3D基础

常用公式

开启 3D 之旅

$$
Q = [x, y, z, w]^T = [u_x sin(\frac{\theta}{2}), u_y sin(\frac{\theta}{2}), u_z sin(\frac{\theta}{2}), cos(\frac{\theta}{2})]^T
$$

$$
\frac{\partial u}{\partial t} = h^2 \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2}\right)
$$

$$
\sum(x)
$$

$$
J_\alpha(x) = \sum_{m=0}^\infty \frac{(-1)^m}{m! \Gamma (m + \alpha + 1)} {\left({ \frac{x}{2} }\right)}
$$

$$
f(x)=\left\{
\begin{align}
x & = \cos(t) \\
y & = \sin(t) \\
z & = \frac xy
\end{align}
\right\}.
$$

$$
F^{HLLC}=\left\{
\begin{array}{rcl}
F_L & & {0 < S_L} \\
F^*_L & & {S_L \leq 0 < S_M} \\
F^*_R & & {S_M \leq 0 < S_R} \\
F_R & & {S_R \leq 0}
\end{array}
\right\}
$$

$$
f(x)=
\begin{cases}
0& \text{x=0} \\
1& \text{x!=0}
\end{cases}
$$