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# iLikeCarrots

Member Since 19 Apr 2012
Offline Last Active Apr 23 2012 08:21 AM

### Invert Transform Matrix [Solved]

21 April 2012 - 09:19 PM

I'm having trouble inverting my object matrix with non-uniform scaling. I have scanned the web and written the multiplication out by hand, but I haven't been able to find my error. I am creating a matrix for OpenGL, and I combine my 4x4 matrix in the order Translation, Rotation, Scale. Where could I be going wrong?

I find the position X,Y,Z in the last column
I find the scaling X,Y,Z as the lengths the first three columns
I use the upper left 3x3 matrix as the rotation
```~ Inv Scale ~	 ~ Inv Rot ~  ~ Inv Pos ~
[1/X  0   0   0]   [\.......]   [1 0 0 -X]
[ 0  1/Y  0   0]   [..flip..]   [0 1 0 -Y]
[ 0   0  1/Z  0]   [diagonal]   [0 0 1 -Z]
[ 0   0   0   1]   [.......\]   [0 0 0  1]
```

After combining the above matrices in that order, I come up with the following code with matrix A as the result:
```(GL Matrix Indices)
[0 4  8 12]
[1 5  9 13]
[2 6 10 14]
[3 7 11 15]

void invertMatrix (float A[], float B[]) {
float sclX = lengthVector(&B[0]);
float sclY = lengthVector(&B[4]);
float sclZ = lengthVector(&B[8]);

A[0] = B[0]/sclX; A[4] = B[1]/sclX; A[8]  = B[2] /sclX;
A[1] = B[4]/sclY; A[5] = B[5]/sclY; A[9]  = B[6] /sclY;
A[2] = B[8]/sclZ; A[6] = B[9]/sclZ; A[10] = B[10]/sclZ;
A[3] = 0.0;	   A[7] = 0.0;	   A[11] = 0.0;

float posX = -B[12],
posY = -B[13],
posZ = -B[14];

A[12] = A[0]*posX + A[4]*posY + A[8] *posZ;
A[13] = A[1]*posX + A[5]*posY + A[9] *posZ;
A[14] = A[2]*posX + A[6]*posY + A[10]*posZ;
A[15] = 1.0;
}
```

To test my inverse, I created a matrix with the following transform:
Position x=0, y=0, z=0
Rotation x=1, y=0, z=0
Scaling x=1, y=1, z=3
I multiply the inverse times the matrix, which always returns the scaling on the diagonal.
```-- Object Matrix --   -- Inverse Matrix -- -- Inverse * Object --
[1.0  0.0  0.0  0.0]  [1.0  0.0  0.0 -0.0]  [1.0  0.0  0.0  0.0]
[0.0  0.5 -2.5  0.0]  [0.0  0.5  0.8 -0.0]  [0.0  1.0 -0.0  0.0]
[0.0  0.8  1.6  0.0]  [0.0 -0.8  0.5  0.0]  [0.0  0.0  3.0  0.0]
[0.0  0.0  0.0  1.0]  [0.0  0.0  0.0  1.0]  [0.0  0.0  0.0  1.0]
```

### Skinning Matrices [Solved]

20 April 2012 - 11:28 PM

I'm attempting to animate a skinned mesh with joints. I have looked at many different materials, and something isn't right with my understanding. All of my nodes hold a local and global matrix. When I load in the joints, I calculate the inverse pose matrix like so:

Pose Matrix = Mesh's Inverse Global * Joint Global
Inverse Pose Matrix = Inverse of Pose Matrix

Then when my joints are updated, I calculate the joint in mesh space and multiply it with the inverse pose matrix.

Joint wrt Mesh = Mesh's Inverse Global * Joint Global
Deform Matrix = Joint wrt Mesh * Inverse Pose Matrix

I uploaded the following video files to demonstrate what is happening to my mesh. Is my algorithm correct in handling the matrices in mesh space and calculating the inverse pose matrix? If I knew that, it would be easier to further study the problem.

Source animation..

My Results..

These are my references -
Introduction to Game Development
UCSD - Skinning powerpoint
Animation in Video Games

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