math.geom2d.spline
Class CubicBezierCurve2D

java.lang.Object
  math.geom2d.curve.AbstractContinuousCurve2D
      math.geom2d.curve.AbstractSmoothCurve2D
          math.geom2d.spline.CubicBezierCurve2D

All Implemented Interfaces:

Serializable, Cloneable, ContinuousCurve2D, Curve2D, SmoothCurve2D, ContinuousOrientedCurve2D, OrientedCurve2D, Shape2D

Direct Known Subclasses:

BezierCurve2D

public class CubicBezierCurve2D
extends AbstractSmoothCurve2D
implements SmoothCurve2D, ContinuousOrientedCurve2D, Cloneable

A cubic bezier curve, defined by 4 points. From javaGeom 0.8.0, this shape does not extends java.awt.geom.CubicCurve2D.Double anymore

Author:

Legland

See Also:

Serialized Form

Field Summary

protected double	ctrlx1
protected double	ctrlx2
protected double	ctrly1
protected double	ctrly2
protected double	x1
protected double	x2
protected double	y1
protected double	y2

Fields inherited from interface math.geom2d.Shape2D

ACCURACY

Constructor Summary

CubicBezierCurve2D()

CubicBezierCurve2D(double[][] coefs)
Build a new Bezier curve from its array of coefficients.

CubicBezierCurve2D(double x1, double y1, double xctrl1, double yctrl1, double xctrl2, double yctrl2, double x2, double y2)
Build a new Bezier curve of degree 3 by specifying position of extreme points and position of 2 control points.

CubicBezierCurve2D(Point2D p1, Point2D ctrl1, Point2D ctrl2, Point2D p2)
Build a new Bezier curve of degree 3 by specifying position of extreme points and position of 2 control points.

CubicBezierCurve2D(Point2D p1, Vector2D v1, Point2D p2, Vector2D v2)
Build a new Bezier curve of degree 3 by specifying position and tangent of first and last points.

Method Summary

GeneralPath	appendPath(GeneralPath path) Append the path of the curve to the given path.
CurveSet2D<? extends CubicBezierCurve2D>	clip(Box2D box) Clip the Bezier curve by a box.
CubicBezierCurve2D	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 p) Checks if the shape contains the given point.
static CubicBezierCurve2D	create(Point2D p1, Point2D c1, Point2D c2, Point2D p2)
static CubicBezierCurve2D	create(Point2D p1, Vector2D v1, Point2D p2, Vector2D v2)
boolean	equals(Object obj)
Box2D	getBoundingBox() Returns the bounding box of the shape.
Point2D	getControl1()
Point2D	getControl2()
Point2D	getCtrlP1()
Point2D	getCtrlP2()
double	getCurvature(double t) returns the curvature of the Curve.
double	getDistance(double x, double y) Compute approximated distance, computed on a polyline.
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.
Point2D	getFirstPoint() Returns the first point of the curve.
GeneralPath	getGeneralPath()
Collection<Point2D>	getIntersections(LinearShape2D line) Use approximation, by replacing Bezier curve with a polyline.
Point2D	getLastPoint() Returns the last point of the curve.
Point2D	getP1()
Point2D	getP2()
double[][]	getParametric() Returns the matrix of parametric representation of the line.
Point2D	getPoint(double t) Gets the point from a parametric representation of the curve.
double	getPosition(Point2D point) Computes position by approximating cubic spline with a polyline.
CubicBezierCurve2D	getReverseCurve() Returns the Bezier curve given by control points taken in reverse order.
double	getSignedDistance(double x, double y) The same as getSignedDistance(Point2D), but by passing 2 double as arguments.
double	getSignedDistance(Point2D point) 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.
CubicBezierCurve2D	getSubCurve(double t0, double t1) Computes portion of BezierCurve.
double	getT0() returns 0, as Bezier curve is parameterized between 0 and 1.
double	getT1() Returns 1, as Bezier curve is parameterized between 0 and 1.
Vector2D	getTangent(double t)
double	getWindingAngle(Point2D point) Use winding angle of approximated polyline
boolean	isBounded() Returns true, a cubic Bezier Curve is always bounded.
boolean	isClosed() The cubic curve is never closed.
boolean	isEmpty() Returns true if the shape does not contain any point.
boolean	isInside(Point2D pt) return true if the point is 'inside' the domain bounded by the curve.
double	project(Point2D point) Computes position by approximating cubic spline with a polyline.
CubicBezierCurve2D	transform(AffineTransform2D trans) Returns the Bezier Curve transformed by the given AffineTransform2D.

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, wrapCurve

Methods inherited from class java.lang.Object

finalize, getClass, hashCode, notify, notifyAll, toString, 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, getSingularPoints, isSingular

Field Detail

x1

protected double x1

y1

protected double y1

ctrlx1

protected double ctrlx1

ctrly1

protected double ctrly1

ctrlx2

protected double ctrlx2

ctrly2

protected double ctrly2

x2

protected double x2

y2

protected double y2

Constructor Detail

CubicBezierCurve2D

public CubicBezierCurve2D()

CubicBezierCurve2D

public CubicBezierCurve2D(double[][] coefs)

Build a new Bezier curve from its array of coefficients. The array must have size 2*4.

Parameters:

coefs - the coefficients of the CubicBezierCurve2D.

CubicBezierCurve2D

public CubicBezierCurve2D(Point2D p1,
                          Point2D ctrl1,
                          Point2D ctrl2,
                          Point2D p2)

Build a new Bezier curve of degree 3 by specifying position of extreme points and position of 2 control points. The resulting curve is totally contained in the convex polygon formed by the 4 control points.

Parameters:

p1 - first point

ctrl1 - first control point

ctrl2 - second control point

p2 - last point

CubicBezierCurve2D

public CubicBezierCurve2D(Point2D p1,
                          Vector2D v1,
                          Point2D p2,
                          Vector2D v2)

Build a new Bezier curve of degree 3 by specifying position and tangent of first and last points.

Parameters:

p1 - first point

v1 - first tangent vector

p2 - position of last point

v2 - last tangent vector

CubicBezierCurve2D

public CubicBezierCurve2D(double x1,
                          double y1,
                          double xctrl1,
                          double yctrl1,
                          double xctrl2,
                          double yctrl2,
                          double x2,
                          double y2)

Build a new Bezier curve of degree 3 by specifying position of extreme points and position of 2 control points. The resulting curve is totally containe in the convex polygon formed by the 4 control points.

Method Detail

create

public static final CubicBezierCurve2D create(Point2D p1,
                                              Point2D c1,
                                              Point2D c2,
                                              Point2D p2)

create

public static final CubicBezierCurve2D create(Point2D p1,
                                              Vector2D v1,
                                              Point2D p2,
                                              Vector2D v2)

getControl1

public Point2D getControl1()

getControl2

public Point2D getControl2()

getP1

public Point2D getP1()

getP2

public Point2D getP2()

getCtrlP1

public Point2D getCtrlP1()

getCtrlP2

public Point2D getCtrlP2()

getParametric

public double[][] getParametric()

Returns the matrix of parametric representation of the line. Result has the form :

[ x0 dx dx2 dx3]

[ y0 dy dy2 dy3]

Coefficients are from the parametric equation : x(t) = x0 + dx*t + dx2*t^2 + dx3*t^3 y(t) = y0 + dy*t + dy2*t^2 + dy3*t^3

getWindingAngle

public double getWindingAngle(Point2D point)

Use winding angle of approximated polyline

Specified by:

getWindingAngle in interface OrientedCurve2D

Parameters:

point - a point of the plane

Returns:

a signed angle

See Also:

OrientedCurve2D.getWindingAngle(java.awt.geom.Point2D)

isInside

public boolean isInside(Point2D pt)

return 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.

getSignedDistance

public double getSignedDistance(Point2D point)

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:

point - 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

See Also:

OrientedCurve2D.getSignedDistance(java.awt.geom.Point2D)

getTangent

public Vector2D getTangent(double t)

Specified by:

getTangent in interface SmoothCurve2D

getCurvature

public double getCurvature(double t)

returns the curvature of the Curve.

Specified by:

getCurvature in interface SmoothCurve2D

isClosed

public boolean isClosed()

The cubic curve is never closed.

Specified by:

isClosed in interface ContinuousCurve2D

getT0

public double getT0()

returns 0, as Bezier curve is parameterized between 0 and 1.

Specified by:

getT0 in interface Curve2D

getT1

public double getT1()

Returns 1, as Bezier curve is parameterized between 0 and 1.

Specified by:

getT1 in interface Curve2D

getIntersections

public Collection<Point2D> getIntersections(LinearShape2D line)

Use approximation, by replacing Bezier curve with a polyline.

Specified by:

getIntersections in interface Curve2D

See Also:

Curve2D.getIntersections(math.geom2d.line.LinearShape2D)

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

See Also:

Curve2D.getPoint(double)

getFirstPoint

public Point2D getFirstPoint()

Returns the first point of the curve.

Specified by:

getFirstPoint in interface Curve2D

Overrides:

getFirstPoint in class AbstractContinuousCurve2D

Returns:

the first point of the curve

getLastPoint

public Point2D getLastPoint()

Returns the last point of the curve.

Specified by:

getLastPoint in interface Curve2D

Overrides:

getLastPoint in class AbstractContinuousCurve2D

Returns:

the last point of the curve.

getPosition

public double getPosition(Point2D point)

Computes position by approximating cubic spline with a polyline.

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)

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

getReverseCurve

public CubicBezierCurve2D getReverseCurve()

Returns the Bezier curve given by control points taken in reverse order.

Specified by:

getReverseCurve in interface ContinuousCurve2D

Specified by:

getReverseCurve in interface Curve2D

Specified by:

getReverseCurve in interface SmoothCurve2D

Specified by:

getReverseCurve in interface ContinuousOrientedCurve2D

Specified by:

getReverseCurve in interface OrientedCurve2D

getSubCurve

public CubicBezierCurve2D getSubCurve(double t0,
                                      double t1)

Computes portion of BezierCurve. 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.

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

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

See Also:

Shape2D.getDistance(java.awt.geom.Point2D)

getDistance

public double getDistance(double x,
                          double y)

Compute approximated distance, computed on a polyline.

Specified by:

getDistance in interface Shape2D

See Also:

Shape2D.getDistance(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 CubicBezierCurve2D> clip(Box2D box)

Clip the Bezier curve by a box. Return a set of CubicBezierCurve2D.

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 CubicBezierCurve2D 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 GeneralPath appendPath(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 GeneralPath getGeneralPath()

equals

public boolean equals(Object obj)

Overrides:

equals in class Object

clone

public CubicBezierCurve2D 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