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When working with 3d graphics, sample shaders USUALLY use the following operation for vector position transformation:

result = mul(matrix, vector);

This obviously means the same as:

result = mul(vector, matrix_transposed);

Also, just to mention, most linear algebra libraries prefer to only leave the vector * matrix multiplication operation for simplicity.

Now: let's say I want to transform some vector (position, for example), using some concrete matrix (to be concrete, let's use D3DX matrix operations). So, I construct simple world-view-projection matrix and then pass it to my shader.

  D3DXMatrixRotationX(&world, 0.05f);

  D3DXMatrixLookAtLH(&view, &D3DXVECTOR3(400.0f, 80.0f, 0.0f),
                            &D3DXVECTOR3(0.1f, 0.1f, 0.0f),
                            &D3DXVECTOR3(0.0f, 1.0f, 0.0f));

  D3DXMatrixPerspectiveFovLH(&projection, 0.5f, 800.0f / 600.0f, 1.0f, 1500.0f);

  D3DXMATRIX wvp = world * view * projection;

  Set Shader Parameter (wvp); // Pseudocode here


And here comes the part I can't understand - if done this way, the shader code should be

result = mul(vector, wvp)

for this transformation to work(vector is multiplied from the left side of the matrix).

Why does this happen? How do most sample shaders have the result = mul(wvp, vector) transformation inside them (and they don't transpose the matrix before setting it as a parameter)?

Where am I wrong?

Thank you.

A bit more information - D3DX matrix has row-major alignment and I am using the corresponding function, which takes a row-major matrix as a parameter (cgSetMatrixParameterfr in my particular case).

Of course, I could "transpose" that matrix by calling the function cgSetMatrixParameterfc, which treats input data as column-major matrix (and "automatically" transposes it), but that would be ridiculous.

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AFAIK the equality v*A=A^T*v does not hold for matrix multiplication. However, (v*A)^T=A^T*v^T does. –  You Sep 20 '10 at 15:20

2 Answers 2

up vote 2 down vote accepted

The convention in mathematics (and thus in programming) is that you multiply the vector by a linear transformation from the right: matrix * vector == transformed vector. So I don't understand you complain. The matrix is already set to the right one. If you want to multiply the vector from the left then you need to transpose the matrix: result = mul(vector, transpose(wvp))

EDIT: OK, Direct3D actually does the opposite. It multiplies vectors from the left (treats them as rows rather than columns). OpenGL, for example, multiplies from the right as normal people do. So you need to load the transposed matrix to the cg program.

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Could you explain then why does the code (DX-specific) generates the matrix, which is transposed comparing to multiplication convention? You could test it yourself, for this code to work shader has to have a mul(vector, matrix) instruction, but not the mul(matrix, vector). –  Yippie-Ki-Yay Sep 20 '10 at 15:28
Yes, I looked at the documentation. See edit. –  ybungalobill Sep 20 '10 at 15:50
Note: The cue was that you wrote world * view * projection. The order here may be right iff you project as vector * world * view * projection. –  ybungalobill Sep 20 '10 at 15:56

If both matrices are diagonal, square and have same size, then the multiplication is commutative.

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