Tech Blog

I just updated Papervision3D to allow the CameraObject3D#unproject method to work when CameraObject3D#useProjectionMatrix = true.

Papervision3D has two methods of ‘projecting’ vectors onto the screen:

1. useProjectionMatrix = false, this is the default ‘fast’ method
2. useProjectionMatrix = true, this is the method where projection is done by a matrix

Note that Papervision3D switches to method #2 in ‘ortho mode’.

So what is the difference exactly between these two kinds of projection? First we need to define what projection is. Projection is what adds ‘perspective’ to a scene and makes sure your scene fits to the viewport. Its the last step in the so-called ‘render pipeline’.

We can derive the ‘fore shortening’ effect of perspective in several ways. Method #1 is simple, effective and fast. It uses the camera’s focus and zoom values. Method #2 uses a more classic way of projection : it uses a dedicated matrix. Tech buffs: very much like OpenGL’s gluPerspective.

Andy Zupko has a great post on unproject using method #1.

We will discuss unproject using method #2, which works slightly different.

The difference is that when #useProjectionMatrix is set to true, then CameraObject3D#unproject returns a point in world-space, rather then a ray. Let me explain with some code:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17

// we want to use a projection matrix
camera.useProjectionMatrix = true;
 
// '0' indicates we want a point on the near plane
var pointOnNearPlane : Number3D = camera.unproject( screenX, screenY, 0 );
 
// '1' indicates we want a point on the far plane
var pointOnFarPlane : Number3D = camera.unproject( screenX, screenY, 1 );
 
// Construct the ray's direction
var dir : Number3D = Number3D.sub( pointOnFarPlane, pointOnNearPlane );
 
// Normalize
dir.normalize();
 
// So, now you have a ray with its origin at 'pointOnNearPlane',
// and direction 'dir'

Optimization: could save some cycles by doing (*not* in ortho mode!, see below):

1
2
3
4
5
6
7

var camPosition : Number3D = new Number3D( camera.x, camera.y, camera.z );
// Construct the ray's direction
var dir : Number3D = Number3D.sub( pointOnFarPlane, camPosition );
// Normalize
dir.normalize();
// So, now you have a ray with its origin at the camera's position
// and direction 'dir'

Why can’t we use above optimization in ortho mode?
In perspective mode all ‘rays’ originate from the camera’s position: the ‘view cone’ has shape of a pyramid. Hence we can assume ‘pointOnNearPlane’ to coincide with the camera’s position.
In ortho mode however the ‘view cone’ has the shape of a cube, all rays are parallel. Hence we need to unproject *two* points to construct our ray.

Now simply follow Andy Zupko ’s post to drag objects around.
Or perform ‘picking’, or…

Update:
Created a little demo to visualize what I’m ranting about, check it out here

Tags: camera, Flash, Papervision3D, unproject