Matrix mult order in Direct3D

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予麋鹿
予麋鹿 2021-02-10 15:37

I\'ve received two conflicting answers in terms of multiplying matrices in Direct3D to achieve results. Tutorials do state to multiply from left to right and that\'s fine but it

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  • 2021-02-10 16:15

    See this answer. In OpenGL, each subsequent operation is a pre-multiplication of all the operations before it, not a post-multiplication. You can see a matrix multiplication of a vector as a function evaluation.

    If what you want is to first rotate a vector and then translate your rotated vector, which you in OpenGL would have solved by first calling glRotatef and then calling glTranslatef, you could express that using function calls as

    myNewVector = translate(rotate(myOldVector))
    

    The rotate function does this

    rotate(anyVector) = rotationMatrix * anyVector
    

    and the translate function does this

    translate(anyOtherVector) = translationMatrix * anyOtherVector
    

    so your equivalent expression using matrix multiplications would look like

    myNewVector = translationMatrix * rotationMatrix * myOldVector
    

    That is, your combined transformation matrix would look be translationMatrix * rotationMatrix.

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  • 2021-02-10 16:40

    The problem is the order you are multiplying the matrices to get the composite transform matrix is reversed from what it should be. You are doing: wm = rotatem * translatem, which follows the order of operations you are doing for OpenGL, but for DirectX the matrix should have been wm = translatem * rotatem

    The fundamental difference between OpenGL and DirectX arises from the fact that OpenGL treats matrices in column major order, while DirectX treats matrics in row major order.

    To go from column major to row major you need to find the transpose ( swap the rows and the columns ) of the OpenGL matrix.

    So, if you write wm = rotatem * translatem in OpenGL, then you want the transpose of that for DirectX, which is:

    wmT = (rotatem*translatem)T = translatemT * rotatemT
    

    which explains why the order of the matrix multiply has to be reversed in DirectX.

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