How does game engine take quaternion into calculation?

Unity Engine
1

Transform matrix is a 4x4 matrix, and quaternion is only 1x4… how is everything happening behind the scene?

2

I’ve heard it said that quaternions are an entire field of specialization in the world of mathematics. I’ve come to accept that it’s a level of mathematical wizardry that I will never achieve. The Quaternion class is a godsend.

3

I believe that quaternion is somehow transformmed back into 4x4 matrix of rotation (rotMatrix) , and later take rotMatrix into calculation, but I am not so sure… I am curious about it,

4

Well, first up, things don’t necessarily have to be the same size to multiply them. Secondly, remember that where a quaternion stores only rotation a 4x4 matrix also stores position and scale data.

I can’t be more precise than that without going into the math, which I do recommend everyone works through for themselves at least once. You’ll rarely have to apply it manually yourself working in something like Unity, but having a solid grasp of how it all works - not just this, but matrix multiplication, the how and where various bits of data are represented, transformations between different representations and knowing the pros and cons of each - will better equip you figure out how to make stuff happen.

5

You can inspect the source code for Quaternion’s operators in MonoDevelop. They are indeed doing the equivalent math of using a rotation matrix.

public static Vector3 operator * (Quaternion rotation, Vector3 point)
{
    float num = rotation.x * 2f;
    float num2 = rotation.y * 2f;
    float num3 = rotation.z * 2f;
    float num4 = rotation.x * num;
    float num5 = rotation.y * num2;
    float num6 = rotation.z * num3;
    float num7 = rotation.x * num2;
    float num8 = rotation.x * num3;
    float num9 = rotation.y * num3;
    float num10 = rotation.w * num;
    float num11 = rotation.w * num2;
    float num12 = rotation.w * num3;
    Vector3 result;
    result.x = (1f - (num5 + num6)) * point.x + (num7 - num12) * point.y + (num8 + num11) * point.z;
    result.y = (num7 + num12) * point.x + (1f - (num4 + num6)) * point.y + (num9 - num10) * point.z;
    result.z = (num8 - num11) * point.x + (num9 + num10) * point.y + (1f - (num4 + num5)) * point.z;
    return result;
}
6

wow,thx…you are really powerful…