transform

行主序矩阵与列主序矩阵

首先要了解的是，对于连续内存数据：

\[m_{11}\ m_{12}\ m_{13}\ m_{14}\ m_{21}\ m_{22}\ m_{23}\ m_{24}\ m_{31}\ m_{32}\ m_{33}\ m_{34}\ m_{41}\ m_{42}\ m_{43}\ m_{44} \]

行主序矩阵是这样解释数据的：

\[M= \begin{bmatrix} m_{11} & m_{12} & m_{13} & m_{14} \\ m_{21} & m_{22} & m_{23} & m_{24} \\ m_{31} & m_{32} & m_{33} & m_{34} \\ m_{41} & m_{42} & m_{43} & m_{44} \end{bmatrix} \]

而列主序矩阵是这样解释数据的：

\[M= \begin{bmatrix} m_{11} & m_{21} & m_{31} & m_{41} \\ m_{12} & m_{22} & m_{32} & m_{42} \\ m_{13} & m_{23} & m_{33} & m_{43} \\ m_{14} & m_{24} & m_{34} & m_{44} \end{bmatrix} \]

DirectX的数学使用的是row major matrix,但是HLSL packs matrices in a column major order

虽然HLSL使用column major order进行packs.但是实际它读取matrices是安装row major order的。

this is the matrix we are passing from our app, which is in row major ordering:

\[\begin{bmatrix} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 10 & 11 & 12 \\ 13 & 14 & 15 & 16 \end{bmatrix} \]

this is how HLSL is storing the matrix:

\[\begin{bmatrix} 1 & 5 & 9 & 13 \\ 2 & 6 & 10 & 14 \\ 3 & 7 & 11 & 15 \\ 4 & 8 & 12 & 16 \end{bmatrix} \]

HLSL code:

\[\text{output.pos} = \text{mul}(\text{input.pos},\text{wvpMat}); \]

HLSL assembly:

0: dp4 r0.x, v0.xyzw, cb0[0].xyzw // r0.x <- output.pos.x 1: dp4 r0.y, v0.xyzw, cb0[1].xyzw // r0.y <- output.pos.y 2: dp4 r0.z, v0.xyzw, cb0[2].xyzw // r0.z <- output.pos.z 3: dp4 r0.w, v0.xyzw, cb0[3].xyzw // r0.w <- output.pos.w

cb0[0] is now this in HLSL (this was a column in our app, but is now a row in HLSL, which makes the multiplication easier):

\[\begin{bmatrix}1 & 5 & 9 & 13\end{bmatrix} \]

World/View/Project Space

View Space

\[\begin{bmatrix} \mathtt{right}.x & \mathtt{up}.x & \mathtt{forward}.x & \mathtt{position}.x \\ \mathtt{right}.y & \mathtt{up}.y & \mathtt{forward}.y & \mathtt{position}.y \\ \mathtt{right}.z & \mathtt{up}.z & \mathtt{forward}.z & \mathtt{position}.z \\ 0 & 0 & 0 & 1 \end{bmatrix} \]

The right, up and forward vector are normalized vectors . The describe the camera's right direction in the virtual world, the up direction, and the forward direction . The position vector is an x,y,z coordinate describing the position of the camera in the virtual world.

Moving From Space to Space

So just to recap, to get a 3d model from object (a.k.a. local) space to projection space, we multiply each vertex by world, then view, then projection. It will look like this:

finalvertex.pos = vertex.pos * worldMatrix * viewMatrix * projectionMatrix;

参考:

!(Transform )[https://www.braynzarsoft.net/viewtutorial/q16390-transformations-and-world-view-projection-space-matrices]