org.opentrafficsim.core.geometry

Class Bezier

java.lang.Object

org.opentrafficsim.core.geometry.Bezier

public final class Bezier
extends Object

Generation of Bézier curves.
The class implements the cubic(...) method to generate a cubic Bézier curve using the following formula: B(t) = (1 - t)³P₀ + 3t(1 - t)² P₁ + 3t² (1 - t) P₂ + t³ P₃ where P₀ and P₃ are the end points, and P₁ and P₂ the control points.
For a smooth movement, one of the standard implementations if the cubic(...) function offered is the case where P₁ is positioned halfway between P₀ and P₃ starting from P₀ in the direction of P₃, and P₂ is positioned halfway between P₃ and P₀ starting from P₃ in the direction of P₀.
Finally, an n-point generalization of the Bézier curve is implemented with the bezier(...) function.

Copyright (c) 2013-2018 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved.
BSD-style license. See OpenTrafficSim License.

$LastChangedDate: 2015-07-24 02:58:59 +0200 (Fri, 24 Jul 2015) $, @version $Revision: 1147 $, by $Author: averbraeck $, initial version Nov 14, 2015

Author:

Alexander Verbraeck, Peter Knoppers

Method Summary

Modifier and Type	Method and Description
static OTSLine3D	bezier(int numPoints, OTSPoint3D... points) Construct a Bézier curve of degree n.
static OTSLine3D	bezier(OTSPoint3D... points) Construct a Bézier curve of degree n.
static OTSLine3D	cubic(DirectedPoint start, DirectedPoint end) Construct a cubic Bézier curve from start to end with two generated control points at half the distance between start and end.
static OTSLine3D	cubic(int numPoints, DirectedPoint start, DirectedPoint end) Construct a cubic Bézier curve from start to end with two generated control points at half the distance between start and end.
static OTSLine3D	cubic(int numPoints, DirectedPoint start, DirectedPoint end, double shape) Construct a cubic Bézier curve from start to end with two generated control points at half the distance between start and end.
static OTSLine3D	cubic(int numPoints, DirectedPoint start, DirectedPoint end, double shape, boolean weighted) Construct a cubic Bézier curve from start to end with two generated control points at half the distance between start and end.
static OTSLine3D	cubic(int numPoints, OTSPoint3D start, OTSPoint3D control1, OTSPoint3D control2, OTSPoint3D end) Construct a cubic Bézier curve from start to end with two control points.
static void	main(String[] args)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

cubic

public static OTSLine3D cubic(int numPoints,
                              OTSPoint3D start,
                              OTSPoint3D control1,
                              OTSPoint3D control2,
                              OTSPoint3D end)
                       throws OTSGeometryException

Construct a cubic Bézier curve from start to end with two control points.

Parameters:

numPoints - the number of points for the Bézier curve

start - the start point of the Bézier curve

control1 - the first control point

control2 - the second control point

end - the end point of the Bézier curve

Returns:

a cubic Bézier curve between start and end, with the two provided control points

Throws:

OTSGeometryException - in case the number of points is less than 2 or the Bézier curve could not be constructed

cubic

public static OTSLine3D cubic(int numPoints,
                              DirectedPoint start,
                              DirectedPoint end)
                       throws OTSGeometryException

Construct a cubic Bézier curve from start to end with two generated control points at half the distance between start and end. The z-value is interpolated in a linear way.

Parameters:

numPoints - the number of points for the Bézier curve

start - the directed start point of the Bézier curve

end - the directed end point of the Bézier curve

Returns:

a cubic Bézier curve between start and end, with the two provided control points

Throws:

OTSGeometryException - in case the number of points is less than 2 or the Bézier curve could not be constructed

cubic

public static OTSLine3D cubic(int numPoints,
                              DirectedPoint start,
                              DirectedPoint end,
                              double shape)
                       throws OTSGeometryException

Construct a cubic Bézier curve from start to end with two generated control points at half the distance between start and end. The z-value is interpolated in a linear way.

Parameters:

numPoints - the number of points for the Bézier curve

start - the directed start point of the Bézier curve

end - the directed end point of the Bézier curve

shape - shape factor; 1 = control points at half the distance between start and end, > 1 results in a pointier shape, < 1 results in a flatter shape, value should be above 0

Returns:

a cubic Bézier curve between start and end, with the two determined control points

Throws:

OTSGeometryException - in case the number of points is less than 2 or the Bézier curve could not be constructed

cubic

public static OTSLine3D cubic(int numPoints,
                              DirectedPoint start,
                              DirectedPoint end,
                              double shape,
                              boolean weighted)
                       throws OTSGeometryException

Construct a cubic Bézier curve from start to end with two generated control points at half the distance between start and end. The z-value is interpolated in a linear way.

Parameters:

numPoints - the number of points for the Bézier curve

start - the directed start point of the Bézier curve

end - the directed end point of the Bézier curve

shape - shape factor; 1 = control points at half the distance between start and end, > 1 results in a pointier shape, < 1 results in a flatter shape, value should be above 0

weighted - boolean; control point distance relates to distance to projected point on extended line from other end

Returns:

a cubic Bézier curve between start and end, with the two determined control points

Throws:

OTSGeometryException - in case the number of points is less than 2 or the Bézier curve could not be constructed

cubic

public static OTSLine3D cubic(DirectedPoint start,
                              DirectedPoint end)
                       throws OTSGeometryException

Construct a cubic Bézier curve from start to end with two generated control points at half the distance between start and end. The z-value is interpolated in a linear way.

Parameters:

start - the directed start point of the Bézier curve

end - the directed end point of the Bézier curve

Returns:

a cubic Bézier curve between start and end, with the two provided control points

Throws:

OTSGeometryException - in case the number of points is less than 2 or the Bézier curve could not be constructed

bezier

public static OTSLine3D bezier(int numPoints,
                               OTSPoint3D... points)
                        throws OTSGeometryException

Construct a Bézier curve of degree n.

Parameters:

numPoints - the number of points for the Bézier curve to be constructed

points - the points of the curve, where the first and last are begin and end point, and the intermediate ones are control points. There should be at least two points.

Returns:

the Bézier value B(t) of degree n, where n is the number of points in the array

Throws:

OTSGeometryException - in case the number of points is less than 2 or the Bézier curve could not be constructed

bezier

public static OTSLine3D bezier(OTSPoint3D... points)
                        throws OTSGeometryException

Construct a Bézier curve of degree n.

Parameters:

points - the points of the curve, where the first and last are begin and end point, and the intermediate ones are control points. There should be at least two points.

Returns:

the Bézier value B(t) of degree n, where n is the number of points in the array

Throws:

OTSGeometryException - in case the number of points is less than 2 or the Bézier curve could not be constructed

main

public static void main(String[] args)
                 throws OTSGeometryException

Parameters:

args - args

Throws:

OTSGeometryException - ne