diff --git a/CMakeLists.txt b/CMakeLists.txt
index f6cce1f..4ce8e36 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -20,8 +20,6 @@ add_executable(DESCSS main.cpp ${sources} ${headers})
target_link_libraries(DESCSS ${Geant4_LIBRARIES})
set(DESCSS_SCRIPTS
- debug.mac
- electron.mac
vis.mac
assets/model.txt
)
diff --git a/G4.code-workspace b/G4.code-workspace
index 3c470bf..79e8674 100644
--- a/G4.code-workspace
+++ b/G4.code-workspace
@@ -10,7 +10,116 @@
"line": "cpp",
"plane": "cpp",
"qrot": "cpp",
- "cmath": "cpp"
+ "cmath": "cpp",
+ "string": "cpp",
+ "vector": "cpp",
+ "algorithm": "cpp",
+ "array": "cpp",
+ "atomic": "cpp",
+ "bit": "cpp",
+ "cctype": "cpp",
+ "cfenv": "cpp",
+ "charconv": "cpp",
+ "chrono": "cpp",
+ "clocale": "cpp",
+ "compare": "cpp",
+ "complex": "cpp",
+ "concepts": "cpp",
+ "condition_variable": "cpp",
+ "csetjmp": "cpp",
+ "csignal": "cpp",
+ "cstdarg": "cpp",
+ "cstddef": "cpp",
+ "cstdint": "cpp",
+ "cstdio": "cpp",
+ "cstdlib": "cpp",
+ "cstring": "cpp",
+ "ctime": "cpp",
+ "cwchar": "cpp",
+ "deque": "cpp",
+ "exception": "cpp",
+ "format": "cpp",
+ "forward_list": "cpp",
+ "fstream": "cpp",
+ "functional": "cpp",
+ "future": "cpp",
+ "initializer_list": "cpp",
+ "iomanip": "cpp",
+ "ios": "cpp",
+ "iosfwd": "cpp",
+ "iostream": "cpp",
+ "istream": "cpp",
+ "iterator": "cpp",
+ "limits": "cpp",
+ "list": "cpp",
+ "locale": "cpp",
+ "map": "cpp",
+ "memory": "cpp",
+ "mutex": "cpp",
+ "new": "cpp",
+ "numeric": "cpp",
+ "optional": "cpp",
+ "ostream": "cpp",
+ "queue": "cpp",
+ "ratio": "cpp",
+ "regex": "cpp",
+ "set": "cpp",
+ "sstream": "cpp",
+ "stack": "cpp",
+ "stdexcept": "cpp",
+ "stop_token": "cpp",
+ "streambuf": "cpp",
+ "system_error": "cpp",
+ "thread": "cpp",
+ "tuple": "cpp",
+ "type_traits": "cpp",
+ "typeinfo": "cpp",
+ "unordered_map": "cpp",
+ "utility": "cpp",
+ "xfacet": "cpp",
+ "xhash": "cpp",
+ "xiosbase": "cpp",
+ "xlocale": "cpp",
+ "xlocbuf": "cpp",
+ "xlocinfo": "cpp",
+ "xlocmes": "cpp",
+ "xlocmon": "cpp",
+ "xlocnum": "cpp",
+ "xloctime": "cpp",
+ "xmemory": "cpp",
+ "xstddef": "cpp",
+ "xstring": "cpp",
+ "xtr1common": "cpp",
+ "xtree": "cpp",
+ "xutility": "cpp",
+ "matrix": "cpp",
+ "vec2f": "cpp",
+ "vec3f": "cpp",
+ "vec4f": "cpp",
+ "sf_vec": "cpp",
+ "sf_vec3f": "cpp",
+ "aida_ntuple": "cpp",
+ "handle": "cpp",
+ "img": "cpp",
+ "mat": "cpp",
+ "mapmanip": "cpp",
+ "basket": "cpp",
+ "branch": "cpp",
+ "dummy": "cpp",
+ "graph": "cpp",
+ "info": "cpp",
+ "iros": "cpp",
+ "leaf": "cpp",
+ "named": "cpp",
+ "obj_array": "cpp",
+ "obj_list": "cpp",
+ "stl_vector": "cpp",
+ "tree_index": "cpp",
+ "vector3": "cpp",
+ "style_parser": "cpp",
+ "vmanip": "cpp",
+ "element": "cpp",
+ "tree": "cpp"
}
}
}
\ No newline at end of file
diff --git a/README.md b/README.md
index 9041dd6..36c889d 100644
--- a/README.md
+++ b/README.md
@@ -207,14 +207,96 @@ $$
double z = rho * cos(theta);
```
-2. 发射方向
-在`Geant4`中，假定粒子的位置矢量为$\vec{r}$，则以$\vec{r}$反方向作为$z$轴正方向建立右手坐标系，粒子的指向为:
+2. 发射方向[^6]
+在`Geant4`中，假定粒子的位置矢量为$\vec{r}$，则以$\vec{r}$反方向作为$z$轴正方向建立右手坐标系（简称为`P`系），随机生成指向$\vec{d}$，为了保证发射方向是朝向球面内，因此需要限制$\theta$的最大角度为$90^{\circ}$。
+ ```c
+ double u = rand();
+ double v = rand();
+ double phi = 2 * pi * u;
+ double theta = arccos(2 * v - 1);
+ double x = sin(theta) * cos(phi);
+ double y = sin(theta) * sin(phi);
+ double z = cos(theta);
+ ```
+
+随后我们需要将$\vec{d}$转化到`World`坐标系（简称为`W`系）中，已知两个坐标系有两个公共点，在`W`系中表示为原点$O$和发射点$\vec{r}=(x_0,y_0,z_0)$，在`P`系中则为$(0,0,\rho)$和原点$O^\prime$,则有：
$$
-P_x = -\sin\theta\cos\phi \\
-P_y = -\sin\theta\sin\phi \\
-P_z = -\cos\theta
+\begin{bmatrix}
+x\\ y\\ z
+\end{bmatrix} = \lambda R \begin{bmatrix}
+u\\ v\\ w
+\end{bmatrix} + \begin{bmatrix}
+x_0\\ y_0\\ z_0
+\end{bmatrix}
+\cdots(1)
$$
-为了保证发射方向是朝向球面内，因此需要限制$\theta$的最大角度为$90^{\circ}$。
+
+其中$\lambda$为尺度比例因子，设置为1；$R$被称为罗德里格矩阵，定义反对称矩阵：
+$$
+S = \begin{bmatrix}
+0,& -c,& -b \\
+c,& 0,& -a \\
+b,& a,& 0
+\end{bmatrix}
+$$
+
+则$R$可表示为$R = (I+S)(I-S)^{-1}$，展开后则有：
+$$
+R = \frac{1}{1+a^2+b^2+c^2}\begin{bmatrix}
+ 1 + a^2 - b^2 - c^2, -2c - 2ab, -2b + 2ac \\
+ 2c - 2ab, 1 - a^2 + b^2 - c^2, -2a - 2bc \\
+ 2b + 2ac, 2a - 2bc, 1 - a^2 - b^2 + c^2
+\end{bmatrix}\cdots(2)
+$$
+
+将两个公共点代入$(1)$，相减则可消去平移项，可得到：
+$$
+\begin{bmatrix}
+x_2-x_1\\ y_2-y_1\\ z_2-z_1
+\end{bmatrix} = R \begin{bmatrix}
+u_2-u_1\\ v_2-v_1\\ w_2-w_1
+\end{bmatrix}
+$$
+
+代入$(2)$则可得到（$u_{21}=u_2-u_1$）：
+$$
+\begin{bmatrix}
+0,& w_{21}+z_{21},& v_{21}+y_{21} \\
+w_{21}+z_{21},& 0,& -u_{21}-x_{21} \\
+-v_{21}-y_{21},& -u_{21}-x_{21},& 0
+\end{bmatrix}\begin{bmatrix}
+a\\ b\\ c
+\end{bmatrix} = \begin{bmatrix}
+u_{21} - x_{21} \\
+v_{21} - y_{21} \\
+w_{21} - z_{21}
+\end{bmatrix}
+$$
+
+代入本题，则有：
+$$
+\begin{bmatrix}
+0,& -\rho+z_0,& y_0 \\
+-\rho+z_0,& 0,& -x_0 \\
+-y_0,& -x_0,& 0
+\end{bmatrix}\begin{bmatrix}
+a\\ b\\ c
+\end{bmatrix} = \begin{bmatrix}
+-x_0 \\
+-y_0 \\
+-\rho-z_0
+\end{bmatrix}
+$$
+
+令$a=1$，则可求得：
+$$
+\begin{cases}
+b = \frac{z_0+\rho-y_0}{x_0} \\
+c = \frac{z_0-\rho+y_0}{x_0}
+\end{cases}
+$$
+
+计算得到$R$，继而根据$(1)$计算得到$\vec{d}$在`W`系中的表达式。
3. 能量
* 俘获电子的函数较为简单，采用`ITM`；（下表中$j_0$已经归一化）
@@ -240,8 +322,12 @@ $$
* 其余`GCR`辐射粒子同样使用`ARM`，生成`100000`个随机数需要`4.5`分钟。
