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Question by AlexPGilbert · Jan 19, 2016 at 07:33 PM · rotationquaternionvertex shader

Quaternion Multiplication in a shader.

Hi All!

I have this math visualization project I am working on which involves stereo-graphically projecting points on the 4 dimensional sphere onto a 3D plane.

I have the prototype working great! (https://www.facebook.com/100008697402693/videos/1513084485658117/?theater)

Anyways, I'm trying to move most of the calculations I am doing off the CPU and onto the GPU. I have most of it working except I cannot for the life of me get quaternion multiplication to work in CG. I really need a function in CG that takes two float4's and multiplies them the same way the * operator works with Unity Quaternions.

The function I am using now looks like:

 float4 mulQuaternion(float4 q1, float4 q2)
                 {
                     float4 q =
                     {
                         (q1.w * q2.x) + (q1.x * q2.w) + (q1.y * q2.z) - (q1.z * q2.y),
                         (q1.w * q2.y) - (q1.x * q2.z) + (q1.y * q2.w) + (q1.z * q2.x),
                         (q1.w * q2.z) + (q1.x * q2.y) - (q1.y * q2.x) + (q1.z * q2.w),
                         (q1.w * q2.w) - (q1.x * q2.x) - (q1.y * q2.y) - (q1.z * q2.z),
                     };
                     return q;
                 }

I'm sure there is a small mistake somewhere, but I have been at this for a while and can't seem to fix it. Any help would be really appreciated. Thank you!

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Answer by cjdev · Jan 19, 2016 at 10:58 PM

It could be that you're doing the multiplication in the wrong order since it's not communicative or you might have the wrong equation. You could try the Hamilton product, which it looks like you either have or are close to.

 float4 q =
         {
             q1.x*q2.x - q1.y*q2.y - q1.z*q2.z - q1.w*q2.w,
             q1.x*q2.y + q1.y*q2.x + q1.z*q2.w - q1.w*q2.z,
             q1.x*q2.z - q1.y*q2.w + q1.z*q2.x + q1.w*q2.y,
             q1.x*q2.w + q1.y*q2.z - q1.z*q2.y + q1.w*q2.x
         }
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