24
votes
Accepted
Using Quaternions: What can I do with them? (without the maths)
Multiplication
At least in terms of Unity's implementation of Quaternions, the multiplication order described in the question is not correct. This is important because 3D rotation is not commutative.
...
- 132k
15
votes
Using Quaternions: What can I do with them? (without the maths)
Where's the dot product used?
In Unity, one of the most common users of the dot product is whenever you check if two quaternions are equal via == or ...
- 611
10
votes
Accepted
Is adding quaternions a useful operation?
I can think of two reasons:
if your quats represent infinitesimal rotations, adding them together actually yields the composite rotation, provided the result is infinitesimal too (i.e. an element of ...
- 3,271
7
votes
Switch axes and handedness of a quaternion?
To convert the Quaternion, we need to convert the imaginary part (xyz) which represents the axis of rotation into the destination coordinate system. In this case, that means exchanging x & y while ...
- 132k
7
votes
Accepted
Rotate from Current Rotation to Another using Angular Velocity
"maybe due to the gimbal nature of Vector3 for angular velocity" ...using Vector3 for angular velocity does not entail gimbals, but converting it to Euler angles does.
Angular velocity is not an ...
- 132k
7
votes
Accepted
Converting a quaternion in a right to left handed coordinate system
A quaternion can be thought of as an angle-axis representation:
quaternion.xyz = sin(angle/2) * axis.xyz
quaternion.w = cos(angle/2)
So, converting them between ...
- 132k
6
votes
How to express and verify euler rotation limits in Unity
Euler angles aren't necessarily a good way of expressing limits over arbitrary ranges, as their behaviour close to zero is very different from their behaviour away from zero.
Below I've visualized ...
- 132k
6
votes
Accepted
Direction vector to quaternion
From http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/
...
- 3,729
6
votes
Combining Quaternion Rotations
Multiplying two quaternions gives you a quaternion equivalent to performing the two rotations they represent in sequence.
...
- 132k
5
votes
Accepted
Unwanted roll when rotating camera with pitch and yaw
As I explained above, this is not an issue with quaternions. Quaternions just represent your rotation.
The problem is that you have mutually conflicting goals for this rotation:
The camera can look ...
- 132k
5
votes
Accepted
Quaternion rotation problems
"Is it wrong that I am counting total rotation and then creating [a] quaternion from it?"
Yes, because rotations do not combine like simple addition.
(In mathematical terms, rotations in three ...
- 132k
5
votes
Convert quaternion to a different coordinate system
Summarizing your two coordinate spaces:
...
- 132k
5
votes
Unity Quaternion.LookRotation meaning
Quaternion.LookRotation(forward, up) constructs an orientation quaternion that...
rotates an object's local z+ axis (0, 0, 1) — the blue arrow on its local ...
- 132k
5
votes
Accepted
Euler angle and Quaternion conversion become weird when yaw is bigger than 90 degrees
Your current code assumes it's always going to get Euler angles where x is between ±90° and z is close to 0.
Meanwhile, glm wants to return Euler angles that are standardized so that y is between ±90°,...
- 132k
5
votes
Does gimbal lock occur only when a combination of local and world rotation axis are used?
Gimbal lock occurs when your internal structure for storing/composing rotations uses a gimbal model:
Image via Wikipedia, attributed: "By Lookang many thanks to Fu-Kwun Hwang and author of Easy ...
- 132k
4
votes
Accepted
Unity's Quaternion.Lerp slows down when target is directly behind turret
Taking a look at your barrel rotation function...
...
- 132k
4
votes
Accepted
LookRotation() make X axis face the target instead of Z
I've answered a few flavours of this before.
The basic idea is to chain together two rotations: one that takes the axes you want to align and points them along z+ and y+ respectively, and then the ...
- 132k
4
votes
Accepted
How to smooth rotations?
Yes, in fact that's what quaternions are often used for - interpolating between two different orientations. Other methods of representing orientation suffer from issues like gimbal lock and wrap-...
- 14.8k
4
votes
Accepted
Storing transformations in game objects. (GLM, C++)
My general recommendation is to keep both the source components of your transformation for ease of manipulation:
local translation vector
local orientation quaternion
local axis-aligned scale triplet,...
- 132k
4
votes
GLM conversion from euler angles to quaternion and back does not hold
The results are not what you expect, but they are not wrong. It’s just that for a given orientation there are at least two “paths” through Euler angles that lead there.
For instance, the identity ...
- 23.8k
4
votes
Accepted
Understanding how to use Quaternion to rotate object
Explaining why quaternions work the way they do and their relation to mainstream linear transformation rotations would require some more advanced mathematics knowledge regarding group theory and how ...
- 338
4
votes
Accepted
How does Unity know where the character is facing?
It doesn't know.
What it does is point the local z axis of the object (that's the blue arrow you see in the scene view when selecting its local transform gizmo) in the ...
- 132k
4
votes
Accepted
How does Unity's FromToRotation work? A major part of its behavior seems undocumented
FromToRotation chooses the shortest possible rotation that maps fromDirection to toDirection....
- 132k
3
votes
Accepted
Quaternion not giving correct value back. What am I doing wrong here?
Rounding.
If you attach the debugger and look at the values of your quaternion:
You'll see that the values are just too small to be displayed with one tenth precision, as the debug value is ...
- 73.2k
3
votes
Applying angular velocity to quaternion
In the following I use a vector hat to represent a quaternion and a unit vector hat to represent a unit quaternion.
Let q(t) represent the quaternion rotation at any point in time. Let r be a ...
- 131
3
votes
Accepted
How to avoid Gimbal Lock on Rubik's Cube
In the case of a puzzle like this you can animate the rotation then reset the model back to its original position but with the cube's stickers rotated.
Look at it like cheating with a real puzzle by ...
- 11.9k
3
votes
Accepted
How should I handle quaternion types, in my game engine?
If your goal is to have quaternion that expresses rotations, and if you want to do operations with them (for eg. rotation composition by multiplying quaternions or convertion a quaternion to a ...
- 466
3
votes
Accepted
How to orbit an object around another object in an oval path in Unity?
You may translate the orbiting object with the coordinates of an elliptical path. You can get the x and y values from the equations.
x = centerX + (semi-major * sin T)
y = centerY + (semi-...
- 2,043
3
votes
Accepted
Unity : how to Rotate GameObject back to Indentity position?
I'd usually approach it like this:
...
- 132k
Only top scored, non community-wiki answers of a minimum length are eligible