Parabola2D

Documentation of 'math.geom2d.conic.Parabola2D' Java class Parabola2D

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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).

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

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

Method Summary

All Methods Static Methods Instance Methods Concrete Methods Deprecated Methods
Modifier and Type	Method and Description
`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()` Deprecated. use copy constructor instead (0.11.2)
`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.
`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()
```
    Empty constructor.
  - 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
```
@Deprecated
public Parabola2D clone()
```
    Deprecated. use copy constructor instead (0.11.2)
    
    Specified by:
    
    clone in interface Curve2D
    
    Specified by:
    
    clone in class AbstractSmoothCurve2D

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Detail:
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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

Constructor Detail

Parabola2D

Parabola2D

Parabola2D

Method Detail

create

getFocus

getParameter

getFocusDistance

getVertex

getVector1

getVector2

getAngle

isDirect

conicType

conicCoefficients

eccentricity

domain

windingAngle

signedDistance

signedDistance

isInside

tangent

curvature

continuousCurves

isClosed

t0

getT0

t1

getT1

point

position

project

intersections

reverse

subCurve

distance

distance

appendPath

fill

isBounded

isEmpty

clip

boundingBox

transform

contains

contains

almostEquals

toString

equals

clone