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No this is not an engine bug or an artifact of a selected rotation illustration (these can occur too, however this impact applies to each system that represents rotations, quaternions included).
You have found an actual reality about how rotation works in three-dimensional area, and it departs from our instinct about different transformations like translation:
Once we compose rotations on a couple of axis, the consequence we get is not simply the entire/internet worth we utilized to every axis (as we would anticipate for translation). The order wherein we apply the rotations modifications the consequence, as every rotation strikes the axes on which the following rotations get utilized (if rotating concerning the object’s native axes), or the connection between the article and the axis (if rotating concerning the world’s axes).
The altering of axis relationships over time can confuse our instinct about what every axis is “supposed” to do. Particularly, sure combos of yaw and pitch rotations give the identical consequence as a roll rotation!
You possibly can confirm that every step is rotating accurately concerning the axis we requested – there is not any engine glitch or artifact in our notation interfering with or second-guessing our enter – the spherical (or hyperspherical / quaternion) nature of rotation simply means our transformations “wrap round” onto one another. They might be orthogonal regionally, for small rotations, however as they pile up we discover they don’t seem to be globally orthogonal.
That is most dramatic and clear for 90-degree turns like these above, however the wandering axes creep in over many small rotations too, as demonstrated within the query.
So, what can we do about it?
If you have already got a pitch-yaw rotation system, one of many quickest methods to remove undesirable roll is to alter one of many rotations to function on the worldwide or father or mother transformation axes as an alternative of the article’s native axes. That means you possibly can’t get cross-contamination between the 2 – one axis stays completely managed.
Here is the identical sequence of pitch-yaw-pitch that turned a roll within the instance above, however now we apply our yaw across the world Y axis as an alternative of the article’s
So we will repair the first-person digital camera with the mantra “Pitch Domestically, Yaw Globally”:
void Replace() {
float velocity = lookSpeed * Time.deltaTime;
rework.Rotate(0f, Enter.GetAxis("Horizontal") * velocity, 0f, House.World);
rework.Rotate(-Enter.GetAxis("Vertical") * velocity, 0f, 0f, House.Self);
}
In case you’re compounding your rotations utilizing multiplication, you’d flip the left/proper order of one of many multiplications to get the identical impact:
// Yaw occurs "over" the present rotation, in world coordinates.
Quaternion yaw = Quaternion.Euler(0f, Enter.GetAxis("Horizontal") * velocity, 0f);
rework.rotation = yaw * rework.rotation; // yaw on the left.
// Pitch occurs "beneath" the present rotation, in native coordinates.
Quaternion pitch = Quaternion.Euler(-Enter.GetAxis("Vertical") * velocity, 0f, 0f);
rework.rotation = rework.rotation * pitch; // pitch on the fitting.
(The particular order will depend upon the multiplication conventions in your surroundings, however left = extra world / proper = extra native is a standard alternative)
That is equal to storing up the web whole yaw and whole pitch you need as float variables, then all the time making use of the web consequence , setting up a single new orientation quaternion or matrix from these angles alone (supplied you retain totalPitch clamped):
// Assemble a brand new orientation quaternion or matrix from Euler/Tait-Bryan angles.
var newRotation = Quaternion.Euler(totalPitch, totalYaw, 0f);
// Apply it to our object.
rework.rotation = newRotation;
or equivalently…
// Kind a view vector utilizing whole pitch & yaw as spherical coordinates.
Vector3 ahead = new Vector3(
Mathf.cos(totalPitch) * Mathf.sin(totalYaw),
Mathf.sin(totalPitch),
Mathf.cos(totalPitch) * Mathf.cos(totalYaw));
// Assemble an orientation or view matrix pointing in that route.
var newRotation = Quaternion.LookRotation(ahead, new Vector3(0, 1, 0));
// Apply it to our object.
rework.rotation = newRotation;
Utilizing this world/native cut up, the rotations haven’t got an opportunity to compound and affect one another, as a result of they’re utilized to impartial units of axes.
The identical concept might help if it is an object on this planet that we need to rotate. For an instance just like the globe, we would typically need to invert it and apply our yaw regionally (so it all the time spins round its poles) and pitch globally (so it ideas towards/away from our view, moderately than towards/away from Australia, wherever it is pointing…)
Limitations
This world/native hybrid technique is not all the time the fitting repair. For instance, in a sport with 3D flight/swimming, you may want to have the ability to level straight up / straight down and nonetheless have full management. However with this setup you may hit gimbal lock – your yaw axis (world up) turns into parallel to your roll axis (native ahead), and you haven’t any strategy to look left or proper with out twisting.
What you are able to do as an alternative in instances like that is to make use of pure native rotations like we began with within the query above (so your controls really feel the identical irrespective of the place you are wanting), which can initially let some roll creep in – however then we appropriate for it.
For instance, we will use native rotations to replace our “ahead” vector, then use that ahead vector along with a reference “up” vector to assemble our remaining orientation. (Utilizing, for instance, Unity’s Quaternion.LookRotation methodology, or manually setting up an orthonormal matrix from these vectors) By controlling the up vector, we management the roll or twist.
For the flight/swimming instance, you may need to apply these corrections progressively over time. If it is too abrupt, the view can lurch in a distracting means. As an alternative, you need to use the participant’s present up vector and trace it towards the vertical, frame-by-frame, till their view ranges out. Making use of this throughout a flip can generally be much less nauseating than twisting the digital camera whereas the participant’s controls are idle.
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