Question Replicating Matrix4x4.TRS() function on the gpu?

Hello, I need to replicate the math of this function
https://docs.unity3d.com/ScriptReference/Matrix4x4.TRS.html

on the gpu. It needs to take in a float3 (For scale), float3 (translation), and float4 (quaternion rotation) and build a float4x4 matrix that can be multiplied with a vertex position (i.e, mul(MYMATRIX, v.vertex) to get the intended transformation.

I looked at the source code for "matrix4x4.cs" from this page: https://github.com/Unity-Technologies/UnityCsReference/blob/master/Runtime/Export/Math/Matrix4x4.cs

which seems to be the math I must reproduce in hlsl. However, my implementation below does not work:

Code (CSharp):

1. float4x4 Scale(float3 vec)
2. {
3.     float4x4 m;
4.     m._m00 = vec.x; m._m01 = 0.0; m._m02 = 0.0; m._m03 = 0.0;
5.     m._m10 = 0.0; m._m11 = vec.y; m._m12 = 0.0; m._m13 = 0.0;
6.     m._m20 = 0.0; m._m21 = 0.0; m._m22 = vec.z; m._m23 = 0.0;
7.     m._m30 = 0.0; m._m31 = 0.0; m._m32 = 0.0; m._m33 = 1.0;
8.     return m;
9. }
10.  
11. // Creates a translation matrix.
12. float4x4 Translate(float3 vec)
13. {
14.     float4x4 m;
15.     m._m00 = 1.0; m._m01 = 0.0; m._m02 = 0.0; m._m03 = vec.x;
16.     m._m10 = 0.0; m._m11 = 1.0; m._m12 = 0.0; m._m13 = vec.y;
17.     m._m20 = 0.0; m._m21 = 0.0; m._m22 = 1.0; m._m23 = vec.z;
18.     m._m30 = 0.0; m._m31 = 0.0; m._m32 = 0.0; m._m33 = 1.0;
19.     return m;
20. }
21.  
22. // Creates a rotation matrix. Note: Assumes unit quaternion
23. float4x4 Rotate(float4 q)
24. {
25.     // Precalculate coordinate products
26.     float x = q.x * 2.0;
27.     float y = q.y * 2.0;
28.     float z = q.z * 2.0;
29.     float xx = q.x * x;
30.     float yy = q.y * y;
31.     float zz = q.z * z;
32.     float xy = q.x * y;
33.     float xz = q.x * z;
34.     float yz = q.y * z;
35.     float wx = q.w * x;
36.     float wy = q.w * y;
37.     float wz = q.w * z;
38.  
39.     // Calculate 3x3 matrix from orthonormal basis
40.     float4x4 m;
41.     m._m00 = 1.0f - (yy + zz); m._m10 = xy + wz; m._m20 = xz - wy; m._m30 = 0.0;
42.     m._m01 = xy - wz; m._m11 = 1.0f - (xx + zz); m._m21 = yz + wx; m._m31 = 0.0;
43.     m._m02 = xz + wy; m._m12 = yz - wx; m._m22 = 1.0f - (xx + yy); m._m32 = 0.0;
44.     m._m03 = 0.0; m._m13 = 0.0; m._m23 = 0.0; m._m33 = 1.0;
45.     return m;
46. }
47.  
48. float4x4 TRS(float4x4 s, float4x4 r, float4x4 t)
49. {
50.     float4x4 final = mul(t, mul(s, r));
51.     return final;
52. }

For the last method there, I tried every combination for ordering t, r, and s. So that is not where the issue lies. Can anyone provide some pointers?

 

If you manually make three matrices with each of rotate45, translate 1,2,3, scale 4,5,6, and then look at the resulting matrices, you will see that the "interesting" terms of these three operations do not overlap at all. Just construct the matrix with the appropriate terms and the appropriate values. Study lines 348 to 391 of the source code, and see how you could do the results of all three in a very similar function.

 

I do not know how to do that. I mean, the function Matrix4x4.TRS takes an input of two vector3 and a quaternion and does some math to make the final matrix4x4. I just want to find that source code so I can translate it into HLSL

 

I also tried this resource, particularly lines 87-141, and it also did not yield correct results: https://gist.github.com/mattatz/86fff4b32d198d0928d0fa4ff32cf6fa

 

Code (CSharp):

1.  
2. float4x4 QuatToMatrix(float4 q)
3. {
4.     float4x4 rotMat = float4x4
5.     (
6.         float4(1 - 2 * q.y * q.y - 2 * q.z * q.z, 2 * q.x * q.y + 2 * q.w * q.z, 2 * q.x * q.z - 2 * q.w * q.y, 0),
7.         float4(2 * q.x * q.y - 2 * q.w * q.z, 1 - 2 * q.x * q.x - 2 * q.z * q.z, 2 * q.y * q.z + 2 * q.w * q.x, 0),
8.         float4(2 * q.x * q.z + 2 * q.w * q.y, 2 * q.y * q.z - 2 * q.w * q.x, 1 - 2 * q.x * q.x - 2 * q.y * q.y, 0),
9.         float4(0, 0, 0, 1)
10.     );
11.     return rotMat;
12. }
13.  
14. float4x4 MakeTRSMatrix(float3 pos, float4 rotQuat, float3 scale)
15. {
16.     float4x4 rotPart = QuatToMatrix(rotQuat);
17.     float4x4 trPart = float4x4(float4(scale.x, 0, 0, 0), float4(0, scale.y, 0, 0), float4(0, 0, scale.z, 0), float4(pos, 1));
18.     return mul(rotPart, trPart);
19. }
20.  

 

Thanks for this, going to try it out and will let you know!

 

@Rukhanka hmmm we are close but this does not give quite the same results as Matrix.TRS() on the CPU. For example, when using the exact same vectors (or floats on the gpu) for translation, rotation, and scale, I get these two different matrices (printed to console at runtime):


From Matrix4x4.TRS():

0.96297 0.00000 -0.26963 -0.54868
0.00000 1.00000 0.00000 0.00000
0.26963 0.00000 0.96297 0.40844
0.00000 0.00000 0.00000 1.00000


From the proposed hlsl functions:


0.96297 0.00000 0.26963 0.00000
0.00000 1.00000 0.00000 0.00000
-0.26963 0.00000 0.96297 0.00000
-0.54868 0.00000 0.40844 1.00000


So they are similar for sure, but for some reason the top right and bottom left are interchanged, two values in the bottom right are interchanged, and there are some signs reversed... anyone know why this is?

 

There are exactly same matrices, but first one is column major and second is row major: https://www.scratchapixel.com/lesso...eometry/row-major-vs-column-major-vector.html
Transpose matrix to convert from one to another.

 

@Rukhanka Thank you man I really appreciate you. Works like a charm. Made my day