Why do we need to use the "transpose" of a transformed matrix? (direct3D11)

I have read the SimpleMath and also read the Programmers guide articles, but I can't seem to put my head around the purpose of transposing a matrix once it has been "transformed"

I mean, I understand what the transpose of a matrix is. I just don't understand why we need to actually take the transpose.

Take this code snippet for example..(assuming the matrices have already been created for the CameraView and the CameraProjection)

World = XMMatrixIdentity();                             

WVP = World * CameraView * CameraProjection;

XMMatrixTranspose(WVP)

So my question is, what is the purpose of getting the transpose of WVP? what purpose does that serve for Direct3D 11?

Solution

First of all, let's see how matrices can be represented in memory. Consider the following matrix.

1 2 3
4 5 6
7 8 9

All values stored in computer memory are stored sequentially, there is no concept of "row" and "column", only address. If you represent the matrix above in row-major order, the float values in the matrix will be stored linearly in memory like this:

Lowest address [ 1 2 3 4 5 6 7 8 9 ] Highest address

If, on the other hand, you represent this same matrix in column-major order, the float values in the matrix will be stored in memory like this:

Lowest address [ 1 4 7 2 5 8 3 6 9 ] Highest address

So in row-major order, consecutive values of rows are contiguous in memory, whereas in column-major order, consecutive values of columns are contiguous in memory.

Now, HLSL requires your matrices to be supplied in column-major order, but DirectXMath stores its matrices in row-major order because its implementation is faster that way, so you have to transpose it so that it gets fed into HLSL shaders in column-major order.

Correction:

HLSL defaults to taking your matrices in column-major order, but DirectXMath stores its matrices in row-major order because its implementation is faster that way, so one solution is to transpose the matrices so that they get fed into HLSL shaders in column-major order. Alternatively, you can override this default so that HLSL takes your matrices in row-major order, and then you wouldn't have to transpose them.