Dot Product Vs Cross Product Turning a Turret Towards A Enemy and firing

Question

http://pastebin.com/iw9DHf7s is code demonstrating dot product turning a turretto a target and firing. It works and chooses best angle to spin.

A problem can occur when game goes faster (better computer) and that threshold no longer applies. Making the threshold bigger obviously stops the turret early.

My friend mentions cross product is the way to fix it. Then he disappears for long periods of time. Doesn't dot product NOT get a inner angle between two vectors? Ok lets just say I agree and dot product doesn't work ever.

So tell me how does vector product do the trick? I'm going from a single scalar that I can get degrees out of to a third orthogonal vector. I've read about cross product and the function and watched a you tube video and I don't get (given the same code pasted) how to use cross product here.

Update: Would this work?

//towerFacing is the at/forward vector of the cannon
Vector v1 = cannonPos - targetPos ;
Vector v2 = towerFacing - cannonPos ;

//The z plane
double cross = v1.x*v2.y - v1.y*v2.x ;
if (cross > 0) { return Direction.Left ; } 
if (cross < 0) { return Direction.Right ; }

Obviously the zero is not what we want to use in games. However The difference is now our zero means our at vector and target is perpendicular and on each other which a x b = 0. The dot product since it uses cosine I used the right vector which is orthogonal with the facing( a . b = 0).

Am I wrong on how the cross product works by what has listed for answers still?

Answer 1

The dot method you have on the pastebin is fine if all objects are on the same plane and it is essentially a 2d problem (regardless of if the game is 2d or 3d). If, however, you are in a 3d environment where you need to adjust cannon yaw & pitch, then the cross method would be better because it would give both the direction to turn(rotate towards target) and the 3d axis to rotate about.

If you crossed the cannon's barrel direction with the direction to the target, it gives the proper axis. If you normalized both before crossing, it would even give the arc-sine of the angle between them if you needed (in the same way a dot product could give the arc-cosine). When crossing, the axis created will give the shortest rotational direction to the target... so does your dot method... but it fails you when the barrel has to change in two dimensions.

Answer 2

Blockquote A problem can occur when game goes faster (better computer) and that threshold no longer applies.

For starters this is a huge mistake to make and you will find your life much more difficult if you rely on the CPU processing speed to determine your game's frame rate. At a minimum I would update your game based on the actual progression of time rather than CPU cycles. You can still run into problems where different machines will have different amounts of time to process each frame, but your physics and other gameplay systems should advance time strictly on how much real world time passes each frame.