| Language version: | ActionScript 3.0 |
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.
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:
length:Number [read-only]
| Language version: | ActionScript 3.0 |
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:Number [read-only]
| Language version: | ActionScript 3.0 |
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
public var w:Number
| Language version: | ActionScript 3.0 |
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
public var x:Number
| Language version: | ActionScript 3.0
|
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.
public var y:Number
| Language version: | ActionScript 3.0
|
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.
public var z:Number
| Language version: | ActionScript 3.0
|
The third element of a Vector3D object, such as
the z coordinate of a point in three-dimensional space. The default value is 0.
public function Vector3D(x:Number = 0., y:Number = 0., z:Number = 0., w:Number = 0.)
| Language version: | ActionScript 3.0 |
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.) |
| |
| y:Number (default = 0.) |
| |
| z:Number (default = 0.) |
| |
| w:Number (default = 0.) |
public function add(a:Vector3D):Vector3D
| Language version: | ActionScript 3.0 |
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.
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
public function addToOutput(a:Vector3D, output:Vector3D):Vector3D
| Language version: | ActionScript 3.0 |
| Runtime version: | AIR 33.1
|
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.
Parameters
| a:Vector3D — A Vector3D object to be added to the current Vector3D object.
|
| |
| output:Vector3D — An optional Vector3D object to be used as the output value, avoiding the creation of a new object
|
Returns
| Vector3D —
A Vector3D object that is the result of adding the current Vector3D object
to another Vector3D object.
|
See also
public static function angleBetween(a:Vector3D, b:Vector3D):Number
| Language version: | ActionScript 3.0 |
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.
|
public function clone():Vector3D
| Language version: | ActionScript 3.0 |
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.
|
public function copyFrom(sourceVector3D:Vector3D):void
| Language version: | ActionScript 3.0
|
Copies all of vector data from the source Vector3D object into the
calling Vector3D object.
Parameters
| sourceVector3D:Vector3D — The Vector3D object from which to copy the data.
|
public function crossProduct(a:Vector3D):Vector3D
| Language version: | ActionScript 3.0 |
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 parallel to each other.
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
Returns
| Vector3D —
A new Vector3D object that is perpendicular to the current Vector3D object and the Vector3D
object specified as the parameter.
|
See also
public function crossProductToOutput(a:Vector3D, output:Vector3D):Vector3D
| Language version: | ActionScript 3.0 |
| Runtime version: | AIR 33.1
|
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 parallel to each other.
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.
|
| |
| output:Vector3D — An optional Vector3D object to be used as the output value, avoiding the creation of a new 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
public function decrementBy(a:Vector3D):void
| Language version: | ActionScript 3.0 |
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
public static function distance(pt1:Vector3D, pt2:Vector3D):Number
| Language version: | ActionScript 3.0 |
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.
|
public function dotProduct(a:Vector3D):Number
| Language version: | ActionScript 3.0 |
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
public function equals(toCompare:Vector3D, allFour:Boolean = false):Boolean
| Language version: | ActionScript 3.0 |
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)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
public function incrementBy(a:Vector3D):void
| Language version: | ActionScript 3.0 |
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
public function nearEquals(toCompare:Vector3D, tolerance:Number, allFour:Boolean = false):Boolean
| Language version: | ActionScript 3.0 |
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)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
public function negate():void
| Language version: | ActionScript 3.0 |
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.
public function normalize():Number
| Language version: | ActionScript 3.0 |
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.
|
public function project():void
| Language version: | ActionScript 3.0 |
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.
public function scaleBy(s:Number):void
| Language version: | ActionScript 3.0 |
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.
|
public function setTo(xa:Number, ya:Number, za:Number):void
| Language version: | ActionScript 3.0
|
Sets the members of Vector3D to the specified values
Parameters
public function subtract(a:Vector3D):Vector3D
| Language version: | ActionScript 3.0 |
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
public function subtractToOutput(a:Vector3D, output:Vector3D):Vector3D
| Language version: | ActionScript 3.0 |
| Runtime version: | AIR 33.1
|
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.
|
| |
| output:Vector3D — An optional Vector3D object to be used as the output value, avoiding the creation of a new object
|
Returns
| Vector3D —
A new Vector3D object that is the difference between the current Vector3D
and the specified Vector3D object.
|
See also
public function toString():String
| Language version: | ActionScript 3.0 |
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.
|
public static const X_AXIS:Vector3D
| Language version: | ActionScript 3.0 |
The x axis defined as a Vector3D object with coordinates (1,0,0).
public static const Y_AXIS:Vector3D
| Language version: | ActionScript 3.0 |
The y axis defined as a Vector3D object with coordinates (0,1,0).
public static const Z_AXIS:Vector3D
| Language version: | ActionScript 3.0 |
The z axis defined as a Vector3D object with coordinates (0,0,1).
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