Parabola2D (java-geom 3.3.1 API)

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

Fields
Modifier and Type	Field and Description
`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

Constructors
Constructor and Description
`Parabola2D()`
`Parabola2D(double xv, double yv, double a, double theta)`
`Parabola2D(Point2D vertex, double a, double theta)`

Method Summary

Methods
Modifier and Type	Method and Description
`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.
`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

Class Parabola2D

Nested Class Summary

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

Field Summary

Fields inherited from interface math.geom2d.Shape2D

Constructor Summary

Method Summary

Methods inherited from class math.geom2d.curve.AbstractSmoothCurve2D

Methods inherited from class math.geom2d.curve.AbstractContinuousCurve2D

Methods inherited from class java.lang.Object

Methods inherited from interface math.geom2d.curve.ContinuousCurve2D

Methods inherited from interface math.geom2d.curve.Curve2D

Field Detail

xv

yv

theta

a

Constructor Detail

Parabola2D

Parabola2D

Parabola2D

Method Detail

create

getFocus

getParameter

getFocusDistance

getVertex

getVector1

getVector2

getAngle

isDirect

getConicType

getConicCoefficients

getEccentricity

getBoundaryCurves

getDomain

getWindingAngle

getSignedDistance

getSignedDistance

isInside

getTangent

getCurvature

isClosed

getT0

getT1

getPoint

getPosition

project

getIntersections

getReverseCurve

getSubCurve

getDistance

getDistance

appendPath

fill

isBounded

isEmpty

clip

getBoundingBox

transform

contains

contains

toString

equals

clone