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http://help.adobe.com/en_US/AS3LCR/Flash_10.0/flash/geom/Matrix3D.html

The documentation shows how the basis is defined for the Matrix3D object. While transforming a unit vector pointing down the...

This smells like an NP-complete problem to me. No real help to offer other than to suggest looking at packing problems and their solutions to see if those offer or lead to any insight. You may have...

For the world positioning issue, I'm not sure exactly what the problem is other than that there is some problem and it deals with "world positioning", whatever that means. Luckily, you seem to be on...

The example still compiles, if that's what you mean. The orientation of the objects is affected by the branch, though. The idea was to have the text aligned such that it appeared 'most upright'. ...

Project the vector of the ball onto the slope('s vector). The projection is the vector of the ball as if it were sliding down the slope, and the difference of the original velocity vector and that...

Another vote for the "this." prefix.

It should be noted that the "this." prefix is implicitly added whenever you access any member variable or member function from within the object. The only...

They are.
http://www.codecogs.com/eqnedit.php?latex=test

A Ray* object.

I would not do this myself as it would force explicit conversions from ray to line/segment, which is almost definitely...

Link to the Actionscript.org thread mentioned.

The reason I mentioned the Dictionary type was that I believed it was AS3's hash or tree structure. The documentation doesn't list it as such or...

A second approach which may be used for detecting collisions between arbitrary convex polytopes is the GJK algorithm(s). From what I have heard, this algorithm is more difficult to implement than...

Ahh I see. My mistake.

As for reducing the total number of comparisons made, some sort of broad phase culling scheme could be implemented. If you have already considered this and ruled it out...

Eberly has a segment-segment distance paper on his documentation page. The general approach described is applicable to a number of problems. The point-triangle paper on the same site describes a...

You could represent the rectangle parametrically and pick a point along the edge by clamping your variables to certain values. The advantage of this is that it will work for any parallelogram in any...

The way this is traditionally done is by using a transformation matrix as a "camera", and then transforming the workspace by the inverse of this camera matrix. This will allow for translating,...

I'll assume you're at least familiar with the dot product.

I don't understand what you're trying to say here, but you may have to adjust the following derivation for your problem. It might be...

package {

import flash.display.DisplayObject;
import flash.display.Sprite;
import flash.geom.Matrix;
import flash.geom.Point;
import flash.text.Font;
import...