Ai System Patches

====== Euler To Quaternion ======

^ short description | Takes 3 rotation angles (x/y/z rot) and converts them to x/y/z/w quaternions |
^ ports | Bank (X) [control/numeric] |
^ ::: | Heading (Y) [control/numeric] |
^ ::: | Altitude (Z) [control/numeric] |
^ ::: | x Quaternion [control/numeric] |
^ ::: | y Quaternion [control/numeric] |
^ ::: | z Quaternion [control/numeric] |
^ ::: | w Quaternion [control/numeric] |

==== used in example ====

{{backlinks>.#ai:examples}}

===== Manual =====
This is not in the manual.

However, there is an extensive explanation in the a.m. example:

>When creating this project I ran into a strange problem: x, y, and z rotation are no independent from each other. I described it like this:
>
>... in AI, the x and y rotation of a screen fixture refer to the world’s x and y axis. However, z rotation refers to the screen’s z axis. This leads to the situation – with x_rot = -90 – that y_rot and z_rot do exactly the same, but the screen cannot be tilted sideways (what z_rotation does).
>
>Dave Green was kind enough to give a thorough explanation of this:
>
>
>> You have discovered one of the draw backs of the Euler angle system we use in to rotate screens in Ai.  Gimbal Lock.  There is a short video explaining the problem here: https://www.youtube.com/watch?v=zc8b2Jo7mno.  The advantage to using the Euler system for angles is that everybody understands it.  But the trade off is that it has limitations in the form of gimbal lock.
>>
>>So you are probably thinking what can I do to resolve this problem?  Well the simplest option is to have a second version of your model which is 'pre-rotated' by 90' on the x axis.  That will allow your z rotation to function as you expect.  That might not be the solution you need in this case, but it is a common solution to the problem.
>>
>>Another option is to use the alternate skin for the Fixture in the stage patch and then connect to the x,y,z,w Quat ports.  I believe these allow you to rotate the fixture using quaternion rotation.  Only problem is I just tried this and I have no idea what data you need to feed into it.  I know this solves this problem though if you can work out what to feed into it.  Ciaran may be able to elaborate here as he added these ports.  There is a short video explaining quaternion rotation here: https://www.youtube.com/watch?v=SCbpxiCN0U0 you should be able to take some math / trig modules in salvation and replicate the conversion detailed in this video if you are feeling brave ;)
>
>And while I was still struggling to find my way through all this Ciaran was so kind to create a patch which is now included as system patch:
>
>>As Dave has said you encounter this problem based on the way Euler angles are defined in Euclidean Space. To get around this we can either use a 4x4 rotation matrix or quaternions. Without getting into the maths too much I have created a patch that should convert your Euler Angles into Quaternions, giving you back full 3 degrees of rotation.

{{:ai:patches:eulertoquaternion.png?450|}}