Package org.djutils.draw.curve

Class Bezier2d

java.lang.Object
org.djutils.draw.curve.Bezier2d
All Implemented Interfaces:
Curve<DirectedPoint2d,Double,Point2d,Flattener2d,PolyLine2d>, Curve2d, Flattener.FlattableCurve<Point2d,Double>
Direct Known Subclasses:
BezierCubic2d
public class Bezier2d extends Object implements Curve2d
Continuous definition of a Bézier curve in 2d. This class is simply a helper class for (and a super of) BezierCubic2d, which uses this class to determine curvature, offset lines, etc.

Copyright (c) 2023-2025 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved.
BSD-style license. See OpenTrafficSim License.

Author:
Alexander Verbraeck, Peter Knoppers, Wouter Schakel
See Also:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    protected final double[]
    x
    The x-coordinates of the points of this Bézier.
    protected final double[]
    y
    The y-coordinates of the points of this Bézier.

  • Constructor Summary

    Constructors
    Constructor
    Description
    Bezier2d(double[] x, double[] y)
    Create a Bézier curve of any order.
    Bezier2d(Point2d... points)
    Create a Bézier curve of any order.

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    curvature(double t)
    Returns the curvature at the given t value.
    Bezier2d
    derivative()
    Returns the derivative for a Bézier, which is a Bézier of 1 order lower.
    boolean
    equals(Object obj)
     
    double
    getLength()
    Return the length of this Curve.
    Point2d
    getPoint(double t)
    Returns the point at the given fraction of this Curve.
    double
    getX(int i)
    Retrieve the x-coordinate of the i'th point of this Bézier curve.
    double
    getY(int i)
    Retrieve the y-coordinate of the i'th point of this Bézier curve.
    int
    hashCode()
     
    int
    size()
    Return the number of points (or x-y pairs) that this Bézier curve is based on.
    PolyLine2d
    toPolyLine(Flattener2d flattener)
    Flatten a Curve into a PolyLine.
    String
    toString()
     

    Methods inherited from class java.lang.Object

    clone, finalize, getClass, notify, notifyAll, wait, wait, wait

    Methods inherited from interface org.djutils.draw.curve.Curve

    getKnots

    Methods inherited from interface org.djutils.draw.curve.Curve2d

    getDirection, getEndDirection, getEndPoint, getStartDirection, getStartPoint

  • Field Details

    • x

      protected final double[] x
      The x-coordinates of the points of this Bézier.

    • y

      protected final double[] y
      The y-coordinates of the points of this Bézier.

  • Constructor Details

    • Bezier2d

      public Bezier2d(Point2d... points)
      Create a Bézier curve of any order.
      Parameters:
      points - Point2d... shape points that define the Bézier curve
      Throws:
      NullPointerException - when points is null, or contains a null value
      IllegalArgumentException - when the length of points is less than 2

    • Bezier2d

      public Bezier2d(double[] x, double[] y)
      Create a Bézier curve of any order.
      Parameters:
      x - the x-coordinates of the points that define the Bézier curve
      y - the y-coordinates of the points that define the Bézier curve
      Throws:
      NullPointerException - when x, or y is null
      IllegalArgumentException - when the length of the x array is not equal to the length of the y array, or less than 2

  • Method Details

    • derivative

      public Bezier2d derivative()
      Returns the derivative for a Bézier, which is a Bézier of 1 order lower.
      Returns:
      derivative Bézier
      Throws:
      IllegalStateException - when the order of this Bezier2d is 1

    • size

      public int size()
      Return the number of points (or x-y pairs) that this Bézier curve is based on.
      Returns:
      the number of points (or x-y pairs) that this Bézier curve is based on

    • getX

      public double getX(int i)
      Retrieve the x-coordinate of the i'th point of this Bézier curve.
      Parameters:
      i - the index
      Returns:
      the x-coordinate of the i'th point of this Bézier curve
      Throws:
      IndexOutOfBoundsException - when i < 0, or i ≥ size()

    • getY

      public double getY(int i)
      Retrieve the y-coordinate of the i'th point of this Bézier curve.
      Parameters:
      i - the index
      Returns:
      the y-coordinate of the i'th point of this Bézier curve
      Throws:
      IndexOutOfBoundsException - when i < 0, or i ≥ size()

    • getPoint

      public Point2d getPoint(double t)
      Description copied from interface: Curve
      Returns the point at the given fraction of this Curve. The fraction may represent any parameter, such as t in a Bézier curve, s in a Clothoid, or simply the fraction of length.
      Specified by:
      getPoint in interface Curve<DirectedPoint2d,Double,Point2d,Flattener2d,PolyLine2d>
      Specified by:
      getPoint in interface Flattener.FlattableCurve<Point2d,Double>
      Parameters:
      t - the fraction
      Returns:
      the point at the given fraction

    • getLength

      public double getLength()
      Description copied from interface: Curve
      Return the length of this Curve.
      Specified by:
      getLength in interface Curve<DirectedPoint2d,Double,Point2d,Flattener2d,PolyLine2d>
      Returns:
      length of this Curve

    • curvature

      public double curvature(double t)
      Returns the curvature at the given t value.
      Parameters:
      t - t value, moving from 0 to 1 along the Bézier.
      Returns:
      double curvature at the given t value.

    • toPolyLine

      public PolyLine2d toPolyLine(Flattener2d flattener)
      Description copied from interface: Curve
      Flatten a Curve into a PolyLine. Implementations should use the flattener when relevant and possible.
      Specified by:
      toPolyLine in interface Curve<DirectedPoint2d,Double,Point2d,Flattener2d,PolyLine2d>
      Parameters:
      flattener - the flattener
      Returns:
      approximation of this Curve as a PolyLine

    • toString

      public String toString()
      Overrides:
      toString in class Object

    • hashCode

      public int hashCode()
      Overrides:
      hashCode in class Object

    • equals

      public boolean equals(Object obj)
      Overrides:
      equals in class Object