Hey Guys,

It's my first post here, been using XNA for a while now and I am currently in the stage of writing the AI for the enemy ships in my space shooter. I get very confused when it comes to calculating angles in 3D, all the angle math functions such as Atan2 seem to return results which I can't get my head around, I seem to have to make the angle negative and substract 90 degrees from it for it to be accurate. I also need the vertical angle and I don't know how you would work that out. A lot of things I read about calculating the angle between two 3D vectors only seem to return one angle, how can you have one angle between a 3D vector? So far I haven't needed to do any angle calculation and this problem is slowing me down, I would appreciate all the help you guys can give.

Thanks,

Oli.

Zebadee2323:

A lot of things I read about calculating the angle between two 3D vectors only seem to return one angle, how can you have one angle between a 3D vector?

Two 3D vectors lie in a plane whose normal is the cross product of them.  The angle between them is the angle between them on the plane.

Ah ha, I think I understand why there is only one angle now! Thanks.

For my rotations I am using quaternions, so far I have had no trouble with them however I still have no idea how I can calculate the pitch, yaw and roll my ship needs to have to point at another vector, is it possible to give me an example? Thanks a lot for your help so far. 

*Update*

I have now successfully calculated the Horizontal and Vertical angles thanks to you guys however I am now encountering another strange problem...

My ships movement is based on its forward vector, this vector is being rotated by the quaternion created using the two new angles I have calculated, the strange thing is the ship moves correctly towards its target but the actual ship model itself is going crazy even though it is using the same rotation quaternion that the forward vector is being rotated by. There isn't anything wrong with the way I am drawing my models because my rotation for everything else (such as the players ship) is fine.

Any Ideas?

Hi, thanks for your reply.

I meant going crazy as in looking in different directions at very fast speeds :P

I tried out your code but the ship seems to smoothly fly off in another direction. However your code did help me create some code of my own which seems to work for some positions, for others Vector3.Dot() will return over 1 or under -1 causing it and angle to become "NaN" and then my ship disappears.

I don't understand enough about quaternions to be able to work out whats wrong (if this is even a quaternion problem).

Thanks for your help so far, I really do appreciate it.

float dot, angle;
Vector3 cross, axis, targetVector;

targetVector = Vector3.Normalize(Target - Position);

dot = Vector3.Dot(Forward, targetVector);
angle = (float)Math.Acos(dot);

cross = Vector3.Cross(Forward, targetVector);
axis = Vector3.Normalize(cross);

RotationQuaternion *= Quaternion.CreateFromAxisAngle(axis, angle);
RotationQuaternion = Quaternion.Normalize(RotationQuaternion);
RotationMatrix = Matrix.CreateFromQuaternion(RotationQuaternion);

Forward = Vector3.TransformNormal(Vector3.Forward, RotationMatrix);
SetVelocity(Forward * 10000 * elapsed);

lordofduct:

Oh and your "Quaternion.CreateFromAxisAngle" doesn't know which direction around the axis you are talking about. ArcCos(angle) returns the closest angle between the two vectors, but it doesn't know if said angle is clockwise or counterClockwise from the forward vector. Hence why it probably only works at certain times, but not all (specifically when the target is a clockwise turn from the forward vector).

Ah yes that is probably why, I think I have ran into a problem similar to this before, I never managed to work out how to calculate which way an object has to turn to face its target the fastest. I don't know how you would do it only knowing the angle returned from Acos() though.

Thanks for your help.

Zebadee2323:

For my rotations I am using quaternions, so far I have had no trouble with them however I still have no idea how I can calculate the pitch, yaw and roll my ship needs to have to point at another vector, is it possible to give me an example? Thanks a lot for your help so far. 

Any Ideas?

Here is a different approach to think about.   If you are pointing one ship at a target, this thread will be helpful http://forums.xna.com/thread/32295.aspx as it shows a different (and for me, much simpler) approach.  The post in the thread that is the most relevant is.. http://forums.xna.com/post/32295.aspx

I have my spaceship world_matrix and a set of quaternions I use for rotations when I update the ship with a controller.  When I want to point the ship at something, I use a variation of the code referenced in the link.   After updating the direciton of the ship (the world_matrix up, forward, and right vectors) using the vector math, I update my quaternions using quaternion.CreateFromRotationMatrix(world_matrix).  

What I am doing now is keeping a vector3 target which I translate around with the controller and simply pass that target to my "point_at" function when I want to move the ship with the controller.   If the ship acquires a target it needs to approach, I simply drop in the position of that target.

best,

Byron

Thanks for the great replies guys, I have successfully got my ships flying to their targets :D. I have managed to implement some battle AI too, it's a very strange experience watching your AI fight each other.

Also just a small off topic question regarding ArrayList performance; I store all the lasers the ships shoot into an ArrayList, when there are a lot of them on screen they seem to "lag" as if I was playing an online game but all my other objects that are not managed by the ArrayList have smooth movement. I was just wondering if ArrayLists run on seperate threads or something and they are not keeping up fast enough with the main loop causing this lag effect? Or am I just talking absolute rubbish? :P