Quaternion

Question

Hi, what's the difference between concatenate and multiply quaternion in C#?? Thanks

Answer 1

It seems that multiplication is *Q1*Q2*, concatenation is *Q2*Q1*.

See the source of Concatenate and Multiply:

• https://referencesource.microsoft.com/#System.Numerics/System/Numerics/Quaternion.cs,59e4bc6d59900151.

Answer 2

The answer is that the rotation order of the new quaternion obtained by the two methods is reversed.
The multiplication of quaternions means to form two rotations: perform one rotation and then perform another rotation, which means that the multiplication of quaternions cannot be commutative.
When we want to get q1*q2, we will use Quaternion.Multiply(q1,q2);
When we want to get q2*q1, we can use Quaternion.Multiply(q2,q1) or Quaternion.Concatenate(q1,q2);
You can see this in the source code of these two methods:

Multiply method：

        public static Quaternion Multiply(Quaternion value1, Quaternion value2)  
        {  
            Quaternion ans;  

            float q1x = value1.X;  
            float q1y = value1.Y;  
            float q1z = value1.Z;  
            float q1w = value1.W;  

            float q2x = value2.X;  
            float q2y = value2.Y;  
            float q2z = value2.Z;  
            float q2w = value2.W;  

            // cross(av, bv)  
            float cx = q1y * q2z - q1z * q2y;  
            float cy = q1z * q2x - q1x * q2z;  
            float cz = q1x * q2y - q1y * q2x;  

            float dot = q1x * q2x + q1y * q2y + q1z * q2z;  

            ans.X = q1x * q2w + q2x * q1w + cx;  
            ans.Y = q1y * q2w + q2y * q1w + cy;  
            ans.Z = q1z * q2w + q2z * q1w + cz;  
            ans.W = q1w * q2w - dot;  

            return ans;  
        }  

Concatenate method:

        public static Quaternion Concatenate(Quaternion value1, Quaternion value2)  
        {  
            Quaternion ans;  

            // Concatenate rotation is actually q2 * q1 instead of q1 * q2.  
            // So that's why value2 goes q1 and value1 goes q2.  
            float q1x = value2.X;  
            float q1y = value2.Y;  
            float q1z = value2.Z;  
            float q1w = value2.W;  

            float q2x = value1.X;  
            float q2y = value1.Y;  
            float q2z = value1.Z;  
            float q2w = value1.W;  

            // cross(av, bv)  
            float cx = q1y * q2z - q1z * q2y;  
            float cy = q1z * q2x - q1x * q2z;  
            float cz = q1x * q2y - q1y * q2x;  

            float dot = q1x * q2x + q1y * q2y + q1z * q2z;  

            ans.X = q1x * q2w + q2x * q1w + cx;  
            ans.Y = q1y * q2w + q2y * q1w + cy;  
            ans.Z = q1z * q2w + q2z * q1w + cz;  
            ans.W = q1w * q2w - dot;  

            return ans;  
        }  

You can see the source code here: referencesource.microsoft.com

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