Hello everyone!

I am trying to make a space RTS where ships have 2 rotation DOF (pitch, yaw) and 3 translation DOF (x,y,z). Each ship has a set of turrets, some of which have their pivot angles restricted. The turret itself pivots around it's yaw axis, and the barrels on their pitch axis, and each axis has its own restrictions. Each turret has one quaternion for the base orientation, and one for the barrel orientation. The turret also has a set traverse speed on each axis.

My problem is that I don't know how to find the rotation needed on each axis to traverse the turret towards it's target. Ofcourse, i also need to find wether it can reach the target at all, or if it should find something else to shoot at. My first thought was to convert the target coordinates into the turrets local space and find the angles using trig (is this possible?). What way would you do it? Do i need to save the local euler orientation or can this be done entirely with quaternions? What is the fastest and easiest way of doing this?

These are the functions i want to make:

private bool isObjectInField (object o)

public bool rotateTowardsPoint (vector v)

But first, some background:

*I am making this inside the Warcraft III engine. The language I use is object oriented and similar to Java.

*Z axis is "up", and X is "forward" (in model space).

*I am using my own vector and quaternion libraries which have most of the funcitons necessary. I would, however, like to refrain from using SLERP since it is too slow.

Any help is very much appreciated. I can uderstand most code languages, so do feel free to post code examples.

Will you only turn in the xy-plane (around the z-axis) or also up and down?

As stated the turret has 2 rotation DOF and rotates both on its pitch and yaw axis. The barrels can only rotate up/down, and the base can only rotate left/right (in local space, ofcourse).

I actually made a small illustration to show what i mean:

[attachment=17765:Illustration.jpg]

The gun base pivots on the Z axis, and has a limited turning field. So does the barrels, except they pivot in the Y axis. The whole gun itself can be oriented in any way on the surface of the ship. Given a target point, i want to find out:

A: if the point is within the turrets target field.

B: how to rotate the turret towards it.

Given your current view direction v1 and the target view direction v2 you can create a quaternion that rotates v1 into v2. The rotation axis is a = v1 x v2 and the rotation angle is found using cos( alpha ) = dot( v1, v2 ). You can google for shortest arc quaternion. There is an article in GPG 1 by Stan Melax which is useful and you can find it nearly completely on Google Books previews.

Once you have the quaternion q = ( x, y, z, w ) which rotates v1 into v2 you can decompose it into its swing and twist components. (Google for swing twist decomposition). After the decomposition you apply the limit to the twist factor and re-build you final quaternion.

You decompose the quaternion as q = q_xy * q_z. Here q_z = ( 0, 0, z, w ) / sqrt( z^2 + w^2 ). You can now compute q_xy = q * conjugate( q_z ). Now apply your limit to q_z and finally find the limited quaternion q' = q_xy * q_z'. If no limit was applied q will be equal to q'.

From your picture you might want to limit the swing of the turret as well and you can use the same principal as described above.

HTH,

-Dirk

Tank you for your reply! That looks like a very elegant sulotion indeed. What i ended up using though was the method i proposed in my first post - calculating the inverse of the ships orientation, and then rotating the relative position of the target by this, and finally just using Atan2 to find the angles. In this case i saved the euler angles separately, since all restrictions are in degrees, it made sense to me to do so. After setting the appropriate pitch/yaw rotations, i reassembled the quaternion from the new values.

Any comments on this? Thank you again for your help.