Package org.gephi.appearance.api

Class Interpolator.BezierInterpolator

java.lang.Object

org.gephi.appearance.api.Interpolator

org.gephi.appearance.api.Interpolator.BezierInterpolator

Enclosing class:

Interpolator

public static class Interpolator.BezierInterpolator
extends Interpolator

Bezier curve interpolator.

Basically, a cubic Bezier curve is created with start point (0,0) and endpoint (1,1). The other two control points (px1, py1) and (px2, py2) are given by the user, where px1, py1, px1, and px2 are all in the range [0,1].

Nested Class Summary

Nested classes/interfaces inherited from class org.gephi.appearance.api.Interpolator

Interpolator.BezierInterpolator

Field Summary

Fields

Modifier and Type	Field	Description
private boolean	isCurveLinear	do the input control points form a line with (0,0) and (1,1), i.e., x1 == y1 and x2 == y2 -- if so, then all x(t) == y(t) for the curve
private static float	SAMPLE_INCREMENT	difference in t used to calculate each of the xSamples values -- power of 2 sample size should provide exact representation of this value and its integer multiples (integer in range of [0..SAMPLE_SIZE]
private static int	SAMPLE_SIZE	power of 2 sample size for lookup table of x values
private float	x1	the coordinates of the 2 2D control points for a cubic Bezier curve, with implicit start point (0,0) and end point (1,1) -- each individual coordinate value must be in range [0,1]
private float	x2	the coordinates of the 2 2D control points for a cubic Bezier curve, with implicit start point (0,0) and end point (1,1) -- each individual coordinate value must be in range [0,1]
private float[]	xSamples	x values for the bezier curve, sampled at increments of 1/SAMPLE_SIZE -- this is used to find the good initial guess for parameter t, given an x
private float	y1	the coordinates of the 2 2D control points for a cubic Bezier curve, with implicit start point (0,0) and end point (1,1) -- each individual coordinate value must be in range [0,1]
private float	y2	the coordinates of the 2 2D control points for a cubic Bezier curve, with implicit start point (0,0) and end point (1,1) -- each individual coordinate value must be in range [0,1]

Fields inherited from class org.gephi.appearance.api.Interpolator

LINEAR, LOG2

Constructor Summary

Constructors

Constructor	Description
BezierInterpolator(float px1, float py1, float px2, float py2)	constructor -- cubic bezier curve will be represented by control points (0,0) (px1,py1) (px2,py2) (1,1) -- px1, py1, px2, py2 all in range [0,1]

Method Summary

Modifier and Type	Method	Description
boolean	equals(Object o)
private float	eval(float t, float p1, float p2)	use Bernstein basis to evaluate 1D cubic Bezier curve (quicker and more numerically stable than power basis) -- 1D control coordinates are (0, p1, p2, 1), where p1 and p2 are in range [0,1], and there is no ordering constraint on p1 and p2, i.e., p1 <= p2 does not have to be true
private float	evalDerivative(float t, float p1, float p2)	evaluate Bernstein basis derivative of 1D cubic Bezier curve, where 1D control points are (0, p1, p2, 1), where p1 and p2 are in range [0,1], and there is no ordering constraint on p1 and p2, i.e., p1 <= p2 does not have to be true
private float	findTForX(float x)	find the parameter t that produces the given x-value for the curve -- uses Newton-Raphson to refine the value as opposed to subdividing until we are within some tolerance
Point2D	getControl1()
Point2D	getControl2()
private float	getInitialGuessForT(float x)	find an initial good guess for what parameter t might produce the x-value on the Bezier curve -- uses linear interpolation on the x-value sample array that was created on construction
int	hashCode()
float	interpolate(float x)	get the y-value of the cubic bezier curve that corresponds to the x input

Methods inherited from class org.gephi.appearance.api.Interpolator

newBezierInterpolator

Methods inherited from class java.lang.Object

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

Field Detail

SAMPLE_SIZE

private static final int SAMPLE_SIZE

power of 2 sample size for lookup table of x values

See Also:

Constant Field Values

SAMPLE_INCREMENT

private static final float SAMPLE_INCREMENT

difference in t used to calculate each of the xSamples values -- power of 2 sample size should provide exact representation of this value and its integer multiples (integer in range of [0..SAMPLE_SIZE]

See Also:

Constant Field Values

x1

private final float x1

the coordinates of the 2 2D control points for a cubic Bezier curve, with implicit start point (0,0) and end point (1,1) -- each individual coordinate value must be in range [0,1]

y1

private final float y1

the coordinates of the 2 2D control points for a cubic Bezier curve, with implicit start point (0,0) and end point (1,1) -- each individual coordinate value must be in range [0,1]

x2

private final float x2

the coordinates of the 2 2D control points for a cubic Bezier curve, with implicit start point (0,0) and end point (1,1) -- each individual coordinate value must be in range [0,1]

y2

private final float y2

the coordinates of the 2 2D control points for a cubic Bezier curve, with implicit start point (0,0) and end point (1,1) -- each individual coordinate value must be in range [0,1]

isCurveLinear

private final boolean isCurveLinear

do the input control points form a line with (0,0) and (1,1), i.e., x1 == y1 and x2 == y2 -- if so, then all x(t) == y(t) for the curve

xSamples

private final float[] xSamples

x values for the bezier curve, sampled at increments of 1/SAMPLE_SIZE -- this is used to find the good initial guess for parameter t, given an x

Constructor Detail

BezierInterpolator

public BezierInterpolator(float px1,
                          float py1,
                          float px2,
                          float py2)

constructor -- cubic bezier curve will be represented by control points (0,0) (px1,py1) (px2,py2) (1,1) -- px1, py1, px2, py2 all in range [0,1]

Parameters:

px1 - is x-coordinate of first control point, in range [0,1]

py1 - is y-coordinate of first control point, in range [0,1]

px2 - is x-coordinate of second control point, in range [0,1]

py2 - is y-coordinate of second control point, in range [0,1]

Method Detail

getControl1

public Point2D getControl1()

getControl2

public Point2D getControl2()

interpolate

public float interpolate(float x)

get the y-value of the cubic bezier curve that corresponds to the x input

Specified by:

interpolate in class Interpolator

Parameters:

x - is x-value of cubic bezier curve, in range [0,1]

Returns:

corresponding y-value of cubic bezier curve -- in range [0,1]

eval

private float eval(float t,
                   float p1,
                   float p2)

use Bernstein basis to evaluate 1D cubic Bezier curve (quicker and more numerically stable than power basis) -- 1D control coordinates are (0, p1, p2, 1), where p1 and p2 are in range [0,1], and there is no ordering constraint on p1 and p2, i.e., p1 <= p2 does not have to be true

Parameters:

t - is the paramaterized value in range [0,1]

p1 - is 1st control point coordinate in range [0,1]

p2 - is 2nd control point coordinate in range [0,1]

Returns:

the value of the Bezier curve at parameter t

evalDerivative

private float evalDerivative(float t,
                             float p1,
                             float p2)

evaluate Bernstein basis derivative of 1D cubic Bezier curve, where 1D control points are (0, p1, p2, 1), where p1 and p2 are in range [0,1], and there is no ordering constraint on p1 and p2, i.e., p1 <= p2 does not have to be true

Parameters:

t - is the paramaterized value in range [0,1]

p1 - is 1st control point coordinate in range [0,1]

p2 - is 2nd control point coordinate in range [0,1]

Returns:

the value of the Bezier curve at parameter t

getInitialGuessForT

private float getInitialGuessForT(float x)

find an initial good guess for what parameter t might produce the x-value on the Bezier curve -- uses linear interpolation on the x-value sample array that was created on construction

Parameters:

x - is x-value of cubic bezier curve, in range [0,1]

Returns:

a good initial guess for parameter t (in range [0,1]) that gives x

findTForX

private float findTForX(float x)

find the parameter t that produces the given x-value for the curve -- uses Newton-Raphson to refine the value as opposed to subdividing until we are within some tolerance

Parameters:

x - is x-value of cubic bezier curve, in range [0,1]

Returns:

the parameter t (in range [0,1]) that produces x

equals

public boolean equals(Object o)

Overrides:

equals in class Object

hashCode

public int hashCode()

Overrides:

hashCode in class Object