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

Question

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?

Kathrinekathryn

Surely it depends on what you're going to actually do with the matrix? – Quadrisect

Well, let's say i just want to create a 3d scene with the camera and the projection in it. If i transpose the transformed matrix, what will that do? – Kathrinekathryn

No, but specifically what mathematical operation do you intend to with WVP? Transposing doesn't really do anything; it just replaces pre-multiplication of column vectors with post-multiplication of row vectors (and vice versa). Without context, that's about all that can be said ;) – Quadrisect

The pattern is that the transpose happens just before setting it into a Constant Buffer which is sent to an HLSL shader... It is in fact to make the row-major matrix into a column-major matrix. – Amadus

Answer 1

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.

Anastomosis

HLSL requires your matrices to be supplied in column-major order ah thank you very much, this explains everything for me now :) – Kathrinekathryn

HLSL doesn't require it, it just defaults to column-major. This is covered explicitly in the DirectXMath Programmer's Guide in the Working with D3DXMath section under Using DirectXMath with Direct3D and a link to the related HLSL docs. In short: DirectXMath supports either left- or right-handed viewing coordinates, but all matrices are row-major. You can tell HLSL to use row-major, but it defaults to column-major which is slightly faster. Hence the transpose just before setting a CB. – Amadus

To make this more explicit, I've added this topic to the SimpleMath docs on the DirectX Tool Kit GitHub wiki. – Amadus