QuadBezierCurve2D

Documentation of 'math.geom2d.spline.QuadBezierCurve2D' Java class QuadBezierCurve2D

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java.lang.Object
- math.geom2d.curve.AbstractContinuousCurve2D
- - math.geom2d.curve.AbstractSmoothCurve2D
  - - math.geom2d.spline.QuadBezierCurve2D

All Implemented Interfaces:

java.lang.Cloneable, ContinuousCurve2D, Curve2D, SmoothCurve2D, ContinuousOrientedCurve2D, OrientedCurve2D, GeometricObject2D, Shape2D
```
public class QuadBezierCurve2D
extends AbstractSmoothCurve2D
implements SmoothCurve2D, ContinuousOrientedCurve2D, java.lang.Cloneable
```
A quadratic Bezier curve, defined by 3 control points. The curve starts at the first control point and finished at the third control point. The second point is used to defined the curvature of the curve. From javaGeom 0.8.0, this shape does not extends. java.awt.geom.QuadCurve2D.Double anymore

Field Summary
- Fields inherited from interface math.geom2d.Shape2D
  ACCURACY

Constructor Summary

Constructors
Constructor and Description
`QuadBezierCurve2D()` Creates an empty quadratic bezier curve.
`QuadBezierCurve2D(double[][] coefs)` Build a new Bezier curve from its array of coefficients.
`QuadBezierCurve2D(double x1, double y1, double xctrl, double yctrl, double x2, double y2)` Build a new quadratic Bezier curve by specifying position of extreme points and position of control point.
`QuadBezierCurve2D(Point2D[] pts)`
`QuadBezierCurve2D(Point2D p1, Point2D ctrl, Point2D p2)` Build a new quadratic Bezier curve by specifying position of extreme points and position of control point.

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)` Append the path of the curve to the given path.
`Polyline2D`	`asPolyline(int n)` Converts this continuous curve to an instance of LinearCurve2D with the given number of edges.
`Box2D`	`boundingBox()` Returns the approximate bounding box of this curve.
`CurveSet2D<? extends QuadBezierCurve2D>`	`clip(Box2D box)` Clip the curve by a box.
`QuadBezierCurve2D`	`clone()` Deprecated. not necessary to clone immutable objects (0.11.2)
`boolean`	`contains(double x, double y)` Checks if the shape contains the planar point defined by (x,y).
`boolean`	`contains(Point2D p)` Checks if the shape contains the given point.
`static QuadBezierCurve2D`	`create(Point2D p1, Point2D p2, Point2D p3)` Deprecated. since 0.11.1
`double`	`curvature(double t)` Returns the curvature of the Curve.
`double`	`distance(double x, double y)` Computes approximated distance, computed on a polyline.
`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.
`boolean`	`equals(java.lang.Object obj)`
`Point2D`	`firstPoint()` Returns the first point of the curve, that corresponds to the first control point.
`Point2D`	`getControl()`
`Point2D`	`getCtrl()`
`java.awt.geom.GeneralPath`	`getGeneralPath()`
`Point2D`	`getP1()`
`Point2D`	`getP2()`
`double[][]`	`getParametric()` Returns the matrix of parametric representation of the line.
`double`	`getT0()` Deprecated. replaced by t0() (since 0.11.1).
`double`	`getT1()` Deprecated. replaced by t1() (since 0.11.1).
`java.util.Collection<Point2D>`	`intersections(LinearShape2D line)` Use approximation, by replacing Bezier curve with a polyline.
`boolean`	`isBounded()` Returns true, a cubic Bezier Curve is always bounded.
`boolean`	`isClosed()` Returns false, as a quadratic curve is never closed.
`boolean`	`isEmpty()` Returns true if the shape does not contain any point.
`boolean`	`isInside(Point2D pt)` Returns true if the point is 'inside' the domain bounded by the curve.
`Point2D`	`lastPoint()` Returns the last point of the curve, that corresponds to the third control point.
`Point2D`	`point(double t)` Returns the point located at the given position on the curve.
`double`	`position(Point2D point)` Computes position by approximating cubic spline with a polyline.
`double`	`project(Point2D point)` Computes position by approximating cubic spline with a polyline.
`QuadBezierCurve2D`	`reverse()` Returns the bezier curve given by control points taken in reverse order.
`double`	`signedDistance(double x, double y)` The same as distanceSigned(Point2D), but by passing 2 double as arguments.
`double`	`signedDistance(Point2D point)` Returns the signed distance of the curve to the given point.
`QuadBezierCurve2D`	`subCurve(double t0, double t1)` Computes portion of BezierCurve.
`double`	`t0()` Returns 0, as Bezier curve is parameterized between 0 and 1.
`double`	`t1()` Returns 1, as Bezier curve is parametrized between 0 and 1.
`Vector2D`	`tangent(double t)` Returns the tangent of the curve at the given position.
`QuadBezierCurve2D`	`transform(AffineTransform2D trans)` Returns the Bezier Curve transformed by the given AffineTransform2D.
`double`	`windingAngle(Point2D point)` Use winding angle of approximated polyline

Methods inherited from class math.geom2d.curve.AbstractSmoothCurve2D
isSingular, leftTangent, normal, rightTangent, singularPoints, smoothPieces, vertices

Methods inherited from class math.geom2d.curve.AbstractContinuousCurve2D
asAwtShape, continuousCurves, draw

Methods inherited from class java.lang.Object
getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface math.geom2d.curve.SmoothCurve2D
normal

Methods inherited from interface math.geom2d.curve.ContinuousCurve2D
leftTangent, rightTangent, smoothPieces

Methods inherited from interface math.geom2d.curve.Curve2D
asAwtShape, continuousCurves, draw, isSingular, singularPoints, vertices

- Constructor Detail
  - QuadBezierCurve2D
```
public QuadBezierCurve2D()
```
    Creates an empty quadratic bezier curve.
  - QuadBezierCurve2D
```
public QuadBezierCurve2D(double[][] coefs)
```
    Build a new Bezier curve from its array of coefficients. The array must have size 2*3.
    
    Parameters:
    
    coefs - the coefficients of the QuadBezierCurve2D.
  - QuadBezierCurve2D
```
public QuadBezierCurve2D(Point2D p1,
                         Point2D ctrl,
                         Point2D p2)
```
    Build a new quadratic Bezier curve by specifying position of extreme points and position of control point. The resulting curve is totally contained in the convex polygon formed by the 3 control points.
    
    Parameters:
    
    p1 - first point
    
    ctrl - control point
    
    p2 - last point
  - QuadBezierCurve2D
```
public QuadBezierCurve2D(Point2D[] pts)
```
  - QuadBezierCurve2D
```
public QuadBezierCurve2D(double x1,
                         double y1,
                         double xctrl,
                         double yctrl,
                         double x2,
                         double y2)
```
    Build a new quadratic Bezier curve by specifying position of extreme points and position of control point. The resulting curve is totally contained in the convex polygon formed by the 3 control points.
- Method Detail
  - create
```
@Deprecated
public static QuadBezierCurve2D create(Point2D p1,
                                                   Point2D p2,
                                                   Point2D p3)
```
    Deprecated. since 0.11.1
    
    Static factory for creating a new Quadratic Bezier curve from 3 points.
  - getControl
```
public Point2D getControl()
```
  - getP1
```
public Point2D getP1()
```
  - getP2
```
public Point2D getP2()
```
  - getCtrl
```
public Point2D getCtrl()
```
  - getParametric
```
public double[][] getParametric()
```
    Returns the matrix of parametric representation of the line. Result is a 2x3 array with coefficients:
    [ cx0 cx1 cx2]
    [ cy0 cy1 cy2]
    Coefficients are from the parametric equation : x(t) = cx0 + cx1*t + cx2*t^2 y(t) = cy0 + cy1*t + cy2*t^2
  - windingAngle
```
public double windingAngle(Point2D point)
```
    Use winding angle of approximated polyline
    
    Specified by:
    
    windingAngle in interface OrientedCurve2D
    
    Parameters:
    
    point - a point of the plane
    
    Returns:
    
    a signed angle
    
    See Also:
    
    OrientedCurve2D.windingAngle(Point2D)
  - isInside
```
public boolean isInside(Point2D pt)
```
    Returns true if the point is 'inside' the domain bounded by the curve. Uses a polyline approximation.
    
    Specified by:
    
    isInside in interface OrientedCurve2D
    
    Parameters:
    
    pt - a point in the plane
    
    Returns:
    
    true if the point is on the left side of the curve.
  - signedDistance
```
public double signedDistance(Point2D point)
```
    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:
    
    point - 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
    
    See Also:
    
    OrientedCurve2D.signedDistance(Point2D)
  - 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 Curve.
    
    Specified by:
    
    curvature in interface ContinuousCurve2D
    
    Parameters:
    
    t - the position on the curve
    
    Returns:
    
    the curvature of the curve for position t
  - isClosed
```
public boolean isClosed()
```
    Returns false, as a quadratic curve is never closed.
    
    Specified by:
    
    isClosed in interface ContinuousCurve2D
  - asPolyline
```
public Polyline2D asPolyline(int n)
```
    Description copied from class: AbstractContinuousCurve2D
    
    Converts this continuous curve to an instance of LinearCurve2D with the given number of edges. Returns either an instance of Polyline2D or LinearRing2D, depending on the curve is closed or not. This method can be overridden to return the correct type.
    
    Specified by:
    
    asPolyline in interface ContinuousCurve2D
    
    Overrides:
    
    asPolyline in class AbstractContinuousCurve2D
    
    Parameters:
    
    n - the number of line segments
    
    Returns:
    
    a polyline with n line segments.
    
    See Also:
    
    ContinuousCurve2D.asPolyline(int)
  - t0
```
public double t0()
```
    Returns 0, as Bezier curve is parameterized between 0 and 1.
    
    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 1, as Bezier curve is parametrized between 0 and 1.
    
    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
  - intersections
```
public java.util.Collection<Point2D> intersections(LinearShape2D line)
```
    Use approximation, by replacing Bezier curve with a polyline.
    
    Specified by:
    
    intersections in interface Curve2D
    
    See Also:
    
    Curve2D.intersections(math.geom2d.line.LinearShape2D)
  - 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
    
    See Also:
    
    Curve2D.point(double)
  - firstPoint
```
public Point2D firstPoint()
```
    Returns the first point of the curve, that corresponds to the first control point.
    
    Specified by:
    
    firstPoint in interface Curve2D
    
    Overrides:
    
    firstPoint in class AbstractContinuousCurve2D
    
    Returns:
    
    the first point of the curve
    
    See Also:
    
    Curve2D.t0(), Curve2D.point(double)
  - lastPoint
```
public Point2D lastPoint()
```
    Returns the last point of the curve, that corresponds to the third control point.
    
    Specified by:
    
    lastPoint in interface Curve2D
    
    Overrides:
    
    lastPoint in class AbstractContinuousCurve2D
    
    Returns:
    
    the last point of the curve.
    
    See Also:
    
    Curve2D.t1(), Curve2D.point(double)
  - position
```
public double position(Point2D point)
```
    Computes position by approximating cubic spline with a polyline.
    
    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)
```
    Computes position by approximating cubic spline with a polyline.
    
    Specified by:
    
    project in interface Curve2D
    
    Parameters:
    
    point - a point to project
    
    Returns:
    
    the position of the closest orthogonal projection
  - reverse
```
public QuadBezierCurve2D reverse()
```
    Returns the bezier curve given by control points taken in reverse order.
    
    Specified by:
    
    reverse in interface ContinuousCurve2D
    
    Specified by:
    
    reverse in interface Curve2D
    
    Specified by:
    
    reverse in interface SmoothCurve2D
    
    Specified by:
    
    reverse in interface ContinuousOrientedCurve2D
    
    Specified by:
    
    reverse in interface OrientedCurve2D
  - subCurve
```
public QuadBezierCurve2D subCurve(double t0,
                                  double t1)
```
    Computes portion of BezierCurve. 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.
  - 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 p)
```
    Description copied from interface: Shape2D
    
    Checks if the shape contains the given point.
    
    Specified by:
    
    contains in interface Shape2D
  - 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
    
    See Also:
    
    Shape2D.distance(Point2D)
  - distance
```
public double distance(double x,
                       double y)
```
    Computes approximated distance, computed on a polyline.
    
    Specified by:
    
    distance in interface Shape2D
    
    See Also:
    
    Shape2D.distance(double, double)
  - isBounded
```
public boolean isBounded()
```
    Returns true, a cubic Bezier Curve is always bounded.
    
    Specified by:
    
    isBounded in interface Shape2D
  - isEmpty
```
public boolean isEmpty()
```
    Description copied from interface: Shape2D
    
    Returns true if the shape does not contain any point. This is the case for example for PointSet2D without any point.
    
    Specified by:
    
    isEmpty in interface Shape2D
    
    Returns:
    
    true if the shape does not contain any point.
  - clip
```
public CurveSet2D<? extends QuadBezierCurve2D> clip(Box2D box)
```
    Clip the curve by a box. The result is an instance of CurveSet2D, which contains only instances of QuadBezierCurve2D. If the curve is not clipped, the result is an instance of CurveSet2D which contains 0 curves.
    
    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()
```
    Returns the approximate bounding box of this curve. Actually, computes the bounding box of the set of control points.
    
    Specified by:
    
    boundingBox in interface Shape2D
    
    Returns:
    
    the bounding box of the shape.
  - transform
```
public QuadBezierCurve2D transform(AffineTransform2D trans)
```
    Returns the Bezier Curve transformed by the given AffineTransform2D. This is simply done by transforming control points of the curve.
    
    Specified by:
    
    transform in interface ContinuousCurve2D
    
    Specified by:
    
    transform in interface Curve2D
    
    Specified by:
    
    transform in interface SmoothCurve2D
    
    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
  - appendPath
```
public java.awt.geom.GeneralPath appendPath(java.awt.geom.GeneralPath path)
```
    Description copied from interface: ContinuousCurve2D
    
    Append the path of the curve to the given path.
    
    Specified by:
    
    appendPath in interface ContinuousCurve2D
    
    Parameters:
    
    path - a path to modify
    
    Returns:
    
    the modified path
  - getGeneralPath
```
public java.awt.geom.GeneralPath getGeneralPath()
```
  - 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
  - equals
```
public boolean equals(java.lang.Object obj)
```
    Overrides:
    
    equals in class java.lang.Object
  - clone
```
@Deprecated
public QuadBezierCurve2D clone()
```
    Deprecated. not necessary to clone immutable objects (0.11.2)
    
    Specified by:
    
    clone in interface Curve2D
    
    Specified by:
    
    clone in class AbstractSmoothCurve2D

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Class QuadBezierCurve2D

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.SmoothCurve2D

Methods inherited from interface math.geom2d.curve.ContinuousCurve2D

Methods inherited from interface math.geom2d.curve.Curve2D

Constructor Detail

QuadBezierCurve2D

QuadBezierCurve2D

QuadBezierCurve2D

QuadBezierCurve2D

QuadBezierCurve2D

Method Detail

create

getControl

getP1

getP2

getCtrl

getParametric

windingAngle

isInside

signedDistance

signedDistance

tangent

curvature

isClosed

asPolyline

t0

getT0

t1

getT1

intersections

point

firstPoint

lastPoint

position

project

reverse

subCurve

contains

contains

distance

distance

isBounded

isEmpty

clip

boundingBox

transform

appendPath

getGeneralPath

almostEquals

equals

clone