float4x4 position, rotation, and scale

I'm exploring float4x4 and created some helper methods to access data from it. Everything works well until the scale is no longer float3(1, 1, 1). To visualize the error I have attached this component to a teapot, and in the scene view I draw it again using a different color. As soon as the scale is changed the two meshes are rendered differently. What's going on here?

Code (CSharp):

1.  
2. public class Float4x4Testing : MonoBehaviour
3. {
4.  
5.     float3 GetPosition(float4x4 m)
6.     {
7.         return new float3(m.c3.x, m.c3.y, m.c3.z);
8.     }
9.  
10.     quaternion GetRotation(float4x4 m)
11.     {
12.         return new quaternion(m);
13.     }
14.  
15.     float3 GetScale(float4x4 m)
16.     {
17.         return new float3(
18.             math.length(new float3(m.c0.x, m.c1.x, m.c2.x)),
19.             math.length(new float3(m.c0.y, m.c1.y, m.c2.y)),
20.             math.length(new float3(m.c0.z, m.c1.z, m.c2.z))
21.         );
22.     }
23.  
24.  
25.     void OnDrawGizmos()
26.     {
27.         var pos = transform.position;
28.         var rot = transform.rotation.normalized;
29.         var scale = transform.lossyScale;
30.  
31.         float4x4 m = float4x4.TRS(pos, rot, scale);
32.  
33.         var p = GetPosition(m);
34.         var q = GetRotation(m);
35.         var s = GetScale(m);
36.  
37.         Gizmos.color = Color.grey;
38.         var mesh = gameObject.GetComponent<MeshFilter>().sharedMesh;
39.         Gizmos.DrawMesh(mesh, 0, p, q, s);
40.     }
41. }
42.  

 

Code (CSharp):

1.     float3 GetPosition(float4x4 m)
2.     {
3.         return new float3(m.c3.x, m.c3.y, m.c3.z);
4.     }
5.     quaternion GetRotation(float4x4 m)
6.     {
7.         return new quaternion(m);
8.     }

Because this is only valid when the transformation matrix has no scale.

If you have scale on your matrix you have to remove it first (it's been a while but I think it's just a division) before calculating position/rotation. This is basically why it's a good idea to avoid scale!