How do i calculate an objects scale using a perspective projection matrix?

Im currently building a little 3D particle engine in flash the uses sprites.

to set the position of each sprite I am using the projectVector function below. (the viewTransform matrix is the particles world matrix concatenated with a perspective projection matrix)

var projectedPoint:Vector3D = Utils3D.projectVector(viewTransform, point);
sprite.x = projectedPoint.x;
sprite.y =  projectedPoint.y;

this wor开发者_如何学JAVAks really well an places the sprites exactly where they should be :D The problem I am having is trying to figure out how to calculate the scale of the each particle based on is distance from the camera..

sprite.scaleX = sprite.scaleY = ??

If I wasn't using a perspective projection matrix I would usually do something like this..

var scaleRatio:Number = (focus * zoom)/(focus + particle.globalz);
particle.depth = scaleRatio;
sprite.x = particle.globalx * scaleRatio;
sprite.y = particle.globaly * scaleRatio;
// set scale..
sprite.scaleX = sprite.scaleY = scaleRatio;

If there is anyone out there able to show me how to calculate the "scaleRatio" using a perspective projection matrix that would be ace

thanks!

I'm sure there's a more succinct way to do this, but since you already know how to project a point, you could do this:

var tl:Point = sprite.getRect(sprite.parent).topLeft;
var br:Point = sprite.getRect(sprite.parent).bottomRight;

var projectedTL:Point = Utils3D.projectVector(viewTransform, tl);
var projectedBR:Point = Utils3D.projectVector(viewTransform, br);

trace("projected width = "+(projectedBR.x - projectedTL.x));
trace("projected height = "+(projectedBR.y - projectedTL.y));