shape

intersects

public boolean intersects(double xr,
                          double yr,
                          double wr,
                          double hr)

Returns true if one of the edges of the rectangle intersects the parabola.

Specified by:

intersects in interface java.awt.Shape

intersects

public boolean intersects(java.awt.geom.Rectangle2D rect)

Returns true if one of the edges of the rectangle intersects the parabola.

Specified by:

intersects in interface java.awt.Shape

contains

public boolean contains(double arg0,
                        double arg1,
                        double arg2,
                        double arg3)

return false, as every curve.

Specified by:

contains in interface java.awt.Shape

contains

public boolean contains(java.awt.geom.Rectangle2D arg0)

return false, as every curve.

Specified by:

contains in interface java.awt.Shape

appendPath

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

returns the appended path of a ParabolaArc2D, with -100

Specified by:

appendPath in interface ContinuousCurve2D

Parameters:

path - a path to modify

Returns:

the modified path

getGeneralPath

public java.awt.geom.GeneralPath getGeneralPath()

compute path of a ParabolaArc2D with -100

getPathIterator

public java.awt.geom.PathIterator getPathIterator(java.awt.geom.AffineTransform trans)

return path iterator of a ParabolaArc2D with -100

Specified by:

getPathIterator in interface java.awt.Shape

getPathIterator

public java.awt.geom.PathIterator getPathIterator(java.awt.geom.AffineTransform trans,
                                                  double flatness)

return path iterator of a ParabolaArc2D with -100

Specified by:

getPathIterator in interface java.awt.Shape

equals

public boolean equals(java.lang.Object obj)

Overrides:

equals in class java.lang.Object