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The
PerspectiveProjection
class in the
flash.geom
package
provides a simple way of applying rudimentary perspective when moving
display objects through 3D space.
If you do not explicitly create a perspective projection for
your 3D space, the 3D engine uses a default PerspectiveProjection
object that exists on the root and is propagated to all its children.
The three properties that define how a PerspectiveProjection
object displays 3D space are:
-
fieldOfView
-
projectionCenter
-
focalLength
Modifying the value of the
fieldOfView
automatically
modifies the value of the
focalLength
and vice-versa,
since they are interdependent.
The formula used to calculate the
focalLength
given
the
fieldOfView
value is:
focalLength = stageWidth/2 * (cos(fieldOfView/2) / sin(fieldOfView/2)
Typically you would modify the
fieldOfView
property
explicitly.
Field of view
By manipulating
the
fieldOfView
property of the PerspectiveProjection
class, you can make a 3D display object approaching the viewer appear
larger and an object receding from the viewer appear smaller.
The
fieldOfView
property specifies an angle
between
0
and 180 degrees that determines the strength of the perspective
projection. The greater the value, the stronger the distortion applied
to a display object moving along its z-axis. A low
fieldOfView
value
results in very little scaling and causes objects to appear to move
only slightly back in space. A high
fieldOfView
value
causes more distortion and the appearance of greater movement. The
maximum value of 179.9999... degrees results in an extreme fish-eye
camera lens effect. The maximum value of
fieldOfView
is
179.9999... and the minimum is 0.00001... Exactly 0 and 180 are
illegal values.
Projection center
The
projectionCenter
property
represents the vanishing point in the perspective projection. It
is applied as an offset to the default registration point (0,0)
in the upper-left corner of the stage.
As an object appears to move further from the viewer, it skews
towards the vanishing point and eventually vanishes. Imagine an
infinitely long hall. As you look down the hall, the edges of the
walls converge to a vanishing point far down the hall.
If the vanishing point is at the center of the stage, the hall
disappears towards a point in the center. The default value for
the
projectionCenter
property is the center of
the stage. If, for example, you want elements to appear on the left of
the stage and a 3D area to appear on the right, set the
projectionCenter
to
a point on the right of the stage to make that the vanishing point
of your 3D viewing area.
Focal length
The
focalLength
property
represents the distance between the origin of the viewpoint (0,0,0)
and the location of the display object on its z-axis.
A long focal length is like a telephoto lens with a narrow view
and compressed distances between objects. A short focal length is
like a wide angle lens, with which you get a wide view with a lot
of distortion. A medium focal length approximates what the human
eye sees.
Typically the
focalLength
is re-calculated dynamically
during perspective transformation as the display object moves, but
you can set it explicitly.
Default perspective projection values
The default PerspectiveProjection object created
on the root has the following values:
-
fieldOfView: 55
-
perspectiveCenter: stagewidth/2, stageHeight/2
-
focalLength: stageWidth/ 2 * ( cos(fieldOfView/2) / sin(fieldOfView/2) )
These are the values that are used if you do not create your
own PerspectiveProjection object.
You can instantiate your own PerspectiveProjection object with
the intention of modifying the
projectionCenter
and
fieldOfView
yourself.
In this case, the default values of the newly created object are
the following, based on a default stage size of 500 by 500:
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