flash.geom.Vector3D - Adobe® Flex® 4 Language Reference (Flex 4)

Package	flash.geom
Class	public class Vector3D
Inheritance	Vector3D Object

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

The Vector3D class represents a point or a location in the three-dimensional space using the Cartesian coordinates x, y, and z. As in a two-dimensional space, the x property represents the horizontal axis and the y property represents the vertical axis. In three-dimensional space, the z property represents depth. The value of the x property increases as the object moves to the right. The value of the y property increases as the object moves down. The z property increases as the object moves farther from the point of view. Using perspective projection and scaling, the object is seen to be bigger when near and smaller when farther away from the screen. As in a right-handed three-dimensional coordinate system, the positive z-axis points away from the viewer and the value of the z property increases as the object moves away from the viewer's eye. The origin point (0,0,0) of the global space is the upper-left corner of the stage.

X, Y, Z Axes

The Vector3D class can also represent a direction, an arrow pointing from the origin of the coordinates, such as (0,0,0), to an endpoint; or a floating-point component of an RGB (Red, Green, Blue) color model.

Quaternion notation introduces a fourth element, the w property, which provides additional orientation information. For example, the w property can define an angle of rotation of a Vector3D object. The combination of the angle of rotation and the coordinates x, y, and z can determine the display object's orientation. Here is a representation of Vector3D elements in matrix notation:

Vector3D elements

Public Properties

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	Property		Defined By
		constructor : Object A reference to the class object or constructor function for a given object instance.	Object
		length : Number [read-only] The length, magnitude, of the current Vector3D object from the origin (0,0,0) to the object's x, y, and z coordinates.	Vector3D
		lengthSquared : Number [read-only] The square of the length of the current Vector3D object, calculated using the x, y, and z properties.	Vector3D
		prototype : Object [static] A reference to the prototype object of a class or function object.	Object
		w : Number The fourth element of a Vector3D object (in addition to the x, y, and z properties) can hold data such as the angle of rotation.	Vector3D
		x : Number The first element of a Vector3D object, such as the x coordinate of a point in the three-dimensional space.	Vector3D
		y : Number The second element of a Vector3D object, such as the y coordinate of a point in the three-dimensional space.	Vector3D
		z : Number The third element of a Vector3D object, such as the z coordinate of a point in three-dimensional space.	Vector3D

Public Methods

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	Method		Defined By
		Vector3D(x:Number = 0., y:Number = 0., z:Number = 0., w:Number = 0.) Creates an instance of a Vector3D object.	Vector3D
		add(a:Vector3D):Vector3D Adds the value of the x, y, and z elements of the current Vector3D object to the values of the x, y, and z elements of another Vector3D object.	Vector3D
		angleBetween(a:Vector3D, b:Vector3D):Number [static] Returns the angle in radians between two vectors.	Vector3D
		clone():Vector3D Returns a new Vector3D object that is an exact copy of the current Vector3D object.	Vector3D
		crossProduct(a:Vector3D):Vector3D Returns a new Vector3D object that is perpendicular (at a right angle) to the current Vector3D and another Vector3D object.	Vector3D
		decrementBy(a:Vector3D):void Decrements the value of the x, y, and z elements of the current Vector3D object by the values of the x, y, and z elements of specified Vector3D object.	Vector3D
		distance(pt1:Vector3D, pt2:Vector3D):Number [static] Returns the distance between two Vector3D objects.	Vector3D
		dotProduct(a:Vector3D):Number If the current Vector3D object and the one specified as the parameter are unit vertices, this method returns the cosine of the angle between the two vertices.	Vector3D
		equals(toCompare:Vector3D, allFour:Boolean = false):Boolean Determines whether two Vector3D objects are equal by comparing the x, y, and z elements of the current Vector3D object with a specified Vector3D object.	Vector3D
		hasOwnProperty(name:String):Boolean Indicates whether an object has a specified property defined.	Object
		incrementBy(a:Vector3D):void Increments the value of the x, y, and z elements of the current Vector3D object by the values of the x, y, and z elements of a specified Vector3D object.	Vector3D
		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
		nearEquals(toCompare:Vector3D, tolerance:Number, allFour:Boolean = false):Boolean Compares the elements of the current Vector3D object with the elements of a specified Vector3D object to determine whether they are nearly equal.	Vector3D
		negate():void Sets the current Vector3D object to its inverse.	Vector3D
		normalize():Number Converts a Vector3D object to a unit vector by dividing the first three elements (x, y, z) by the length of the vector.	Vector3D
		project():void Divides the value of the x, y, and z properties of the current Vector3D object by the value of its w property.	Vector3D
		propertyIsEnumerable(name:String):Boolean Indicates whether the specified property exists and is enumerable.	Object
		scaleBy(s:Number):void Scales the current Vector3D object by a scalar, a magnitude.	Vector3D
		setPropertyIsEnumerable(name:String, isEnum:Boolean = true):void Sets the availability of a dynamic property for loop operations.	Object
		subtract(a:Vector3D):Vector3D Subtracts the value of the x, y, and z elements of the current Vector3D object from the values of the x, y, and z elements of another Vector3D object.	Vector3D
		toLocaleString():String Returns the string representation of this object, formatted according to locale-specific conventions.	Object
		toString():String Returns a string representation of the current Vector3D object.	Vector3D
		valueOf():Object Returns the primitive value of the specified object.	Object

Public Constants

	Constant		Defined By
		X_AXIS : Vector3D [static] The x axis defined as a Vector3D object with coordinates (1,0,0).	Vector3D
		Y_AXIS : Vector3D [static] The y axis defined as a Vector3D object with coordinates (0,1,0).	Vector3D
		Z_AXIS : Vector3D [static] The z axis defined as a Vector3D object with coordinates (0,0,1).	Vector3D

Property Detail

length

property

length:Number [read-only]

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

The length, magnitude, of the current Vector3D object from the origin (0,0,0) to the object's x, y, and z coordinates. The w property is ignored. A unit vector has a length or magnitude of one.

Implementation
public function get length():Number

See also

lengthSquared

property

lengthSquared:Number [read-only]

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

The square of the length of the current Vector3D object, calculated using the x, y, and z properties. The w property is ignored. Use the lengthSquared() method whenever possible instead of the slower Math.sqrt() method call of the Vector3D.length() method.

Implementation
public function get lengthSquared():Number

See also

length

w

property

public var w:Number

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

The fourth element of a Vector3D object (in addition to the x, y, and z properties) can hold data such as the angle of rotation. The default value is 0.

Quaternion notation employs an angle as the fourth element in its calculation of three-dimensional rotation. The w property can be used to define the angle of rotation about the Vector3D object. The combination of the rotation angle and the coordinates (x,y,z) determines the display object's orientation.

In addition, the w property can be used as a perspective warp factor for a projected three-dimensional position or as a projection transform value in representing a three-dimensional coordinate projected into the two-dimensional space. For example, you can create a projection matrix using the Matrix3D.rawData property, that, when applied to a Vector3D object, produces a transform value in the Vector3D object's fourth element (the w property). Dividing the Vector3D object's other elements by the transform value then produces a projected Vector3D object. You can use the Vector3D.project() method to divide the first three elements of a Vector3D object by its fourth element.

See also

project()

x

property

public var x:Number

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

The first element of a Vector3D object, such as the x coordinate of a point in the three-dimensional space. The default value is 0.

y

property

public var y:Number

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

The second element of a Vector3D object, such as the y coordinate of a point in the three-dimensional space. The default value is 0.

z

property

public var z:Number

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

The third element of a Vector3D object, such as the z coordinate of a point in three-dimensional space. The default value is 0.

Constructor Detail

Vector3D

()

Constructor

public function Vector3D(x:Number = 0., y:Number = 0., z:Number = 0., w:Number = 0.)

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Creates an instance of a Vector3D object. If you do not specify a parameter for the constructor, a Vector3D object is created with the elements (0,0,0,0).

Parameters

	`x:Number` (default = `0.`) — The first element, such as the x coordinate.

	`y:Number` (default = `0.`) — The second element, such as the y coordinate.

	`z:Number` (default = `0.`) — The third element, such as the z coordinate.

	`w:Number` (default = `0.`) — An optional element for additional data such as the angle of rotation.

Method Detail

add

()

method

public function add(a:Vector3D):Vector3D

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Adds the value of the x, y, and z elements of the current Vector3D object to the values of the x, y, and z elements of another Vector3D object. The add() method does not change the current Vector3D object. Instead, it returns a new Vector3D object with the new values.

The result of adding two vectors together is a resultant vector. One way to visualize the result is by drawing a vector from the origin or tail of the first vector to the end or head of the second vector. The resultant vector is the distance between the origin point of the first vector and the end point of the second vector.

Resultant Vector3D

Parameters

a:Vector3D — A Vector3D object to be added to the current Vector3D object.

Returns

Vector3D — A Vector3D object that is the result of adding the current Vector3D object to another Vector3D object.

See also

incrementBy()

angleBetween

()

method

public static function angleBetween(a:Vector3D, b:Vector3D):Number

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Returns the angle in radians between two vectors. The returned angle is the smallest radian the first Vector3D object rotates until it aligns with the second Vector3D object.

The angleBetween() method is a static method. You can use it directly as a method of the Vector3D class.

To convert a degree to a radian, you can use the following formula:

radian = Math.PI/180 * degree

Parameters

	`a:Vector3D` — The first Vector3D object.

	`b:Vector3D` — The second Vector3D object.

Returns

Number — The angle between two Vector3D objects.

clone

()

method

public function clone():Vector3D

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Returns a new Vector3D object that is an exact copy of the current Vector3D object.

Returns

Vector3D — A new Vector3D object that is a copy of the current Vector3D object.

crossProduct

()

method

public function crossProduct(a:Vector3D):Vector3D

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Returns a new Vector3D object that is perpendicular (at a right angle) to the current Vector3D and another Vector3D object. If the returned Vector3D object's coordinates are (0,0,0), then the two Vector3D objects are perpendicular to each other.

Cross Product

You can use the normalized cross product of two vertices of a polygon surface with the normalized vector of the camera or eye viewpoint to get a dot product. The value of the dot product can identify whether a surface of a three-dimensional object is hidden from the viewpoint.

Parameters

a:Vector3D — A second Vector3D object.

Returns

Vector3D — A new Vector3D object that is perpendicular to the current Vector3D object and the Vector3D object specified as the parameter.

See also

dotProduct()
normalize()

decrementBy

()

method

public function decrementBy(a:Vector3D):void

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Decrements the value of the x, y, and z elements of the current Vector3D object by the values of the x, y, and z elements of specified Vector3D object. Unlike the Vector3D.subtract() method, the decrementBy() method changes the current Vector3D object and does not return a new Vector3D object.

Parameters

a:Vector3D — The Vector3D object containing the values to subtract from the current Vector3D object.

See also

subtract()

distance

()

method

public static function distance(pt1:Vector3D, pt2:Vector3D):Number

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Returns the distance between two Vector3D objects. The distance() method is a static method. You can use it directly as a method of the Vector3D class to get the Euclidean distance between two three-dimensional points.

Parameters

	`pt1:Vector3D` — A Vector3D object as the first three-dimensional point.

	`pt2:Vector3D` — A Vector3D object as the second three-dimensional point.

Returns

Number — The distance between two Vector3D objects.

dotProduct

()

method

public function dotProduct(a:Vector3D):Number

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

If the current Vector3D object and the one specified as the parameter are unit vertices, this method returns the cosine of the angle between the two vertices. Unit vertices are vertices that point to the same direction but their length is one. They remove the length of the vector as a factor in the result. You can use the normalize() method to convert a vector to a unit vector.

The dotProduct() method finds the angle between two vertices. It is also used in backface culling or lighting calculations. Backface culling is a procedure for determining which surfaces are hidden from the viewpoint. You can use the normalized vertices from the camera, or eye, viewpoint and the cross product of the vertices of a polygon surface to get the dot product. If the dot product is less than zero, then the surface is facing the camera or the viewer. If the two unit vertices are perpendicular to each other, they are orthogonal and the dot product is zero. If the two vertices are parallel to each other, the dot product is one.

Parameters

a:Vector3D — The second Vector3D object.

Returns

Number — A scalar which is the dot product of the current Vector3D object and the specified Vector3D object.

See also

crossProduct()
normalize()

equals

()

method

public function equals(toCompare:Vector3D, allFour:Boolean = false):Boolean

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Determines whether two Vector3D objects are equal by comparing the x, y, and z elements of the current Vector3D object with a specified Vector3D object. If the values of these elements are the same, the two Vector3D objects are equal. If the second optional parameter is set to true, all four elements of the Vector3D objects, including the w property, are compared.

Parameters

	`toCompare:Vector3D` — The Vector3D object to be compared with the current Vector3D object.

	`allFour:Boolean` (default = `false`) — An optional parameter that specifies whether the `w` property of the Vector3D objects is used in the comparison.

Returns

Boolean — A value of true if the specified Vector3D object is equal to the current Vector3D object; false if it is not equal.

See also

nearEquals()

incrementBy

()

method

public function incrementBy(a:Vector3D):void

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Increments the value of the x, y, and z elements of the current Vector3D object by the values of the x, y, and z elements of a specified Vector3D object. Unlike the Vector3D.add() method, the incrementBy() method changes the current Vector3D object and does not return a new Vector3D object.

Parameters

a:Vector3D — The Vector3D object to be added to the current Vector3D object.

See also

add()

nearEquals

()

method

public function nearEquals(toCompare:Vector3D, tolerance:Number, allFour:Boolean = false):Boolean

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Compares the elements of the current Vector3D object with the elements of a specified Vector3D object to determine whether they are nearly equal. The two Vector3D objects are nearly equal if the value of all the elements of the two vertices are equal, or the result of the comparison is within the tolerance range. The difference between two elements must be less than the number specified as the tolerance parameter. If the third optional parameter is set to true, all four elements of the Vector3D objects, including the w property, are compared. Otherwise, only the x, y, and z elements are included in the comparison.

Parameters

	`toCompare:Vector3D` — The Vector3D object to be compared with the current Vector3D object.

	`tolerance:Number` — A number determining the tolerance factor. If the difference between the values of the Vector3D element specified in the `toCompare` parameter and the current Vector3D element is less than the tolerance number, the two values are considered nearly equal.

	`allFour:Boolean` (default = `false`) — An optional parameter that specifies whether the `w` property of the Vector3D objects is used in the comparison.

Returns

Boolean — A value of true if the specified Vector3D object is nearly equal to the current Vector3D object; false if it is not equal.

See also

equals()

negate

()

method

public function negate():void

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Sets the current Vector3D object to its inverse. The inverse object is also considered the opposite of the original object. The value of the x, y, and z properties of the current Vector3D object is changed to -x, -y, and -z.

normalize

()

method

public function normalize():Number

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Converts a Vector3D object to a unit vector by dividing the first three elements (x, y, z) by the length of the vector. Unit vertices are vertices that have a direction but their length is one. They simplify vector calculations by removing length as a factor.

Returns

Number — The length of the current Vector3D object.

project

()

method

public function project():void

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Divides the value of the x, y, and z properties of the current Vector3D object by the value of its w property.

If the current Vector3D object is the result of multiplying a Vector3D object by a projection Matrix3D object, the w property can hold the transform value. The project() method then can complete the projection by dividing the elements by the w property. Use the Matrix3D.rawData property to create a projection Matrix3D object.

scaleBy

()

method

public function scaleBy(s:Number):void

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Scales the current Vector3D object by a scalar, a magnitude. The Vector3D object's x, y, and z elements are multiplied by the scalar number specified in the parameter. For example, if the vector is scaled by ten, the result is a vector that is ten times longer. The scalar can also change the direction of the vector. Multiplying the vector by a negative number reverses its direction.

Parameters

s:Number — A multiplier (scalar) used to scale a Vector3D object.

subtract

()

method

public function subtract(a:Vector3D):Vector3D

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Subtracts the value of the x, y, and z elements of the current Vector3D object from the values of the x, y, and z elements of another Vector3D object. The subtract() method does not change the current Vector3D object. Instead, this method returns a new Vector3D object with the new values.

Parameters

a:Vector3D — The Vector3D object to be subtracted from the current Vector3D object.

Returns

Vector3D — A new Vector3D object that is the difference between the current Vector3D and the specified Vector3D object.

See also

decrementBy()

toString

()

method

public function toString():String

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

Returns a string representation of the current Vector3D object. The string contains the values of the x, y, and z properties.

Returns

String — A string containing the values of the x, y, and z properties.

Constant Detail

X_AXIS

Constant

public static const X_AXIS:Vector3D

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

The x axis defined as a Vector3D object with coordinates (1,0,0).

Y_AXIS

Constant

public static const Y_AXIS:Vector3D

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

The y axis defined as a Vector3D object with coordinates (0,1,0).

Z_AXIS

Constant

public static const Z_AXIS:Vector3D

Language Version:

ActionScript 3.0

Runtime Versions:

Flash Player 10, AIR 1.5

The z axis defined as a Vector3D object with coordinates (0,0,1).