fl.motion.BezierSegment - ActionScript® 3.0 Reference for the Adobe® Flash® Platform

Package	fl.motion
Class	public class BezierSegment
Inheritance	BezierSegment Object

Language Version:

ActionScript 3.0

Product Version:

Flash CS3

Runtime Versions:

Flash Player 9.0.28.0, AIR 1.0

A Bezier segment consists of four Point objects that define a single cubic Bezier curve. The BezierSegment class also contains methods to find coordinate values along the curve.

Related API Elements

Motion XML Elements

Public Properties

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	Property		Defined By
		a : Point The first point of the Bezier curve.	BezierSegment
		b : Point The second point of the Bezier curve.	BezierSegment
		c : Point The third point of the Bezier curve.	BezierSegment
		constructor : Object A reference to the class object or constructor function for a given object instance.	Object
		d : Point The fourth point of the Bezier curve.	BezierSegment
		prototype : Object [static] A reference to the prototype object of a class or function object.	Object

Public Methods

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	Method		Defined By
		BezierSegment(a:Point, b:Point, c:Point, d:Point) Constructor for BezierSegment instances.	BezierSegment
		getCubicCoefficients(a:Number, b:Number, c:Number, d:Number):Array [static] Calculates the coefficients for a cubic polynomial equation, given the values of the corresponding cubic Bezier equation.	BezierSegment
		getCubicRoots(a:Number = 0, b:Number = 0, c:Number = 0, d:Number = 0):Array [static] Finds the real solutions, if they exist, to a cubic polynomial equation of the form: at^3 + bt^2 + ct + d.	BezierSegment
		getQuadraticRoots(a:Number, b:Number, c:Number):Array [static] Finds the real solutions, if they exist, to a quadratic equation of the form: at^2 + bt + c.	BezierSegment
		getSingleValue(t:Number, a:Number = 0, b:Number = 0, c:Number = 0, d:Number = 0):Number [static] Calculates the value of a one-dimensional cubic Bezier equation at a specific time.	BezierSegment
		getValue(t:Number):Point Calculates the location of a two-dimensional cubic Bezier curve at a specific time.	BezierSegment
		getYForX(x:Number, coefficients:Array = null):Number Finds the y value of a cubic Bezier curve at a given x coordinate.	BezierSegment
		hasOwnProperty(name:String):Boolean Indicates whether an object has a specified property defined.	Object
		isPrototypeOf(theClass:Object):Boolean Indicates whether an instance of the Object class is in the prototype chain of the object specified as the parameter.	Object
		propertyIsEnumerable(name:String):Boolean Indicates whether the specified property exists and is enumerable.	Object
		setPropertyIsEnumerable(name:String, isEnum:Boolean = true):void Sets the availability of a dynamic property for loop operations.	Object
		toLocaleString():String Returns the string representation of this object, formatted according to locale-specific conventions.	Object
		toString():String Returns the string representation of the specified object.	Object
		valueOf():Object Returns the primitive value of the specified object.	Object

Property Detail

a

property

public var a:Point

Language Version:

ActionScript 3.0

Product Version:

Flash CS3

Runtime Versions:

Flash Player 9.0.28.0, AIR 1.0

The first point of the Bezier curve. It is a node, which means it falls directly on the curve.

b

property

public var b:Point

Language Version:

ActionScript 3.0

Product Version:

Flash CS3

Runtime Versions:

Flash Player 9.0.28.0, AIR 1.0

The second point of the Bezier curve. It is a control point, which means the curve moves toward it, but usually does not pass through it.

c

property

public var c:Point

Language Version:

ActionScript 3.0

Product Version:

Flash CS3

Runtime Versions:

Flash Player 9.0.28.0, AIR 1.0

The third point of the Bezier curve. It is a control point, which means the curve moves toward it, but usually does not pass through it.

d

property

public var d:Point

Language Version:

ActionScript 3.0

Product Version:

Flash CS3

Runtime Versions:

Flash Player 9.0.28.0, AIR 1.0

The fourth point of the Bezier curve. It is a node, which means it falls directly on the curve.

Constructor Detail

BezierSegment

()

Constructor

public function BezierSegment(a:Point, b:Point, c:Point, d:Point)

Language Version:

ActionScript 3.0

Product Version:

Flash CS3

Runtime Versions:

Flash Player 9.0.28.0, AIR 1.0

Constructor for BezierSegment instances.

Parameters

	`a:Point` — The first point of the curve, a node.

	`b:Point` — The second point of the curve, a control point.

	`c:Point` — The third point of the curve, a control point.

	`d:Point` — The fourth point of the curve, a node.

Related API Elements

property details

Method Detail

getCubicCoefficients

()

method

public static function getCubicCoefficients(a:Number, b:Number, c:Number, d:Number):Array

Language Version:

ActionScript 3.0

Product Version:

Flash CS3

Runtime Versions:

Flash Player 9.0.28.0, AIR 1.0

Calculates the coefficients for a cubic polynomial equation, given the values of the corresponding cubic Bezier equation.

Parameters

	`a:Number` — The first value of the Bezier equation.

	`b:Number` — The second value of the Bezier equation.

	`c:Number` — The third value of the Bezier equation.

	`d:Number` — The fourth value of the Bezier equation.

Returns

Array — An array containing four number values, which are the coefficients for a cubic polynomial. The coefficients are ordered from the highest degree to the lowest, so the first number in the array would be multiplied by t^3, the second by t^2, and so on.

Related API Elements

getCubicRoots()

getCubicRoots

()

method

public static function getCubicRoots(a:Number = 0, b:Number = 0, c:Number = 0, d:Number = 0):Array

Language Version:

ActionScript 3.0

Product Version:

Flash CS3

Runtime Versions:

Flash Player 9.0.28.0, AIR 1.0

Finds the real solutions, if they exist, to a cubic polynomial equation of the form: at^3 + bt^2 + ct + d. This method is used to evaluate custom easing curves.

Parameters

	`a:Number` (default = `0`) — The first coefficient of the cubic equation, which is multiplied by the cubed variable (t^3).

	`b:Number` (default = `0`) — The second coefficient of the cubic equation, which is multiplied by the squared variable (t^2).

	`c:Number` (default = `0`) — The third coefficient of the cubic equation, which is multiplied by the linear variable (t).

	`d:Number` (default = `0`) — The fourth coefficient of the cubic equation, which is the constant.

Returns

Array — An array of number values, indicating the real roots of the equation. There may be no roots, or as many as three. Imaginary or complex roots are ignored.

getQuadraticRoots

()

method

public static function getQuadraticRoots(a:Number, b:Number, c:Number):Array

Language Version:

ActionScript 3.0

Product Version:

Flash CS3

Runtime Versions:

Flash Player 9.0.28.0, AIR 1.0

Finds the real solutions, if they exist, to a quadratic equation of the form: at^2 + bt + c.

Parameters

	`a:Number` — The first coefficient of the quadratic equation, which is multiplied by the squared variable (t^2).

	`b:Number` — The second coefficient of the quadratic equation, which is multiplied by the linear variable (t).

	`c:Number` — The third coefficient of the quadratic equation, which is the constant.

Returns

Array — An array of number values, indicating the real roots of the equation. There may be no roots, or as many as two. Imaginary or complex roots are ignored.

getSingleValue

()

method

public static function getSingleValue(t:Number, a:Number = 0, b:Number = 0, c:Number = 0, d:Number = 0):Number

Language Version:

ActionScript 3.0

Product Version:

Flash CS3

Runtime Versions:

Flash Player 9.0.28.0, AIR 1.0

Calculates the value of a one-dimensional cubic Bezier equation at a specific time. By contrast, a Bezier curve is usually two-dimensional and uses two of these equations, one for the x coordinate and one for the y coordinate.

Parameters

	`t:Number` — The `time` or degree of progress along the curve, as a decimal value between `0` and `1`. Note: The `t` parameter does not necessarily move along the curve at a uniform speed. For example, a `t` value of `0.5` does not always produce a value halfway along the curve.

	`a:Number` (default = `0`) — The first value of the Bezier equation.

	`b:Number` (default = `0`) — The second value of the Bezier equation.

	`c:Number` (default = `0`) — The third value of the Bezier equation.

	`d:Number` (default = `0`) — The fourth value of the Bezier equation.

Returns

Number — The value of the Bezier equation at the specified time.

getValue

()

method

public function getValue(t:Number):Point

Language Version:

ActionScript 3.0

Product Version:

Flash CS3

Runtime Versions:

Flash Player 9.0.28.0, AIR 1.0

Calculates the location of a two-dimensional cubic Bezier curve at a specific time.

Parameters

t:Number — The time or degree of progress along the curve, as a decimal value between 0 and 1.

Note: The t parameter does not necessarily move along the curve at a uniform speed. For example, a t value of 0.5 does not always produce a value halfway along the curve.

Returns

Point — A point object containing the x and y coordinates of the Bezier curve at the specified time.

getYForX

()

method

public function getYForX(x:Number, coefficients:Array = null):Number

Language Version:

ActionScript 3.0

Product Version:

Flash CS3

Runtime Versions:

Flash Player 9.0.28.0, AIR 1.0

Finds the y value of a cubic Bezier curve at a given x coordinate. Some Bezier curves overlap themselves horizontally, resulting in more than one y value for a given x value. In that case, this method will return whichever value is most logical. Used by CustomEase and BezierEase interpolation.

Parameters

	`x:Number` — An x coordinate that lies between the first and last point, inclusive.

	`coefficients:Array` (default = `null`) — An optional array of number values that represent the polynomial coefficients for the Bezier. This array can be used to optimize performance by precalculating values that are the same everywhere on the curve and do not need to be recalculated for each iteration.

Returns

Number — The y value of the cubic Bezier curve at the given x coordinate.

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Classes x

a

b

c

d

BezierSegment

getCubicCoefficients

getCubicRoots

getQuadraticRoots

getSingleValue

getValue

getYForX